**Meet the editor**

Prof. Dongmei Chen is currently an associate professor at the Department of Geography, Queen's University in Kingston, Canada. She is also crossed-appointed at the Department of Environmental Science. She received her BA from Peking University, China, her MS from the Institute of Remote Sensing Application, Chinese Academic of Science, and her PhD in Geography from

the joint doctoral program of San Diego State University and University of California at Santa Barbara, USA. Prof. Chen worked at the Environmental Systems Research Institute (ESRI), California as a GIS product specialist for two years. Her research interests focus mainly on understanding and modeling of interactions between human activities and physical environment by using geographic information science, remote sensing, spatial analysis and modeling technologies. She has worked on more than twenty funded environmental- and health-related research projects, and published over fifty journal articles and book chapters. Prof. Chen has received research awards from American Society for Photogrammetry and Remote Sensing, Canada Foundation of Innovation, Chinese Academic of Science and International Geographic Information Foundation.

Contents

**Preface IX** 

Claus-Peter Rückemann

Othniel K. Likkason

Chapter 2 **Spectral Analysis of Geophysical Data 27**

Chapter 1 **Queueing Aspects of Integrated Information and** 

Chapter 3 **Quantitative Evaluation of Spatial Interpolation** 

Xuejun Liu, Jiapei Hu and Jinjuan Ma

Chapter 4 **Integrated Geochemical and Geophysical** 

Emmanuel Abiodun Ariyibi

Chapter 5 **Regularity Analysis of Airborne Natural Gamma Ray Data** 

Chapter 6 **Two-Dimensional Multifractional** 

Ahmad Bilal

Saïd Gaci and Naïma Zaourar

**Models Based on a Data-Independent Method 53** 

**Approach to Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 71** 

**Measured in the Hoggar Area (Algeria) 93** 

Chapter 7 **3D Seismic Sedimentology of Nearshore Subaqueous Fans –** 

**Along the Syrian Rift – NW the Arabian Plate 139** 

**Brownian Motion- Based Investigation of Heterogeneities from a Core Image 109** 

Yang Fengli, Zhao Wenfang, Sun Zhuan, Cheng Haisheng and Peng Yunxin

Chapter 8 **Mapping and Analyzing the Volcano-Petrology and Tectono-Seismicity Characteristics** 

Saïd Gaci, Naïma Zaourar, Louis Briqueu and Mohamed Hamoudi

**A Case Study from Dongying Depression, Eastern China 125** 

**Computing Systems in Geosciences and Natural Sciences 1** 

## Contents

#### **Preface XI**

Ahmad Bilal


X Contents


## Preface

Geoscience is one of the most broad and rapidly developed fields in last three decades. With the rapid diffusion of geospace technologies and growing attention on global environmental and climate change, many new data, methods and models have been applied to various aspects of geoscience. The focus of this book is on the recent advances in data, analysis methods and their applications in geoscience and environmental change studies. One of the problems associated with such a rich selection of themes is the organization challenge of bringing together a variety of techniques, applications, study areas and data. After the review process, a collection of sixteen articles written by scholars from thirteen countries has been selected for this book. These articles cover a wide range of data analysis methods and modeling techniques, and provide an excellent profile of their applications in geology, geophysics, hydrology and environmental change in different regions of the world.

One of the most obvious technological revolutions in last half century is the development and application of computer information technology. Modern geoscience research widely relies on information technologies, especially geographic information systems (GIS). In the first chapter, Rückemann shows how geoscience research greatly benefits from modern development of information and computing systems, especially high performance computing. He reviews the general information technology advances and discusses issues from hardware, system architecture, software, legal and collaborational aspects that prevent interest groups in geoscience and natural science from building complex integrated computing systems on a long term base. At the end of the chapter, he also presents successful case studies of integrated computing systems used in geoscience and natural science.

Many quantitative methods are widely used in geoscience. Chapters 2 and 3 are review papers on two common analysis methods for geoscience and natural science. In Chapter 2, Likkason covers different spectral analysis methods and tools that can be used to analyze and interpret geophysical data obtained in the field. He discusses the detailed treatment and analysis of periodic and aperiodic functions in Fourier methods, as well as the sampling theorem and Fourier analysis. These Fourier-based methods have found usefulness in the analysis of geophysical data. In Chapter 3, Liu et al. review spatial interpolation algorithms that are widely used to estimate values of properties at unsampled locations for spatial continuous data. There are many factors

#### XII Preface

affecting the performance of spatial interpolation methods and growing concerns on the accuracy obtained from different interpolation methods. They propose a dataindependent GIS-based evaluation process flow to quantitatively analyze and evaluate different spatial interpolation models.

Preface XI

diamonds, Kimberlite magmas are invaluable to scientific and exploration communities. Kamenetsky et al. (Chapter 10) use data from the newly developed study of the diamondiferous Udachnaya-East kimberlite pipe in Siberia to understand chemical and physical characteristics of kimberlite magma. To optimize oil reservoir development and production planning, geological models that can capture uncertainty

Maucec et al. (Chapter 11) review recent advances in technology for building highresolution geological models and its role in state-of-the-art and future reservoir management decisions for hydrocarbon field development. They introduce some basic tools and concepts of geostatistical spatial analysis and modeling, and present a fundamentally novel method to resolve most of the common geocellular modeling

Chapters 12 to 14 present studies in hydrological models and their applications. Sediment yield exported by a basic (or catchment) over a period of time is important for the size of sediment storage capability of a dam and estimate of a reservoir life. Therefore, sediment yield prediction from catchments is very important for many dam plans and designs in places where water resources sedimentation is a serious problem. Preksedis Ndomba (Chapter 12) reports a study of sediment yields based on the relationship between sediment yield and various climatic regions in Tanzania. They develop simple sediment yield-fill equations on each catchment area and recommend them as simple and efficient planning tools for water-supply schemes of small reservoirs with limited local data. In Chapter 13, Ndomba et al. evaluate the suitability of a commonly used hydrological model, the Soil and Water Assessment Tool (SWAT)

Many geo-objects or phenomena do not have clear boundaries and are often mixed together. Fuzzy set theories have been developed to model the uncertainty in transition or mixed regions. In Chapter 14, Barreto-Neto develops a fuzzy rule-based hydrologic model within a GIS environment to predict runoff in the Quilomo River watershed located in South of the State of São Paulo, Brazil. They found that the incorporation of the fuzzy theory to the hydrologic model made a better run off estimation than the traditional Boolean model, and confirm the advantage of fuzzy

Environmental change has been causing global concerns, and remote sensing technology has played an important role in monitoring environmental change. Chapter 15 written by Zhang et al. provides a good example of how remotely sensed images can be used to detect changes on the earth surface. They use time series MODIS satellite images to get the classified land cover classification maps to assess the

The evolution of species on earth is the topic of the last chapter (Chapter 16). Using fossil records in the Lower Eocene crustancean burrow system in the southwestern

for sediment yield estimation in three catchments of Eastern Africa.

theory in the representation of natural phenomena.

rock desertification problems in Guangxi Province of China.

are needed for hydrocarbon field development.

issues.

The following chapters 4 to 11 consist of eight articles on different data, methods, models and their applications used in geophysics and geology studies. Ariyibi and Joshua (Chapter 4) summarize the basic principles of using data acquired by the dual frequency global positioning system (GPS) receivers to understand variation and dynamics of the ionosphere. They use the total electron content (TEC) and S4 index data recorded from GPS receiver at a low-latitude station of Ile – Ife to study the ionospheric condition during low geomagnetic activity period and during geomagnetic storm events.

The airborne Gamma Ray (GR) measurements have been used in geophysical research for decades. The information provided by a gamma-ray spectrometer can be used for tracing the amounts of mineral deposits in rocks. Gaci et al. (Chapter 5) conducts a mono (two)-dimensional fractal analysis of natural radioactivity measurements recorded over the Hoggar's area of Algeria. They found that the fractal behavior of the GR measurement is not affected by pre-processing operations.

Core samples are commonly used to study the evolution of climate, species and sedimentary composition from geologic history. Gaci and Zaourar (Chapter 6) overview different numerical analysis methods used for the study and investigation of core images. They used a new fractal-based model with the two-dimensional multifractional Brownian motion (2D-mBm) in order to explore the spatial evolution of the local regularity in digitized core images. They demonstrated that the regularity maps obtained by 2D multiple filter techniques from the digitized core images could characterize heterogeneities of the analyzed core.

The use of seismic data to study sedimentary rocks and their forming processes is the focus of seismic sedimentology. Yang et al. (Chapter 7) present a case study on 3D seismic sedimentology of nearshore subaqueous fans from Dongying Depression, Eastern China. In Chapter 8, Bilal presents a study on mapping and analyzing the volcano activities and seismicity characteristics to understand the nature and composition of the underlying lithospheric mantle along the Syrian rift.

The microstructures of geomaterials and their evolution under different environmental conditions are critical for understanding their mechanical behavior and performance in engineering environments. In Chapter 9, Sorgi and De Gennaro present results from a research program to evaluate the mechanical behavior of chalk in the shallow underground mine of Estreux, Northern France. Different techniques are used to analyze the process at the site, laboratory and microscopic scales.

Diamond mining and oil field planning are always hot topics in geoscience because of their high economic implication. Due to the close association of Kimberlite rocks with diamonds, Kimberlite magmas are invaluable to scientific and exploration communities. Kamenetsky et al. (Chapter 10) use data from the newly developed study of the diamondiferous Udachnaya-East kimberlite pipe in Siberia to understand chemical and physical characteristics of kimberlite magma. To optimize oil reservoir development and production planning, geological models that can capture uncertainty are needed for hydrocarbon field development.

X Preface

different spatial interpolation models.

geomagnetic storm events.

affecting the performance of spatial interpolation methods and growing concerns on the accuracy obtained from different interpolation methods. They propose a dataindependent GIS-based evaluation process flow to quantitatively analyze and evaluate

The following chapters 4 to 11 consist of eight articles on different data, methods, models and their applications used in geophysics and geology studies. Ariyibi and Joshua (Chapter 4) summarize the basic principles of using data acquired by the dual frequency global positioning system (GPS) receivers to understand variation and dynamics of the ionosphere. They use the total electron content (TEC) and S4 index data recorded from GPS receiver at a low-latitude station of Ile – Ife to study the ionospheric condition during low geomagnetic activity period and during

The airborne Gamma Ray (GR) measurements have been used in geophysical research for decades. The information provided by a gamma-ray spectrometer can be used for tracing the amounts of mineral deposits in rocks. Gaci et al. (Chapter 5) conducts a mono (two)-dimensional fractal analysis of natural radioactivity measurements recorded over the Hoggar's area of Algeria. They found that the fractal behavior of the

Core samples are commonly used to study the evolution of climate, species and sedimentary composition from geologic history. Gaci and Zaourar (Chapter 6) overview different numerical analysis methods used for the study and investigation of core images. They used a new fractal-based model with the two-dimensional multifractional Brownian motion (2D-mBm) in order to explore the spatial evolution of the local regularity in digitized core images. They demonstrated that the regularity maps obtained by 2D multiple filter techniques from the digitized core images could

The use of seismic data to study sedimentary rocks and their forming processes is the focus of seismic sedimentology. Yang et al. (Chapter 7) present a case study on 3D seismic sedimentology of nearshore subaqueous fans from Dongying Depression, Eastern China. In Chapter 8, Bilal presents a study on mapping and analyzing the volcano activities and seismicity characteristics to understand the nature and

The microstructures of geomaterials and their evolution under different environmental conditions are critical for understanding their mechanical behavior and performance in engineering environments. In Chapter 9, Sorgi and De Gennaro present results from a research program to evaluate the mechanical behavior of chalk in the shallow underground mine of Estreux, Northern France. Different techniques

Diamond mining and oil field planning are always hot topics in geoscience because of their high economic implication. Due to the close association of Kimberlite rocks with

composition of the underlying lithospheric mantle along the Syrian rift.

are used to analyze the process at the site, laboratory and microscopic scales.

GR measurement is not affected by pre-processing operations.

characterize heterogeneities of the analyzed core.

Maucec et al. (Chapter 11) review recent advances in technology for building highresolution geological models and its role in state-of-the-art and future reservoir management decisions for hydrocarbon field development. They introduce some basic tools and concepts of geostatistical spatial analysis and modeling, and present a fundamentally novel method to resolve most of the common geocellular modeling issues.

Chapters 12 to 14 present studies in hydrological models and their applications. Sediment yield exported by a basic (or catchment) over a period of time is important for the size of sediment storage capability of a dam and estimate of a reservoir life. Therefore, sediment yield prediction from catchments is very important for many dam plans and designs in places where water resources sedimentation is a serious problem. Preksedis Ndomba (Chapter 12) reports a study of sediment yields based on the relationship between sediment yield and various climatic regions in Tanzania. They develop simple sediment yield-fill equations on each catchment area and recommend them as simple and efficient planning tools for water-supply schemes of small reservoirs with limited local data. In Chapter 13, Ndomba et al. evaluate the suitability of a commonly used hydrological model, the Soil and Water Assessment Tool (SWAT) for sediment yield estimation in three catchments of Eastern Africa.

Many geo-objects or phenomena do not have clear boundaries and are often mixed together. Fuzzy set theories have been developed to model the uncertainty in transition or mixed regions. In Chapter 14, Barreto-Neto develops a fuzzy rule-based hydrologic model within a GIS environment to predict runoff in the Quilomo River watershed located in South of the State of São Paulo, Brazil. They found that the incorporation of the fuzzy theory to the hydrologic model made a better run off estimation than the traditional Boolean model, and confirm the advantage of fuzzy theory in the representation of natural phenomena.

Environmental change has been causing global concerns, and remote sensing technology has played an important role in monitoring environmental change. Chapter 15 written by Zhang et al. provides a good example of how remotely sensed images can be used to detect changes on the earth surface. They use time series MODIS satellite images to get the classified land cover classification maps to assess the rock desertification problems in Guangxi Province of China.

The evolution of species on earth is the topic of the last chapter (Chapter 16). Using fossil records in the Lower Eocene crustancean burrow system in the southwestern

#### XIV Preface

Israel, Lewy et al. demonstrate the change of breeding mode from K-type to r-type during the end-Cretaceous biological crisis.

As a collection of edited research and review papers, this book attempts to create a sense of the current state of art in methods, technology and their applications in geoscience, as well as the direction currently pursued by the research community around the world. I hope that readers will find this book of benefit in understanding the current developments and trends in the merging areas of analysis methods, models, techniques, and applications in geoscience. However, considering the wide range of themes and rapid technology progress in geoscience, the topics covered in this book are only a small part of methods, models, techniques used in geoscience.

Above all, I would like to thank Mirna Cvijic, Dejan Grgur, and other publishing managers at InTech for their support and help, as well as acknowledge the efforts of the authors. All credits and responsibilities of each included article belong to the corresponding contributors

> **Dongmei Chen**  Associate Professor at the Department of Geography, Queen's University in Kingston, Canada

## **Queueing Aspects of Integrated Information and Computing Systems in Geosciences and Natural Sciences**

Claus-Peter Rückemann

*Westfälische Wilhelms-Universität Münster (WWU), Leibniz Universität Hannover, North-German Supercomputing Alliance (HLRN) Germany*

#### **1. Introduction**

Modern geosciences widely rely on information science technologies. In most cases of scientific research applications, tools, and state of the art hardware architectures are infamously neglected and therefore their development is not pressed ahead and not documented, a fault for continuous and future developments. Information Systems and Computing Systems up to now live an isolated life, rarely integrated and mostly lacking essential features for future application. Although in general technology advances and new tools arise, there is a number of aspects that prevent interest groups from building complex integrated systems and components on a long term base. These issues, from hardware and system architecture aspects to software, legal, and collaborational aspects, are top in the queue for realisation show-stoppers. This chapter presents the current status of integrated information and computing systems. It discusses the most prominent technical and legal aspects for applications in geosciences and natural sciences. Todays state of the art information systems provide a plethora of features for nearly any field of application. Present computing systems can provide various distributed and high end compute power. Compute resources in most cases have to be supported by highly performing storage resources. The most prominent disciplines on up to date resources are natural sciences like geosciences, geophysics, physics, and many other fields with theoretical and applied usage scenarios. For geosciences both information systems as well as computing resources are essential means of day to day work. The most immanent limitation is that there are only a very few facilities with these systems combining the information systems features with powerful compute resources. The goal we have to work on for the next years is to facilitate this integration of information and computing systems. Modern information systems can provide various information and visualise context for different purposes beyond standard Geoscientific Information Systems (GIS). Fields demanding for handling, processing, and analysing geoscientific data are manyfold. Geophysics as well as applied sciences provide various methods as to name magnetic methods, gravity methods, seismic methods, tomography, electromagnetic methods, resistivity methods, induced polarisation, radioactivity methods, well logging and various

main potential for insight on their own, merely not from context. Capability computing will

<sup>3</sup> Queueing Aspects of Integrated Information

The more interesting along with the development of the next generation of system architectures is the opening of capacity computing for complex information systems. These systems provide capacity for many small or medium sized jobs. Job processing of several parallel jobs is suitable for these resources. The single job itself may be used for parameter studies, design alternatives, exploring pre-development stages, and in general these jobs on their own have less potential for insight. Making use of capacity computing resources many instances of compute jobs will run on a resource. This is what we need to enliven conventional

There is a number of different paradigms and resources that can be considered for this purpose and used from various geosciences disciplines. The topmost category for High End Computing (HEC) are High Performance Computing (HPC) and Supercomputing resources. These will in nearly all use cases be used in a non distributed manner. The lower end, Distributed Computing (DC) and services computing resources, are for example built on base of paradigms like Sky Computing, Cloud Computing, Grid Computing, Cluster Computing,

What do we have to expect to be the machines behind these paradigms? The answer is a performance pyramid. The performance pyramid for computing resources shows the

The obstacles for operating complex resources with interactive systems with efficient and effective operation can be overcome while reacting on several levels, architectures, hardware, frameworks and middleware, applications, energy consumption, competence resources,

information system implementations with new features, leading to new insights.

usually not be the first association with information systems.

and Computing Systems in Geosciences and Natural Sciences

**2.2 Capacity computing**

**3. Computing resources**

**3.1 Paradigms**

Mobile Computing.

following structure.

• Workstations, • Mobile devices.

**4. Computing obstacles**

consultancy, and support.

Top sector:

**3.2 Performance pyramid**

• International supercomputers, • National supercomputers, • Regional supercomputers. Medium and bottom sector:

• Local and dedicated compute servers and clusters,

assisting and integrated methods and techniques. Integrating these methods with information systems and the support of remote sensing, cartography, depth imaging, and infrastructural and social sources a more and more holistic view on the earth system will be possible. This will help to gain insight in the fields of seismology, meteorology, climatology, prospection and exploration, medical geology, epidemiology, environmental planning and many more disciplines. The resulting information systems and applications are not only used for scientific research but for public information, education, disaster management, expert systems and many more. In various application areas the surplus value arises with intelligent combination of information. A cartographic system only displaying spatial data is of less significance for a seismological disaster management application if there are no additional information and features provided. Provisioning these information will in many case result in interactive computation. For some use cases requests for points of interest, dynamical cartography, event programming, flexible event triggering, long-term monitoring like in seismology, catastrophe management and meteorology are necessary, for others simulation or modeling of scenarios are essential. All these fields of application contain tasks that cannot be handled in extend for large and complex systems on one local compute and storage resource only. Processes like processing jobs, visualisation, traveling salesman problems, and multimedia production have to be transferred to systems with the capacity necessary for multiple requests at the same time. We should not isolate scholarly research from long term information science concepts and architectures used in geosciences disciplines. Therefore the overall goal is to integrate systems, concepts, software, hardware and other components on a higher level of collaboration and strategical decision. As many application scenarios arise from geosciences and natural sciences, a number of examples are given based on implementations from these disciplines and case studies done over the last decade. Present activities and future work to be done on development and strategies level are presented to help overcome the stagnancy in the evolution of integrated systems. This chapter will show the components that in most other cases are discussed independently and presents a basic concept for integrating systems as successfully used with geosciences and natural sciences case studies.

#### **2. Capability versus capacity**

The high end computing world vastly used by geosciences researchers can be described with capability computing on the one hand and capacity computing on the other hand which provide complex tools to expand the means and methods of research by continuously expanding the limits of feasibility.

#### **2.1 Capability computing**

Capability computing means to target the grand challenge problems in certain fields. This will for example be the case with earthquake simulation, multi-dimensional modeling of the earth's underground, tornado simulation, atmosphere simulation, galaxy cluster simulation, non-linear computation of complex structures, life-sciences and epidemiological simulation, archaeological and architectural simulation. For the foreseeable future complex information and computing systems will be a topic on this list as soon as resources evolve. Systems for capability computing have to provide capacity for a few large jobs. Job processing for single-job scenarios can handle larger problems or faster solution. For these single jobs have main potential for insight on their own, merely not from context. Capability computing will usually not be the first association with information systems.

#### **2.2 Capacity computing**

2 Will-be-set-by-IN-TECH

assisting and integrated methods and techniques. Integrating these methods with information systems and the support of remote sensing, cartography, depth imaging, and infrastructural and social sources a more and more holistic view on the earth system will be possible. This will help to gain insight in the fields of seismology, meteorology, climatology, prospection and exploration, medical geology, epidemiology, environmental planning and many more disciplines. The resulting information systems and applications are not only used for scientific research but for public information, education, disaster management, expert systems and many more. In various application areas the surplus value arises with intelligent combination of information. A cartographic system only displaying spatial data is of less significance for a seismological disaster management application if there are no additional information and features provided. Provisioning these information will in many case result in interactive computation. For some use cases requests for points of interest, dynamical cartography, event programming, flexible event triggering, long-term monitoring like in seismology, catastrophe management and meteorology are necessary, for others simulation or modeling of scenarios are essential. All these fields of application contain tasks that cannot be handled in extend for large and complex systems on one local compute and storage resource only. Processes like processing jobs, visualisation, traveling salesman problems, and multimedia production have to be transferred to systems with the capacity necessary for multiple requests at the same time. We should not isolate scholarly research from long term information science concepts and architectures used in geosciences disciplines. Therefore the overall goal is to integrate systems, concepts, software, hardware and other components on a higher level of collaboration and strategical decision. As many application scenarios arise from geosciences and natural sciences, a number of examples are given based on implementations from these disciplines and case studies done over the last decade. Present activities and future work to be done on development and strategies level are presented to help overcome the stagnancy in the evolution of integrated systems. This chapter will show the components that in most other cases are discussed independently and presents a basic concept for integrating systems

as successfully used with geosciences and natural sciences case studies.

The high end computing world vastly used by geosciences researchers can be described with capability computing on the one hand and capacity computing on the other hand which provide complex tools to expand the means and methods of research by continuously

Capability computing means to target the grand challenge problems in certain fields. This will for example be the case with earthquake simulation, multi-dimensional modeling of the earth's underground, tornado simulation, atmosphere simulation, galaxy cluster simulation, non-linear computation of complex structures, life-sciences and epidemiological simulation, archaeological and architectural simulation. For the foreseeable future complex information and computing systems will be a topic on this list as soon as resources evolve. Systems for capability computing have to provide capacity for a few large jobs. Job processing for single-job scenarios can handle larger problems or faster solution. For these single jobs have

**2. Capability versus capacity**

expanding the limits of feasibility.

**2.1 Capability computing**

The more interesting along with the development of the next generation of system architectures is the opening of capacity computing for complex information systems. These systems provide capacity for many small or medium sized jobs. Job processing of several parallel jobs is suitable for these resources. The single job itself may be used for parameter studies, design alternatives, exploring pre-development stages, and in general these jobs on their own have less potential for insight. Making use of capacity computing resources many instances of compute jobs will run on a resource. This is what we need to enliven conventional information system implementations with new features, leading to new insights.

#### **3. Computing resources**

#### **3.1 Paradigms**

There is a number of different paradigms and resources that can be considered for this purpose and used from various geosciences disciplines. The topmost category for High End Computing (HEC) are High Performance Computing (HPC) and Supercomputing resources. These will in nearly all use cases be used in a non distributed manner. The lower end, Distributed Computing (DC) and services computing resources, are for example built on base of paradigms like Sky Computing, Cloud Computing, Grid Computing, Cluster Computing, Mobile Computing.

#### **3.2 Performance pyramid**

What do we have to expect to be the machines behind these paradigms? The answer is a performance pyramid. The performance pyramid for computing resources shows the following structure.

Top sector:


Medium and bottom sector:


#### **4. Computing obstacles**

The obstacles for operating complex resources with interactive systems with efficient and effective operation can be overcome while reacting on several levels, architectures, hardware, frameworks and middleware, applications, energy consumption, competence resources, consultancy, and support.

**5. Hardware resources**

and Computing Systems in Geosciences and Natural Sciences

hardware components.

**5.2 Resources cooling**

water-cooling (SGI, 2011).

**5.1 Resources infrastructure**

electronical and physical security measures.

Most scientific projects consider software and hardware issues to be treated separately. This would most likely be a problem for developing integrated systems on a solid holistic base. As for overall costs, for example with power consumption and staff, only very few institutions will be able to operate and develop those systems. The more complex these systems get, the less can the distinction between infrastructure resources and systems resources be recognised. As for understanding the complexity of these issues to be inseparable in the dimension of future integrated systems, the following paragraphs will illustrate some most important

<sup>5</sup> Queueing Aspects of Integrated Information

An unabdicable premise for safe and reliable operation complex and large systems are concepts and implementation of power resources, unbreakable power supplies, air conditioning, electronics, physical security and many more infrastructure components. Figure 1 shows infrastructure components necessary to operate a larger computer installation for the purpose of scientific computing: generator, air conditioning, power supplies, and

Fig. 1. Infrastructure components necessary to operate larger computer installations.

Besides the infrastructure, various measures associated directly with the computer systems are necessary and this will depend on the type of installation. Figure 2 shows one type of rack

As far as High End Computing (HEC) being a genus for High Performance Computing and various other ambitioned computing paradigms is an issue of national interest for most countries, reliability and security are the most important factors for operating these services. Science and Research is depending on the results of their computations. Just with this, everyone is depending on systems and operating systems used. So problems most imminent arise especially with the


With the increasing number of requests and interactivity the communication size, size of data, transfer band width, scalability, and mean times for failure get more important. An intelligent arrangement and configuration of system components and an overall management of system components gets into the focus.

The most prominent problem with the next generation of resources is quantity of components. The handling of quantity leads –besides many other challenges– to increased demands for encryption, IO, PCI, on-chip features, error correction (ECC), research and development, scientific and academic staff and supporting maintenance, operative and administrative staff, as well as for secondary dependencies like energy resources and unbreakable power supplies.

#### **4.1 Consumption**

The most prominent problem with quantity, besides the computing obstacles, is consumption. State of the art power and energy measures are for example Low Voltage memory (LV DIMM), Light Load Efficiency Mode (LLEM), multiple Power Supplies, watercooler chassis & air conditioning, higher temperature cooling, hot water cooling, hybrid cooling systems, Energy and Power Manager (Active Energy Manager, AEM and others), application/energy frequency optimisation, energy reduced low frequency Processors, Power Management, and Energy Management.

#### **4.2 Shortcommings**

Besides that modular, dynamical applications are rare, even in geosciences, shortcommings regarding application context and how to handle these aspects are obvious:


#### **5. Hardware resources**

4 Will-be-set-by-IN-TECH

As far as High End Computing (HEC) being a genus for High Performance Computing and various other ambitioned computing paradigms is an issue of national interest for most countries, reliability and security are the most important factors for operating these services. Science and Research is depending on the results of their computations. Just with this, everyone is depending on systems and operating systems used. So problems most imminent

With the increasing number of requests and interactivity the communication size, size of data, transfer band width, scalability, and mean times for failure get more important. An intelligent arrangement and configuration of system components and an overall management of system

The most prominent problem with the next generation of resources is quantity of components. The handling of quantity leads –besides many other challenges– to increased demands for encryption, IO, PCI, on-chip features, error correction (ECC), research and development, scientific and academic staff and supporting maintenance, operative and administrative staff, as well as for secondary dependencies like energy resources and unbreakable power supplies.

The most prominent problem with quantity, besides the computing obstacles, is consumption. State of the art power and energy measures are for example Low Voltage memory (LV DIMM), Light Load Efficiency Mode (LLEM), multiple Power Supplies, watercooler chassis & air conditioning, higher temperature cooling, hot water cooling, hybrid cooling systems, Energy and Power Manager (Active Energy Manager, AEM and others), application/energy frequency optimisation, energy reduced low frequency Processors, Power Management, and

Besides that modular, dynamical applications are rare, even in geosciences, shortcommings

regarding application context and how to handle these aspects are obvious:

• Architectures (CPU, GPU, GPGPU, FPGA, . . .), • Languages (high level languages, CUDA, . . .),

• Fast and broad band Networks,

arise especially with the • Large number of cores, • Large number of nodes, • Distributed memory usage,

• Large number of large hard disks, • Read and write speed of storage.

components gets into the focus.

**4.1 Consumption**

Energy Management.

**4.2 Shortcommings**

• Memory,

• Efficiency,

• Manageability, . . .

Most scientific projects consider software and hardware issues to be treated separately. This would most likely be a problem for developing integrated systems on a solid holistic base. As for overall costs, for example with power consumption and staff, only very few institutions will be able to operate and develop those systems. The more complex these systems get, the less can the distinction between infrastructure resources and systems resources be recognised. As for understanding the complexity of these issues to be inseparable in the dimension of future integrated systems, the following paragraphs will illustrate some most important hardware components.

#### **5.1 Resources infrastructure**

An unabdicable premise for safe and reliable operation complex and large systems are concepts and implementation of power resources, unbreakable power supplies, air conditioning, electronics, physical security and many more infrastructure components. Figure 1 shows infrastructure components necessary to operate a larger computer installation for the purpose of scientific computing: generator, air conditioning, power supplies, and electronical and physical security measures.

Fig. 1. Infrastructure components necessary to operate larger computer installations.

#### **5.2 Resources cooling**

Besides the infrastructure, various measures associated directly with the computer systems are necessary and this will depend on the type of installation. Figure 2 shows one type of rack water-cooling (SGI, 2011).

Fig. 4. Networks, cabling, switches.

connection for maintenance or emergencies.

and Computing Systems in Geosciences and Natural Sciences

appropriate RAID level, and redundant meta data storage servers.

Linking high end resources is an important factor for ensuring economical use and enabling for access. In many cases these connections are built for redundancy, in order to switch

<sup>7</sup> Queueing Aspects of Integrated Information

Not only systems connections can be created using fallbacks. Figure 5 shows a network switch connecting some compute resources on redundant pathes. With large numbers of components the rate of failure increases. Redundancy and appropriate concepts will minimise the risk due to component failures. Large resources, as we have seen, not only need redundant cores and memory but various additional redundancies. Figure 5 further shows redundant rack power supplies, redundant disk drive enclosures with redundant disks, for example with

Fig. 5. Redundancy with linking resources, rack power supplies, disk drive enclosures and

**5.6 Systems connection**

**5.7 System redundancy**

disks, meta data storage servers.

Fig. 2. Water-cooling in rack.

#### **5.3 System core resources**

For the main purpose of computing, large numbers of compute nodes are needed. The main system resources are cores and memory. The first two images in Figure 3 show a rack with compute nodes (SGI, 2011) and some thousand memory sticks needed for one supercomputer installation.

Fig. 3. Core resources and storage: compute nodes, memory, and disk storage unit.

#### **5.4 System networks**

With the increase of core resources, the more networks infrastructure is needed to operate these resources and make them accessible as a system. Figure 4 shows cabling and switches. Currently the significance of networks is rapidly increasing. Fibre optics are used to efficiently and effectively implementing networks. No wonder that in the year 2009 the physics Nobel Prize was dedicated to fibre optics, for the ground breaking achievements concerning the transmission of light in fibers for optical communication.

#### **5.5 System storage**

Besides cores, memory, and networks large storage capabilities are necessary for permanent storage. Figure 3 shows a disk storage unit consisting of several racks of hard disk drives, controllers, and servers.

Fig. 4. Networks, cabling, switches.

#### **5.6 Systems connection**

6 Will-be-set-by-IN-TECH

For the main purpose of computing, large numbers of compute nodes are needed. The main system resources are cores and memory. The first two images in Figure 3 show a rack with compute nodes (SGI, 2011) and some thousand memory sticks needed for one supercomputer

Fig. 3. Core resources and storage: compute nodes, memory, and disk storage unit.

transmission of light in fibers for optical communication.

With the increase of core resources, the more networks infrastructure is needed to operate these resources and make them accessible as a system. Figure 4 shows cabling and switches. Currently the significance of networks is rapidly increasing. Fibre optics are used to efficiently and effectively implementing networks. No wonder that in the year 2009 the physics Nobel Prize was dedicated to fibre optics, for the ground breaking achievements concerning the

Besides cores, memory, and networks large storage capabilities are necessary for permanent storage. Figure 3 shows a disk storage unit consisting of several racks of hard disk drives,

Fig. 2. Water-cooling in rack.

**5.3 System core resources**

installation.

**5.4 System networks**

**5.5 System storage**

controllers, and servers.

Linking high end resources is an important factor for ensuring economical use and enabling for access. In many cases these connections are built for redundancy, in order to switch connection for maintenance or emergencies.

#### **5.7 System redundancy**

Not only systems connections can be created using fallbacks. Figure 5 shows a network switch connecting some compute resources on redundant pathes. With large numbers of components the rate of failure increases. Redundancy and appropriate concepts will minimise the risk due to component failures. Large resources, as we have seen, not only need redundant cores and memory but various additional redundancies. Figure 5 further shows redundant rack power supplies, redundant disk drive enclosures with redundant disks, for example with appropriate RAID level, and redundant meta data storage servers.

Fig. 5. Redundancy with linking resources, rack power supplies, disk drive enclosures and disks, meta data storage servers.

**7. Software needs hardware**

components and resources.

economy.

et al., 2009).

and environment be handled?

**7.1 Geoexploration and integrated systems**

and Computing Systems in Geosciences and Natural Sciences

The next sections will present some examples on how these resources are used in geosciences and geoinformatics with integrated systems. It will show the complexity of the next generation of system architectures and usage that arises from integrating the necessary

<sup>9</sup> Queueing Aspects of Integrated Information

These sections present information system use cases and geoscientific application components that will profit from integrated information and computing systems using high end resources. It discusses features, concepts and frameworks, legal issues, technical requirements, and techniques needed for implementing these integrated systems. High Performance Computing has been recognised as one of the key technologies for the 21st century. It shows up with the problems existing today with implementing and using computing resources not only in batch mode but in combination with quasi interactive applications and it gives an outlook for future systems, components, and frameworks, and the work packages that have to be done by geoscientific disciplines, services and support, and resources providers from academia and

There are two main objectives for interfacing modular complex integrated information and computing systems: "trust in computing" and "trust in information". This goal for a long-term strategy means to concentrate on implementing methods for flexible use of envelope interfaces for use with integrated information and computing systems for managing objects and strengthen trust with systems from natural and geosciences, spatial sciences, and remote sensing as to be used for application, e.g., in environment management, healthcare or archaeology. Spatial means are tools, for the sciences involved. Therefore processing and computing is referred to the content which is embedded and used from the visual domain. Over the last years a long-term project, Geo Exploration and Information (GEXI) (GEXI, 1996, 1999, 2011) for analysing national and international case studies and creating as well as testing various implementation scenarios, has shown the two trust groups of systems, reflected by the collaboration matrices (Rückemann, 2010a). It has examined chances to overcome the deficits, built a collaboration framework and illuminated legal aspects and benefits (EULISP, 2011; Rückemann, 2010b). The information and instructions handled within these systems is one of the crucial points while systems are evolving by information-driven transformation (Mackert

For computing and information intensive systems the limiting constraints are manyfold. Recycling of architecture native and application centric algorithms is very welcome. In order to reuse information about these tasks and jobs, it is necessary to enable users to separate the respective information for system and application components. This can be done by structured envelope-like descriptions containing essential workflow information, algorithms, instructions, data, and meta data. The container concept developed has been called Compute Envelope (CEN). The idea of envelope-like descriptive containers has been inspired by the good experiences with the concept of Self Contained applications (SFC) (Rückemann, 2001). Envelopes can be used to integrate descriptive and generic processing information. Main questions regarding the topics of computing envelope interfaces are: Which content can be embedded or referenced in envelopes? How will these envelope objects be integrated into an information and computing system and how can the content be used? How can the context

#### **5.8 System operating**

System operating will have to ensure local system access, component and services monitoring as well as hardware, physical and logical maintenance. Figure 6 illustrates operating access using local console, remote access, monitoring and physical maintenance.

Fig. 6. Operating using local console access, remote access, monitoring and physical maintenance.

#### **6. Resources prerequisites**

The complexity of these aspects shows why the integration of computing resources has takes so much time and why this is on the turn now. When we want do the planning for future resources and consumptive prerequisites there are essential requirements for technical and competence resources. For the technical resources we have to implement efficient and effective general purpose system installations, for loosely as well as for massively parallel processing:


For the competence resources a sustainable infrastructure has to be built, regarding research, scientific consulting, staff, operation, systems management, technical consulting, and administrative measures. Goals with using these resources are dynamically provisioning of secondary information, calculation and computation results, modeling and simulation. For exploiting the existing and future compute and storage resources, the basic "trust in computing" and "trust in information" requirements have therefore to be implemented in complex environments. For many scenarios this leads to international collaborations for data collection and use as well as to modular development and operation of components. The geosciences as other natural sciences cannot fulfill these requirements without interdisciplinary research and collaboration.

#### **7. Software needs hardware**

8 Will-be-set-by-IN-TECH

System operating will have to ensure local system access, component and services monitoring as well as hardware, physical and logical maintenance. Figure 6 illustrates operating access

using local console, remote access, monitoring and physical maintenance.

Fig. 6. Operating using local console access, remote access, monitoring and physical

• Accessing Computing Power (MPI / OpenMP / loosely coupled interactive),

• Efficiency (Computing Power / Power Consumption),

without interdisciplinary research and collaboration.

The complexity of these aspects shows why the integration of computing resources has takes so much time and why this is on the turn now. When we want do the planning for future resources and consumptive prerequisites there are essential requirements for technical and competence resources. For the technical resources we have to implement efficient and effective general purpose system installations, for loosely as well as for massively parallel processing: • Architecture (e.g. MPP Massively Parallel Processing / SMP Symmetric Multi-Processing),

For the competence resources a sustainable infrastructure has to be built, regarding research, scientific consulting, staff, operation, systems management, technical consulting, and administrative measures. Goals with using these resources are dynamically provisioning of secondary information, calculation and computation results, modeling and simulation. For exploiting the existing and future compute and storage resources, the basic "trust in computing" and "trust in information" requirements have therefore to be implemented in complex environments. For many scenarios this leads to international collaborations for data collection and use as well as to modular development and operation of components. The geosciences as other natural sciences cannot fulfill these requirements

**5.8 System operating**

maintenance.

**6. Resources prerequisites**

• Storage and Archive.

The next sections will present some examples on how these resources are used in geosciences and geoinformatics with integrated systems. It will show the complexity of the next generation of system architectures and usage that arises from integrating the necessary components and resources.

#### **7.1 Geoexploration and integrated systems**

These sections present information system use cases and geoscientific application components that will profit from integrated information and computing systems using high end resources. It discusses features, concepts and frameworks, legal issues, technical requirements, and techniques needed for implementing these integrated systems. High Performance Computing has been recognised as one of the key technologies for the 21st century. It shows up with the problems existing today with implementing and using computing resources not only in batch mode but in combination with quasi interactive applications and it gives an outlook for future systems, components, and frameworks, and the work packages that have to be done by geoscientific disciplines, services and support, and resources providers from academia and economy.

There are two main objectives for interfacing modular complex integrated information and computing systems: "trust in computing" and "trust in information". This goal for a long-term strategy means to concentrate on implementing methods for flexible use of envelope interfaces for use with integrated information and computing systems for managing objects and strengthen trust with systems from natural and geosciences, spatial sciences, and remote sensing as to be used for application, e.g., in environment management, healthcare or archaeology. Spatial means are tools, for the sciences involved. Therefore processing and computing is referred to the content which is embedded and used from the visual domain. Over the last years a long-term project, Geo Exploration and Information (GEXI) (GEXI, 1996, 1999, 2011) for analysing national and international case studies and creating as well as testing various implementation scenarios, has shown the two trust groups of systems, reflected by the collaboration matrices (Rückemann, 2010a). It has examined chances to overcome the deficits, built a collaboration framework and illuminated legal aspects and benefits (EULISP, 2011; Rückemann, 2010b). The information and instructions handled within these systems is one of the crucial points while systems are evolving by information-driven transformation (Mackert et al., 2009).

For computing and information intensive systems the limiting constraints are manyfold. Recycling of architecture native and application centric algorithms is very welcome. In order to reuse information about these tasks and jobs, it is necessary to enable users to separate the respective information for system and application components. This can be done by structured envelope-like descriptions containing essential workflow information, algorithms, instructions, data, and meta data. The container concept developed has been called Compute Envelope (CEN). The idea of envelope-like descriptive containers has been inspired by the good experiences with the concept of Self Contained applications (SFC) (Rückemann, 2001). Envelopes can be used to integrate descriptive and generic processing information. Main questions regarding the topics of computing envelope interfaces are: Which content can be embedded or referenced in envelopes? How will these envelope objects be integrated into an information and computing system and how can the content be used? How can the context and environment be handled?

and data collections. These architectures can be centralised or distributed. For the different purposes the implementations will use database software, file systems structures, meta data collection or combinations of more than one mechanism. In any case there should be a flexible and standardised way to interface and access the information. The information created within the LX Project has been subject of a long-term research initiative. It covers and combines for example educationary treatises, individual and definitions and descriptions, scientific results, as well as Point of Interest (POI) information. It is capable of handling categorisation, ergonomic multi-lingual representations as well as information alternatives for various different purposes. It integrates typesetting issues and publishing, including formulas, customised sorting, indexing, and timeline functions for the information objects.

<sup>11</sup> Queueing Aspects of Integrated Information

 Caldera %-GP%-XX%---: Caldera [Vulkanologie, Geologie]: %-GP%-DE%---: \lxidx{Schüsselkrater}, %-GP%-DE%---: \lxidx{Chaldera}, %-GP%-DE%---: \lxidx{Caldera}, %-GP%-DE%---: \lxidx{cauldron}, %-GP%-DE%---: \lxidx{Kessel}.

<sup>8</sup> %-GP%-EN%---: \lxidx{Chaldera}, <sup>9</sup> %-GP%-EN%---: \lxidx{Schüsselkrater},

<sup>10</sup> %-GP%-EN%---: \lxidx{Caldera}, <sup>11</sup> %-GP%-EN%---: \lxidx{cauldron}, <sup>12</sup> %-GP%-EN%---: \lxidx{Kessel}.

<sup>14</sup> %-GP%-DE%---: s. auch Capping stage <sup>15</sup> %-GP%-EN%---: s. also Capping stage

The integration of interactive and batch resources usage with dynamical applications does need flexibility in terms of interfaces and configuration. Various use cases studied distributed resources like capacity resources with Condor for example on ZIVcluster resources and on the other hand with High Performance Computing resources for example on ZIVSMP and HLRN

As well as analysing and separating the essential layers for building complex integrated systems, it is essential that these allow a holistic view on the overall system, for operation, development, and strategies level. The framework developed (Rückemann, 2010b) and studied for integrated information and computing is the Grid-GIS house (Figure 8) (Rückemann, 2009). An implementation of this kind is very complex and can only be handled with a modular architecture being able to separate tasks and responsibilities for resources (HEC, HPC), services, and disciplines. Figure 9 illustrates the logical components for integrated monitoring, accounting, and billing architecture for distributed resources and data usage. The legal aspects of combined usage of geo applications with services and distributed

<sup>17</sup> %-GP%-XX%---: %%NET: http://...

Listing 1 shows a simple example for an LX Encyclopedia entry.

and Computing Systems in Geosciences and Natural Sciences

<sup>7</sup> %-GP%-DE%---: ...

<sup>13</sup> %-GP%-EN%---: ...

(HLRN, 2011; ZIVGrid, 2008; ZIVHPC, 2011; ZIVSMP, 2011).

**8. Integration framework – resources, services, disciplines**

Listing 1. Example LX Encyclopedia entry.

**7.4 High End Computing**

<sup>16</sup> %-GP%-XX%---: %%SRC: ...

#### **7.2 Geoscientific Information Systems and Active Source**

One of the most essential components for integrating geoexploration components and the access to computing resources are dynamical Geoscientific Information Systems (GIS) (Rückemann, 2001). Some screenshots of a dynamical GIS (Rückemann, 2009) illustrate the facettes: Using dynamical data, raster, vector, secondary data, and events (Figure 7a), embedding dynamical components into components (Figure 7b), interacting with external components (Figure 7c), extending the user interface (Figure 7d).

(a) Raster, vector, secondary data, and events. (b) Embed dynamical components into components.

(c) Interact with external components. (d) Extend the user interface.

Fig. 7. Facettes of an Integrated Information System.

#### **7.3 Information databases**

Information databases are the base for many components in Information Systems. There are various concepts built on classical database architectures, special information structures, 10 Will-be-set-by-IN-TECH

One of the most essential components for integrating geoexploration components and the access to computing resources are dynamical Geoscientific Information Systems (GIS) (Rückemann, 2001). Some screenshots of a dynamical GIS (Rückemann, 2009) illustrate the facettes: Using dynamical data, raster, vector, secondary data, and events (Figure 7a), embedding dynamical components into components (Figure 7b), interacting with external

(a) Raster, vector, secondary data, and events. (b) Embed dynamical components into components.

(c) Interact with external components. (d) Extend the user interface.

Information databases are the base for many components in Information Systems. There are various concepts built on classical database architectures, special information structures,

Fig. 7. Facettes of an Integrated Information System.

**7.3 Information databases**

**7.2 Geoscientific Information Systems and Active Source**

components (Figure 7c), extending the user interface (Figure 7d).

and data collections. These architectures can be centralised or distributed. For the different purposes the implementations will use database software, file systems structures, meta data collection or combinations of more than one mechanism. In any case there should be a flexible and standardised way to interface and access the information. The information created within the LX Project has been subject of a long-term research initiative. It covers and combines for example educationary treatises, individual and definitions and descriptions, scientific results, as well as Point of Interest (POI) information. It is capable of handling categorisation, ergonomic multi-lingual representations as well as information alternatives for various different purposes. It integrates typesetting issues and publishing, including formulas, customised sorting, indexing, and timeline functions for the information objects. Listing 1 shows a simple example for an LX Encyclopedia entry.


Listing 1. Example LX Encyclopedia entry.

#### **7.4 High End Computing**

The integration of interactive and batch resources usage with dynamical applications does need flexibility in terms of interfaces and configuration. Various use cases studied distributed resources like capacity resources with Condor for example on ZIVcluster resources and on the other hand with High Performance Computing resources for example on ZIVSMP and HLRN (HLRN, 2011; ZIVGrid, 2008; ZIVHPC, 2011; ZIVSMP, 2011).

#### **8. Integration framework – resources, services, disciplines**

As well as analysing and separating the essential layers for building complex integrated systems, it is essential that these allow a holistic view on the overall system, for operation, development, and strategies level. The framework developed (Rückemann, 2010b) and studied for integrated information and computing is the Grid-GIS house (Figure 8) (Rückemann, 2009). An implementation of this kind is very complex and can only be handled with a modular architecture being able to separate tasks and responsibilities for resources (HEC, HPC), services, and disciplines. Figure 9 illustrates the logical components for integrated monitoring, accounting, and billing architecture for distributed resources and data usage. The legal aspects of combined usage of geo applications with services and distributed

**Local Law**

**Transfer Trusted Comp. Recherche/search Georeferencing Referencing Access**

**Automation**

**Privacy QoS Pricing**

and Computing Systems in Geosciences and Natural Sciences

**Exploration Environment**

**Location**

**Physical security**

**9. Integrated – InfoPoints using distributed resources**

• interactive dynamical applications (frontend),

**Tracking**

**Content**

**Time QoD Pricing**

usage.

procedures and data.

components are:

**DC**

<sup>13</sup> Queueing Aspects of Integrated Information

**Service security**

**Accounting Billing**

**Access**

**Network security Data security**

**Geo HPC**

derivatives and C (Tcl Developer Site, 2010), like the actmap application and Active Map

Using auto-events, dynamical cartography, and geocognostic aspects, views and applications using distributed compute and storage resources can be created very flexibly. As with the concept presented resources available from Distributed Systems, High Performance Computing, Grid and Cloud services, and available networks can be used. The main

• distributed resources, compute and storage, configured for interactive and batch use, • parallel applications and components (backend), as available on the resources, • a framework with interfaces for using parallel applications interactively.

Besides the traditional visualisation a lot of disciplines like geo-resources and energy exploration, archaeology, medicine, epidemology and for example various applications within the tourism industry can profit from the e-Science components. These e-Science components can be used for Geoscientific Information Systems for dynamical InfoPoints and multimedia,

Fig. 10. Legal aspects of combined geo applications, services, and distributed resources

**Algorithms Licenses Policies**

**Physical security**

**High Availability**

**Pricing**

**Shared/exclusive access**

Fig. 8. Framework for integrated information and computing.

Fig. 9. Integrated monitoring, accounting, and billing architecture.

resources (Rückemann, 2010a;b) is shown in Figure 10. As the various components need dynamical and user-space interfaces, scripting mechanisms are unabdicable. The following sections discuss an example of a dynamical application using different distributed resources via flexible methods. Dynamical components and interfaces are implemented with Tcl and 12 Will-be-set-by-IN-TECH

**Geo− Geoscientific**

**companies, universities ... Provider, Scientific institutions,**

**Geoinformatics, Geophysics, Geology, Geography, ...**

**Geo services: Web Services / Grid−GIS services**

**Navigation Integration**

**Geo−Information, Customers, Service,**

**Multiscale geo−data Integration/fusion GIS**

**Visualisation Service chains Quality management**

**Simulation Geo−scientific processing**

**Services**

**Visualisation Resource requirements**

**Workflows Data management**

**GIS**

**Grid middleware**

**High Performance Computing and Grid resources**

**monitoring job mon.**

**resource mon.**

**accounting**

**transmission of accounting data**

**monitoring data possible) (direct transmission of**

**billing**

resources (Rückemann, 2010a;b) is shown in Figure 10. As the various components need dynamical and user-space interfaces, scripting mechanisms are unabdicable. The following sections discuss an example of a dynamical application using different distributed resources via flexible methods. Dynamical components and interfaces are implemented with Tcl and

**resources**

**R R R R**

Fig. 8. Framework for integrated information and computing.

**resource assignment**

**status information**

**valuation**

**resource**

**e.g. global User ID user information**

Fig. 9. Integrated monitoring, accounting, and billing architecture.

**Distributed/mobile**

**Grid services**

**Data Collection/Automation Data Processing Data Transfer**

**Security**

**components**

**Geo−data**

**computing Trusted &**

**Distributed**

**records accounting**

> **records billing**

**VO management**

**storage**

**data access**

**access data storage**

**data monitoring storage of**

> **monitoring records**

**computing res. data storage**

**Distributed**

**monitoring**

**MPI Interactive**

**Batch**

**NG−Arch. Design**

**information and accounting of monitoring**

**visualisation**

**accounting CSM data**

**access accounting records**

**data monitoring**

**Legal**

**Framework**

**Point/Line**

**Metadata**

**Algorithms**

**Tracking Geo monitoring**

**2D/2.5D**

**3D/4D MMedia/POI**

**Parallel.**

**Interface Vector data**

**Data Service**

**Broadband**

**Raster data**

**Accounting**

**Networks InfiniBand**

**specification resource**

**resource broker**

**request**

**resource description & valuation**

**meta scheduler**

**transmission of billing/accounting information**

**Customers Market**

**Virtualisation**

**Exploration Ecology**

**Generalisation**

**HPC**

**job user**

**resource description**

**Computing Services Distrib.**

**Market Service Provider**

**Sciences Energy− Sciences Environm.**

Fig. 10. Legal aspects of combined geo applications, services, and distributed resources usage.

derivatives and C (Tcl Developer Site, 2010), like the actmap application and Active Map procedures and data.

#### **9. Integrated – InfoPoints using distributed resources**

Using auto-events, dynamical cartography, and geocognostic aspects, views and applications using distributed compute and storage resources can be created very flexibly. As with the concept presented resources available from Distributed Systems, High Performance Computing, Grid and Cloud services, and available networks can be used. The main components are:


Besides the traditional visualisation a lot of disciplines like geo-resources and energy exploration, archaeology, medicine, epidemology and for example various applications within the tourism industry can profit from the e-Science components. These e-Science components can be used for Geoscientific Information Systems for dynamical InfoPoints and multimedia,

<sup>1</sup> #

<sup>3</sup> # 4 <sup>5</sup> #

<sup>7</sup> # 8

11

15

18

<sup>9</sup> erasePict

<sup>17</sup> removeGrid

framework (Listing 3).

**9.4 InfoPoints Active Source**

(as shown in Figure **??**).

<sup>7</sup> **global** w <sup>8</sup> # Yucatan

<sup>17</sup> **global** w

<sup>12</sup> ...

<sup>14</sup> } 15

<sup>19</sup> ##EOF:

<sup>6</sup> # Active map of Mexico

<sup>16</sup> openSource mexico.gas

<sup>10</sup> \$w configure -background turquoise

<sup>13</sup> .poly .line .rect .oval .setcolor <sup>14</sup> pack **forget** .popupmode .optmen\_zoom

Listing 2. Example InfoPoint Binding Data.

<sup>1</sup> /home/cpr/gisig/actmap\_sb.sfc mexico.bnd Listing 3. Example creating the dynamical application.

<sup>1</sup> #BCMT-------------------------------------------------

<sup>5</sup> #ECMT-------------------------------------------------

<sup>9</sup> \$w create polygon 9.691339i 4.547244i 9.667717i \ <sup>10</sup> 4.541732i 9.644094i 4.535433i 9.620472i 4.523622i \ <sup>11</sup> 9.596850i 4.511811i 9.573228i 4.506299i 9.531496i \

<sup>2</sup> ###EN \gisigsnip{Object Data: Country Mexico} <sup>3</sup> ###EN Minimal Active Source example with InfoPoint:

<sup>4</sup> ###EN Yucatan (Cancun, Chichen Itza, Tulum).

<sup>6</sup> **proc** create\_country\_mexico {} {

<sup>16</sup> **proc** create\_country\_mexico\_bind {} {

<sup>19</sup> \$w bind province\_quintana\_roo <Button-1> \

<sup>12</sup> pack **forget** .scale .drawmode .tagborderwidth \

and Computing Systems in Geosciences and Natural Sciences

<sup>2</sup> # actmap example -- (c) Claus-Peter R\"uckemann, 2008, 2009

<sup>15</sup> Queueing Aspects of Integrated Information

This dynamical application can be created by loading the Active Source data with the actmap

The following Active Source code (Listing 4) shows a tiny excerpt of the Active Source for the interactive Map of México containing some main functional parts for the InfoPoint Yucatán

<sup>13</sup> -outline #000000 -width 2 -fill green -tags {itemshape province\_yucatan}

<sup>18</sup> \$w bind province\_yucatan <Button-1> {showName "Province Yucatan"}

<sup>20</sup> {showName "Province Quintana Roo"}

Points of Interest based on Active Source (Active POI), dynamical mapping, and dynamical applications.

#### **9.1 InfoPoints and dynamical cartography**

With the integration of interactive dynamical components and dynamical cartography various surplus values can be used. Figure **??**a shows an interactive Map of México (Rückemann, 2009). The yellow circle is an event sensitive Active Source object containing a collection of references for particular objects in the application. This type of object has been named InfoPoint. InfoPoints can use any type of start and stop routines triggered by events. Figure **??**b shows a defined assortment of information, a view set, fetched and presented by triggering an event on the InfoPoint. The information has been referenced from within

(a) Interactive México with InfoPoint Yucatán. (b) Sample view set of InfoPoint Yucatán.

Fig. 11. Integrated interactive dynamical components and InfoPoints.

the World Wide Web in this case. InfoPoints can depend on the cognitive context within the application as this is a basic feature of Active Source: Creating an application data set it is for example possible to define the Level of Detail (LoD) for zoom levels and how the application handles different kinds of objects like Points of Interest (PoI) or resolution of photos in the focus area of the pointing device.

#### **9.2 Inside InfoPoints**

The following passages show all the minimal components necessary for a fully functional InfoPoint. The example for this case study is mainly based on the Active Source framework. Triggered program execution ("Geoevents") of applications is shown with event bindings, start and stop routines for the data.

#### **9.3 InfoPoints bindings and creation**

Listing 2 shows the creation of the canvas for the InfoPoint and loading of the Active Source via bindings.

14 Will-be-set-by-IN-TECH

Points of Interest based on Active Source (Active POI), dynamical mapping, and dynamical

With the integration of interactive dynamical components and dynamical cartography various surplus values can be used. Figure **??**a shows an interactive Map of México (Rückemann, 2009). The yellow circle is an event sensitive Active Source object containing a collection of references for particular objects in the application. This type of object has been named InfoPoint. InfoPoints can use any type of start and stop routines triggered by events. Figure **??**b shows a defined assortment of information, a view set, fetched and presented by triggering an event on the InfoPoint. The information has been referenced from within

(a) Interactive México with InfoPoint Yucatán. (b) Sample view set of InfoPoint Yucatán.

the World Wide Web in this case. InfoPoints can depend on the cognitive context within the application as this is a basic feature of Active Source: Creating an application data set it is for example possible to define the Level of Detail (LoD) for zoom levels and how the application handles different kinds of objects like Points of Interest (PoI) or resolution of photos in the

The following passages show all the minimal components necessary for a fully functional InfoPoint. The example for this case study is mainly based on the Active Source framework. Triggered program execution ("Geoevents") of applications is shown with event bindings,

Listing 2 shows the creation of the canvas for the InfoPoint and loading of the Active Source

Fig. 11. Integrated interactive dynamical components and InfoPoints.

focus area of the pointing device.

start and stop routines for the data.

**9.3 InfoPoints bindings and creation**

**9.2 Inside InfoPoints**

via bindings.

applications.

**9.1 InfoPoints and dynamical cartography**

```
1 #
2 # actmap example -- (c) Claus-Peter R\"uckemann, 2008, 2009
3 #
4
5 #
6 # Active map of Mexico
7 #
8
9 erasePict
10 $w configure -background turquoise
11
12 pack forget .scale .drawmode .tagborderwidth \
13 .poly .line .rect .oval .setcolor
14 pack forget .popupmode .optmen_zoom
15
16 openSource mexico.gas
17 removeGrid
18
19 ##EOF:
```
Listing 2. Example InfoPoint Binding Data.

This dynamical application can be created by loading the Active Source data with the actmap framework (Listing 3).

```
1 /home/cpr/gisig/actmap_sb.sfc mexico.bnd
```
Listing 3. Example creating the dynamical application.

#### **9.4 InfoPoints Active Source**

The following Active Source code (Listing 4) shows a tiny excerpt of the Active Source for the interactive Map of México containing some main functional parts for the InfoPoint Yucatán (as shown in Figure **??**).

```
1 #BCMT-------------------------------------------------
2 ###EN \gisigsnip{Object Data: Country Mexico}
3 ###EN Minimal Active Source example with InfoPoint:
4 ###EN Yucatan (Cancun, Chichen Itza, Tulum).
5 #ECMT-------------------------------------------------
6 proc create_country_mexico {} {
7 global w
8 # Yucatan
9 $w create polygon 9.691339i 4.547244i 9.667717i \
10 4.541732i 9.644094i 4.535433i 9.620472i 4.523622i \
11 9.596850i 4.511811i 9.573228i 4.506299i 9.531496i \
12 ...
13 -outline #000000 -width 2 -fill green -tags {itemshape province_yucatan}
14 }
15
16 proc create_country_mexico_bind {} {
17 global w
18 $w bind province_yucatan <Button-1> {showName "Province Yucatan"}
19 $w bind province_quintana_roo <Button-1> \
20 {showName "Province Quintana Roo"}
```
**proc** create\_country\_mexico\_application\_ballons {} {

and Computing Systems in Geosciences and Natural Sciences

create\_country\_mexico\_application\_ballons

Listing 4. Example InfoPoint Active Source data.

depicted in the source are the procedures for:

 gisig:set\_balloon \$is1.country "Notation of State and Site" gisig:set\_balloon \$is1.color "Symbolic Color od State and Site"

The source contains a minimal example with the active objects for the province Yucatán in México. The full data set contains all provinces as shown in Figure **??**. The functional parts

<sup>17</sup> Queueing Aspects of Integrated Information

The cartographic mapping data (polygon data in this example only) including attribute

The event bindings for the provinces. Active Source functions are called, displaying

Selected site names on the map and the active objects for site objects including the InfoPoint object. The classification of the InfoPoint is done using the tag legend\_infopoint. Any internal or external actions like context dependent scripting can be triggered by single

Some autoevents with the event definitions for the objects (Enter and Leave events in this

• Call section: The call section contains function calls for creating the components for the Active Source application at the start of the application, in this case the above procedures

Any number of groups of objects can be build. This excerpt only contains Cancun, Chichen Itza and Tulum. A more complex for this example data set will group data within topics, any category can be distinguished into subcategories in order to calculate specific views and

 **global** w **global** is1

 create\_country\_mexico create\_country\_mexico\_bind create\_country\_mexico\_sites create\_country\_mexico\_autoevents

scaleAllCanvas 0.8

• create\_country\_mexico:

• create\_country\_mexico\_bind:

• create\_country\_mexico\_sites:

objects or groups of objects.

and scaling at startup.

• create\_country\_mexico\_autoevents:

• island (Isla Mujeres, Isla Cozumel),

• create\_country\_mexico\_application\_ballons:

Information for this data used within the Active Source application.

multimedia information, for example for the category site used here:

• city (México City, Valladolid, Mérida, Playa del Carmen),

and tag data.

province names.

example).

 } 

##EOF

```
21 }
22
23 proc create_country_mexico_sites {} {
24 global w
25 global text_site_name_cancun
26 global text_site_name_chichen_itza
27 global text_site_name_tulum
28 set text_site_name_cancun "Cancún"
29 set text_site_name_chichen_itza "Chichén Itzá"
30 set text_site_name_tulum "Tulum"
31
32 $w create oval 8.80i 4.00i 9.30i 4.50i \
33 -fill yellow -width 3 \
34 -tags {itemshape site legend_infopoint}
35 $w bind legend_infopoint <Button-1> \
36 {showName "Legend InfoPoint"}
37 $w bind legend_infopoint <Shift-Button-3> \
38 {exec browedit$t_suff}
39
40 $w create oval 9.93i 4.60i 9.98i 4.65i \
41 -fill white -width 1 \
42 -tags {itemshape site cancun}
43 $w bind cancun <Button-1> \
44 {showName "$text_site_name_cancun"}
45 $w bind cancun <Shift-Button-3> \
46 {exec browedit$t_suff}
47
48 $w create oval 9.30i 4.85i 9.36i 4.90i \
49 -fill white -width 1 \
50 -tags {itemshape site chichen_itza}
51 $w bind chichen_itza <Button-1> \
52 {showName "$text_site_name_chichen_itza"}
53 $w bind chichen_itza <Shift-Button-3> \
54 {exec browedit$t_suff}
55 ...
56 }
57
58 proc create_country_mexico_autoevents {} {
59 global w
60 $w bind legend_infopoint <Any-Enter> {set killatleave \
61 [exec ./mexico_legend_infopoint_viewall.sh $op_parallel ] }
62 $w bind legend_infopoint <Any-Leave> \
63 {exec ./mexico_legend_infopoint_kaxv.sh }
64
65 $w bind cancun <Any-Enter> {set killatleave \
66 [exec $appl_image_viewer -geometry +800+400 \
67 ./mexico_site_name_cancun.jpg $op_parallel ] }
68 $w bind cancun <Any-Leave> {exec kill -9 $killatleave }
69
70 $w bind chichen_itza <Any-Enter> {set killatleave \
71 [exec $appl_image_viewer -geometry +800+100 \
72 ./mexico_site_name_chichen_itza.jpg $op_parallel ] }
73 $w bind chichen_itza <Any-Leave> {exec kill -9 $killatleave }
74 ...
75 }
76
```

```
77 proc create_country_mexico_application_ballons {} {
78 global w
79 global is1
80 gisig:set_balloon $is1.country "Notation of State and Site"
81 gisig:set_balloon $is1.color "Symbolic Color od State and Site"
82 }
83
84 create_country_mexico
85 create_country_mexico_bind
86 create_country_mexico_sites
87 create_country_mexico_autoevents
88 create_country_mexico_application_ballons
89 scaleAllCanvas 0.8
90 ##EOF
```
Listing 4. Example InfoPoint Active Source data.

The source contains a minimal example with the active objects for the province Yucatán in México. The full data set contains all provinces as shown in Figure **??**. The functional parts depicted in the source are the procedures for:

• create\_country\_mexico:

Will-be-set-by-IN-TECH

 } 

 ... } 

 ... } 

**global** w

**global** w

**proc** create\_country\_mexico\_sites {} {

 **set** text\_site\_name\_cancun "Cancún" **set** text\_site\_name\_chichen\_itza "Chichén Itzá"

**set** text\_site\_name\_tulum "Tulum"

\$w create oval 8.80i 4.00i 9.30i 4.50i \

 -tags {itemshape site legend\_infopoint} \$w bind legend\_infopoint <Button-1> \ {showName "Legend InfoPoint"}

\$w bind legend\_infopoint <Shift-Button-3> \

\$w create oval 9.93i 4.60i 9.98i 4.65i \

 {showName "\$text\_site\_name\_cancun"} \$w bind cancun <Shift-Button-3> \

\$w create oval 9.30i 4.85i 9.36i 4.90i \

 {showName "\$text\_site\_name\_chichen\_itza"} \$w bind chichen\_itza <Shift-Button-3> \

**proc** create\_country\_mexico\_autoevents {} {

\$w bind cancun <Any-Enter> {**set** killatleave \

 \$w bind legend\_infopoint <Any-Leave> \ {**exec** ./mexico\_legend\_infopoint\_kaxv.sh }

\$w bind legend\_infopoint <Any-Enter> {**set** killatleave \

\$w bind cancun <Any-Leave> {**exec** kill -9 \$killatleave }

\$w bind chichen\_itza <Any-Enter> {**set** killatleave \

[**exec** ./mexico\_legend\_infopoint\_viewall.sh \$op\_parallel ] }

 [**exec** \$appl\_image\_viewer -geometry +800+400 \ ./mexico\_site\_name\_cancun.jpg \$op\_parallel ] }

[**exec** \$appl\_image\_viewer -geometry +800+100 \

\$w bind chichen\_itza <Any-Leave> {**exec** kill -9 \$killatleave }

./mexico\_site\_name\_chichen\_itza.jpg \$op\_parallel ] }

 -tags {itemshape site chichen\_itza} \$w bind chichen\_itza <Button-1> \

 **global** text\_site\_name\_cancun **global** text\_site\_name\_chichen\_itza

**global** text\_site\_name\_tulum


{**exec** browedit\$t\_suff}


{**exec** browedit\$t\_suff}


{**exec** browedit\$t\_suff}

 -tags {itemshape site cancun} \$w bind cancun <Button-1> \

The cartographic mapping data (polygon data in this example only) including attribute and tag data.


Any number of groups of objects can be build. This excerpt only contains Cancun, Chichen Itza and Tulum. A more complex for this example data set will group data within topics, any category can be distinguished into subcategories in order to calculate specific views and multimedia information, for example for the category site used here:


<sup>1</sup> <ObjectEnvelope><!-- ObjectEnvelope (OEN)-->

and Computing Systems in Geosciences and Natural Sciences

<sup>6</sup> <DateCreated>2010-08-01:221114</DateCreated> <sup>7</sup> <DateModified>2010-08-01:222029</DateModified> <sup>8</sup> <**ID**>...</**ID**><CertificateID>...</CertificateID>

Listing 7. Example for an Object Envelope (OEN).

<sup>3</sup> <Filename>GIS\_Case\_Study\_20090804.jpg</Filename>

<sup>10</sup> <Content><ContentData>...</ContentData></Content>

small example for an OEN file using a content DataReference.

<sup>3</sup> <Filename>GIS\_Case\_Study\_20090804.jpg</Filename>

<sup>10</sup> <Content><DataReference>https://doi...</DataReference></Content>

**9.8 Implemented solution for integrated systems with massive resources requirements** For most interactive information system components a configuration of the distributed resources environment was needed. In opposite to OEN use, making it necessary to have referenced instead of embedded data for huge data sets, for CEN it should be possible to embed the essential instruction data. So there is less need for minimising data overhead and communication. Envelope technology is meant to be a generic extensible concept for information and computing system components (Rückemann, 2011). Figure 12 shows the workflow with application scenarios from GEXI case studies (Rückemann, 2010b). Future

<sup>1</sup> <ObjectEnvelope><!-- ObjectEnvelope (OEN)-->

<sup>6</sup> <DateCreated>2010-08-01:221114</DateCreated> <sup>7</sup> <DateModified>2010-08-01:222029</DateModified> <sup>8</sup> <**ID**>...</**ID**><CertificateID>...</CertificateID>

An end-user public client application may be implemented via a browser plugin, based on appropriate services. With OEN instructions embedded in envelopes, for example as XML-based element structure representation, content can be handled as content-stream or as content-reference. The way this will have to be implemented for different use cases depends on the situation, and in many cases on the size and number of data objects. Listing 8 shows a

<sup>19</sup> Queueing Aspects of Integrated Information

<sup>2</sup> <Object>

<sup>11</sup> </Object>

<sup>2</sup> <Object>

<sup>11</sup> </Object>

<sup>12</sup> </ObjectEnvelope>

<sup>4</sup> <Md5sum>...</Md5sum> <sup>5</sup> <Sha1sum>...</Sha1sum>

<sup>9</sup> <Signature>...</Signature>

Listing 8. OEN referencing signed data.

objectives for client components are:

• Verify signed objects on demand.

• Channels for limiting communication traffic, • Qualified signature services and accounting, • Using signed objects without verification,

<sup>12</sup> </ObjectEnvelope>

<sup>4</sup> <Md5sum>...</Md5sum> <sup>5</sup> <Sha1sum>...</Sha1sum>

<sup>9</sup> <Signature>...</Signature>


Objects can belong to more than one category or subcategory as for example some categories or all of these as well as single objects can be classified touristic. The data, as contained in the procedures here (mapping data, events, autoevents, objects, bindings and so on) can be put into a database for handling huge data collections.

#### **9.5 Start an InfoPoint**

Listing 5 shows the start routine data (as shown in Figure **??**). For simplicity various images are loaded in several application instances (xv) on the X Window System. Various other API calls like Web-Get fetchWget for fetching distributed objects via HTTP requests can be used and defined.

```
1 xv -geometry +1280+0 -expand 0.8 mexico_site_name_cancun_map.jpg &
2 xv -geometry +1280+263 -expand 0.97 mexico_site_name_cancun_map_hot.jpg &
3
4 xv -geometry +980+0 -expand 0.5 mexico_site_name_cancun.jpg &
5 xv -geometry +980+228 -expand 0.61 mexico_site_name_cancun_hotel.jpg &
6 xv -geometry +980+450 -expand 0.60 mexico_site_name_cancun_mall.jpg &
7 xv -geometry +980+620 -expand 0.55 mexico_site_name_cancun_night.jpg &
8
9 xv -geometry +740+0 -expand 0.4 mexico_site_name_chichen_itza.jpg &
10 xv -geometry +740+220 -expand 0.8 mexico_site_name_cenote.jpg &
11 xv -geometry +740+420 -expand 0.6 mexico_site_name_tulum_temple.jpg &
12 #xv -geometry +740+500 -expand 0.3 mexico_site_name_tulum.jpg &
13 xv -geometry +740+629 -expand 0.6 mexico_site_name_palm.jpg &
```
Listing 5. Example InfoPoint event start routine data.

#### **9.6 Stop an InfoPoint**

Listing 6 shows the stop routine data. For simplicity all instances of the applications started with the start routine are removed via system calls.

```
1 killall -9 --user cpr --exact xv
```
Listing 6. Example InfoPoint event stop routine data.

Using Active Source applications any forget or delete modes as well as using Inter Process Communication (IPC) are possible.

#### **9.7 Integration and trust**

Integrating components for mission critical systems does expect methods for handling "Trust in computation" and "Trust in information". This is what Object Envelopes (OEN) and Compute Envelopes (CEN) have been developed for (Rückemann, 2011). Listing 7 shows a small example for a generic OEN file.

18 Will-be-set-by-IN-TECH

• archaeological (Cobá, Mayapan, Ek Balam, Aktumal, Templo Maya de Ixchel, Tumba

Objects can belong to more than one category or subcategory as for example some categories or all of these as well as single objects can be classified touristic. The data, as contained in the procedures here (mapping data, events, autoevents, objects, bindings and so on) can be

Listing 5 shows the start routine data (as shown in Figure **??**). For simplicity various images are loaded in several application instances (xv) on the X Window System. Various other API calls like Web-Get fetchWget for fetching distributed objects via HTTP requests can be used

<sup>1</sup> xv -geometry +1280+0 -expand 0.8 mexico\_site\_name\_cancun\_map.jpg & <sup>2</sup> xv -geometry +1280+263 -expand 0.97 mexico\_site\_name\_cancun\_map\_hot.jpg &

<sup>5</sup> xv -geometry +980+228 -expand 0.61 mexico\_site\_name\_cancun\_hotel.jpg & <sup>6</sup> xv -geometry +980+450 -expand 0.60 mexico\_site\_name\_cancun\_mall.jpg & <sup>7</sup> xv -geometry +980+620 -expand 0.55 mexico\_site\_name\_cancun\_night.jpg &

 xv -geometry +740+0 -expand 0.4 mexico\_site\_name\_chichen\_itza.jpg & xv -geometry +740+220 -expand 0.8 mexico\_site\_name\_cenote.jpg & xv -geometry +740+420 -expand 0.6 mexico\_site\_name\_tulum\_temple.jpg & #xv -geometry +740+500 -expand 0.3 mexico\_site\_name\_tulum.jpg & xv -geometry +740+629 -expand 0.6 mexico\_site\_name\_palm.jpg &

Listing 6 shows the stop routine data. For simplicity all instances of the applications started

Using Active Source applications any forget or delete modes as well as using Inter Process

Integrating components for mission critical systems does expect methods for handling "Trust in computation" and "Trust in information". This is what Object Envelopes (OEN) and Compute Envelopes (CEN) have been developed for (Rückemann, 2011). Listing 7 shows

<sup>4</sup> xv -geometry +980+0 -expand 0.5 mexico\_site\_name\_cancun.jpg &

• geological (Chicxulub, Actun Chen, Sac Actun, Ik Kil),

put into a database for handling huge data collections.

Listing 5. Example InfoPoint event start routine data.

with the start routine are removed via system calls.

Listing 6. Example InfoPoint event stop routine data.

<sup>1</sup> killall -9 --user cpr --exact xv

Communication (IPC) are possible.

a small example for a generic OEN file.

**9.7 Integration and trust**

• marine (Xel Há, Holbox, Palancar).

de Caracol),

**9.5 Start an InfoPoint**

**9.6 Stop an InfoPoint**

and defined.

3

8

```
1 <ObjectEnvelope><!-- ObjectEnvelope (OEN)-->
2 <Object>
3 <Filename>GIS_Case_Study_20090804.jpg</Filename>
4 <Md5sum>...</Md5sum>
5 <Sha1sum>...</Sha1sum>
6 <DateCreated>2010-08-01:221114</DateCreated>
7 <DateModified>2010-08-01:222029</DateModified>
8 <ID>...</ID><CertificateID>...</CertificateID>
9 <Signature>...</Signature>
10 <Content><ContentData>...</ContentData></Content>
11 </Object>
12 </ObjectEnvelope>
```
Listing 7. Example for an Object Envelope (OEN).

An end-user public client application may be implemented via a browser plugin, based on appropriate services. With OEN instructions embedded in envelopes, for example as XML-based element structure representation, content can be handled as content-stream or as content-reference. The way this will have to be implemented for different use cases depends on the situation, and in many cases on the size and number of data objects. Listing 8 shows a small example for an OEN file using a content DataReference.

```
1 <ObjectEnvelope><!-- ObjectEnvelope (OEN)-->
2 <Object>
3 <Filename>GIS_Case_Study_20090804.jpg</Filename>
4 <Md5sum>...</Md5sum>
5 <Sha1sum>...</Sha1sum>
6 <DateCreated>2010-08-01:221114</DateCreated>
7 <DateModified>2010-08-01:222029</DateModified>
8 <ID>...</ID><CertificateID>...</CertificateID>
9 <Signature>...</Signature>
10 <Content><DataReference>https://doi...</DataReference></Content>
11 </Object>
12 </ObjectEnvelope>
```
Listing 8. OEN referencing signed data.

#### **9.8 Implemented solution for integrated systems with massive resources requirements**

For most interactive information system components a configuration of the distributed resources environment was needed. In opposite to OEN use, making it necessary to have referenced instead of embedded data for huge data sets, for CEN it should be possible to embed the essential instruction data. So there is less need for minimising data overhead and communication. Envelope technology is meant to be a generic extensible concept for information and computing system components (Rückemann, 2011). Figure 12 shows the workflow with application scenarios from GEXI case studies (Rückemann, 2010b). Future objectives for client components are:


 ###EN \gisigsnip{Compute Data: Compute Envelope (CEN)} #ECMT--------------------------------------------------

and Computing Systems in Geosciences and Natural Sciences

<sup>21</sup> Queueing Aspects of Integrated Information

##CEN <Filename>Processing\_Bat\_GIS515.torque</Filename>

\$w bind legend\_infopoint <Any-Enter> {**set** killatleave \

./mexico\_site\_name\_tulum\_temple.jpg \$op\_parallel ] }

[**exec** ./mexico\_legend\_infopoint\_viewall.sh \$op\_parallel ] }

Interactive applications based on Active Source have been used on Grid, Cluster, and HPC

Using CEN features, it is possible to implement resources access on base of validation, verification, and execution. The sources (Listing 10, 11) can be generated semi-automatically and called from a set of files or can be embedded into an actmap component, depending on

 ##CEN <DateCreated>2010-09-12:230012</DateCreated> ##CEN <DateModified>2010-09-12:235052</DateModified> ##CEN <ID>...</ID><CertificateID>...</CertificateID>

 #BCEN <ComputeEnvelope> ##CEN <Instruction>

 ##CEN </Instruction> #ECEN </ComputeEnvelope>

...

**global** w

} ...

(MPP, SMP) systems.

**9.10 Resources interface**

the field of application.

<Instruction>

<**ID**>...</**ID**>

<Script><Pbs>

 <Md5sum>...</Md5sum> <Sha1sum>...</Sha1sum> <Sha512sum>...</Sha512sum>

 ##CEN <Md5sum>...</Md5sum> ##CEN <Sha1sum>...</Sha1sum> ##CEN <Sha512sum>...</Sha512sum>

 ##CEN <Signature>...</Signature> ##CEN <Content>...</Content>

**proc** create\_country\_mexico\_autoevents {} {

 \$w bind legend\_infopoint <Any-Leave> \ {**exec** ./mexico\_legend\_infopoint\_kaxv.sh } \$w bind tulum <Any-Enter> {**set** killatleave \ [**exec** \$appl\_image\_viewer -geometry +800+400 \

Listing 9. CEN embedded with Active Source.

<ComputeEnvelope><!-- ComputeEnvelope (CEN)-->

 <DateCreated>2010-08-01:201057</DateCreated> <DateModified>2010-08-01:211804</DateModified>

<CertificateID>...</CertificateID>

<Signature>...</Signature>

<Shell>#!/bin/bash</Shell>

<Filename>Processing\_Batch\_GIS612.pbs</Filename>

<Content><DataReference>https://doi...</DataReference></Content>

 \$w bind tulum <Any-Leave> \ {**exec** kill -9 \$killatleave }

Fig. 12. Workflow with application scenarios from the GEXI case studies.

The tests done for proof of concept have been in development stage. A more suitable solution has now been created on a generic envelope base. An end-user public client application may be implemented via a browser plugin, based on appropriate services. The current solution is based on CEN files containing XML structures for handling and embedding data and information. This is so important because even in standard cases we easily have to handle hundreds of thousands of compute request from these components. In the easiest case it will be static information from information databases, for advanced cases it is for example conditional processing and simulation for thousands of objects like multimedia data or borehole depth profiling.

#### **9.9 Integrated components in practice**

When taking a look onto different batch and scheduling environments one can see large differences in capabilities, handling different environments and architectures. In the last years experiences have been gained in handling simple features for different environments for High Throughput Computing like Condor (Condor, 2010), workload schedulers like LoadLeveler (IBM, 2005) and Grid Engine (SGE, 2010), and batch system environments like Moab / Torque (Moab, 2010; Torque, 2010). Batch and interactive features are integrated with Active Source event management (Rückemann, 2001). Listing 9 shows a small example of a CEN embedded into an Active Source component.

```
1 #BCMT--------------------------------------------------
2 ###EN \gisigsnip{Object Data: Country Mexico}
3 #ECMT--------------------------------------------------
4 proc create_country_mexico {} {
5 global w
6 # Sonora
7 $w create polygon 0.938583i 0.354331i 2.055118i ...
8 #BCMT--------------------------------------------------
```
Will-be-set-by-IN-TECH

Fig. 12. Workflow with application scenarios from the GEXI case studies.

#BCMT--------------------------------------------------

#ECMT--------------------------------------------------

 \$w create polygon 0.938583i 0.354331i 2.055118i ... #BCMT--------------------------------------------------

###EN \gisigsnip{Object Data: Country Mexico}

or borehole depth profiling.

**9.9 Integrated components in practice**

into an Active Source component.

 **global** w # Sonora

**proc** create\_country\_mexico {} {

The tests done for proof of concept have been in development stage. A more suitable solution has now been created on a generic envelope base. An end-user public client application may be implemented via a browser plugin, based on appropriate services. The current solution is based on CEN files containing XML structures for handling and embedding data and information. This is so important because even in standard cases we easily have to handle hundreds of thousands of compute request from these components. In the easiest case it will be static information from information databases, for advanced cases it is for example conditional processing and simulation for thousands of objects like multimedia data

When taking a look onto different batch and scheduling environments one can see large differences in capabilities, handling different environments and architectures. In the last years experiences have been gained in handling simple features for different environments for High Throughput Computing like Condor (Condor, 2010), workload schedulers like LoadLeveler (IBM, 2005) and Grid Engine (SGE, 2010), and batch system environments like Moab / Torque (Moab, 2010; Torque, 2010). Batch and interactive features are integrated with Active Source event management (Rückemann, 2001). Listing 9 shows a small example of a CEN embedded

```
9 ###EN \gisigsnip{Compute Data: Compute Envelope (CEN)}
10 #ECMT--------------------------------------------------
11 #BCEN <ComputeEnvelope>
12 ##CEN <Instruction>
13 ##CEN <Filename>Processing_Bat_GIS515.torque</Filename>
14 ##CEN <Md5sum>...</Md5sum>
15 ##CEN <Sha1sum>...</Sha1sum>
16 ##CEN <Sha512sum>...</Sha512sum>
17 ##CEN <DateCreated>2010-09-12:230012</DateCreated>
18 ##CEN <DateModified>2010-09-12:235052</DateModified>
19 ##CEN <ID>...</ID><CertificateID>...</CertificateID>
20 ##CEN <Signature>...</Signature>
21 ##CEN <Content>...</Content>
22 ##CEN </Instruction>
23 #ECEN </ComputeEnvelope>
24 ...
25 proc create_country_mexico_autoevents {} {
26 global w
27 $w bind legend_infopoint <Any-Enter> {set killatleave \
28 [exec ./mexico_legend_infopoint_viewall.sh $op_parallel ] }
29 $w bind legend_infopoint <Any-Leave> \
30 {exec ./mexico_legend_infopoint_kaxv.sh }
31 $w bind tulum <Any-Enter> {set killatleave \
32 [exec $appl_image_viewer -geometry +800+400 \
33 ./mexico_site_name_tulum_temple.jpg $op_parallel ] }
34 $w bind tulum <Any-Leave> \
35 {exec kill -9 $killatleave }
36 } ...
```
Listing 9. CEN embedded with Active Source.

Interactive applications based on Active Source have been used on Grid, Cluster, and HPC (MPP, SMP) systems.

#### **9.10 Resources interface**

Using CEN features, it is possible to implement resources access on base of validation, verification, and execution. The sources (Listing 10, 11) can be generated semi-automatically and called from a set of files or can be embedded into an actmap component, depending on the field of application.

```
1 <ComputeEnvelope><!-- ComputeEnvelope (CEN)-->
2 <Instruction>
3 <Filename>Processing_Batch_GIS612.pbs</Filename>
4 <Md5sum>...</Md5sum>
5 <Sha1sum>...</Sha1sum>
6 <Sha512sum>...</Sha512sum>
7 <DateCreated>2010-08-01:201057</DateCreated>
8 <DateModified>2010-08-01:211804</DateModified>
9 <ID>...</ID>
10 <CertificateID>...</CertificateID>
11 <Signature>...</Signature>
12 <Content><DataReference>https://doi...</DataReference></Content>
13 <Script><Pbs>
14 <Shell>#!/bin/bash</Shell>
```
<sup>30</sup> </Instruction> <sup>31</sup> </ComputeEnvelope>

**9.11 Service and operation**

**10. Evaluation**

restrictions.

Listing 11. Embedded Active Source Condor script.

and Computing Systems in Geosciences and Natural Sciences

With Actmap CRI being part of Active Source, calls to parallel processing interfaces, e.g., using InfiniBand, can be used, for example MPI (Message Passing Interface) and OpenMP, already described for standalone job scripts for this purpose, working analogical (Rückemann, 2009).

<sup>23</sup> Queueing Aspects of Integrated Information

With the complexity of the high level integration of disciplines, services, and resources there are various aspects that cannot be handled in general as they will depend on scenario, collaboration partners, state of current technology, and many other. Based on the collaboration framework operation can integrate Service Oriented Architectures (SOA) and Resources Oriented Architectures (ROA). Based on the pre-implementation case studies and application scenarios it will be necessary to define agreements on the low level of services (S-Level) and operation (O-Level). For the S-Level integrated systems will need to collect Service Level Requests (SLR), define Service Level Specifications (SLS), and specify appropriate Service Level Agreements (SLA). According to these, on the O-Level Operational Level Agreements (OLA) have to be arranged. In all practical cases these agreements together with the underlying Service Level Management (SLM) should clearly take up less than two to five percent of the overall capacity for the collaboration for an efficient and effective system. The most important mostly non-technical factor for planning complex integrated systems therefore is to limit the dominance and growth of management, administrative, and operational tasks. Economic target centred contracts can be a solution to set limits to possible

usuriousness, for example to restrict against "hydrocephalic" reporting and auditing.

industry partners involved in the case studies emphasised that the key factors are:

• Information, instructions, and meta data have to be self explanatory.

• Information has to be stored in a common non proprietary way.

• Information and components have to be widely portable.

processable along with each other.

• Component atoms need to be recyclable.

The case studies demonstrated that integrated systems can be successfully implemented with enormous potential for flexible solutions. Disciplines, services, and resources level can be handled under one integrated concept. Interactive dynamical information systems components have been enabled to use an efficient abstraction and to handle thousands of subjobs for parallel processing, in demanding cases without the disadvantages of distributed systems. With the results of the case studies we can answer one additional question: What are the essential key factors for long-term use of integrated components? The academic and

• Multi-lingual information need appropriate interfaces in order to be editable and

• Tools for processing and interfacing the information have to be available without

```
15 <JobName>#PBS -N myjob</JobName>
16 <Oe>#PBS -j oe</Oe>
17 <Walltime>#PBS -l walltime=00:10:00</Walltime>
18 <NodesPpn>#PBS -l nodes=8:ppn=4</NodesPpn>
19 <Feature>#PBS -l feature=ice</Feature>
20 <Partition>#PBS -l partition=hannover</Partition>
21 <Accesspolicy>#PBS -l naccesspolicy=singlejob</Accesspolicy>
22 <Module>module load mpt</Module>
23 <Cd>cd $PBS_O_WORKDIR</Cd>
24 <Np>np=$(cat $PBS_NODEFILE | wc -l)</Np>
25 <Exec>mpiexec_mpt -np $np ./dyna.out 2>&1</Exec>
26 </Pbs></Script>
27 </Instruction>
28 </ComputeEnvelope>
```
Listing 10. Embedded Active Source MPI script.

Examples for using High Performance Computing and Grid Computing resources include batch system interfaces and job handling. Job scripts from this type will on demand (event binding) be sent to the batch system for processing. The Actmap Computing Resources Interface (CRI) is an example for an actmap library (actlcri) containing functions and procedures and even platform specific parts in a portable way. CRI can be used for handling computing resources, loading Tcl or TBC dynamically into the stack (Tcl Developer Site, 2010) when given set behaviour\_loadlib\_actlib "yes".

```
1 <ComputeEnvelope><!-- ComputeEnvelope (CEN)-->
2 <Instruction>
3 <Filename>Processing_Batch_GIS612.pbs</Filename>
4 <Md5sum>...</Md5sum>
5 <Sha1sum>...</Sha1sum>
6 <Sha512sum>...</Sha512sum>
7 <DateCreated>2010-08-01:201057</DateCreated>
8 <DateModified>2010-08-01:211804</DateModified>
9 <ID>...</ID>
10 <CertificateID>...</CertificateID>
11 <Signature>...</Signature>
12 <Content><DataReference>https://doi...</DataReference></Content>
13 <Script><Condor>
14 <Environment>universe = standard</Environment>
15 <Exec>executable = /home/cpr/grid/job.exe</Exec>
16 <TransferFiles>should_transfer_files = YES</TransferFiles>
17 <TransferInputFiles>transfer_input_files = job.exe,job.input
18 </TransferInputFiles>
19 <Input>input = job.input</Input>
20 <Output>output = job.output</Output>
21 <Error>error = job.error</Error>
22 <Log>log = job.log</Log>
23 <NotifyMail>notify_user = ruckema@uni-muenster.de</NotifyMail>
24 <Requirements>
25 requirements = (Memory >= 50)
26 requirements = ( ( (OpSys=="Linux")||(OpSys=="AIX"))&&(Memory >= 500) )
27 </Requirements>
28 <Action>queue</Action>
29 </Condor></Script>
```

```
30 </Instruction>
31 </ComputeEnvelope>
```
22 Will-be-set-by-IN-TECH

Examples for using High Performance Computing and Grid Computing resources include batch system interfaces and job handling. Job scripts from this type will on demand (event binding) be sent to the batch system for processing. The Actmap Computing Resources Interface (CRI) is an example for an actmap library (actlcri) containing functions and procedures and even platform specific parts in a portable way. CRI can be used for handling computing resources, loading Tcl or TBC dynamically into the stack (Tcl Developer Site, 2010)

<sup>15</sup> <JobName>#PBS -N myjob</JobName>

<sup>22</sup> <Module>module load mpt</Module> <sup>23</sup> <Cd>cd \$PBS\_O\_WORKDIR</Cd>

<sup>24</sup> <Np>np=\$(cat \$PBS\_NODEFILE | wc -l)</Np>

Listing 10. Embedded Active Source MPI script.

<sup>17</sup> <Walltime>#PBS -l walltime=00:10:00</Walltime> <sup>18</sup> <NodesPpn>#PBS -l nodes=8:ppn=4</NodesPpn> <sup>19</sup> <Feature>#PBS -l feature=ice</Feature>

<sup>20</sup> <Partition>#PBS -l partition=hannover</Partition>

<sup>25</sup> <Exec>mpiexec\_mpt -np \$np ./dyna.out 2>&1</Exec>

when given set behaviour\_loadlib\_actlib "yes".

<sup>1</sup> <ComputeEnvelope><!-- ComputeEnvelope (CEN)-->

<sup>7</sup> <DateCreated>2010-08-01:201057</DateCreated> <sup>8</sup> <DateModified>2010-08-01:211804</DateModified>

<sup>14</sup> <Environment>universe = standard</Environment> <sup>15</sup> <Exec>executable = /home/cpr/grid/job.exe</Exec>

<sup>10</sup> <CertificateID>...</CertificateID>

<sup>19</sup> <Input>input = job.input</Input> <sup>20</sup> <Output>output = job.output</Output> <sup>21</sup> <Error>error = job.error</Error>

<sup>11</sup> <Signature>...</Signature>

<sup>3</sup> <Filename>Processing\_Batch\_GIS612.pbs</Filename>

<sup>12</sup> <Content><DataReference>https://doi...</DataReference></Content>

<sup>16</sup> <TransferFiles>should\_transfer\_files = YES</TransferFiles> <sup>17</sup> <TransferInputFiles>transfer\_input\_files = job.exe,job.input

<sup>23</sup> <NotifyMail>notify\_user = ruckema@uni-muenster.de</NotifyMail>

<sup>26</sup> requirements = ( ( (OpSys=="Linux")||(OpSys=="AIX"))&&(Memory >= 500) )

<sup>21</sup> <Accesspolicy>#PBS -l naccesspolicy=singlejob</Accesspolicy>

<sup>16</sup> <Oe>#PBS -j oe</Oe>

<sup>26</sup> </Pbs></Script> <sup>27</sup> </Instruction> <sup>28</sup> </ComputeEnvelope>

<sup>2</sup> <Instruction>

<sup>9</sup> <**ID**>...</**ID**>

<sup>13</sup> <Script><Condor>

<sup>24</sup> <Requirements>

<sup>27</sup> </Requirements>

<sup>18</sup> </TransferInputFiles>

<sup>22</sup> <Log>log = job.log</Log>

<sup>28</sup> <Action>queue</Action> <sup>29</sup> </Condor></Script>

<sup>25</sup> requirements = (Memory >= 50)

<sup>4</sup> <Md5sum>...</Md5sum> <sup>5</sup> <Sha1sum>...</Sha1sum> <sup>6</sup> <Sha512sum>...</Sha512sum> Listing 11. Embedded Active Source Condor script.

With Actmap CRI being part of Active Source, calls to parallel processing interfaces, e.g., using InfiniBand, can be used, for example MPI (Message Passing Interface) and OpenMP, already described for standalone job scripts for this purpose, working analogical (Rückemann, 2009).

#### **9.11 Service and operation**

With the complexity of the high level integration of disciplines, services, and resources there are various aspects that cannot be handled in general as they will depend on scenario, collaboration partners, state of current technology, and many other. Based on the collaboration framework operation can integrate Service Oriented Architectures (SOA) and Resources Oriented Architectures (ROA). Based on the pre-implementation case studies and application scenarios it will be necessary to define agreements on the low level of services (S-Level) and operation (O-Level). For the S-Level integrated systems will need to collect Service Level Requests (SLR), define Service Level Specifications (SLS), and specify appropriate Service Level Agreements (SLA). According to these, on the O-Level Operational Level Agreements (OLA) have to be arranged. In all practical cases these agreements together with the underlying Service Level Management (SLM) should clearly take up less than two to five percent of the overall capacity for the collaboration for an efficient and effective system. The most important mostly non-technical factor for planning complex integrated systems therefore is to limit the dominance and growth of management, administrative, and operational tasks. Economic target centred contracts can be a solution to set limits to possible usuriousness, for example to restrict against "hydrocephalic" reporting and auditing.

#### **10. Evaluation**

The case studies demonstrated that integrated systems can be successfully implemented with enormous potential for flexible solutions. Disciplines, services, and resources level can be handled under one integrated concept. Interactive dynamical information systems components have been enabled to use an efficient abstraction and to handle thousands of subjobs for parallel processing, in demanding cases without the disadvantages of distributed systems. With the results of the case studies we can answer one additional question: What are the essential key factors for long-term use of integrated components? The academic and industry partners involved in the case studies emphasised that the key factors are:


Legal Informatics, Leibniz Universität Hannover (IRI / LUH). URL: http://www.

für Hoch- und Höchstleistungsrechnen). URL: http://www.hlrn.de [accessed:

*of Information Technology*, IGI Global, pp. 217–232. Chapter XII, in: Pankowska, M. (ed.), Infonomics for Distributed Business and Decision-Making Environments: Creating Information System Ecology, ISBN: 1-60566-890-7, DOI:

*Geoinformationssysteme. Ein Konzept zur ereignisgesteuerten und dynamischen Visualisierung und Aufbereitung geowissenschaftlicher Daten*, Diss., Westfälische Wilhelms-Universität, Münster, Deutschland. 161 (xxii+139) S., URL: http://wwwmath.uni-muenster.de/cs/u/ruckema/x/dis/download/

*International Journal on Advances in Software* **2**(2). ISSN: 1942-2628, URL: http://

Systems Using a Collaboration Framework Respecting Implementation, Legal Issues, and Security, *International Journal on Advances in Security* 3(3&4): 91–103. Savola, R., (ed.), VTT Technical Research Centre of Finland, Finland, URL: http: //www.iariajournals.org/security/sec\_v3\_n34\_2010\_paged.pdf [accessed: 2011-07-10], URL: http://www.iariajournals.org/security/

Computing in Geosciences and Exploration, *Proceedings of the Int. Conf. on Digital Society (ICDS 2010), The Int. Conf. on Technical and Legal Aspects of the e-Society (CYBERLAWS 2010), February 10–16, 2010, St. Maarten, Netherlands Antilles*, IEEE Computer Society Press, IEEE Xplore Digital Library, pp. 339–344. ISBN: 978-0-7695-3953-9, URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?

High Performance Computing and Information Systems, *Proceedings International Conference on Advanced Geographic Information Systems, Applications, and Services (GEOProcessing 2011), February 23–28, 2011, Gosier, Guadeloupe, France / GEOProcessing 2011, ICDS 2011, ACHI 2011, ICQNM 2011, CYBERLAWS 2011, eTELEMED 2011, eL&mL 2011, eKNOW 2011 / DigitalWorld 2011*, XPS, Xpert Publishing

GEXI (1996, 1999, 2011). Geo Exploration and Information (GEXI). URL: http: //www.user.uni-hannover.de/cpr/x/rprojs/en/index.html#GEXI

<sup>25</sup> Queueing Aspects of Integrated Information

HLRN (2011). HLRN, North-German Supercomputing Alliance (Norddeutscher Verbund

IBM (2005). IBM Tivoli Workload Scheduler LoadLeveler. URL: http://www-03.ibm.com/

Mackert, M., Whitten, P. & Holtz, B. (2009). *Health Infonomics: Intelligent Applications*

URL: http://www.clusterresources.com [accessed: 2010-10-10]. Rückemann, C.-P. (2001). *Beitrag zur Realisierung portabler Komponenten für*

Rückemann, C.-P. (2009). Dynamical Parallel Applications on Distributed and HPC Systems,

Rückemann, C.-P. (2010a). Integrating Future High End Computing and Information

Rückemann, C.-P. (2010b). Legal Issues Regarding Distributed and High Performance

Rückemann, C.-P. (2011). Envelope Interfaces for Geoscientific Processing with

www.iariajournals.org/software/ [accessed: 2009-11-16].

systems/software/loadleveler/ [accessed: 2010-10-10].

eulisp.de [accessed: 2011-01-01].

and Computing Systems in Geosciences and Natural Sciences

(Information) [accessed: 2010-05-02].

10.4018/978-1-60566-890-1.ch010. Moab (2010). Moab: Admin Manual, Users Guide.

dis3acro.pdf [accessed: 2009-11-16].

tp=&arnumber=5432414 [accessed: 2010-03-28].

[accessed: 2011-07-10].

2011-07-10].

#### **11. Outlook**

There are a number of aspects that have to be addressed in future work. These are mostly not only on the technology but on collaborational, organisational, and funding level with integrated information and computing systems. For geosciences and natural sciences algorithms and concepts for processing, visualisation, and extended use of data and information are available. The grand challenge with the wisdom will be to succeed in overcoming the fate of decision makers on scientific funding, that gathering a critical mass of acceptance in the society is vital.

#### **12. Conclusion**

This chapter has shown some prominent aspects of the complexity of the next generation of system architectures that arises from integrating the necessary components and computing resources, used in geosciences and geoinformatics. With technology advances new tools arise for geosciences research and Information Systems and Computing Systems will become more widely available. Due to the complexity and vast efforts necessary to implement and operate these systems and resources there is a strong need to enable economic and efficient use and operation. Hardware and software system components cannot be neglected anymore and viewed isolated. System architecture issues to software, legal, and collaborational aspects are in the focus and must be handled for operation, development, and strategies level. Various application scenarios from geosciences and natural sciences profit from the new means and concepts and will help to push the development not only of Geoscientific Information Systems and Computing Systems but of Information Systems and Computing Systems for the geosciences.

#### **13. Acknowledgements**

I am grateful to all national and international academic and industry partners in the GEXI cooperations for the innovative constructive work and case study support as well as to the colleagues at the Leibniz Universität Hannover, at the Institut für Rechtsinformatik (IRI), the North-German Supercomputing Alliance (HLRN), the Westfälische Wilhelms-Universität (WWU) Münster, at the Zentrum für Informationsverarbeitung (ZIV) Münster, in the German Grid Initiative D-Grid and the participants of the postgraduate European Legal Informatics Study Programme (EULISP) and of the WGGEOSP work group as well as the colleagues at the last years GEOWS, GEOProcessing, CYBERLAWS, ICDS, and INFOCOMP international conferences for prolific discussion of scientific, legal, and technical aspects as well as to the staff at ZIV and the partner institutes and associated HPC companies for supporting this work by managing and providing HEC resources over the years. I am especially grateful to Hans-Günther Müller, SGI, for fruitful discussion and providing support with hardware photos.

#### **14. References**

Condor (2010). Condor, High Throughput Computing. URL: http://www.cs.wisc.edu/ condor/ [accessed: 2010-10-10].

EULISP (2011). *Fundamental Aspects of Information Science, Security, and Computing (Lecture)*, EULISP Lecture Notes, European Legal Informatics Study Programme, Institute for 24 Will-be-set-by-IN-TECH

There are a number of aspects that have to be addressed in future work. These are mostly not only on the technology but on collaborational, organisational, and funding level with integrated information and computing systems. For geosciences and natural sciences algorithms and concepts for processing, visualisation, and extended use of data and information are available. The grand challenge with the wisdom will be to succeed in overcoming the fate of decision makers on scientific funding, that gathering a critical mass of

This chapter has shown some prominent aspects of the complexity of the next generation of system architectures that arises from integrating the necessary components and computing resources, used in geosciences and geoinformatics. With technology advances new tools arise for geosciences research and Information Systems and Computing Systems will become more widely available. Due to the complexity and vast efforts necessary to implement and operate these systems and resources there is a strong need to enable economic and efficient use and operation. Hardware and software system components cannot be neglected anymore and viewed isolated. System architecture issues to software, legal, and collaborational aspects are in the focus and must be handled for operation, development, and strategies level. Various application scenarios from geosciences and natural sciences profit from the new means and concepts and will help to push the development not only of Geoscientific Information Systems and Computing Systems but of Information Systems and Computing Systems for the

I am grateful to all national and international academic and industry partners in the GEXI cooperations for the innovative constructive work and case study support as well as to the colleagues at the Leibniz Universität Hannover, at the Institut für Rechtsinformatik (IRI), the North-German Supercomputing Alliance (HLRN), the Westfälische Wilhelms-Universität (WWU) Münster, at the Zentrum für Informationsverarbeitung (ZIV) Münster, in the German Grid Initiative D-Grid and the participants of the postgraduate European Legal Informatics Study Programme (EULISP) and of the WGGEOSP work group as well as the colleagues at the last years GEOWS, GEOProcessing, CYBERLAWS, ICDS, and INFOCOMP international conferences for prolific discussion of scientific, legal, and technical aspects as well as to the staff at ZIV and the partner institutes and associated HPC companies for supporting this work by managing and providing HEC resources over the years. I am especially grateful to Hans-Günther Müller, SGI, for fruitful discussion and providing support with hardware

Condor (2010). Condor, High Throughput Computing. URL: http://www.cs.wisc.edu/

EULISP (2011). *Fundamental Aspects of Information Science, Security, and Computing (Lecture)*,

EULISP Lecture Notes, European Legal Informatics Study Programme, Institute for

**11. Outlook**

**12. Conclusion**

geosciences.

photos.

**14. References**

condor/ [accessed: 2010-10-10].

**13. Acknowledgements**

acceptance in the society is vital.

Legal Informatics, Leibniz Universität Hannover (IRI / LUH). URL: http://www. eulisp.de [accessed: 2011-01-01].


URL: http://www.clusterresources.com [accessed: 2010-10-10].


**2** 

 *Nigeria* 

Othniel K. Likkason *Physics Programme,* 

*Abubakar Tafawa Balewa University, Bauchi,* 

**Spectral Analysis of Geophysical Data** 

The usefulness of a geophysical method for a particular purpose depends, to a large extent, on the characteristics of the target proposition (exploration target) which differentiate it from the surrounding media. For example, in the detection of structures associated with oil and gas (such as faults, anticlines, synclines, salt domes and other large scale structures), we can exploit the elastic properties of the rocks. Depending on the type of minerals sought, we can take advantage of their variations with respect to the host environment, of the electric conductivity, local changes in gravity, magnetic, radioactive or geothermal values to provide information to be analysed and interpreted that will lead to parameter estimation of

This chapter deals with some tools that can be used to analyse and interpret geophysical data so obtained in the field. We shall be having in mind potential field data (from gravity, magnetic or electrical surveys). For example, the gravity data may be the records of Bouguer gravity anomalies (in milligals), the magnetic data may be the total magnetic field intensity anomaly (in gammas) and data from electrical survey may be records of resistivity measurements (in ohm-metre). There are other thematic ways in which data from these surveys can be expressed; depicting some other attributes of the exploration target and the

Potential fields for now are mostly displayed in 1-D (profile form), 2-D (map form) or 3-D (map form and depth display). Whichever form, the 1-D and 2-D data are usually displayed in magnitudes against space (spatial data). When data express thematic values against space (profile distance) or thematic values against time, they are called time-series data or timedomain data. The changes or variations in the magnitudes (thematic values) with space and/or time may reflect significant changes in the nature and attributes of the causative agents. We therefore use these variations to carefully interpret the nature and the structural

Most at times the picture of the events painted in the time-domain is poor and undiscernable possibly because of noise effects and other measurement errors. A noise in any set of data is any effects that are not related to the chosen target proposition. Even where such noise and measurements errors are minimized, some features of the data need to be gained/enhanced for proper accentuation. The only recourse to this problem is to make a transformation of the time-domain data to other forms or use some time-domain tools to analyse the data for improve signal to noise ratio; both of which must be

**1. Introduction** 

the deposits.

host environments.

features of the causative agents.

Solutions, pp. 23–28. Rückemann, C.-P., Wolfson, O. (eds.), 6 pages, ISBN: 978-1-61208-003-1, URL: http://www.thinkmind.org/download.php? articleid=geoprocessing\_2011\_2\_10\_30030 [accessed: 2011-07-10].


URL: http://dev.scriptics.com/ [accessed: 2010-10-10].


ZIVHPC (2011). ZIVHPC, HPC Computing Resources.

URL: https://www.uni-muenster.de/ZIV/Technik/ZIVHPC/index.html [accessed: 2011-02-20].

	- URL: https://www.uni-muenster.de/ZIV/Technik/ZIVHPC/ZIVSMP. html [accessed: 2011-02-20].

## **Spectral Analysis of Geophysical Data**

#### Othniel K. Likkason

*Physics Programme, Abubakar Tafawa Balewa University, Bauchi, Nigeria* 

#### **1. Introduction**

26 Will-be-set-by-IN-TECH

26 Advances in Data, Methods, Models and Their Applications in Geoscience

articleid=geoprocessing\_2011\_2\_10\_30030 [accessed: 2011-07-10]. SGE (2010). Sun Grid Engine. URL: http://gridengine.sunsource.net/ [accessed:

SGI (2011). SGI, Silicon Graphics GmbH. URL: http://www.sgi.com [accessed:

Torque (2010). Torque Admin Manual. URL: http://www.clusterresources.com/

ZIVGrid (2008). ZIV der WWU Münster – ZIVGrid. URL: http://www.uni-muenster.

URL: https://www.uni-muenster.de/ZIV/Technik/ZIVHPC/index.html

URL: https://www.uni-muenster.de/ZIV/Technik/ZIVHPC/ZIVSMP.

URL: http://dev.scriptics.com/ [accessed: 2010-10-10].

de/ZIV/Server/ZIVGrid/ [accessed: 2008-12-23].

2010-10-10].

2011-07-10].

Tcl Developer Site (2010). Tcl Developer Site.

[accessed: 2011-02-20].

html [accessed: 2011-02-20].

torquedocs21/ [accessed: 2010-10-10].

ZIVHPC (2011). ZIVHPC, HPC Computing Resources.

ZIVSMP (2011). ZIVSMP, SMP Computing Resources.

Solutions, pp. 23–28. Rückemann, C.-P., Wolfson, O. (eds.), 6 pages, ISBN: 978-1-61208-003-1, URL: http://www.thinkmind.org/download.php?

> The usefulness of a geophysical method for a particular purpose depends, to a large extent, on the characteristics of the target proposition (exploration target) which differentiate it from the surrounding media. For example, in the detection of structures associated with oil and gas (such as faults, anticlines, synclines, salt domes and other large scale structures), we can exploit the elastic properties of the rocks. Depending on the type of minerals sought, we can take advantage of their variations with respect to the host environment, of the electric conductivity, local changes in gravity, magnetic, radioactive or geothermal values to provide information to be analysed and interpreted that will lead to parameter estimation of the deposits.

> This chapter deals with some tools that can be used to analyse and interpret geophysical data so obtained in the field. We shall be having in mind potential field data (from gravity, magnetic or electrical surveys). For example, the gravity data may be the records of Bouguer gravity anomalies (in milligals), the magnetic data may be the total magnetic field intensity anomaly (in gammas) and data from electrical survey may be records of resistivity measurements (in ohm-metre). There are other thematic ways in which data from these surveys can be expressed; depicting some other attributes of the exploration target and the host environments.

> Potential fields for now are mostly displayed in 1-D (profile form), 2-D (map form) or 3-D (map form and depth display). Whichever form, the 1-D and 2-D data are usually displayed in magnitudes against space (spatial data). When data express thematic values against space (profile distance) or thematic values against time, they are called time-series data or timedomain data. The changes or variations in the magnitudes (thematic values) with space and/or time may reflect significant changes in the nature and attributes of the causative agents. We therefore use these variations to carefully interpret the nature and the structural features of the causative agents.

> Most at times the picture of the events painted in the time-domain is poor and undiscernable possibly because of noise effects and other measurement errors. A noise in any set of data is any effects that are not related to the chosen target proposition. Even where such noise and measurements errors are minimized, some features of the data need to be gained/enhanced for proper accentuation. The only recourse to this problem is to make a transformation of the time-domain data to other forms or use some time-domain tools to analyse the data for improve signal to noise ratio; both of which must be

Spectral Analysis of Geophysical Data 29

To recover a function f(t) from its digital form, the sampling points must be sufficiently close to each other. There is actually a maximum sampling period particular to the function

According to the sampling theorem (or Shannon theorem), a function can be fully recovered by the sampling process provided (a) it is a reasonably well-behaved function and (b) band-

Condition (a) implies that the function be continuous with no abnormal behaviour such as discontinuities (sharp breaks or singularities). This condition is practically always fulfilled in the case of functions representing natural processes (such as Laplacian fields). The bandlimitedness of a function as a second condition, refers to a function which possesses a Fourier transform of non-zero value outside it. Most functions involving natural processes

If a function is digitized with equal sampling interval, τ, the period present in that function which can be recovered by the process is 2τ, since we need a minimum of two sampling

in the subject of digitization. The frequency, fN is referred to as the folding or Nyquist frequency. The parameter, τ represents the maximum limit for the sampling period with which we can fully specify a function whose lowest period is 2τ. However, the sampling cut-

It has been shown that the continuous function, f(t) which is band-limited can be reconstructed from the digital values fn by using the formula (Papoulis, 1962; Bath, 1974)

> ��� ���� �� ���� ���� �� ����

Where ωc = 2πfc. We see that to recover the continuous function, f(t) from the digital version, the nth sample is replaced by the sinc function (i.e. [sinωct]/ωct) which is scaled by the sample value fn and placed at time, nτ. The scaled and shifted sinc functions are then added together to give the original time function, f(t). Complete recovery also means running

Aliasing is a kind of spectrum distortion which is brought about as a result of too coarse sampling. Fine sampling (implying fN>fc) and critical sampling (implying fN = fc), produce no aliasing effects. Coarse sampling (implying fN<fc) is undersampling and there will be considerable overlap between adjacent spectra in the recovered analogue function. Thus to

���� = ∑ ��

� ���� ��) has a special significance

��� ��(����) ��(����)

Fig. 1. Sampling a continuous signal fn

limited (Bath, 1974).

also fulfill this condition.

off frequency, fC (=�

�

concerned, with which the complete recovery may be achieved.

intervals to define one period. The equivalent frequency (�� <sup>=</sup> �

�(�) = ∑ ��

�

) and so fC = 2fN.

values from n = -**∞** to +**∞**, which is practically impossible.

accomplished without compromising the quality of the original data. Even where the picture of the time-domain data 'looks good", we can perform further analyses on the signal for correlation, improvement and enhancement purposes. There are many time-domain and frequency-domain tools for these purposes. This is the reason for this chapter.

We shall be exploring the uses of some tools for the analyses and interpretations of geophysical potential fields under the banner of Spectral Analysis of Geophysical Data.

The first section of the chapter covers the treatment and analysis of periodic and aperiodic functions by means of Fourier methods, the second section develops the concept of spectra and possible applications and the third section covers spectrum of random fields; ending with an application to synthetic and real (field) data.

#### **2. Periodic and aperiodic functions**

A periodic function of time, t can be defined as f(t) = f(t+T), where T is the smallest constant, called the period which satisfies the relation. In general f(t) = f(t+NT), where N is an integer other than zero. As an example, we can find the period of a function such as f(t) = cos t/3 + cos t/4. If this function is periodic, with a period, T, then f(t) = f(t+T). Using the relation cosθ = cos(θ + 2πm), m = 0, ±1, ±2, ..., we can compute the period of this function to be T = 24π.

Aperiodic function, on the other hand, is a function that is not periodic in the finite sense of time. We can say that an aperiodic function can be taken to be periodic at some infinite time, where the time period, T = **∞**.

A function f(t) is even if and only if f(t) = f(-t) and odd if f(t) = -f(-t).

#### **3. Sampling theorem**

A function, f which is defined in some neighbourhood of c is said to be continuous at c provided (1) the function has a definite finite value f(c) at c and (2) as t approaches c, f(t) approaches f(c) as limit, i.e. lim��� �(�) � �(�). If a function is continuous at all points of an interval a≤t≤b (or a<t<b, etc), then it is said to be continuous on or in that interval. A function f(t) = t2 is a continuous function that satisfies the two conditions above.

A graph of a function that is continuous on an interval a≤t≤b is an unbroken curve over that interval. In practical sense, it is possible to sketch a continuous curve by constructing a table of values (t, f(t)), plotting relatively few points from this table and then sketching a continuous (unbroken) curve through these points.

A function that is not continuous at a point t = c is said to be discontinuous or to have a discontinuity at t = c. The function, f(t) = 1/t is discontinuous at t = 0 as the two requirements for continuity above are violated at t = 0. This discontinuity cannot be removed. On the other hand, a function, f(t) = ����� � has a removable discontinuity at t = 0, even though the formula is not valid at t = 0. We can therefore extend the domain of f(t) to include the origin, as f(0) = 1.

A continuous function, f(t) can be sampled at regular intervals such that the value of the function at each digitized point is fn, with n = 0, ±1, ±2, ±3, ... (Fig. 1).

It will appear as if the time domain function f(t) versus t is transformed into a digitized form domain (fn versus n).

accomplished without compromising the quality of the original data. Even where the picture of the time-domain data 'looks good", we can perform further analyses on the signal for correlation, improvement and enhancement purposes. There are many time-domain and

We shall be exploring the uses of some tools for the analyses and interpretations of geophysical potential fields under the banner of Spectral Analysis of Geophysical Data. The first section of the chapter covers the treatment and analysis of periodic and aperiodic functions by means of Fourier methods, the second section develops the concept of spectra and possible applications and the third section covers spectrum of random fields; ending

A periodic function of time, t can be defined as f(t) = f(t+T), where T is the smallest constant, called the period which satisfies the relation. In general f(t) = f(t+NT), where N is an integer other than zero. As an example, we can find the period of a function such as f(t) = cos t/3 + cos t/4. If this function is periodic, with a period, T, then f(t) = f(t+T). Using the relation cosθ = cos(θ + 2πm), m = 0, ±1, ±2, ..., we can compute the period of this

Aperiodic function, on the other hand, is a function that is not periodic in the finite sense of time. We can say that an aperiodic function can be taken to be periodic at some infinite time,

A function, f which is defined in some neighbourhood of c is said to be continuous at c provided (1) the function has a definite finite value f(c) at c and (2) as t approaches c, f(t) approaches f(c) as limit, i.e. lim��� �(�) � �(�). If a function is continuous at all points of an interval a≤t≤b (or a<t<b, etc), then it is said to be continuous on or in that interval. A

A graph of a function that is continuous on an interval a≤t≤b is an unbroken curve over that interval. In practical sense, it is possible to sketch a continuous curve by constructing a table of values (t, f(t)), plotting relatively few points from this table and then sketching a

A function that is not continuous at a point t = c is said to be discontinuous or to have a discontinuity at t = c. The function, f(t) = 1/t is discontinuous at t = 0 as the two requirements for continuity above are violated at t = 0. This discontinuity cannot be

even though the formula is not valid at t = 0. We can therefore extend the domain of f(t) to

A continuous function, f(t) can be sampled at regular intervals such that the value of the

It will appear as if the time domain function f(t) versus t is transformed into a digitized form

� has a removable discontinuity at t = 0,

function f(t) = t2 is a continuous function that satisfies the two conditions above.

A function f(t) is even if and only if f(t) = f(-t) and odd if f(t) = -f(-t).

continuous (unbroken) curve through these points.

removed. On the other hand, a function, f(t) = �����

function at each digitized point is fn, with n = 0, ±1, ±2, ±3, ... (Fig. 1).

frequency-domain tools for these purposes. This is the reason for this chapter.

with an application to synthetic and real (field) data.

**2. Periodic and aperiodic functions**

function to be T = 24π.

**3. Sampling theorem**

where the time period, T = **∞**.

include the origin, as f(0) = 1.

domain (fn versus n).

Fig. 1. Sampling a continuous signal fn

To recover a function f(t) from its digital form, the sampling points must be sufficiently close to each other. There is actually a maximum sampling period particular to the function concerned, with which the complete recovery may be achieved.

According to the sampling theorem (or Shannon theorem), a function can be fully recovered by the sampling process provided (a) it is a reasonably well-behaved function and (b) bandlimited (Bath, 1974).

Condition (a) implies that the function be continuous with no abnormal behaviour such as discontinuities (sharp breaks or singularities). This condition is practically always fulfilled in the case of functions representing natural processes (such as Laplacian fields). The bandlimitedness of a function as a second condition, refers to a function which possesses a Fourier transform of non-zero value outside it. Most functions involving natural processes also fulfill this condition.

If a function is digitized with equal sampling interval, τ, the period present in that function which can be recovered by the process is 2τ, since we need a minimum of two sampling intervals to define one period. The equivalent frequency (�� <sup>=</sup> � ��) has a special significance in the subject of digitization. The frequency, fN is referred to as the folding or Nyquist frequency. The parameter, τ represents the maximum limit for the sampling period with which we can fully specify a function whose lowest period is 2τ. However, the sampling cutoff frequency, fC (=� � ) and so fC = 2fN.

It has been shown that the continuous function, f(t) which is band-limited can be reconstructed from the digital values fn by using the formula (Papoulis, 1962; Bath, 1974)

$$f(t) = \sum\_{n=-\infty}^{\infty} f\_n \frac{\sin \pi [\binom{t}{t} - n]}{\pi [\binom{t}{t} \pi] - n]} = \sum\_{n=-\infty}^{\infty} f\_n \frac{\sin \omega\_c(t - n\pi)}{\omega\_c(t - n\pi)}$$

Where ωc = 2πfc. We see that to recover the continuous function, f(t) from the digital version, the nth sample is replaced by the sinc function (i.e. [sinωct]/ωct) which is scaled by the sample value fn and placed at time, nτ. The scaled and shifted sinc functions are then added together to give the original time function, f(t). Complete recovery also means running values from n = -**∞** to +**∞**, which is practically impossible.

Aliasing is a kind of spectrum distortion which is brought about as a result of too coarse sampling. Fine sampling (implying fN>fc) and critical sampling (implying fN = fc), produce no aliasing effects. Coarse sampling (implying fN<fc) is undersampling and there will be considerable overlap between adjacent spectra in the recovered analogue function. Thus to

$$f(\mathbf{x}) = \frac{a\_0}{2} + \sum\_{n=1}^{\infty} (a\_n \cos nx + b\_n \sin nx) \tag{1}$$

 $a\_n = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(x) \cos nx \, dx$  ( $n = 0, 1, 2, 3 \dots$ ) ,  $b\_n = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(x) \sin nx \, dx$  ( $n = 1, 2, 3 \dots$ )

$$f(t) = \frac{a\_0}{2} + \sum\_{n=1}^{\infty} (a\_n \cos nt + b\_n \sin nt) \tag{2}$$

$$a\_0 = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(t) \, dt$$

$$a\_n = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(t) \cos nt \, dt \text{ ( $n = 1, 2, 3 \dots$ )}\tag{3}$$

$$b\_n = \frac{1}{\pi} \int\_{-\pi}^{\pi} f(t) \sin nt \, dt \text{ ( $n = 1, 2, 3 \dots$ )}\tag{4}$$

$$f(t) = \frac{a\_o}{2} + \Sigma\_{n=1}^{\infty} (a\_n \cos nt) \tag{4}$$

$$f(t) = \sum\_{n=1}^{\infty} \mathbf{b}\_n \sin nt \,\mathrm{f} \tag{5}$$

$$f(t) = \frac{a\_0}{2} + \sum\_{n=1}^{\infty} (a\_n \cos \frac{n \pi t}{T} + b\_n \sin \frac{n \pi t}{T}) \text{ -T} \le t \le T \tag{6}$$

$$f(t) = \Sigma\_{n=-\infty}^{\circ \circ} \mathcal{C}\_n e^{i n \pi t} / \tau \text{ [-T, T]} \tag{7}$$

$$\mathcal{L}\_n = \frac{1}{2\mathcal{T}} \int\_{-T}^{T} f(t)e^{-in\pi t}/\_T dt \tag{8}$$

$$f(\mathbf{t}) = \frac{1}{2\mathsf{T}} \int\_{-\mathsf{T}}^{\mathsf{T}} f(\lambda) d\lambda + \Sigma\_{n=1}^{\diamondsuit} \frac{1}{\mathsf{T}} \int\_{-\mathsf{T}}^{\mathsf{T}} f(\lambda) d\lambda \cos\frac{n\pi}{\mathsf{T}}(\mathsf{t} - \lambda) d\lambda \tag{9}$$

$$f(t) = \frac{1}{2T} \int\_{-T}^{T} f(\lambda) d\lambda + \Sigma\_{n=1}^{\text{op}} \frac{\Delta\omega}{\pi} \int\_{-T}^{T} f(\lambda) d\lambda \cos\,\omega\_{n}(t-\lambda) d\lambda \tag{10}$$


$$f(\mathbf{t}) = \frac{1}{\pi} \int\_0^\infty d\omega \int\_{-\infty}^\infty f(\lambda) \cos \omega(\mathbf{t} - \lambda) d\lambda \tag{11a}$$

$$f(t) = \frac{1}{\pi} \int\_0^\infty d\omega \int\_{-\infty}^\infty f(\lambda) \cos\omega \lambda \cos\omega t \,d\lambda + \frac{1}{\pi} \int\_0^\infty d\omega \int\_{-\infty}^\infty f(\lambda) \sin\omega \lambda \sin\omega t \,d\lambda$$

$$= \int\_0^\infty \left[ \frac{1}{\pi} \int\_{-\infty}^\infty f(\lambda) \cos\omega \lambda \,d\lambda \right] \cos\omega t \,d\omega + \int\_0^\infty \left[ \frac{1}{\pi} \int\_{-\infty}^\infty f(\lambda) \sin\omega \lambda \,d\lambda \right] \sin\omega t \,d\omega$$

 $f(t) = \int\_0^\alpha A(\omega) \cos \omega t \, d\omega + \int\_0^\alpha B(\omega) \sin \omega t \, d\omega$ 
$$= \int\_0^\alpha [A(\omega) \cos \omega t + B(\omega) \sin \omega t] \, d\omega \tag{11b}$$
 $\text{where } A(\omega) = \frac{1}{\pi} \int\_{-\infty}^\omega f(\lambda) \cos \omega \lambda \, d\lambda \text{ and } B(\omega) = \frac{1}{\pi} \int\_{-\infty}^\infty f(\lambda) \sin \omega \lambda \, d\lambda$ 

$$\mathcal{L}\{\omega\} = \frac{1}{2\pi} \int\_{-\infty}^{\infty} f(t)e^{-l\omega t}dt\tag{12}$$

$$f(t) = \int\_{-\infty}^{\infty} \mathcal{C}(\omega) e^{i\omega t} d\omega \tag{13}$$

$$F(\omega) = \frac{1}{2\pi} \int\_{-\infty}^{\infty} f(t)e^{-i\omega t}dt\tag{14}$$

$$f(t) = \frac{1}{2\pi} \int\_{-\infty}^{\infty} F(\omega)e^{i\omega t} d\omega \tag{15}$$

$$F(\overrightarrow{\mathbf{k}}) = \frac{1}{(2\pi)^{3/2}} \iiint\_{-\infty}^{\infty} f(\overrightarrow{r}) e^{-i\overrightarrow{\mathbf{k}}\cdot\overrightarrow{r}} \,d^3r \text{ and } f(\overrightarrow{r}) = \frac{1}{(2\pi)^{3/2}} \iiint\_{-\infty}^{\infty} F(\overrightarrow{\mathbf{k}}) e^{i\overrightarrow{\mathbf{k}}\cdot\overrightarrow{r}} \,d^3k$$

$$f\_1(\mathfrak{t}).f\_2(\mathfrak{t}) \leftrightarrow \frac{1}{2\pi}F\_1(\omega) \ast F\_2(\omega) \text{ and } f\_1(\mathfrak{t}) \ast f\_2(\mathfrak{t}) \leftrightarrow F\_1(\omega).F\_2(\omega)$$

$$[f\_1(\mathfrak{t}).f\_2(\mathfrak{t}).f\_3(\mathfrak{t})\dots f\_n(\mathfrak{t})] \leftrightarrow \left(\frac{1}{2\pi}\right)^{n-1} [F\_1(\omega)\ast F\_2(\omega)\ast F\_3(\omega)\dots F\_n(\omega)].$$

$$f\_1(t) \* f\_2(t) = \int\_{-\infty}^{\infty} f\_1(\tau) f\_2(t - \tau) d\tau$$

$$F\_1(\omega) \* F\_2(\omega) = \int\_{-\infty}^{\omega} F\_1(p) f\_2(\omega - p) dp.$$


$$\int\_{-\infty}^{\infty} f\_1(t)f\_2(t)dt = \frac{1}{2\pi} \int\_{-\infty}^{\infty} F\_1^\*(\omega)F\_2(\omega)d\omega$$

$$\mathbf{f\_1(t) = f\_2(t) = f(t)}$$

$$\mathbf{F\_1(co) = F\_2(co) = F(co)'}$$

$$\int\_{-\infty}^{\infty} [f(t)]^2 dt = \frac{1}{2\pi} \int\_{-\infty}^{\infty} [F(\omega)]^2 d\omega$$

$$E\_T = \frac{1}{2\pi} \int\_{-\infty}^{\infty} [F(\omega)]^2 d\omega.$$

$$\phi\_{12}\left(\tau\right) = \int\_{-\infty}^{\infty} f\_1(t)f\_2(t+\tau)dt = \int\_{-\infty}^{\infty} f\_1(t-\tau)f\_2(t)dt$$

$$\Phi\_{11}(\mathfrak{r}) = \int\_{-\infty}^{\infty} f(t)f(t+\mathfrak{r}) \, dt$$

$$\Phi\_{12}(\mathfrak{r}) \leftrightarrow \mathcal{E}\_{12}(\mathfrak{a}) \text{ or } \Phi\_{12}(\mathfrak{r}) \leftrightarrow \mathcal{F}\_1(\mathfrak{a}) . F\_2^\*(\mathfrak{a})$$

$$\Phi\_{11}(\mathfrak{r}) \leftrightarrow \mathcal{E}\_{11}(\mathfrak{a}) \text{ or } \Phi\_{11}(\mathfrak{r}) \leftrightarrow [F\_1(\mathfrak{a})]^2$$

Spectral Analysis of Geophysical Data 37

The computation of the inverse FFT is very similar to the forward FFT because of the identical nature of the two. Estimation of power spectrum of a signal can be done by means

Though we have mentioned spectra or spectrum in our previous discussions, we shall formally explain it here. The word spectrum (plural: spectra) is used to describe the variation of certain quantities such as energy or amplitude as a function of some parameter, normally frequency or wavelength. Optical spectrum of white light (colour spectrum) dispersed by a glass prism or some other refractive bodies (such as water) is a good

When a signal is expressed as a function of frequency, it is said to have been transformed into a frequency spectrum. Thus, mathematically, a time-domain signal, f(t) can be expressed by F(ω), where ω represents angular frequency (ω = 2πf; f being the linear


The modulus |�(�)| is normally called the amplitude spectrum and the argument �(�) is

In modern analysis, the time function may be expressed through certain mathematical transformation into a function of frequency. The discrete Fourier transform views both the time domain and the frequency domain as periodic. This can be confusing and inconvenient

The most serious consequence of time domain periodicity is time domain aliasing. Naturally, if we take time domain signal and pass it through DFT, we find the frequency spectrum. If we could immediately pass this frequency spectrum through the inverse DFT to reconstruct the original time domain signal, we are expected to recover this signal, save for spill over from one period into several periods – a problem of circular convolution. Periodicity in the frequency domain behaves in much the same way (as frequency aliasing),

Equations (14) and (15) or any of their similar versions give the Fourier transform pair for a periodic function. For non-repetitive (or aperiodic) signal, the period T→**∞** and the Fourier

�(�) � ���� � = �� ��� ��� ��� �

frequency). The function F(ω) is in general complex and may be represented by

1. The sum of real and imaginary parts: *F*(*ω*) = *a*(*ω*) + *ib*(*ω*) 2. The product of real and complex parts: �(�) = |�(�)|���(�)

�(�) = ����� �(�)

of FFT.

example.

Where

and

called the phase spectrum.

but is more complicated.

transform pair are expressed as

**5.1 Spectral analysis of periodic functions** 

since most of the real time signals are not periodic.

**5.2 Spectral analysis of aperiodic functions** 

**5. The concept of spectra** 

multiplication of the amplitude spectrum. Auto-correlation of two wavelets is equal to the convolution of the first wavelet with the time-reverse of the second wavelet.

#### **4.6 Fast Fourier transform**

It is important to find the discrete forms of the continuous Fourier transform pair in equations (12) and (13). These can be written as (Smith, 1999)

$$G(n) = \sum\_{k=0}^{N-1} g(k)e^{-l\frac{2\pi nk}{N}}\tag{16}$$

and

$$g(k) = \frac{1}{N} \Sigma\_{n=0}^{N-1} G(n) e^{l\frac{2\pi nk}{N}} \tag{17}$$

Both G(n), the discrete amplitude spectrum and the digitized time domain signal, g(k) are periodic as they repeat at every N points. The amplitude spectrum is symmetric while the phase spectrum is antisymmetric.

For real applications, each of equations (16) and (17) will have to be decomposed into the real and imaginary parts with trigonometric argument of �� <sup>=</sup> ���� � . Thus an N point time domain signal is contained in arrays of N real parts and N imaginary parts for each equation.

Calculating the discrete Fourier transform (DFT) equations takes a considerable time even with high speed computers because of the cycles of computations that must be run. The raw computations of DFT can either be done by use of simultaneous equations (very inefficient for practical use) or by correlation method in which signals can be decomposed into orthogonal basis functions using correlation (not too useful a method). The third and the most efficient method for calculating the DFT is by Fast Fourier Transform (FFT). This is an ingenious algorithm that decomposes a DFT with N points into N DFTs each with a single point. The FFT is typically hundreds of times faster than the other methods. In actual practice, correlation is the preferred techniques if the DFT has less than 32 points, otherwise the FFT is used.

Cooley & Tukey (1965) have the credit for bringing the FFT to the scientific world. The FFT, a complicated algorithm is based on the complex DFT; a more sophisticated version of the real DFT and operates by first decomposing an N – point time-domain signal into N time domain signals, each composed of a single point. The second step is to calculate the N frequency spectra corresponding to these N time domain signals. Lastly, the N spectra are synthesized into a single frequency spectrum.

An interlaced decomposition is used each time a signal is broken into two, that is, the signal is separated into its even and odd numbered samples. There will be Log2N stages required in the decomposition and Nlog2N multiplications instead of NxN multiplications without the FFT use. For instance, a 16-point signal (24) requires 4 stages, 512-point signal (27) requires 7 stages, a 4096-point signal (212) requires 12 stages of signal decomposition and so on. The FFT algorithm works on a data length of 2M, where M is a positive integer (≥5). If the data length is not up to the requirement for FFT operation, then "zeros" are sufficiently added. The decomposition is nothing more than a reordering of the samples in the signal. After the decomposition, the FFT algorithm finds the frequency spectra of a 1-point time domain signal (easy!) and then combine the N frequency spectra in the exact reverse order that the time domain decomposition took place.

The computation of the inverse FFT is very similar to the forward FFT because of the identical nature of the two. Estimation of power spectrum of a signal can be done by means of FFT.

#### **5. The concept of spectra**

Though we have mentioned spectra or spectrum in our previous discussions, we shall formally explain it here. The word spectrum (plural: spectra) is used to describe the variation of certain quantities such as energy or amplitude as a function of some parameter, normally frequency or wavelength. Optical spectrum of white light (colour spectrum) dispersed by a glass prism or some other refractive bodies (such as water) is a good example.

When a signal is expressed as a function of frequency, it is said to have been transformed into a frequency spectrum. Thus, mathematically, a time-domain signal, f(t) can be expressed by F(ω), where ω represents angular frequency (ω = 2πf; f being the linear frequency). The function F(ω) is in general complex and may be represented by

1. The sum of real and imaginary parts: *F*(*ω*) = *a*(*ω*) + *ib*(*ω*)

2. The product of real and complex parts: �(�) = |�(�)|���(�) Where

$$|F(\omega)| = \sqrt{a^2(\omega) + b^2(\omega)}$$

and

36 Advances in Data, Methods, Models and Their Applications in Geoscience

multiplication of the amplitude spectrum. Auto-correlation of two wavelets is equal to the

It is important to find the discrete forms of the continuous Fourier transform pair in

�(�) <sup>=</sup> <sup>∑</sup> �(�)������� � ���

� <sup>∑</sup> �(�)��

Both G(n), the discrete amplitude spectrum and the digitized time domain signal, g(k) are periodic as they repeat at every N points. The amplitude spectrum is symmetric while the

For real applications, each of equations (16) and (17) will have to be decomposed into the

domain signal is contained in arrays of N real parts and N imaginary parts for each

Calculating the discrete Fourier transform (DFT) equations takes a considerable time even with high speed computers because of the cycles of computations that must be run. The raw computations of DFT can either be done by use of simultaneous equations (very inefficient for practical use) or by correlation method in which signals can be decomposed into orthogonal basis functions using correlation (not too useful a method). The third and the most efficient method for calculating the DFT is by Fast Fourier Transform (FFT). This is an ingenious algorithm that decomposes a DFT with N points into N DFTs each with a single point. The FFT is typically hundreds of times faster than the other methods. In actual practice, correlation is the preferred techniques if the DFT has less than 32 points, otherwise

Cooley & Tukey (1965) have the credit for bringing the FFT to the scientific world. The FFT, a complicated algorithm is based on the complex DFT; a more sophisticated version of the real DFT and operates by first decomposing an N – point time-domain signal into N time domain signals, each composed of a single point. The second step is to calculate the N frequency spectra corresponding to these N time domain signals. Lastly, the N spectra are

An interlaced decomposition is used each time a signal is broken into two, that is, the signal is separated into its even and odd numbered samples. There will be Log2N stages required in the decomposition and Nlog2N multiplications instead of NxN multiplications without the FFT use. For instance, a 16-point signal (24) requires 4 stages, 512-point signal (27) requires 7 stages, a 4096-point signal (212) requires 12 stages of signal decomposition and so on. The FFT algorithm works on a data length of 2M, where M is a positive integer (≥5). If the data length is not up to the requirement for FFT operation, then "zeros" are sufficiently added. The decomposition is nothing more than a reordering of the samples in the signal. After the decomposition, the FFT algorithm finds the frequency spectra of a 1-point time domain signal (easy!) and then combine the N frequency spectra in the exact reverse order

��� (16)

���� ��� � ��� (17)

� . Thus an N point time

convolution of the first wavelet with the time-reverse of the second wavelet.

�(�) <sup>=</sup> �

real and imaginary parts with trigonometric argument of �� <sup>=</sup> ����

equations (12) and (13). These can be written as (Smith, 1999)

**4.6 Fast Fourier transform** 

phase spectrum is antisymmetric.

synthesized into a single frequency spectrum.

that the time domain decomposition took place.

and

equation.

the FFT is used.

$$\varphi(\omega) = \tan^{-1} \frac{b(\omega)}{a(\omega)} + 2\pi n; n = 0, \pm 1, \pm 2, \pm 3, \dots$$

The modulus |�(�)| is normally called the amplitude spectrum and the argument �(�) is called the phase spectrum.

#### **5.1 Spectral analysis of periodic functions**

In modern analysis, the time function may be expressed through certain mathematical transformation into a function of frequency. The discrete Fourier transform views both the time domain and the frequency domain as periodic. This can be confusing and inconvenient since most of the real time signals are not periodic.

The most serious consequence of time domain periodicity is time domain aliasing. Naturally, if we take time domain signal and pass it through DFT, we find the frequency spectrum. If we could immediately pass this frequency spectrum through the inverse DFT to reconstruct the original time domain signal, we are expected to recover this signal, save for spill over from one period into several periods – a problem of circular convolution. Periodicity in the frequency domain behaves in much the same way (as frequency aliasing), but is more complicated.

#### **5.2 Spectral analysis of aperiodic functions**

Equations (14) and (15) or any of their similar versions give the Fourier transform pair for a periodic function. For non-repetitive (or aperiodic) signal, the period T→**∞** and the Fourier transform pair are expressed as

$$f(t) = \frac{1}{2\pi} \int\_{-\infty}^{\infty} F(\omega)e^{i\omega t} d\omega \tag{18}$$

Spectral Analysis of Geophysical Data 39

that truncating a signal brings about a spectrum modification expressed by the convolution operation between the two spectra, F(ω) and W(ω). The truncation of a signal, therefore, introduces a smoothing effect whose severity depends on the window length. The shorter the window length, the greater the degree of smoothing and vice-versa. The truncated Fourier transform Ftr(ω) is often called the average or weighted spectrum (Blackman & Tukey, 1959). Since all observational data or signals have finite length, truncation effect can

In order to minimize spectral distortion from the signal truncation, other types of time windows may be applied. In general, a window which tapers off gradually towards both ends of the signal introduces less distortion than a window which has near-vertical sides (like the box-car function). A least distortive time window should have the following

a. The time interval must be as long as possible. This implies that its corresponding Fourier transform or the spectral window has its energy concentrated to its main lobe. b. The shape must be as smooth as possible and free of sharp corners. The more smooth the time window is, the smaller the side lobes of the corresponding spectral window

At this juncture, we shall mention some popular time windows. These include the box-car (rectangular), Bartlett (triangular), Blackman, Daniell, Hamming, Hanning (raised cosine), Parzan, Welch and tapered (rectangular windows). Excellent treatise on spectral windows

In general, the Fourier transforms of time domain windows have central main lobe and side lobes in each transform and the magnitudes of the side lobes emphasize the differences between them. Ideally, the main lobe width should be narrow, and the side lobe amplitude

Windows are also extensively used in designing filters and the window parameters (side lobe amplitude, transition width and stopband attenuation) must be used for the design.

To compute the spectrum of a function f(t) which obeys Dirichlet conditions, Fourier transform is applied to it directly, particularly the use of Fourier integral equations. We can

The common types of functions which are usually subjected to Fourier analysis are those obtained by some kind of physical measurements. Functions which represent observational data are normally converted into digital form (if presented as a continuous plot in profile or map forms) so that their spectra can be computed by numerical Fourier transformation. Observational functions are usually not continuous and not infinite as the theory of Fourier transformation demands. For this reason, observational spectra suffer from two types of distortions: (1) truncation effect (by a window function) and (2) digitization effect. When a signal is digitized, its spectrum becomes periodic and so the original spectrum (scaled by the inverse of sampling period) becomes repetitive with the same frequency as that used in sampling the signal. Coarse digitization results in distorted spectrum. The extent of digitization effect depends on the sampling frequency as well as on the cut-off frequency of

� . Thus ���(�) <sup>=</sup> �

�� �(�) � � ��� ��

� . This shows

W(ω) of the rectangular pulse, w(t) as <sup>2</sup> ��� ��

become (the box-car function is a dirty window!).

**5.6 Fourier spectrum of observational data** 

use the basic theorems already presented to evaluate the transforms.

never be avoided.

properties:

can be consulted.

should be small.

the signal (see Section 3).

$$F(\omega) = \int\_{-\infty}^{\infty} f(t)e^{-i\omega t}dt\tag{19}$$

Note again that f(t) is real time domain signal, while F(ω), the amplitude spectrum is a complex function.

#### **5.3 Fourier spectrum**

A time function, f(t) such as gravity field may be transform into another function, F(ω), where the amplitude of all frequency components present in f(t) and their corresponding phases are expressed as function of frequency. The two transform relations are already given in equations (18) and (19).

The complex function, *F*(*ω*), is called the Fourier spectrum and its modulus and arguments as earlier explained are called amplitude and phase spectra respectively. The cosine transform part of *F*(*ω*)[ = *a*(*ω*) + *ib*(*ω*)], *a*(*ω*) is called the co-spectrum and the sine transform part, *b*(*ω*) is called the quadrature spectrum.

#### **5.4 Power spectrum**

If �� is the mean power of a real function, f(t) whose period is T, then (Thompson 1982)

$$E = \lim\_{T \to \infty} \frac{1}{2T} \int\_{-T}^{T} (f(t))^2 dt \tag{20}$$

Where (f(t))2 is termed the instantaneous energy and the complete integration in equation (20) is the total (mean) energy of the function.

We have already noted that for two Fourier pairs, f1(t)↔F1(ω) and f2(t)↔F2(ω), then

$$\text{f}\_1(\text{t}).\text{f}\_2(\text{t}) \longleftrightarrow \frac{1}{2\pi}F\_1^\*(\omega) \ast F\_2(\omega)$$

and that

 $\int\_{-\infty}^{\infty} (f(t))^2 \, dt = \frac{1}{2\pi} \int\_{-\infty}^{\infty} |F(\omega)|^2 \, d\omega$   $[\text{Parseval's theorem}].$ 

The power spectrum |�(�)| � and its total energy ET are then related by

$$E\_{\Gamma} = \frac{1}{2\pi} \int\_{-\infty}^{\infty} |F(\omega)|^2 d\omega = \frac{1}{\pi} \int\_{0}^{\infty} |F(\omega)|^2 d\omega \dots$$

where the power spectrum |�(�)| � is a real quantity.

#### **5.5 Spectral windows and their uses**

When we were discussing the convolution theorem, we noted that we might run into convolution operations in truncating lengthy data (signal) by use of window functions.

Data windowing can be viewed as the truncation of an infinitely long function, f(t). A boxcar function, w(t) = 1, -T<t<T and w(t) = 0 elsewhere, has a value 1 over the required length (2T) and zero elsewhere. The function, w(t), a time window can be used to truncate f(t) and the truncated time function, ftr(t) = f(t).w(t). Using the convolution theorem, the Fourier transform, Ftr(ω) of the truncated function, ftr(t) is given by ���(�) <sup>=</sup> � �� �(�) ∗ �(�), where F(ω) and W(ω) are the Fourier transforms of f(t) and w(t) respectively. We can compute the

�(�) <sup>=</sup> � �(�)������� �

Note again that f(t) is real time domain signal, while F(ω), the amplitude spectrum is a

A time function, f(t) such as gravity field may be transform into another function, F(ω), where the amplitude of all frequency components present in f(t) and their corresponding phases are expressed as function of frequency. The two transform relations are already

The complex function, *F*(*ω*), is called the Fourier spectrum and its modulus and arguments as earlier explained are called amplitude and phase spectra respectively. The cosine transform part of *F*(*ω*)[ = *a*(*ω*) + *ib*(*ω*)], *a*(*ω*) is called the co-spectrum and the sine transform

If �� is the mean power of a real function, f(t) whose period is T, then (Thompson 1982)

We have already noted that for two Fourier pairs, f1(t)↔F1(ω) and f2(t)↔F2(ω), then

�� � |�(�)| ��� �

� is a real quantity.

When we were discussing the convolution theorem, we noted that we might run into convolution operations in truncating lengthy data (signal) by use of window functions. Data windowing can be viewed as the truncation of an infinitely long function, f(t). A boxcar function, w(t) = 1, -T<t<T and w(t) = 0 elsewhere, has a value 1 over the required length (2T) and zero elsewhere. The function, w(t), a time window can be used to truncate f(t) and the truncated time function, ftr(t) = f(t).w(t). Using the convolution theorem, the Fourier

F(ω) and W(ω) are the Fourier transforms of f(t) and w(t) respectively. We can compute the

�� ��

�

Where (f(t))2 is termed the instantaneous energy and the complete integration in equation

�� � (�(�))��� �

∗(�) ∗ ��(�)

� and its total energy ET are then related by

�� [Parseval's theorem].

� � |�(�)| ��� � � ,

�� = lim���

f1(t).f2(t)↔ �

�� � |�(�)| ��� � �� <sup>=</sup> �

transform, Ftr(ω) of the truncated function, ftr(t) is given by ���(�) <sup>=</sup> �

�� � �(�)������ �

�� (18)

�� (19)

�� (20)

�� �(�) ∗ �(�), where

�(�) <sup>=</sup> �

complex function.

**5.3 Fourier spectrum** 

**5.4 Power spectrum** 

The power spectrum |�(�)|

where the power spectrum |�(�)|

**5.5 Spectral windows and their uses** 

and that

given in equations (18) and (19).

part, *b*(*ω*) is called the quadrature spectrum.

(20) is the total (mean) energy of the function.

� (�(�)) � � �� �� = �

ET = �

W(ω) of the rectangular pulse, w(t) as <sup>2</sup> ��� �� � . Thus ���(�) <sup>=</sup> � �� �(�) � � ��� �� � . This shows that truncating a signal brings about a spectrum modification expressed by the convolution operation between the two spectra, F(ω) and W(ω). The truncation of a signal, therefore, introduces a smoothing effect whose severity depends on the window length. The shorter the window length, the greater the degree of smoothing and vice-versa. The truncated Fourier transform Ftr(ω) is often called the average or weighted spectrum (Blackman & Tukey, 1959). Since all observational data or signals have finite length, truncation effect can never be avoided.

In order to minimize spectral distortion from the signal truncation, other types of time windows may be applied. In general, a window which tapers off gradually towards both ends of the signal introduces less distortion than a window which has near-vertical sides (like the box-car function). A least distortive time window should have the following properties:


At this juncture, we shall mention some popular time windows. These include the box-car (rectangular), Bartlett (triangular), Blackman, Daniell, Hamming, Hanning (raised cosine), Parzan, Welch and tapered (rectangular windows). Excellent treatise on spectral windows can be consulted.

In general, the Fourier transforms of time domain windows have central main lobe and side lobes in each transform and the magnitudes of the side lobes emphasize the differences between them. Ideally, the main lobe width should be narrow, and the side lobe amplitude should be small.

Windows are also extensively used in designing filters and the window parameters (side lobe amplitude, transition width and stopband attenuation) must be used for the design.

#### **5.6 Fourier spectrum of observational data**

To compute the spectrum of a function f(t) which obeys Dirichlet conditions, Fourier transform is applied to it directly, particularly the use of Fourier integral equations. We can use the basic theorems already presented to evaluate the transforms.

The common types of functions which are usually subjected to Fourier analysis are those obtained by some kind of physical measurements. Functions which represent observational data are normally converted into digital form (if presented as a continuous plot in profile or map forms) so that their spectra can be computed by numerical Fourier transformation.

Observational functions are usually not continuous and not infinite as the theory of Fourier transformation demands. For this reason, observational spectra suffer from two types of distortions: (1) truncation effect (by a window function) and (2) digitization effect. When a signal is digitized, its spectrum becomes periodic and so the original spectrum (scaled by the inverse of sampling period) becomes repetitive with the same frequency as that used in sampling the signal. Coarse digitization results in distorted spectrum. The extent of digitization effect depends on the sampling frequency as well as on the cut-off frequency of the signal (see Section 3).

Spectral Analysis of Geophysical Data 41

Electric current flowing from an isolated point electrode embedded in a continuous homogeneous ground provides a physical illustration of the significance of the inverse square law. All the current leaving the electrode must cross any closed surface that surrounds it. Usually the surface is spherical, concentric with the electrode and the same function of the total current will cross each unit area on the surface of the sphere. The current per unit area will be inversely proportional to the total surface (half-space) of 2πr2.

The potential fields of either gravity, magnetic or electrical fields are the ones given by either the Laplace or Poisson equations. Some of the useful properties of �(x, y, z) are (i) given this potential field (scalar) over any plane, we can compute the primary or force field (vector) at almost all points in the space by analytic continuation and (ii) the points where the force field cannot be computed are the so-called singular points. A closed surface enclosing all such singular points also encloses the sources which give rise to the potential field. Thus the

All these properties are best described and accentuated in the Fourier domain. We shall therefore express the Fourier transformation of the potential field in two or three dimensions (see Section 4.5). In two dimensions, the Fourier transform pair, (u, v) and its

Φ(�, �) <sup>=</sup> <sup>∬</sup> �(�, �) exp[−�(�� � ��)] ���� �

Where here, u and v are coordinates of the Fourier plane. Equation (24) is also known as the

<sup>∬</sup> |�(�, �)|���� � � � �� : a condition generally not satisfied in most geophysical situations except for an isolated anomaly (Roy, 2008). However, the Fourier transform of a real function in two dimensions

Φ(�, �) = Φ∗(−�, −�), Φ(−�, �) = Φ∗(�, −�)

Φ(0,0) <sup>=</sup> <sup>∬</sup> �(�, �)���� �

If �(x, y, z) is the potential field on a plane z, satisfying the Laplace equation (equation (21)),

Where H(u, v, z) is to be determined by requiring that it also satisfies the Laplace equation

��� <sup>−</sup> (�� � ��)�=0 , whose solution is H(u, v, z) = e s z for all values of z, where � = √�� � ��. For z ≥ 0 equation

��� <sup>∬</sup> Φ(�, �)�(�, �, �) exp[−�(�� � ��)] ���� �

Fourier integral representation of �(x, y). Equation (23) exists only if and only if

��� <sup>∬</sup> Φ(�, �) exp[�(�� � ��)] ���� �

�� (23)

�� (24)

�� (25)

�� (26)

Current flow in the earth, however, is modified drastically by conductivity variation.

singularities of the potential field are confined to the region filled with sources.

�(�, �) <sup>=</sup> �

its Fourier integral representation is given by (Naidu 1987)

���

�(�, �, �) <sup>=</sup> �

and is only true if it satisfies the differential equation

inverse �(x, y) are given by

possesses the following symmetry:

and

(26) becomes

#### **6. Spectrum of random fields**

#### **6.1 Random functions**

A random variable is a real-valued function defined on the events of probability system. A random variable, f(t) emanates from a random or stochastic process: a process developing in time and controlled by probabilistic laws. A random (or stochastic) process is an ensemble or set of functions of some parameter (usually time, t) together with a probability measure by which we can determine that any member, or a group of members has certain statistical properties. Like any other functions, random processes can either be discrete or continuous. At any point in a medium, a unit mass or a unit charge or a unit magnetic pole experiences a certain force. This force will be a force of attraction in the case of gravitational field. It will be a force of attraction or repulsion when two unit charges or two magnetic monopoles of opposite or same polarity are brought close to each other. Every mass in space is associated with a gravitational force of attraction. This force has both magnitude and direction. For gravitational field, the force of attraction will be between two masses along a line joining the bodies. For electrostatic, magnetostatic and direct current flow fields, the direction of the field will be tangential to any point of observation. These forces produce force fields. These fields, either global or man-made local fields are used to quantitatively estimate some

Most geophysical potential fields, in particular gravity and magnetic fields are caused by an ensemble of sources distributed in some complex manner, which may be best described in a stochastic or random framework. We shall examine some characteristics of these fields.

#### **6.2 Geophysical potential fields**

physical properties at every point in a medium.

The potential field, ϕ(x, y, z) in free space (i.e. without sources) satisfies the Laplace equation

$$
\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + \frac{\partial^2 \phi}{\partial z^2} = 0 \tag{21}
$$

When sources are present, the potential fields satisfy the so-called Poisson equation

$$\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + \frac{\partial^2 \phi}{\partial z^2} = -\rho(\mathbf{x}, \mathbf{y}, \mathbf{z})\tag{22}$$

Where ρ(x,y,z) stands for the density, magnetization or conductivity depending opun whether � stands for gravity, magnetic or electric potential respectively. It is important to know that both global or local fields are subject to inverse square law attenuation of the signal strengths. It is at its simple peak in gravity work where the field due to a point mass is inversely proportional to the square of the distance from the mass, and the constant of proportionality (the gravitational constant, G) is invariant. Magnetic fields, though complex, also obey the inverse square law. The fact that their strength is, in principle, modified by the permeability of the medium, is irrelevant in most geophysical work, where measurements are made in either air or water. Magnetic sources are, however, essentially bipolar and the modifications to the simple inverse-square law due to this fact are important. A dipole here consists of equal-strength positive and negative point sources: a very small distance apart. Field strength here decreases as the inverse cube of distance and both strength and direction change with "latitude" (inclination) of the Earth's magnetic field. The intensity of the field at a point on a dipole axis is double the intensity at a point, the same distance away on the dipole "equator", and in the opposite direction.

Electric current flowing from an isolated point electrode embedded in a continuous homogeneous ground provides a physical illustration of the significance of the inverse square law. All the current leaving the electrode must cross any closed surface that surrounds it. Usually the surface is spherical, concentric with the electrode and the same function of the total current will cross each unit area on the surface of the sphere. The current per unit area will be inversely proportional to the total surface (half-space) of 2πr2. Current flow in the earth, however, is modified drastically by conductivity variation.

The potential fields of either gravity, magnetic or electrical fields are the ones given by either the Laplace or Poisson equations. Some of the useful properties of �(x, y, z) are (i) given this potential field (scalar) over any plane, we can compute the primary or force field (vector) at almost all points in the space by analytic continuation and (ii) the points where the force field cannot be computed are the so-called singular points. A closed surface enclosing all such singular points also encloses the sources which give rise to the potential field. Thus the singularities of the potential field are confined to the region filled with sources.

All these properties are best described and accentuated in the Fourier domain. We shall therefore express the Fourier transformation of the potential field in two or three dimensions (see Section 4.5). In two dimensions, the Fourier transform pair, (u, v) and its inverse �(x, y) are given by

$$\Phi(u,v) = \iint\_{-\infty}^{\infty} \Phi(\mathbf{x}, \mathbf{y}) \exp[-i(ux+vy)] \, d\mathbf{x} dy \tag{23}$$

and

40 Advances in Data, Methods, Models and Their Applications in Geoscience

A random variable is a real-valued function defined on the events of probability system. A random variable, f(t) emanates from a random or stochastic process: a process developing in time and controlled by probabilistic laws. A random (or stochastic) process is an ensemble or set of functions of some parameter (usually time, t) together with a probability measure by which we can determine that any member, or a group of members has certain statistical properties. Like any other functions, random processes can either be discrete or continuous. At any point in a medium, a unit mass or a unit charge or a unit magnetic pole experiences a certain force. This force will be a force of attraction in the case of gravitational field. It will be a force of attraction or repulsion when two unit charges or two magnetic monopoles of opposite or same polarity are brought close to each other. Every mass in space is associated with a gravitational force of attraction. This force has both magnitude and direction. For gravitational field, the force of attraction will be between two masses along a line joining the bodies. For electrostatic, magnetostatic and direct current flow fields, the direction of the field will be tangential to any point of observation. These forces produce force fields. These fields, either global or man-made local fields are used to quantitatively estimate some

Most geophysical potential fields, in particular gravity and magnetic fields are caused by an ensemble of sources distributed in some complex manner, which may be best described in a stochastic or random framework. We shall examine some characteristics of these fields.

The potential field, ϕ(x, y, z) in free space (i.e. without sources) satisfies the Laplace equation

��� <sup>+</sup> ���

Where ρ(x,y,z) stands for the density, magnetization or conductivity depending opun whether � stands for gravity, magnetic or electric potential respectively. It is important to know that both global or local fields are subject to inverse square law attenuation of the signal strengths. It is at its simple peak in gravity work where the field due to a point mass is inversely proportional to the square of the distance from the mass, and the constant of proportionality (the gravitational constant, G) is invariant. Magnetic fields, though complex, also obey the inverse square law. The fact that their strength is, in principle, modified by the permeability of the medium, is irrelevant in most geophysical work, where measurements are made in either air or water. Magnetic sources are, however, essentially bipolar and the modifications to the simple inverse-square law due to this fact are important. A dipole here consists of equal-strength positive and negative point sources: a very small distance apart. Field strength here decreases as the inverse cube of distance and both strength and direction change with "latitude" (inclination) of the Earth's magnetic field. The intensity of the field at a point on a dipole axis is double the intensity at a point, the same distance away on the

��� = 0 (21)

��� = ����� �� �� (22)

��� ��� <sup>+</sup> ���

��� ��� <sup>+</sup> ���

When sources are present, the potential fields satisfy the so-called Poisson equation

��� <sup>+</sup> ���

**6. Spectrum of random fields** 

physical properties at every point in a medium.

dipole "equator", and in the opposite direction.

**6.2 Geophysical potential fields** 

**6.1 Random functions** 

$$\phi(\mathbf{x}, \mathbf{y}) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \Phi(\mathbf{u}, \upsilon) \exp[i(\mathbf{u}\mathbf{x} + \upsilon\mathbf{y})] \, d\mathbf{u} d\upsilon \tag{24}$$

Where here, u and v are coordinates of the Fourier plane. Equation (24) is also known as the Fourier integral representation of �(x, y). Equation (23) exists only if and only if

> <sup>∬</sup> |�(�, �)|���� � � � �� :

a condition generally not satisfied in most geophysical situations except for an isolated anomaly (Roy, 2008). However, the Fourier transform of a real function in two dimensions possesses the following symmetry:

$$\Phi(u,\upsilon) = \Phi^\*(-u,-\upsilon), \Phi(-u,\upsilon) = \Phi^\*(u,-\upsilon)$$

$$\Phi(0,0) = \iint\_{-\infty}^{\infty} \phi(x,y)dxdy \tag{25}$$

If �(x, y, z) is the potential field on a plane z, satisfying the Laplace equation (equation (21)), its Fourier integral representation is given by (Naidu 1987)

$$\Phi(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \Phi(\mathbf{u}, \mathbf{v}) H(\mathbf{u}, \mathbf{v}, \mathbf{z}) \exp[-i(\mathbf{u}\mathbf{x} + \mathbf{v}\mathbf{y})] \, d\mathbf{u} d\mathbf{v} \tag{26}$$

Where H(u, v, z) is to be determined by requiring that it also satisfies the Laplace equation and is only true if it satisfies the differential equation

 $\frac{d^2H}{dx^2} - (u^2 + v^2)H = 0$  ,

whose solution is H(u, v, z) = e s z for all values of z, where � = √�� � ��. For z ≥ 0 equation (26) becomes

$$\Phi(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \Phi(\mathbf{u}, \mathbf{v}) e^{-s\mathbf{z}} e^{l(\mathbf{u}\mathbf{x} + \mathbf{v}\mathbf{y})} d\mathbf{u} d\mathbf{v} \tag{27}$$

$$f(\mathbf{x}, \mathbf{y}) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \mathrm{dF}(u, v) \exp[i(u\mathbf{x} + v\mathbf{y})] \tag{28}$$

$$\text{dF}(\mathbf{u}, \mathbf{v}) = \text{F}(\mathbf{u} + \mathbf{du}, \mathbf{v} + \mathbf{dv}) - \text{F}(\mathbf{u}, \mathbf{v}), \text{ (du, dv)} \to 0$$

$$\text{i.}\qquad E\left\{\frac{1}{4\pi^2}dF(u,v)\right\} = E[f(\mathfrak{x},\mathfrak{y})] \\ \colon u=v=0$$

$$=0 \colon (\mathbf{u}, \mathbf{v}) \neq 0$$

$$E\left\{\frac{1}{4\pi^2}dF(u,\upsilon).\frac{1}{4\pi^2}dF^\*(u,\upsilon)\right\}=\frac{1}{4\pi^2}S\_f(u,\upsilon)dud\upsilon$$

$$\Phi(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \mathrm{d}\Phi(\mathbf{u}, \mathbf{v}) H(\mathbf{u}, \mathbf{v}, \mathbf{z}) \exp[i(\mathbf{u}\mathbf{x} + \mathbf{v}\mathbf{y})] \tag{29}$$

$$\frac{d^2H(u,v,z)}{dz^2} - (u^2 + v^2)H = 0$$

$$H(u,v,\mathbf{z}) = \exp[\pm\sqrt{u^2+v^2}\,\mathbf{z}]$$

$$\Phi(\mathbf{x}, \mathbf{y}, \mathbf{z}) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \mathbf{d}\Phi(\mathbf{u}, \mathbf{v}) \exp(-\mathbf{s}\mathbf{z}) \exp[i(\mathbf{u}\mathbf{x} + \mathbf{v}\mathbf{y})] \tag{30}$$

$$\left[f\_{\chi}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = -\frac{\partial \phi}{\partial \mathbf{x}}, f\_{\mathbf{y}}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = -\frac{\partial \phi}{\partial \mathbf{y}}, etc{\right]$$

$$f\_2(\mathbf{x}, \mathbf{y}, h) = -\iint\_{-\infty}^{\infty} \int\_0^{\Delta x} \frac{G \Delta \rho (h + x\_0)}{\left[ (\mathbf{x} - \mathbf{x}\_0)^2 + (\mathbf{y} - \mathbf{y}\_0)^2 + (h + x\_0)^2 \right]^{\frac{1}{2}}} d\mathbf{x}\_0 d\mathbf{y}\_0 d\mathbf{z}\_0 \tag{31}$$

$$f\_{\mathbf{z}}(\mathbf{x}, \mathbf{y}, h) = -\frac{1}{2\pi} G \Delta \rho \iint\_{-\infty}^{\infty} \sum\_{n=1}^{\infty} d\Delta Z\_n(\mathbf{u}, \nu) \frac{(-\mathbf{s})^{n-1}}{n!} \exp\{-\mathbf{s} h\} \exp[i(\mathbf{u}\mathbf{x} + \nu \mathbf{y})] \tag{32}$$

$$\Delta \mathbf{z}^{n}(\mathbf{x}, \mathbf{y}) = \frac{1}{4\pi^{2}} \iint\_{-\infty}^{\infty} d\Delta Z\_{n}(\mathbf{u}, \mathbf{v}) \exp[i(\mu \mathbf{x} + \nu \mathbf{y})],$$

$$f\_z(\mathbf{x}, \mathbf{y}, h) = -\frac{1}{2\pi} G \Delta \rho \iint\_{-\infty}^{\infty} d\Delta Z(\mathbf{u}, \nu) \exp(-sh) \exp[i(\mathbf{u}\mathbf{x} + \nu\mathbf{y})] \tag{33}$$

 $H\_{\chi} = -\frac{\partial \phi}{\partial x}$  and  $H\_{\mathbf{z}} = -\frac{\partial \phi}{\partial \mathbf{z}}$ .

$$f\_T(\mathbf{x}, \mathbf{y}, h) = -\frac{1}{2\pi} G \Delta \rho \iint\_{-\infty}^{\infty} \frac{\Gamma(\mathbf{u}, \mathbf{v})}{\mathbf{s}} \sum\_{\mathbf{n}=1}^{\infty} \mathbf{d} \Delta \mathbf{Z}\_{\mathbf{n}}(\mathbf{u}, \mathbf{v}) \frac{(-\mathbf{s})^{\mathbf{n}-1}}{\mathbf{n}!} \exp\{-\mathbf{s} h\} \exp[l(\mathbf{u}\mathbf{x} + \mathbf{v}\mathbf{y})] \tag{34}$$

$$f\_{\mathcal{T}}(\mathbf{x}, \mathbf{y}, h) = -\frac{1}{2\pi} \iint\_{-\infty}^{\infty} \frac{\Gamma(\mathbf{u}, \mathbf{v})}{\mathbf{s}} \exp(-\mathbf{s}h) \, \mathrm{d}\Delta \mathcal{Z}(\mathbf{u}, \mathbf{v}) \exp[i(\mathbf{u}\mathbf{x} + \mathbf{v}\mathbf{y})] \tag{35}$$

$$f(m,n) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \mathrm{dF}(\mu, \nu) \exp[l(\mu m + \nu n)]\tag{36a}$$

$$\mathcal{W}\_0(m,n) = \frac{1}{4\pi^2} \iint\_{-\infty}^{\infty} \mathcal{W}\_0(\mu, \nu) \exp[l(\mu m + \nu n)] dud\nu\tag{36b}$$

$$f\_0(\mathcal{m}, n) = f(\mathcal{m}, n) . \mathcal{w}\_0(\mathcal{m}, n)$$

$$= \frac{1}{4\pi^2} \iint\_{-\pi}^{\pi} \mathcal{F}\_0(u, v) \exp[i(\mathcal{um} + vn)] du dv \tag{36c}$$

$$F\_0(u,v) = \frac{1}{4\pi^2} \iint\_{-\pi}^{\pi} dF(u',v')W\_0(u-u',v-v').$$

$$F\_0(k,l) = \frac{1}{4\pi^2} \iint\_{-\pi}^{\pi} dF(u',v') \mathcal{W}\_0(\frac{2\pi k}{M} - u', \frac{2\pi l}{N} - v') \tag{37}$$

$$S\_{f\_0}(k,l) = E\left\{\frac{1}{MN}|F\_0(k,l)|^2\right\}$$

$$=\frac{1}{4\pi^2}\iint\_{-\pi}^{\pi}S\_f(u',v')\left|W\_0(\frac{2\pi k}{M}-u',\frac{2\pi l}{N}-v')\right|^2 du'dv'\tag{38}$$


Spectral Analysis of Geophysical Data 47

Where h is depth to the magnetic layer, I0 is the direction of the current earth's magnetic field, , and are directional cosines while 0 is the declination of the earth's magnetic field. The non-exponent component of equation (44) is exactly the same as the square of Γ(u, v) expressed in equation (34). The angular spectrum, Anorm(θ) may now be expressed

Anorm(θ) = Ω[γ2 + (α2 + β2)cos2(θ - θ0)]2 Where Ω is a constant. Thus the angular spectrum is a maximum in the direction of polarization vector. Naidu (1970) had earlier shown that the shape of the angular spectrum is a product of a number of factors such as rock type, strike and polarization vector, but the latter two factors influence the shape of the spectrum significantly. Thus the presence of

On the other hand, the radial spectrum gives a measure of the rate of decay with respect to radial frequency of the spectral power, which may represent a deep-seated phenomenon

We shall apply the concept of radial and angular spectra to synthetic and real data. For the synthetic data, we have taken the field over a magnetic dipole buried at a depth of 4 km. Other parameters of the dipole include: inclination and declination of the inducing field (and remanent field of the dipole) on the dipole are respectively 6o and 8o (i.e. at low magnetic latitudes), where the field strength of the inducing field is 33510 nT and the magnetization intensity is 0.01 A/m, while its susceptibility is assumed as 9.5 x 10-5cgs (0.0012 SI). For space, the anomaly map is not shown. In computing the angular spectrum of this dipole anomaly, the 50x50 data grid was padded with sufficient zeros and cosine tapered to make data matrix amenable for FFT computations. This resulted in a data matrix size of 64x64. The angular spectrum is then calculated for three frequency sub-bands (1-10, 10-20 and 20-30 frequency numbers) for angular interval of 180o. The highest frequency in

Figure 3 shows the curves representing the low (1-10), middle (10-20) and high (20-30) frequency numbers. Observation of these curves shows that 8o and 90o spectral peaks appear in the three frequency subbands followed by a peak at 156o in the mid to high frequency sub-bands though with reduced magnitude. Thus we see the emergence in the three frequency sub-bands, of 8o: the declination of both the inducing and remanents fields. The other angular feature (90o) at subdued level is due to the tapered window used in the analysis. The other peak (156o) corresponds to the direction of the polarization in the

The real data used for the computation of radial and angular spectra were obtained from aeromagnetic total field intensity of the Middle Benue Trough, Nigeria(MBT) collected from 1974 to 1976. The MBT is the central part of the main Benue Trough of Nigeria. The Benue trough is linked genetically to the oil/gas bearing rocks of the inland Nigerian Niger Delta area. With an upbeat in petroleum efforts in the inland basins, attention is now focused on

The composite total field intensity data were corrected for the main field using the IGRF 1975 model and this resulted in the residual field map (Fig. 4) used for the present analysis.

the Benue trough with more emphasis laid on the structural setting of the basin.

peaks in the angular spectrum gives an indication of linear features in the map.

(Bhattacharyya, 1966; Naidu, 1970, Spector & Grant, 1970).

direction of the inducing field at this magnetic latitude.

**6.6 Estimation of radial and angular spectra of aeromagnetic data** 

as

the data is 32.

#### **6.5 Angular and radial spectra of the field**

Naidu (1969) and Mishra & Naidu (1974) gave the spectrum of a two-dimensional magnetic survey as

$$S\_K(\mu, \upsilon) = \frac{1}{K} \sum\_{k=-1}^{K} \frac{1}{L\_x L\_y} \left| X\_k(\mu, \upsilon) \right|^2 \tag{39a}$$

Where S (u, v) is the power spectrum of a 2-D aeromagnetic field, X (u, v) is the Fourier transform of the field, Lx and Ly are length dimensions, and u and v are frequency in the x and y directions respectively given as u = 2π/Lx and v = 2π/Ly. A two-dimensional spectrum can be expressed in a condensed form as one-dimensional spectra; radial and angular (Spector & Grant, 1970; Mishra & Naidu, 1974; Naidu, 1980; Naidu & Mishra, 1980; Naidu & Mathew, 1998). The radial spectrum is defined as

$$\mathbf{R}(\mathbf{s}) = \frac{1}{2\pi} \int\_0^{2\pi} \mathbf{S}\_f(s\cos\theta, s\sin\theta)d\theta \tag{39b}$$

Where again � � √�� � �� is the magnitude of the frequency vector and = tan-1 (v/u) is the direction of the frequency vector in the spatial frequency plane v and u (in radian/km) in the x- and y-directions respectively. The angular spectrum is defined as

$$\mathbf{A(\theta)} = \frac{1}{\Delta s} \int\_{s\_0}^{s\_0 + \Delta s} S\_f(s \cos \theta, s \sin \theta) ds \tag{40}$$

Where, s is the radial frequency band starting from s0 to s0 + s, over which the averaging is carried out. It is useful as a rule to look at power spectra in one-dimensional or profile form rather than in two-dimensional or map form. This is because S is a somewhat bumpy function of (Fedi et al., 1997) when the width of the model is moderately large, and the bumpiness imparts a certain irregularity to the contours (Spector & Grant, 1970). The power spectra in one-dimension also enables ensemble of magnetic block parameters (average magnetic moment/unit depth, average depths to top, average thickness and average widths) to be factored out completely for effective analysis.

Usually the angular spectrum is normalized with respect to the radial spectrum so as to free this spectrum from any radial variation. In this case (Naidu & Mathew, 1998)

$$\mathbf{A}\_{\rm norm}(\theta) = \frac{1}{\Delta s} \int\_{s\_0}^{s\_0 + \Delta s} \frac{\mathcal{S}\_f \{s \cos \theta, s \sin \theta\}}{\mathcal{R}\_f \{s\}} ds \tag{41}$$

The computations of spectra in equations (40) and (41) may require the use of template. The radial spectrum is computed by averaging the 2D spectrum over a series of annular regions while the angular spectrum is computed by averaging over angular sectors in the template. Naidu (1980) and Naidu & Mathew (1998) have shown that the angular spectrum of the total field of a uniform magnetized layer having an uncorrelated random magnetization is given by

$$\mathbf{S}\_{\rm IT} \begin{pmatrix} \mathbf{u}, \mathbf{v} \end{pmatrix} = \, e^{-2\text{ks}} I\_0^2 s^4 \left[ \gamma^2 + (\alpha^2 + \beta^2) \cos^2(\theta - \theta\_0) \right]^2 \tag{42}$$

Naidu (1969) and Mishra & Naidu (1974) gave the spectrum of a two-dimensional magnetic

 <sup>2</sup> 1 1 1 , , *K K k k x y S uv X uv K LL*

Where S (u, v) is the power spectrum of a 2-D aeromagnetic field, X (u, v) is the Fourier transform of the field, Lx and Ly are length dimensions, and u and v are frequency in the x and y directions respectively given as u = 2π/Lx and v = 2π/Ly. A two-dimensional spectrum can be expressed in a condensed form as one-dimensional spectra; radial and angular (Spector & Grant, 1970; Mishra & Naidu, 1974; Naidu, 1980; Naidu & Mishra, 1980;

> <sup>1</sup> ( cos , sin ) <sup>2</sup> *Ss s d <sup>f</sup>*

> <sup>1</sup> ( cos , sin )

*S s s ds*

*f*

Where, s is the radial frequency band starting from s0 to s0 + s, over which the averaging is carried out. It is useful as a rule to look at power spectra in one-dimensional or profile form rather than in two-dimensional or map form. This is because S is a somewhat bumpy function of (Fedi et al., 1997) when the width of the model is moderately large, and the bumpiness imparts a certain irregularity to the contours (Spector & Grant, 1970). The power spectra in one-dimension also enables ensemble of magnetic block parameters (average magnetic moment/unit depth, average depths to top, average thickness and average

Usually the angular spectrum is normalized with respect to the radial spectrum so as to free

1 ( cos , sin )

0 0 ( )cos ( ) *hs e Is*

*s Rs*

The computations of spectra in equations (40) and (41) may require the use of template. The radial spectrum is computed by averaging the 2D spectrum over a series of annular regions while the angular spectrum is computed by averaging over angular sectors in the template. Naidu (1980) and Naidu & Mathew (1998) have shown that the angular spectrum of the total field of a uniform magnetized layer having an uncorrelated random magnetization is given by

*Ss s*

( )

*ds*

 (42)

(41)

 

Where again � � √�� � �� is the magnitude of the frequency vector and = tan-1 (v/u) is the direction of the frequency vector in the spatial frequency plane v and u (in radian/km) in

  

> 

2

0

0

*s*

this spectrum from any radial variation. In this case (Naidu & Mathew, 1998)

SfT (u,v) = 2 24 2 2 2 2 2

0

*s s f f s*

0

 

*s s*

0

*s*

the x- and y-directions respectively. The angular spectrum is defined as

(39a)

(39b)

(40)

**6.5 Angular and radial spectra of the field** 

Naidu & Mathew, 1998). The radial spectrum is defined as

widths) to be factored out completely for effective analysis.

Rf(s) =

A() =

Anorm()=

survey as

Where h is depth to the magnetic layer, I0 is the direction of the current earth's magnetic field, , and are directional cosines while 0 is the declination of the earth's magnetic field. The non-exponent component of equation (44) is exactly the same as the square of Γ(u, v) expressed in equation (34). The angular spectrum, Anorm(θ) may now be expressed as

$$\mathbf{A}\_{\mathrm{norm}}(\boldsymbol{\theta}) = \boldsymbol{\Omega} [\boldsymbol{\chi}^2 + (\mathbf{a}^2 + \boldsymbol{\beta}^2) \cos^2(\boldsymbol{\theta} - \boldsymbol{\theta}\_0)]^2$$

Where Ω is a constant. Thus the angular spectrum is a maximum in the direction of polarization vector. Naidu (1970) had earlier shown that the shape of the angular spectrum is a product of a number of factors such as rock type, strike and polarization vector, but the latter two factors influence the shape of the spectrum significantly. Thus the presence of peaks in the angular spectrum gives an indication of linear features in the map.

On the other hand, the radial spectrum gives a measure of the rate of decay with respect to radial frequency of the spectral power, which may represent a deep-seated phenomenon (Bhattacharyya, 1966; Naidu, 1970, Spector & Grant, 1970).

#### **6.6 Estimation of radial and angular spectra of aeromagnetic data**

We shall apply the concept of radial and angular spectra to synthetic and real data. For the synthetic data, we have taken the field over a magnetic dipole buried at a depth of 4 km. Other parameters of the dipole include: inclination and declination of the inducing field (and remanent field of the dipole) on the dipole are respectively 6o and 8o (i.e. at low magnetic latitudes), where the field strength of the inducing field is 33510 nT and the magnetization intensity is 0.01 A/m, while its susceptibility is assumed as 9.5 x 10-5cgs (0.0012 SI). For space, the anomaly map is not shown. In computing the angular spectrum of this dipole anomaly, the 50x50 data grid was padded with sufficient zeros and cosine tapered to make data matrix amenable for FFT computations. This resulted in a data matrix size of 64x64. The angular spectrum is then calculated for three frequency sub-bands (1-10, 10-20 and 20-30 frequency numbers) for angular interval of 180o. The highest frequency in the data is 32.

Figure 3 shows the curves representing the low (1-10), middle (10-20) and high (20-30) frequency numbers. Observation of these curves shows that 8o and 90o spectral peaks appear in the three frequency subbands followed by a peak at 156o in the mid to high frequency sub-bands though with reduced magnitude. Thus we see the emergence in the three frequency sub-bands, of 8o: the declination of both the inducing and remanents fields. The other angular feature (90o) at subdued level is due to the tapered window used in the analysis. The other peak (156o) corresponds to the direction of the polarization in the direction of the inducing field at this magnetic latitude.

The real data used for the computation of radial and angular spectra were obtained from aeromagnetic total field intensity of the Middle Benue Trough, Nigeria(MBT) collected from 1974 to 1976. The MBT is the central part of the main Benue Trough of Nigeria. The Benue trough is linked genetically to the oil/gas bearing rocks of the inland Nigerian Niger Delta area. With an upbeat in petroleum efforts in the inland basins, attention is now focused on the Benue trough with more emphasis laid on the structural setting of the basin.

The composite total field intensity data were corrected for the main field using the IGRF 1975 model and this resulted in the residual field map (Fig. 4) used for the present analysis.

Spectral Analysis of Geophysical Data 49

The angular and radial spectra of the residual total field magnetic map (Fig. 4) were computed. First, for detailed delineation of angular features, the map was divided into two sub-areas: north/south or upper/lower. The upper part (enclosing nearly 90% of the sediments) has a size of 128x128 and the lower portion has a size of 57x120. It is computationally efficient to use the Fast Fourier Transform (FFT) algorithm to accomplish the analysis of the angular and radial spectra. The upper part of the map (128x128) is already amenable for FFT application since the matrix size is already 2N, where N is an integer. The lower part however, is cosine tapered and then padded with sufficient zeros to make data matrix amenable for FFT application. This resulted into another data of 128x128. Next, the averaging was carried out over three frequency bands (1-20, 20-40 and 40-60 frequency numbers) for each data matrix. This division represents the low frequency band (1-20), mid frequency band (20-40) and high frequency band (40-60), noting that the highest frequency number in the data is 64. The angular spectra for the three sub-bands in each subarea of the map are shown (Figs. 6a and b). Figure 6a shows correspondences between the three spectra indicating peaks at 4o, 36o, 56o, 75o, 102o, 140o and 169o; where the first peak (4o) appears in the three sub-bands, while the other six peaks appear in the mid and high frequency bands. A similar pattern is obtained in the lower part of the map area where also 4o peak appears in the three sub-bands (Fig. 6b) and prominent peaks at 12o and 157o at the

> 0 20 40 60 80 100 Radial Frequency Number

The 4o peak appearing in the three sub-bands corresponds to the value of the inclination of the Earth's magnetic field in the area. The peak at 56o corresponds to the general trend of the Benue Trough (N56E). Other angular values have been fully mapped in the area (Benkhelil,

**C (Depth = 1.43 km)**

Fig. 5. Radial spectrum plotted against frequency number of the total field magnetic anomaly over the Middle Benue Trough, Nigeria. Five linear segments are marked (A, B, C,

**D (Depth = 3.54 km)**

**E (Depth = 20.62 km)**

**B (Depth = 0.73 km)**

**A (Depth = 0.26 km)**

mid and high frequency sub-bands amid a subdued peak at 149o.

4

D, E). Estimates of depths from slopes are indicated.

1982, 1989; Likkason, 2005).

8

12

L og o f R a d ia l S pec trum

16

20

24

Fig. 3. Angu lar spectrum of the dipole anomaly (properties described in Section 6.6) with labels as follows: (a) low frequency band (1-10), (b) mid frequency band (10-20) and (c) high frequency band (20-30)

Fig. 4. Total field magnetic anomaly over the Middle Benue Trough, Nigeria. The 1975 IGRF model (epoch date 1st January 1974) field has been removed. Approximate sedimentarybasement boundary is indicated in dashed lines. Contour interval is 10 nT.

0 40 80 120 160 200 Angle (deg)

Fig. 3. Angu lar spectrum of the dipole anomaly (properties described in Section 6.6) with labels as follows: (a) low frequency band (1-10), (b) mid frequency band (10-20) and (c) high

Fig. 4. Total field magnetic anomaly over the Middle Benue Trough, Nigeria. The 1975 IGRF model (epoch date 1st January 1974) field has been removed. Approximate sedimentary-

**9:00E 11:00E**

basement boundary is indicated in dashed lines. Contour interval is 10 nT.

90o

156o

0

**9:30N**

**7:00N**

frequency band (20-30)

400

800

1200

Angular Spectrum

1600

a

b

c

2000

8o

The angular and radial spectra of the residual total field magnetic map (Fig. 4) were computed. First, for detailed delineation of angular features, the map was divided into two sub-areas: north/south or upper/lower. The upper part (enclosing nearly 90% of the sediments) has a size of 128x128 and the lower portion has a size of 57x120. It is computationally efficient to use the Fast Fourier Transform (FFT) algorithm to accomplish the analysis of the angular and radial spectra. The upper part of the map (128x128) is already amenable for FFT application since the matrix size is already 2N, where N is an integer. The lower part however, is cosine tapered and then padded with sufficient zeros to make data matrix amenable for FFT application. This resulted into another data of 128x128. Next, the averaging was carried out over three frequency bands (1-20, 20-40 and 40-60 frequency numbers) for each data matrix. This division represents the low frequency band (1-20), mid frequency band (20-40) and high frequency band (40-60), noting that the highest frequency number in the data is 64. The angular spectra for the three sub-bands in each subarea of the map are shown (Figs. 6a and b). Figure 6a shows correspondences between the three spectra indicating peaks at 4o, 36o, 56o, 75o, 102o, 140o and 169o; where the first peak (4o) appears in the three sub-bands, while the other six peaks appear in the mid and high frequency bands. A similar pattern is obtained in the lower part of the map area where also 4o peak appears in the three sub-bands (Fig. 6b) and prominent peaks at 12o and 157o at the mid and high frequency sub-bands amid a subdued peak at 149o.

Fig. 5. Radial spectrum plotted against frequency number of the total field magnetic anomaly over the Middle Benue Trough, Nigeria. Five linear segments are marked (A, B, C, D, E). Estimates of depths from slopes are indicated.

The 4o peak appearing in the three sub-bands corresponds to the value of the inclination of the Earth's magnetic field in the area. The peak at 56o corresponds to the general trend of the Benue Trough (N56E). Other angular values have been fully mapped in the area (Benkhelil, 1982, 1989; Likkason, 2005).

Spectral Analysis of Geophysical Data 51

0 40 80 120 160 200 Angle (deg)

(B) Fig. 6. Angular spectrum of the total field magnetic anomaly over (A) the upper sub-area and (B) the lower sub-area of the Middle Benue Trough, Nigeria. In each of the curves, the labels represent as follows: (a) the low frequency band (1-20), (b) the mid-frequency band

Spectrum analysis is a basic tool in signal processing and shows how the signal power is distributed as a function of spatial frequencies. These Fourier-based methods have found usefulness in the analysis of geophysical data and what has been presented in this chapter is just tip of the iceberg. It is important as a rule to have a good understanding of the signal and the corrupting noise. This will lead to a successful extraction of the desired signal from the observed map data. Parameter estimation from such processes have to be carefully done as some operations involved in the processes bear on the resultant data. For example, the effect of the window function bears to some extent on the final outcomes of the computations of angular spectra of both the synthetic and real aeromagnetic field data used

in the last section. The window effects must be recognized and pointed out.

149o

157o (c)

(a)

(b)

1.00E+001

(20-40) and (c) the high frequency band (40-60).

**7. Conclusion** 

1.00E+002

1.00E+003

1.00E+004

Angular Spectrum

1.00E+005

1.00E+006

1.00E+001

1.00E+002

1.00E+003

1.00E+004

Angular Spectrum

1.00E+005

1.00E+006

1.00E+007

4o

4o

12o

To get the overall picture of the depth estimates of the area, the radial spectrum and its log of the aeromagnetic field of the Middle Benue Trough, Nigeria were computed and the latter plotted against frequency number (Fig. 5). Logarithmic spectra are preferred for the analysis than linear spectra because of the additive property of the former, which gives better performance of ensemble average parameters (Spector and Grant 1970) as influences simply add. The plotted radial spectrum seems to support the possibility of five linear segments (marked **A**, **B, C, D** and **E**). The segment marked **E** represents the spectrumdominated by deep-seated contribution, while the mid-layers marked **D, C** and **B** come from near-surface contribution and other plate sources of intermediate depths. The low gradient portion (marked **A**) represents two contributions: from near-surface structures and magnetic terrain effect. From the slopes of the segments at these points it may be inferred that the depths to corresponding magnetic layers are 20.62 km (portion **E**), 3.54 km (portion **D**), 1.43 km (portion **C**), 0.73 km (portion **B**) and 0.26 km (portion **A**). Flight height above mean sea level (m s l) in the survey area is 0.275 km. We suggest that the deep band at 20.62 km is probabily the lowest boundary of static magnetic sources.

Fig. 6. (continued)

To get the overall picture of the depth estimates of the area, the radial spectrum and its log of the aeromagnetic field of the Middle Benue Trough, Nigeria were computed and the latter plotted against frequency number (Fig. 5). Logarithmic spectra are preferred for the analysis than linear spectra because of the additive property of the former, which gives better performance of ensemble average parameters (Spector and Grant 1970) as influences simply add. The plotted radial spectrum seems to support the possibility of five linear segments (marked **A**, **B, C, D** and **E**). The segment marked **E** represents the spectrumdominated by deep-seated contribution, while the mid-layers marked **D, C** and **B** come from near-surface contribution and other plate sources of intermediate depths. The low gradient portion (marked **A**) represents two contributions: from near-surface structures and magnetic terrain effect. From the slopes of the segments at these points it may be inferred that the depths to corresponding magnetic layers are 20.62 km (portion **E**), 3.54 km (portion **D**), 1.43 km (portion **C**), 0.73 km (portion **B**) and 0.26 km (portion **A**). Flight height above mean sea level (m s l) in the survey area is 0.275 km. We suggest that the deep band at

> 0 40 80 120 160 200 Angle (deg)

> > (A)

102o

36o 56o 75o

(c)

169o

140o

(a)

(b)

1.00E+001

1.00E+002

1.00E+003

1.00E+004

Angular Spectrum

Fig. 6. (continued)

1.00E+005

1.00E+006

1.00E+001

1.00E+002

1.00E+003

1.00E+004

Angular Spectrum

1.00E+005

1.00E+006

1.00E+007

4o

20.62 km is probabily the lowest boundary of static magnetic sources.

4o

Fig. 6. Angular spectrum of the total field magnetic anomaly over (A) the upper sub-area and (B) the lower sub-area of the Middle Benue Trough, Nigeria. In each of the curves, the labels represent as follows: (a) the low frequency band (1-20), (b) the mid-frequency band (20-40) and (c) the high frequency band (40-60).

#### **7. Conclusion**

Spectrum analysis is a basic tool in signal processing and shows how the signal power is distributed as a function of spatial frequencies. These Fourier-based methods have found usefulness in the analysis of geophysical data and what has been presented in this chapter is just tip of the iceberg. It is important as a rule to have a good understanding of the signal and the corrupting noise. This will lead to a successful extraction of the desired signal from the observed map data. Parameter estimation from such processes have to be carefully done as some operations involved in the processes bear on the resultant data. For example, the effect of the window function bears to some extent on the final outcomes of the computations of angular spectra of both the synthetic and real aeromagnetic field data used in the last section. The window effects must be recognized and pointed out.

**3** 

*China* 

**Quantitative Evaluation of Spatial** 

*School of Geography Science, Nanjing Normal University, Nanjing,* 

*Key Laboratory of Virtual Geographic Environment (Nanjing Normal University),* 

Spatial interpolation, i.e. the procedure of estimating the value of properties at unsampled sites within areas covered by existing observations (Algarni & Hassan, 2001), appears various models using local/global, exact/approximate and deterministic/geostatistical methods. As being an essential tool for estimating spatial continuous data which plays a significant role in planning, risk assessment and decision making, interpolation methods have been applied to various disciplines concerned with the Earth's surface, such as cartography (Declercq, 1996), geography (Weng, 2002), hydrology (Lin & Chen, 2004), climatology (Attorre et al, 2007), ecology (Stefanoni & Ponce, 2006), agriculture and pedology (Wang et al, 2005; Robinson & Metternicht, 2006), landscape architecture (Fencik &

Since spatial interpolation is based on statistics, there are inevitably a certain assumptions and optimizations. As a result, errors introduced by spatial interpolation and their propagation in analysis models will certainly influence the quality of any decision-making supported by spatial data. This has been one of the hot issues of geographical information science in recent years (David et al, 2004; Shi, W. Z, et al, 2005; Weng, 2006). There are many factors affecting the performance of spatial interpolation methods. The errors are mainly generated from sample data density (Stahl et al., 2006), sample spatial distribution (Collins and Bolstad, 1996), data variance (Schloeder et al., 2001), grid size or resolution (Hengl, 2007), surface types (Zimmerman et al., 1999) and interpolation algorithms (Weng, 2006). However, there are no consistent findings about how these factors affect the performance of the spatial interpolators (Li & Heap, 2011). Therefore, it is difficult to select an appropriate

With the increasing applications of spatial interpolation methods, there is a growing concern about their accuracies and evaluation measures (Hartkamp et al., 1999). The previous studies have greatly focused on individual evaluation methods of spatial interpolation (Weber & Englund, 1992 & 1994; Erxleben et al, 2002; Chaplot, 2006; Weng, 2006; Erdogan, 2009; Bater & Coops, 2009). It is necessary to explore comprehensive evaluation methods of interpolation accuracy. Two fundamental issues related to assessment measures of

**1. Introduction** 

Vajsablova, 2006) and so on.

interpolation method for a given input dataset.

interpolation are addressed here as follows.

**Interpolation Models Based on a** 

**Data-Independent Method** 

Xuejun Liu, Jiapei Hu and Jinjuan Ma

*Ministry of Education, Nanjing,* 

#### **8. References**

Bath, M. (1974). *Spectral analysis in geophysics*, Elsevier Amsterdam


## **Quantitative Evaluation of Spatial Interpolation Models Based on a Data-Independent Method**

Xuejun Liu, Jiapei Hu and Jinjuan Ma

*Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing, School of Geography Science, Nanjing Normal University, Nanjing, China* 

#### **1. Introduction**

52 Advances in Data, Methods, Models and Their Applications in Geoscience

Benkhelil, M. J. (1989). The origin and evolution of the Cretaceous Benue Trough, Nigeria, *J.* 

Bhattacharyya, B. K. (1966). Continuous spectrum of the total magnetic field anomaly due to

Blackman, R. B. & Tukey, J. W. (1959). *The measurement of power spectrum*, Dover

Cooley, J. W. & Tukey, J. W. (1965). An algorithm for the machine computation of complex

Fedi, M., Quarta, T. & De Santis, A. (1997). Inherent power-law behaviour of magnetic field power spectra from a Spector and Grant ensemble, *Geophysics* 62, 1143-1150

Likkason, O. K. , Ajayi, C. O., Shemang, E. M. & Dike, E. F. C. (2005). Indication of fault

Naidu, P. S. (1969). Estimation of spectrum and cross spectrum of aeromagnetic field using fast digital Fourier transform (FDFT) techniques, *Geophys. Prosp.* 17, 344-361

Naidu, P. S. (1980). Spectrum of potential fields due to randomly distributed sources,

Naidu, P. S. (1987). Characterization of potential field signal in frequency domain, *J. Assoc.* 

Naidu, P. S. & Mathew, M. P. (1998). Digital analysis of aeromagnetic maps: detection of a

Naidu, P. S. & Mishra, D. C. (1980). Radial and angular spectrum in geophysical map

Smith, S. W. (1999). *The Scientist and Engineer's guide to digital signal processing* (2nd

Spector, A. & Grant, F. S. (1970). Statistical models for interpreting aeromagnetic data,

Telford, W. M., Geldart, L. P., Sheriff, R. E. & Keys, D. A. (1990). *Applied geophysics,*

Thompson, D. J. (1982). Spectrum estimation and harmonic analysis, *Proc. IEEE* 70 (7), 1055 –

Yaglom, A. H. (1962). *Introduction to theory of stationary random functions*, Prentice Hall, New

analysis, In: *Application of Information and Control Systems* (D.G. Lainiotis and N. S.

Middl;e Benue Trough, Nigeria, *J. Mining and Geology* 41 (2), 205 – 227 Mishra, D. C. & Naidu, P. S. (1974). Two-dimensional power spectral analysis of

Naidu, P. S. (1970). Statistical structure of aeromagnetic field, *Geophysics* 35, 279-292

Tzannes, Eds.). Riedel Publishing Co., Dordrecht, 447-454 Papoulis, A. (1962). *The Fourier integral and its application*, McGraw Hill, New York

Roy, K. K. (2008). *Potential theory in applied geophysics*, Springer, New York

expressions from filtered and Werner deconvolution of aeromagnetic data of the

Bath, M. (1974). *Spectral analysis in geophysics*, Elsevier Amsterdam

a rectangular prismatic body, *Geophysics* 31, 97-121

Kay, S. M. (1989), *Modern spectrum analysis*, Prentice Hall, New Jersey

aeromagnetic fields, *Geophys. Prosp.* 22, 345-353

Fourier series, *Math. Comput*. 19, 297 – 301

*Afric. Earth Sci*. 8, 251-282

Publications, New York

*Geophysics* 33, 337-345

*Geophysics* 35, 293-302

1096

Jersey

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fault, *J. Applied Geophysics* 38,169-179

edition), California Technical Publishing

Cambridge University Press, London

Benkhelil, M. J. (1982). Benue Trough and Benue Chain, *Geol. Mag.* 119, 155-168

**8. References** 

Spatial interpolation, i.e. the procedure of estimating the value of properties at unsampled sites within areas covered by existing observations (Algarni & Hassan, 2001), appears various models using local/global, exact/approximate and deterministic/geostatistical methods. As being an essential tool for estimating spatial continuous data which plays a significant role in planning, risk assessment and decision making, interpolation methods have been applied to various disciplines concerned with the Earth's surface, such as cartography (Declercq, 1996), geography (Weng, 2002), hydrology (Lin & Chen, 2004), climatology (Attorre et al, 2007), ecology (Stefanoni & Ponce, 2006), agriculture and pedology (Wang et al, 2005; Robinson & Metternicht, 2006), landscape architecture (Fencik & Vajsablova, 2006) and so on.

Since spatial interpolation is based on statistics, there are inevitably a certain assumptions and optimizations. As a result, errors introduced by spatial interpolation and their propagation in analysis models will certainly influence the quality of any decision-making supported by spatial data. This has been one of the hot issues of geographical information science in recent years (David et al, 2004; Shi, W. Z, et al, 2005; Weng, 2006). There are many factors affecting the performance of spatial interpolation methods. The errors are mainly generated from sample data density (Stahl et al., 2006), sample spatial distribution (Collins and Bolstad, 1996), data variance (Schloeder et al., 2001), grid size or resolution (Hengl, 2007), surface types (Zimmerman et al., 1999) and interpolation algorithms (Weng, 2006). However, there are no consistent findings about how these factors affect the performance of the spatial interpolators (Li & Heap, 2011). Therefore, it is difficult to select an appropriate interpolation method for a given input dataset.

With the increasing applications of spatial interpolation methods, there is a growing concern about their accuracies and evaluation measures (Hartkamp et al., 1999). The previous studies have greatly focused on individual evaluation methods of spatial interpolation (Weber & Englund, 1992 & 1994; Erxleben et al, 2002; Chaplot, 2006; Weng, 2006; Erdogan, 2009; Bater & Coops, 2009). It is necessary to explore comprehensive evaluation methods of interpolation accuracy. Two fundamental issues related to assessment measures of interpolation are addressed here as follows.

Quantitative Evaluation of Spatial Interpolation

interpolation model, just as follows:

this study have been separately listed in Tab. 1.

Z

1 Z [] *n*

*i*

*n p ii i*

*n p i i i*

*i i*

*Z wRd T x y*

*w Z* 

*wz m m*

( ) (,)

*wi*

number of sample points.

Interpolation

IDW, Inverse Distance

> MC, Minimum

Weighted 1

Kriging p

Curvature 1

Models Based on a Data-Independent Method 55

correlations between the known points, while the combined functions are the performance of interpolations in mathematics, both of which constitute the commonality of interpolation functions in mathematics and physics. Therefore, they can be unified as one general

Z 11 22 ... *<sup>p</sup> w Z w Z w Z m WZ m n n* (1)

where Z*<sup>p</sup>* is the estimated value of an interpolated point P(x , ) *p p y* , Zi denotes a sample point with w*<sup>i</sup>* indicating its corresponding weight, m presents a constant, and n is the total

In this united model shown as Formula 1, any interpolation function can be regarded as a linear combination of sample points, with the difference of rules for weight allocation. In other words, the determination of the weight vector W is essential and critical for interpolations. For example, IDW determines its weight according to the distance between sample points directly, while NNI employs Thiessen polygons and Kriging uses semivariable functions instead. As for the moving curved surface fitting interpolation, though, the weight function is not obvious, surface-fit functions are employed to allocate weights, implying the spatial relationships of data points. The united interpolation models of the eight interpolation algorithms discussed in

It has been proved in Tab. 1 that in spite of various interpolation algorithms and models, they have the same intrinsic interpolation mechanism, and any common interpolation method can be transformed into a united model. From the mathematical mechanism, any spatial interpolation is actually a process of assigning weights to sample points, and

models Interpolation functions Weight vector(W) Constant (m) Parameter

*w*

*wi Txy* (,)

1

*d*

*<sup>0</sup>*

1 (1 ) *n i i m w* 

*k i <sup>i</sup> <sup>n</sup> <sup>k</sup> i i*

 

*d*

Specification

*<sup>i</sup> d* : the distance between P0 and Pi; *k* : a power parameter

*<sup>i</sup> d* : the distance between P0 and Pi; ( ) *R di* : the principal curvature function; *Txy* (,) : a 'trend' function


To overcome the above-mentioned problems, the author (2002, 2003 & 2004) developed a quantitative, data-independent method to evaluate algorithms in Digital Terrain Analysis. With this method, six slope/aspect algorithms and five flow routing algorithms were evaluated properly. Here we hope to employ this method to comprehensively evaluate spatial interpolation models and identify a set of accuracy measures.

#### **2. Unified interpolation models**

So far, more than ten spatial interpolation models have been developed in different fields. Here eight commonly used interpolation algorithms are examined and discussed, e.g. Inverse Distance Weighted (IDW), Kriging, Minimum Curvature (MC), Natural Neighbor Interpolation (NNI), Modified Shepard's Method (MSM), Local Polynomial (LP), Triangulation with Linear Interpolation (TLI) and Thin Plate Spline (TPS). According to the range of interpolation, these interpolations can be classified as global interpolation, block interpolation and point-by-point interpolation. While in view of mathematical mechanism, they can also be grouped into deterministic algorithms and geostatistical algorithms.

Although there are various spatial interpolation algorithms with diverse functions, they share the same essential factors, i.e. on the basis of describing the relationships between data points, and computing the values of unmeasured points through different function combinations of sample points. In another word, the relationships depict the spatial

1. Comparison results: most commonly used methods for evaluation of spatial interpolation models compare the measured data with the interpolated data. However, it is no doubt that measured data are always unsatisfactory. This leads to unknown errors inherent in measured data (Zhou & Liu, 2002). The results may not always keep consistent and even get some controversial conclusions. For example, Laslett et al. (1987), Javis & Stuart (2001) and Erdogan (2009) thought Thin Plate Spline interpolation model can give better interpolated results, while Bater & Coops (2009) argued that Nature Neighbour Interpolation is with more accurate interpolated value. Meanwhile, some researchers (Hosseini et al., 1993; Gotway et al., 1996; Zimmerman et al. 1999; Erxleben et al., 2002; Vicente-Serrano et al., 2003; Attorre et al, 2007; Piazza et al, 2011) found that Kriging is the best one among all the existing interpolation models. Another phenomenon should be mentioned is that the frequency of interpolation methods compared varies considerably among methods and different studies have compared a

suite of different methods, which makes it difficult to draw general conclusions. 2. Assessment indices: there are two typical assessment indices, i.e. statistical measures and spatial accuracy measures. The statistical measures such as Root Mean Squared Error (RMSE), Standard Deviation (SD) and Mean Error (ME) are most frequently used (Weber & Englund, 1994; Weng, 2002; Vicente-Serrano et al., 2003; Hu et al., 2004; Weng, 2006; Tewolde, 2010), whereas incapable of describing the spatial pattern of errors. Then the morphological accuracy measures such as accuracy surface and spatial autocorrelation (Weng, 2002; Weng, 2006; Tewolde, 2010) are employed. However, in order to obtain full evaluation of the interpolations, following problems should be further addressed: (1) most of the evaluations are still concentrated on the statistical measures, while the spatial accuracy ones are likely to be ignored relatively; (2) the maintenance of integrity of an interpolated surface has attracted little attention and a suitable quantitative index is still lack; (3) without consideration of the robustness of

To overcome the above-mentioned problems, the author (2002, 2003 & 2004) developed a quantitative, data-independent method to evaluate algorithms in Digital Terrain Analysis. With this method, six slope/aspect algorithms and five flow routing algorithms were evaluated properly. Here we hope to employ this method to comprehensively evaluate

So far, more than ten spatial interpolation models have been developed in different fields. Here eight commonly used interpolation algorithms are examined and discussed, e.g. Inverse Distance Weighted (IDW), Kriging, Minimum Curvature (MC), Natural Neighbor Interpolation (NNI), Modified Shepard's Method (MSM), Local Polynomial (LP), Triangulation with Linear Interpolation (TLI) and Thin Plate Spline (TPS). According to the range of interpolation, these interpolations can be classified as global interpolation, block interpolation and point-by-point interpolation. While in view of mathematical mechanism,

Although there are various spatial interpolation algorithms with diverse functions, they share the same essential factors, i.e. on the basis of describing the relationships between data points, and computing the values of unmeasured points through different function combinations of sample points. In another word, the relationships depict the spatial

they can also be grouped into deterministic algorithms and geostatistical algorithms.

interpolation algorithms to data errors.

**2. Unified interpolation models** 

spatial interpolation models and identify a set of accuracy measures.

correlations between the known points, while the combined functions are the performance of interpolations in mathematics, both of which constitute the commonality of interpolation functions in mathematics and physics. Therefore, they can be unified as one general interpolation model, just as follows:

$$\mathbf{Z}\_p = w\_1 \mathbf{Z}\_1 + w\_2 \mathbf{Z}\_2 + \dots + w\_n \mathbf{Z}\_n + m = \text{V}\mathbf{V}\mathbf{Z} + m\tag{1}$$

where Z*<sup>p</sup>* is the estimated value of an interpolated point P(x , ) *p p y* , Zi denotes a sample point with w*<sup>i</sup>* indicating its corresponding weight, m presents a constant, and n is the total number of sample points.

In this united model shown as Formula 1, any interpolation function can be regarded as a linear combination of sample points, with the difference of rules for weight allocation. In other words, the determination of the weight vector W is essential and critical for interpolations. For example, IDW determines its weight according to the distance between sample points directly, while NNI employs Thiessen polygons and Kriging uses semivariable functions instead. As for the moving curved surface fitting interpolation, though, the weight function is not obvious, surface-fit functions are employed to allocate weights, implying the spatial relationships of data points. The united interpolation models of the eight interpolation algorithms discussed in this study have been separately listed in Tab. 1.

It has been proved in Tab. 1 that in spite of various interpolation algorithms and models, they have the same intrinsic interpolation mechanism, and any common interpolation method can be transformed into a united model. From the mathematical mechanism, any spatial interpolation is actually a process of assigning weights to sample points, and


Quantitative Evaluation of Spatial Interpolation

**3. Methods and procedures** 

models.

Models Based on a Data-Independent Method 57

different interpolation models have different patterns of weight allocation. While concerning the meaning of geography, the essence of interpolations lies in the spatial correlations between unmeasured points and sample points, reflected during the course of weight allocation. Both sides of mathematics and geography mentioned here can not only give a hypostatic explanation for the spatial interpolation physical mechanism, but can also provide certain guidance for further analysis and evaluation of spatial interpolation

In order to achieve the objectives proposed above, a data-independent experiment has been carried out, which allowed us to quantitatively analyze and evaluate different spatial interpolation models. Fig. 1 shows the flowchart of the whole process employed for our experiment. More specific procedures are illustrated as follows: (1) Constructing a mathematical surface with a known-formula; (2) Discretizing the mathematical surface and then randomly sample N points from those discrete ones; (3) Adding errors with varying levels to the randomly sampling points, so that we can get discrete points with the same distribution but varying error-levels; (4) Making interpolated operations separately on the sampling points without errors and the ones with varying error-levels, using the eight interpolation models mentioned above; (5) Analyzing and evaluating the results acquired

from different interpolation algorithms according to different evaluation indices.

validations, the linear model is selected in this study.

**3.1 Design of mathematical surfaces** 

equations below:

It is noted that all of the eight interpolation algorithms applied in this study are fulfilled by Surfer 8.0, a powerful contouring, gridding and 3D surface mapping package. Another aspect should be indicated is about the parameter-setting during interpolation. The parameters here mainly consist of three kinds: (1) a search neighhood including its search radius and the number of sampling points, which should be set for the local interpolation methods such as LP, IDW, MSM and TPS; (2) the maximum residual and the maximum number of cycles when gridding with MC method; (3) variogram models like linear, gaussian and logarithmic models for Kriging interpolator. Except variogram models used in Kriging interpolation, the parameters in the others interpolation methods are control parameters and can be set as default of Surfer 8.0, for they have no effect on weight allocation. While for Kriging, the choice of variogram models has a close connection with weight allocation and may affect the results of interpolation. Through repeated tests and

In this study, we took the similar approach as reported by Zhou and Liu (2002, 2003 & 2004) by employing pre-defined standard surfaces for testing and comparing selected algorithms. As a result, the 'true' attribute value of any point on the standard surfaces which are pre-defined by known mathematical formulas can be acquired without errors. Our focus is on the difference between the values calculated by interpolation methods and the 'true' valuesto compare these interpolation algorithms objectively. According to the complexity of the surfaces, three surfaces have been selected for test, namely a simple surface, a more complex surface and a Gauss synthetic surface, which are defined by the


\* In this study, the power parameter k of IDW function is set as 2, as well as MSM; the quadratic polynomial is applied in LP interpolation.

Table 1. Unified interpolation models of common spatial interpolation algorithms

models Interpolation functions Weight vector(W) Constant (m) Parameter

*i a*

1

*d*

*<sup>0</sup>*

*k i <sup>i</sup> <sup>n</sup> <sup>k</sup> i i*

 

*d*

*w*

*<sup>p</sup> AP P P Z* <sup>1</sup> [ ] *W AP P P T T <sup>0</sup>*

*W AP*<sup>1</sup> *<sup>0</sup>*

*wi wn*<sup>1</sup>

\* In this study, the power parameter k of IDW function is set as 2, as well as MSM; the

Table 1. Unified interpolation models of common spatial interpolation algorithms

*<sup>a</sup> <sup>0</sup>*

*w*

*<sup>i</sup>*

Specification

*<sup>i</sup> a* : area of Thiessen polygon(Pi); *a* : the total areas of all Thiessen polygons

*Qi* : a quadratic polynomial at the interpolated point Pi; *<sup>i</sup> d* : the distance between P0 and Pi; *k* : a power parameter

*A* : position vector of unknown point; *P* : position vector of known points

*A* : position vector of unknown point; *P* : position vector of known points

*<sup>i</sup> d* : the distance between P0 and Pi; : the optimal parameter

Interpolation

NNI, Nature Neighbor

> MSM, Modified Shepard's Method

LP, Local Polynomial

TLI, Triangulation with Linear Interpolation

TPS, Thin

Interpolation 1

Z *<sup>i</sup> <sup>n</sup> <sup>i</sup> p p i*

1

<sup>1</sup> Z [] *T T*

<sup>1</sup> *Z AP Z <sup>p</sup>*

Plate Spline <sup>1</sup> 1

*n*

*i*

Z ( . )ln( . )

quadratic polynomial is applied in LP interpolation.

*p ii i n*

*wd dw*

 

*n p i i i Z wQ* 

*a z a*

different interpolation models have different patterns of weight allocation. While concerning the meaning of geography, the essence of interpolations lies in the spatial correlations between unmeasured points and sample points, reflected during the course of weight allocation. Both sides of mathematics and geography mentioned here can not only give a hypostatic explanation for the spatial interpolation physical mechanism, but can also provide certain guidance for further analysis and evaluation of spatial interpolation models.

#### **3. Methods and procedures**

In order to achieve the objectives proposed above, a data-independent experiment has been carried out, which allowed us to quantitatively analyze and evaluate different spatial interpolation models. Fig. 1 shows the flowchart of the whole process employed for our experiment. More specific procedures are illustrated as follows: (1) Constructing a mathematical surface with a known-formula; (2) Discretizing the mathematical surface and then randomly sample N points from those discrete ones; (3) Adding errors with varying levels to the randomly sampling points, so that we can get discrete points with the same distribution but varying error-levels; (4) Making interpolated operations separately on the sampling points without errors and the ones with varying error-levels, using the eight interpolation models mentioned above; (5) Analyzing and evaluating the results acquired from different interpolation algorithms according to different evaluation indices.

It is noted that all of the eight interpolation algorithms applied in this study are fulfilled by Surfer 8.0, a powerful contouring, gridding and 3D surface mapping package. Another aspect should be indicated is about the parameter-setting during interpolation. The parameters here mainly consist of three kinds: (1) a search neighhood including its search radius and the number of sampling points, which should be set for the local interpolation methods such as LP, IDW, MSM and TPS; (2) the maximum residual and the maximum number of cycles when gridding with MC method; (3) variogram models like linear, gaussian and logarithmic models for Kriging interpolator. Except variogram models used in Kriging interpolation, the parameters in the others interpolation methods are control parameters and can be set as default of Surfer 8.0, for they have no effect on weight allocation. While for Kriging, the choice of variogram models has a close connection with weight allocation and may affect the results of interpolation. Through repeated tests and validations, the linear model is selected in this study.

#### **3.1 Design of mathematical surfaces**

In this study, we took the similar approach as reported by Zhou and Liu (2002, 2003 & 2004) by employing pre-defined standard surfaces for testing and comparing selected algorithms. As a result, the 'true' attribute value of any point on the standard surfaces which are pre-defined by known mathematical formulas can be acquired without errors. Our focus is on the difference between the values calculated by interpolation methods and the 'true' valuesto compare these interpolation algorithms objectively. According to the complexity of the surfaces, three surfaces have been selected for test, namely a simple surface, a more complex surface and a Gauss synthetic surface, which are defined by the equations below:

Quantitative Evaluation of Spatial Interpolation

Mathematic al surfaces

Randomly sample points

**3.2 Design of evaluation indices** 

lost leading to a fault result.

Models Based on a Data-Independent Method 59

Table 2. Mathematical surfaces and distribution of randomly sample points

considered for the accuracy assessment of the interpolation results as well.

The interpolation result can be regarded as an original surface recovered by sample points. It has two implications, i.e. one is to reflect the closeness between the original surface and the recovered one on the value, and the other one is to recover the structural features of the original surface. It means that the interpolated surface should as far as possible keep the characteristics of the original surface both on statistics and structures, which should be

The evaluation indices about statistical features mainly include RMSE (Root Mean Square Error), ME (Mean Error) and spatial autocorrelation. In this study, RMSE and ME are selected to describe the quality of the interpolation functions. For following the first law of geography (Tobler, 1970), the original surface itself has a strong spatial autocorrelation, so as to the whole interpolated surface. As a result, the surface acquired by interpolations should keep the spatial autocorrelation measured by Moran'I here, or else leading to a meaningless result with an almost randomly interpolated surface. What's more, another two spatial indices, volume and surface area are chosen to reflect the maintenance of overall performance after interpolation. The volume stands for the room above a datum plane and under an original surface or an interpolated surface whose area is measured by surface area. Structural characteristic is the other important evaluation method. It can be regarded as the skeleton of a surface, determining its geometric shape and basic trend, on which the interpolated surface should be in accord with the original one. For the integrity of the structural characteristic, so far there is lack of a suitable quantitative index. In this study, a method of contour-matching has been applied to compare and analyze different interpolations qualitatively, by means of overlaying the contours generated from an interpolated surface and the original one. If these overlaid contours match generally without great deviation or distortion, it can be induced that the structural characteristic of the surface has been kept well after being interpolated, or the structural characteristic will be

Surface 1 (S1) Surface 2 (S2) Surface 3 (S3)

Fig. 1. Flowchart of the scheme to analyze and evaluate the spatial interpolation models

$$\text{Surface1}: \n0 \, f(\text{x}, y) = 30 \times \sin(\frac{\text{x}}{60}) \times \cos(\frac{y}{100}) + y \times \frac{20}{100} \, (\n0 \le x \le 150; 0 \le y \le 100) \tag{2}$$

$$\text{Surface2}: \n0 \, f(\text{x}, y) = (\sin(\frac{x}{y}) - \sin(\frac{x \times y}{800})) \times 10 + 100 \, \text{(} -100 \le x \le 0 \text{;} 10 \le y \le 110\text{)}\tag{3}$$

$$\text{Surface3 : } \nS : \{ (\mathbf{x}, y) = 3(1 - \mathbf{x}^2)e^{-\mathbf{x}^2 - (y+1)^2} - 10(0.2\mathbf{x} - \mathbf{x}^3 - y^5)e^{-\mathbf{x}^2 - y^2} - \frac{1}{3e^{-(\mathbf{x}+1)^2 - y^2}} $$

$$\{-50 \le \mathbf{x} \le 50; -50 \le y \le 50\} \tag{4}$$

Then the three selected surfaces are separately scattered into discrete points, from which one thousand points were randomly sampled. All of the three simulated mathematical surfaces are showed in Tab. 2, as well as the distribution of their randomly sample points. After that, add different errors with the same mean 0 but varying Root Mean Square Errors (RMSE), which are in turn 0.5, 1, 1.5, 2, 4, 6, 8, 10, to these sample points, making their errors with the same distribution but different levels of values.

Fig. 1. Flowchart of the scheme to analyze and evaluate the spatial interpolation models

2 ( 1) 3 5

Then the three selected surfaces are separately scattered into discrete points, from which one thousand points were randomly sampled. All of the three simulated mathematical surfaces are showed in Tab. 2, as well as the distribution of their randomly sample points. After that, add different errors with the same mean 0 but varying Root Mean Square Errors (RMSE), which are in turn 0.5, 1, 1.5, 2, 4, 6, 8, 10, to these sample points, making their errors with the

<sup>1</sup> ( , ) 3(1 ) 10(0.2 )

*x y x y <sup>x</sup> <sup>y</sup> fxy x e xx ye*

 

*<sup>x</sup> <sup>y</sup> fxy <sup>y</sup>* \ (50 150;0 100) *x y* (2)

\ ( 100 0;10 110) *x y* (3)

( 50 50; 50 50) *x y* (4)

2 2

( 1)

3

*e*

Surface1:\ <sup>20</sup> ( , ) 30 sin( ) cos( ) 60 100 100

 Surface2:\ ( , ) (sin( ) sin( )) 10 100 <sup>800</sup> *<sup>x</sup> x y fxy y*

same distribution but different levels of values.

Surface3:\ 2 2 2 2

Table 2. Mathematical surfaces and distribution of randomly sample points

#### **3.2 Design of evaluation indices**

The interpolation result can be regarded as an original surface recovered by sample points. It has two implications, i.e. one is to reflect the closeness between the original surface and the recovered one on the value, and the other one is to recover the structural features of the original surface. It means that the interpolated surface should as far as possible keep the characteristics of the original surface both on statistics and structures, which should be considered for the accuracy assessment of the interpolation results as well.

The evaluation indices about statistical features mainly include RMSE (Root Mean Square Error), ME (Mean Error) and spatial autocorrelation. In this study, RMSE and ME are selected to describe the quality of the interpolation functions. For following the first law of geography (Tobler, 1970), the original surface itself has a strong spatial autocorrelation, so as to the whole interpolated surface. As a result, the surface acquired by interpolations should keep the spatial autocorrelation measured by Moran'I here, or else leading to a meaningless result with an almost randomly interpolated surface. What's more, another two spatial indices, volume and surface area are chosen to reflect the maintenance of overall performance after interpolation. The volume stands for the room above a datum plane and under an original surface or an interpolated surface whose area is measured by surface area. Structural characteristic is the other important evaluation method. It can be regarded as the skeleton of a surface, determining its geometric shape and basic trend, on which the interpolated surface should be in accord with the original one. For the integrity of the structural characteristic, so far there is lack of a suitable quantitative index. In this study, a method of contour-matching has been applied to compare and analyze different interpolations qualitatively, by means of overlaying the contours generated from an interpolated surface and the original one. If these overlaid contours match generally without great deviation or distortion, it can be induced that the structural characteristic of the surface has been kept well after being interpolated, or the structural characteristic will be lost leading to a fault result.

Quantitative Evaluation of Spatial Interpolation

Models Based on a Data-Independent Method 61

Actually, it is not difficult to explain the results. When sample points have no errors or small errors, these sample points themselves can portray the characteristics of the original surface in a relatively accurate degree. Using semi-variogram, the geostatistical method of Kriging recovers the spatial correlation of the original surface exactly, while TPS and MSM are means of finding a proper way to allocate weights to sample points according to the distance between known points and interpolated points. With the increasing of sample data errors, the surface generated by sample points starts to deviate from the original surface, meaning the sample surface can no longer describe the characteristics of the original surface completely. No matter Kriging or TPS, the surfaces they want to depict or recover are just sample surfaces. For LP, although not all of the sample points are strictly passed through, this interpolated method can make a certain restraint on the original data errors, showing a role of peak-clipping and valley-filling for the interpolation. Furthermore, the restraining effect can also reflect the variation tendency of the surfaces created by sample points, bringing about a higher interpolated precision. The interpolated results for the three surfaces with different complexity levels have been showed by Fig. 3. On the whole, the changing tendencies of these three surfaces present a roughly consistent pace, that is to say the largest change of RMSE before and after adding errors belongs to MSM with the minimum belonging to LP, and an ascending order between the two extremes are as follows: TPS, MC, TLI, NNI and IDW. It has been further proved that the interpolated method of LP is less vulnerable to data errors appearing a superior resistance to errors,

Fig. 3. Changes in RMSEs of the three surfaces before and after adding errors

while MSM is extremely sensitive to data errors showing a worst error-resistance.

The Moran'I statistics of S1 with no data-errors and higher data-errors acquired from different interpolation methods have been compared in Fig. 4 and Fig. 5. For the data without errors, the Moran'I of Kriging 0.9980 reaches the topmost showing the best spatial correlation, then followed by LP, TPS and IDW with a better spatial correlation, and the lowest Moran'I belongs to MC whose spatial correlation is the worst (refer to Fig. 4). However, with the increasing of the sample data errors, the Moran'I of LP, 0.9977, changes to the highest with the optimal spatial correlation and by contrast, MSM turns to the lowest as shown by Fig. 5. The other two surfaces present a similar variation regularity or tendency for the entire, although there are a few differences among individual interpolation methods. In order to further interpret the impact caused by the increasing data-errors on spatial

**4.2 Moran'I index** 

#### **4. Results and discussion**

#### **4.1 RMSE and ME**

As the RMSE statistics of the interpolated results from the three surfaces shown in Tab. 3, it is not difficult to identify that all of the three interpolated surfaces present similar variation tendency as a whole. The RMSEs of the interpolated surfaces keep pace with the increasing errors of the original surface, leading to a decreasing interpolated accuracy.


\* 1) 0, 1, 10 are the RMSE added to the original sample points; 2) For the interpolation methods of NNI and TLI cannot deal with the boundary problem well, therefore their boundary values which are replaced with the maximum have been excluded when calculated in statistics.

Table 3. RMSE statistics of the interpolated results from the three surfaces

As shown in Tab.3, Fig. 2 and Fig. 3, when sample points have no errors, the RMSEs of the interpolated results for different methods have an decreasing sequence as LP > IDW, MC > NNI, TLI > Kriging, MSM, TPS. However, the interpolated results vary with the augment of data errors. When the RMSE of sample points increases to 10, the RMSE of the surface interpolated by MSM achieves the maximum, with the minimum gained by LP and the sequence of RMSE for different interpolations changes to MSM > TPS, MC > TLI, Kriging, NNI > IDW > LP. The results show that if the original data has a better quality, the methods of TPS, MSM and Kriging can get a high precision for the interpolated results, while the quality of the original data becomes poorly, the result of LP turns to be relatively reliable.

Fig. 2. RMSE statistics of interpolated results from S1

As the RMSE statistics of the interpolated results from the three surfaces shown in Tab. 3, it is not difficult to identify that all of the three interpolated surfaces present similar variation tendency as a whole. The RMSEs of the interpolated surfaces keep pace with the increasing

S1 S2 S3

\* 1) 0, 1, 10 are the RMSE added to the original sample points; 2) For the interpolation methods of NNI and TLI cannot deal with the boundary problem well, therefore their boundary values which are

As shown in Tab.3, Fig. 2 and Fig. 3, when sample points have no errors, the RMSEs of the interpolated results for different methods have an decreasing sequence as LP > IDW, MC > NNI, TLI > Kriging, MSM, TPS. However, the interpolated results vary with the augment of data errors. When the RMSE of sample points increases to 10, the RMSE of the surface interpolated by MSM achieves the maximum, with the minimum gained by LP and the sequence of RMSE for different interpolations changes to MSM > TPS, MC > TLI, Kriging, NNI > IDW > LP. The results show that if the original data has a better quality, the methods of TPS, MSM and Kriging can get a high precision for the interpolated results, while the quality of the original data becomes poorly, the result of LP turns to be relatively reliable.

replaced with the maximum have been excluded when calculated in statistics. Table 3. RMSE statistics of the interpolated results from the three surfaces

Fig. 2. RMSE statistics of interpolated results from S1

 0 1 10 0 1 10 0 1 10 IDW 0.13 0.46 1.38 1.14 1.19 1.72 0.25 0.50 1.30 Kriging 0.02 0.65 2.13 0.11 0.65 1.99 0.01 0.67 1.98 MC 0.07 0.83 2.79 0.29 0.90 2.53 0.06 0.88 2.51 NNI 0.03 0.62 2.02 0.27 0.67 1.91 0.05 0.64 1.88 MSM 0.02 1.07 3.62 0.29 1.07 3.22 0.01 1.11 3.28 LP 0.22 0.25 0.43 2.51 2.49 2.50 0.56 0.58 0.69 TLI 0.03 0.70 2.31 0.26 0.76 2.17 0.05 0.72 2.14 TPS 0.02 0.84 2.86 0.07 0.87 2.58 0.01 0.90 2.56

errors of the original surface, leading to a decreasing interpolated accuracy.

**4. Results and discussion** 

**4.1 RMSE and ME** 

Fig. 3. Changes in RMSEs of the three surfaces before and after adding errors

Actually, it is not difficult to explain the results. When sample points have no errors or small errors, these sample points themselves can portray the characteristics of the original surface in a relatively accurate degree. Using semi-variogram, the geostatistical method of Kriging recovers the spatial correlation of the original surface exactly, while TPS and MSM are means of finding a proper way to allocate weights to sample points according to the distance between known points and interpolated points. With the increasing of sample data errors, the surface generated by sample points starts to deviate from the original surface, meaning the sample surface can no longer describe the characteristics of the original surface completely. No matter Kriging or TPS, the surfaces they want to depict or recover are just sample surfaces. For LP, although not all of the sample points are strictly passed through, this interpolated method can make a certain restraint on the original data errors, showing a role of peak-clipping and valley-filling for the interpolation. Furthermore, the restraining effect can also reflect the variation tendency of the surfaces created by sample points, bringing about a higher interpolated precision. The interpolated results for the three surfaces with different complexity levels have been showed by Fig. 3. On the whole, the changing tendencies of these three surfaces present a roughly consistent pace, that is to say the largest change of RMSE before and after adding errors belongs to MSM with the minimum belonging to LP, and an ascending order between the two extremes are as follows: TPS, MC, TLI, NNI and IDW. It has been further proved that the interpolated method of LP is less vulnerable to data errors appearing a superior resistance to errors, while MSM is extremely sensitive to data errors showing a worst error-resistance.

#### **4.2 Moran'I index**

The Moran'I statistics of S1 with no data-errors and higher data-errors acquired from different interpolation methods have been compared in Fig. 4 and Fig. 5. For the data without errors, the Moran'I of Kriging 0.9980 reaches the topmost showing the best spatial correlation, then followed by LP, TPS and IDW with a better spatial correlation, and the lowest Moran'I belongs to MC whose spatial correlation is the worst (refer to Fig. 4). However, with the increasing of the sample data errors, the Moran'I of LP, 0.9977, changes to the highest with the optimal spatial correlation and by contrast, MSM turns to the lowest as shown by Fig. 5. The other two surfaces present a similar variation regularity or tendency for the entire, although there are a few differences among individual interpolation methods. In order to further interpret the impact caused by the increasing data-errors on spatial

Quantitative Evaluation of Spatial Interpolation

different interpolated surfaces areas.

Fig. 7. Absolute volume differences of S1

Fig. 8. Absolute surface area differences of S1

**4.4 Contour matching** 

Models Based on a Data-Independent Method 63

for the difference of the 'true' volume and the volume between an interpolated surface and

As shown in Fig. 7, when the original data has no error, the absolute volume differences of MSM, TPS and Kriging are smaller, and by comparison, LP, MC and IDW are relatively larger, with the minimum belonging to MSM and the maximum belonging to LP. However, their relationships make changes after adding a certain errors, similar as the variation of RMSE in Section 4.1. Aside from LP, the absolute volume differences of other interpolation methods are increased with mounting errors, keeping a consistent sequence of LP < IDW < Kriging < TPS < MC < MSM. Beyond doubt, the above analysis results are approximately accordant with the results of RMSE, ME and Moran'I. Moreover, judging from the variation tendency, MSM changes greatest with LP changing least, which has demonstrated the powerful robustness of LP to data errors again. Similar conclusions as volume index can be got from Fig. 8, which presents the absolute differences of the 'true' surface area and

Comparison between the contours of the original surface and those of the interpolated surfaces will be discussed in this section. Fig .9 takes the second surface for instance to present the comparisons when the original data is without errors. As shown in Fig. 9, the contours generated by Kriging, MSM and TPS perform preferably smooth, matching with contours of the original surface well. For NNI and TLI, the inside shapes of the contours maintain well with smooth lines, however, some abnormalities like figure losses appear on the boundary, further verifying their boundary effect mentioned above. Though the shapes of contours produced by LP keep well too, it is easy to notice that their positions shift on the

the datum plane whose elevation is 0. All of the results are calculated by Surfer 8.0.

Fig. 4. Moran'I statistics of S1 (RMSE = 0)

Fig. 5. Moran'I statistics of S1 (RMSE = 10)

Fig. 6. Comparisons of Moran'I reductions among three surfaces

correlation, Fig. 6 reveals the overall variations of the three surfaces. Though Moran'I reductions of the three surfaces have a few differences, they share the same changing tendency. No matter what surface it is, the Moran'I reductions caused by interpolation LP is the smallest with its spatial correlation kept best, while MSM loses most. And the increasing sequence between LP and MSM is listed as follows: IDW, Kriging, NNI < MC, TLI, TPS, which is nearly in accordance with the statistical results of RMSE and ME given in Section 4.1.

#### **4.3 Volume and surface area**

To further analyze the maintenance of overall performance after interpolation, the absolute differences between the 'true' volume and volumes calculated by surfaces interpolated by different models have been compared, except NNI and TLI for their boundary effect. Still taking the first surface for example, the absolute volume difference showed in Fig. 7 stands

Fig. 4. Moran'I statistics of S1 (RMSE = 0)

Fig. 5. Moran'I statistics of S1 (RMSE = 10)

**4.3 Volume and surface area** 

Fig. 6. Comparisons of Moran'I reductions among three surfaces

correlation, Fig. 6 reveals the overall variations of the three surfaces. Though Moran'I reductions of the three surfaces have a few differences, they share the same changing tendency. No matter what surface it is, the Moran'I reductions caused by interpolation LP is the smallest with its spatial correlation kept best, while MSM loses most. And the increasing sequence between LP and MSM is listed as follows: IDW, Kriging, NNI < MC, TLI, TPS, which

To further analyze the maintenance of overall performance after interpolation, the absolute differences between the 'true' volume and volumes calculated by surfaces interpolated by different models have been compared, except NNI and TLI for their boundary effect. Still taking the first surface for example, the absolute volume difference showed in Fig. 7 stands

is nearly in accordance with the statistical results of RMSE and ME given in Section 4.1.

for the difference of the 'true' volume and the volume between an interpolated surface and the datum plane whose elevation is 0. All of the results are calculated by Surfer 8.0.

As shown in Fig. 7, when the original data has no error, the absolute volume differences of MSM, TPS and Kriging are smaller, and by comparison, LP, MC and IDW are relatively larger, with the minimum belonging to MSM and the maximum belonging to LP. However, their relationships make changes after adding a certain errors, similar as the variation of RMSE in Section 4.1. Aside from LP, the absolute volume differences of other interpolation methods are increased with mounting errors, keeping a consistent sequence of LP < IDW < Kriging < TPS < MC < MSM. Beyond doubt, the above analysis results are approximately accordant with the results of RMSE, ME and Moran'I. Moreover, judging from the variation tendency, MSM changes greatest with LP changing least, which has demonstrated the powerful robustness of LP to data errors again. Similar conclusions as volume index can be got from Fig. 8, which presents the absolute differences of the 'true' surface area and different interpolated surfaces areas.

Fig. 7. Absolute volume differences of S1

Fig. 8. Absolute surface area differences of S1

#### **4.4 Contour matching**

Comparison between the contours of the original surface and those of the interpolated surfaces will be discussed in this section. Fig .9 takes the second surface for instance to present the comparisons when the original data is without errors. As shown in Fig. 9, the contours generated by Kriging, MSM and TPS perform preferably smooth, matching with contours of the original surface well. For NNI and TLI, the inside shapes of the contours maintain well with smooth lines, however, some abnormalities like figure losses appear on the boundary, further verifying their boundary effect mentioned above. Though the shapes of contours produced by LP keep well too, it is easy to notice that their positions shift on the

Quantitative Evaluation of Spatial Interpolation

kept relatively intact, showing a powerful robustness to errors.

Models Based on a Data-Independent Method 65

When RMSE of sample points rises to 8, the contours produced by the same eight interpolation methods have been showed in Fig. 10, most of them deforming or distorting drastically except LP. More specifically, the shape or distribution of the deformed contours can be divided into two cases: as for IDW, Kriging, MC, MSM and TPS, the bull's eye effect appears in the regions with high errors, and for TLI and NNI, their contours display as roughly fold-lines with an uneven intensity. Compared with other methods, the contours of LP, though, are not that smooth as the original ones, their shape and distribution are both

S2 IDW Kriging

MC NNI MSM

Fig. 10. Contour comparison among different interpolated surfaces when RMSE of original

data is 8 (cell size = 1m)

whole. On the contrary, the contours of IDW and MC display evident deformation and distortion, especially an obvious bull's eye effect appears for IDW. By contrast, contours of MSM which shares a similar interpolation theory as IDW maintain a better shape without the bull's eye effect, for its improvement in the weight function. As a result, it has been proved again that weight allocation and its corresponding spatial relationship between interpolated points and known points are the ultimate causes for the results of different interpolation methods.

Fig. 9. Contour comparison among different interpolated surfaces from non-error original data (cell size = 1m)

whole. On the contrary, the contours of IDW and MC display evident deformation and distortion, especially an obvious bull's eye effect appears for IDW. By contrast, contours of MSM which shares a similar interpolation theory as IDW maintain a better shape without the bull's eye effect, for its improvement in the weight function. As a result, it has been proved again that weight allocation and its corresponding spatial relationship between interpolated points and known points are the ultimate causes for the results of different

S2 IDW Kriging

MC NNI MSM

Fig. 9. Contour comparison among different interpolated surfaces from non-error original

interpolation methods.

data (cell size = 1m)

When RMSE of sample points rises to 8, the contours produced by the same eight interpolation methods have been showed in Fig. 10, most of them deforming or distorting drastically except LP. More specifically, the shape or distribution of the deformed contours can be divided into two cases: as for IDW, Kriging, MC, MSM and TPS, the bull's eye effect appears in the regions with high errors, and for TLI and NNI, their contours display as roughly fold-lines with an uneven intensity. Compared with other methods, the contours of LP, though, are not that smooth as the original ones, their shape and distribution are both kept relatively intact, showing a powerful robustness to errors.

Fig. 10. Contour comparison among different interpolated surfaces when RMSE of original data is 8 (cell size = 1m)

Quantitative Evaluation of Spatial Interpolation

the interpolated accuracy.

**6. Acknowledgements** 

Education Institutions.

141.

Barbara, CA.

23(3): 128–44.

Environmental Epidemiology 14: 404–415.

**7. References** 

Models Based on a Data-Independent Method 67

smooth process or data precision improvement method can be an effective way to advance

In order to further quantitatively depict the differences of morphological characteristics between original surfaces and interpolated surfaces, further studies will be focused on developing a visually quantitative index, such as an area enclosed between homologous contours (two level contours separately derived from an original surface and an interpolated surface). The real-world tests will also be conducted to compare with the findings by the

This study is supported by the National High Technology Research and Development Program of China (No. 2011AA120304) the National Natural Science Foundation of China (No. 40971230), the Doctoral Fund of Ministry of Education of China (No. 20093207110009) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher

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#### **4.5 Comprehensive evaluation**

Combing the various evaluation indices discussed above, Tab. 4 gives a comprehensive evaluation for various interpolation models. The levels of interpolation accuracy are defined as: lowest, lower, high, higher and highest, while the levels of robustness to errors are set as: weakest, weaker, strong, stronger and strongest. When the original data has no errors, the interpolation accuracy of TPS is the highest, followed by MSM, and MC is the lowest. After higher errors being added to the original data, the interpolation accuracy of TPS changes from the highest to the lowest, while the precision of LP alters from lower to the highest. As a result, the strongest robustness to errors is LP, and the weakest is MSM by contrast. As for MC, regardless of the original data with errors or not, its interpolation accuracy always keeps lower.


Table 4. Comprehensive Evaluation for interpolation models

#### **5. Conclusions**

From the mechanism of spatial interpolation, weight allocation and its corresponding spatial relationship between interpolated points and known points, this article proposes an evaluation and analysis approach of spatial interpolation in GIS based on data-independent method, with the construction of mathematical surfaces without errors to objectively reflect the precision of different interpolation algorithms and with the addition of varying degreeerrors to examine their robustness to errors. Based on our study, following conclusions can be given: (1) when the quality of original data is relatively well, TPS and Kriging can acquire more reliable results; (2) when the quality of original data becomes worse, for its resistance to data errors, LP can maintain a preferable interpolated precision, showing a powerful robustness to errors; (3) the validity of weight function and its corresponding spatial relationship are the kernel for design and analysis of weight function; (4) a kind of data smooth process or data precision improvement method can be an effective way to advance the interpolated accuracy.

In order to further quantitatively depict the differences of morphological characteristics between original surfaces and interpolated surfaces, further studies will be focused on developing a visually quantitative index, such as an area enclosed between homologous contours (two level contours separately derived from an original surface and an interpolated surface). The real-world tests will also be conducted to compare with the findings by the theoretical analysis and a set of high-accuracy data should be needed for test.

#### **6. Acknowledgements**

This study is supported by the National High Technology Research and Development Program of China (No. 2011AA120304) the National Natural Science Foundation of China (No. 40971230), the Doctoral Fund of Ministry of Education of China (No. 20093207110009) and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

### **7. References**

66 Advances in Data, Methods, Models and Their Applications in Geoscience

Combing the various evaluation indices discussed above, Tab. 4 gives a comprehensive evaluation for various interpolation models. The levels of interpolation accuracy are defined as: lowest, lower, high, higher and highest, while the levels of robustness to errors are set as: weakest, weaker, strong, stronger and strongest. When the original data has no errors, the interpolation accuracy of TPS is the highest, followed by MSM, and MC is the lowest. After higher errors being added to the original data, the interpolation accuracy of TPS changes from the highest to the lowest, while the precision of LP alters from lower to the highest. As a result, the strongest robustness to errors is LP, and the weakest is MSM by contrast. As for MC, regardless of the original data with errors or not, its interpolation accuracy always

**IDW** lower higher stronger

**MC** lowest lower weaker

**NNI** high high stronger

**MSM** higher lowest weakest

**LP** lower highest strongest

**TLI** high lower weaker

**TPS** highest lower weaker

From the mechanism of spatial interpolation, weight allocation and its corresponding spatial relationship between interpolated points and known points, this article proposes an evaluation and analysis approach of spatial interpolation in GIS based on data-independent method, with the construction of mathematical surfaces without errors to objectively reflect the precision of different interpolation algorithms and with the addition of varying degreeerrors to examine their robustness to errors. Based on our study, following conclusions can be given: (1) when the quality of original data is relatively well, TPS and Kriging can acquire more reliable results; (2) when the quality of original data becomes worse, for its resistance to data errors, LP can maintain a preferable interpolated precision, showing a powerful robustness to errors; (3) the validity of weight function and its corresponding spatial relationship are the kernel for design and analysis of weight function; (4) a kind of data

**Kriging** high higher strong

**Accuracy with** 

**error data Robustness** 

**4.5 Comprehensive evaluation** 

**Models Accuracy with** 

**non-error data** 

Table 4. Comprehensive Evaluation for interpolation models

keeps lower.

**5. Conclusions** 


Quantitative Evaluation of Spatial Interpolation

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**Integrated Geochemical and Geophysical** 

The crust of the earth is composed of solid rocks. When the rocks are closely examined, they are found to be composed of discrete grains of different sizes, shapes, and colours. These

The formation of soils from rocks generally involves the combination of mechanical and chemical weathering resulting from surface processes. Climatic conditions under which the weathering is affected determine which of the two forms of weathering becomes more pronounced than the other. In arid climates where there is little or no water and where there are appreciable diurnal variations in temperature, chemical weathering is considerably subordinated to mechanical weathering and the rocks simply become broken into increasingly small grains and pieces in which the individual minerals that constitute the rock are easily recognized. If, on the other hand, the climate is warm and humid with appreciable rainfall, chemical weathering becomes markedly pronounced and the individual minerals that form the rock are each subjected to rather intense chemical and comparatively modest mechanical weathering with the formation of different products which are all constituents of soils (Adewunmi,1984). In most Basement Complex rocks, weathered products, reflect certain

Previous studies by Ako et al. (1979), Ako (1980), Ajayi (1988) and Elueze (1977) on the Ilesa area have been suggestive ofsulphide mineralization but the scope of coverage have been limited to the Amphibolite and the area around the Iwara fault. The present work is regional in scope and seeks to uniquely use an integrated geochemical and geophysical approach around the Ilesa area which is within the Schist belt of southwestern Nigeria and consists of Schist Undifferentiated, Gneiss and Migmatite Undifferentiated, Pegmatite, Schist Epidiorite Complex, Quartzite and Quartz Schist, Granite Gneiss, Ampibolite, Schist Pegmatised and Granulite and Gneiss aimed at delineating the area for mineral exploration. The geochemical data from 61 sampling locations were subjected to multivariate analysis and interpreted to delineate geochemical anomalous zone. The geophysical investigation of the anomalous

grains are minerals, which are the building blocks of all rocks (Mazzullo, 1996).

characteristics (geochemical and mineralogical) of the parent rock.

**1. Introduction** 

**Approach to Mineral Prospecting –** 

**A Case Study on the Basement** 

**Complex of Ilesa Area, Nigeria** 

Emmanuel Abiodun Ariyibi

*Department of Physics,* 

*Nigeria* 

*Earth and Space Physics Research Laboratory,* 

 *Obafemi Awolowo University (OAU), le – Ife,* 

Zhou, Q. & Liu, X. (2004). Analysis of errors of derived slope and aspect related to DEM data properties. Computers & Geosciences 30: 369–378. **4** 

## **Integrated Geochemical and Geophysical Approach to Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria**

Emmanuel Abiodun Ariyibi

*Earth and Space Physics Research Laboratory, Department of Physics, Obafemi Awolowo University (OAU), le – Ife, Nigeria* 

#### **1. Introduction**

70 Advances in Data, Methods, Models and Their Applications in Geoscience

Zhou, Q. & Liu, X. (2004). Analysis of errors of derived slope and aspect related to DEM

The crust of the earth is composed of solid rocks. When the rocks are closely examined, they are found to be composed of discrete grains of different sizes, shapes, and colours. These grains are minerals, which are the building blocks of all rocks (Mazzullo, 1996).

The formation of soils from rocks generally involves the combination of mechanical and chemical weathering resulting from surface processes. Climatic conditions under which the weathering is affected determine which of the two forms of weathering becomes more pronounced than the other. In arid climates where there is little or no water and where there are appreciable diurnal variations in temperature, chemical weathering is considerably subordinated to mechanical weathering and the rocks simply become broken into increasingly small grains and pieces in which the individual minerals that constitute the rock are easily recognized. If, on the other hand, the climate is warm and humid with appreciable rainfall, chemical weathering becomes markedly pronounced and the individual minerals that form the rock are each subjected to rather intense chemical and comparatively modest mechanical weathering with the formation of different products which are all constituents of soils (Adewunmi,1984). In most Basement Complex rocks, weathered products, reflect certain characteristics (geochemical and mineralogical) of the parent rock.

Previous studies by Ako et al. (1979), Ako (1980), Ajayi (1988) and Elueze (1977) on the Ilesa area have been suggestive ofsulphide mineralization but the scope of coverage have been limited to the Amphibolite and the area around the Iwara fault. The present work is regional in scope and seeks to uniquely use an integrated geochemical and geophysical approach around the Ilesa area which is within the Schist belt of southwestern Nigeria and consists of Schist Undifferentiated, Gneiss and Migmatite Undifferentiated, Pegmatite, Schist Epidiorite Complex, Quartzite and Quartz Schist, Granite Gneiss, Ampibolite, Schist Pegmatised and Granulite and Gneiss aimed at delineating the area for mineral exploration. The geochemical data from 61 sampling locations were subjected to multivariate analysis and interpreted to delineate geochemical anomalous zone. The geophysical investigation of the anomalous

Integrated Geochemical and Geophysical Approach to

Elueze, 1977; Klemm et al, 1979, 1984).

**4. Research methodology** 

topographical and geochemical anomaly maps.

Indian, Australian, and South African Precambrian shield areas.

**3. Location, geomorphology and relief of study area** 

De Swardt (1953) reflect the erosion cycles that separately occur in the area.

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 73

The Schist Belts group of which Ilesa area is part have been variously termed" Newer Metasediments" (Oyawoye, 1964), "Younger metasediments" (McCurry, 1976); "Schist belts" (Ajibade, 1976) and" Slightly migmatized to non-migmatized metasedimentary and meta-igneous rocks" (Rahaman, 1988). The Nigerian Schist belts occur as prominent N-S trending features in the Nigerian Basement Complex. Lithologically, the schist belt consists of metamorphosed pelitic to semi-pelitic rocks, quartzites, calc-silicates rocks, metaconglomerates and pebbly schists; amphibolites and metavolcanic rocks. On the basis of lithology, metamorphism, structure, geochemical characteristics such as the tholeitic affinities of the amphibolites, and economic potentials, the schist belts show similarities to typical Archaean greenstone belts of the world (Wright and McCurry, 1970; Hubbard, 1975;

However, certain differences exist between these schist belts and typical greenstone belts. Though the schist belts of Nigeria have the sedimentary and ultramafic rock groups as defined by Anhaeusser et al, (1969), the so-called, "greenstone group" comprising serpentinites, crystalline limestones, rhyolites, banded ironstones of chemical origin and massive carbonated "greenstones" are either absent or less conspicuous. Also the ratio of metasediments to metavolcanics is much higher in the Schists belts of Nigeria than in the typical Archaean greenstone belts (Wright and McCurry, 1970). Mineralization is also not strongly developed in the schist's belts as in well known greenstone belts of the Canadian,

The area of study is located in the southern part of Ilesa and is geographically enclosed within Latitude 70 30`N to 7036` N and Longitude 40 38`E to 40 50`E. It covers an area of about 1200 square kilometers. There are a good number of major and minor roads that link up the towns and villages in the study area. There are also main paths and footpaths linking the communities. These make the entire study area fairly accessible. The landscape of the area of study can be generally described as undulating, rising gently to steeply, but in some areas is punctuated by hilly ridges. The ridges are formed by quartz-schist or quartzite that rises abruptly from the enveloping basins and trend in the North to South direction. On the other hand, hills which are probably products of fragments of coarse-grained batholitic granite or resistance gneisses have a positive relief and are covered up by vegetation. Dissected topography also develops over the easily eroded basic rocks which according to

Preliminary work in the survey area took the form of a reconnaissance geological mapping followed by the statistical analysis of geochemical data to delineate areas with geochemical anomalies indicative of possible mineralization (Ariyibi et. al. 2010). This was aimed at studying the geology and selecting geophysical traverses approximately normal to the strike of the geochemical anomaly. In some cases however, the dense vegetation necessitated the cutting of traverses, although most of the traverses used were along existing roads and footpaths. The field data acquisition involved ground magnetic, electrical resistivity and VLF – EM survey methods. Essentially, the magnetic and VLF - EM measurements were carried out simultaneously on the chosen traverses located on the delineated area using

zone that follows employed the Very – Low Frequency Electromagnetic (VLF – EM), Electrical resistivityand magnetic methods.

#### **2. Geologic setting**

The Ilesa area, lies within the Southwest Nigerian Basement Complex (Schist Belt) which is of Precambrian age (De Swardt, 1953). De Swardt (1947) and Russ (1957) suggested that the Nigerian Basement Complex is Polycyclic. This was confirmed by Hurley (1966, 1970) who used radiometric method to determine the age of the rocks. The Nigerian basement is believed to have had structural complexity as a result of folding, igneous and metamorphic activities with five major rock units recognized within the Basement Complex by Rahaman (1976). These are:

The migmatite-gneiss-quartzite complex


Geochronological data on all these rock groups were summarized by Rahaman (1988). The geological map of Ilesa area is as shown in Figure 1.

Fig. 1. Geological map of the study area (After Adebayo, 2008 and Adelusil, 2005)

The Schist Belts group of which Ilesa area is part have been variously termed" Newer Metasediments" (Oyawoye, 1964), "Younger metasediments" (McCurry, 1976); "Schist belts" (Ajibade, 1976) and" Slightly migmatized to non-migmatized metasedimentary and meta-igneous rocks" (Rahaman, 1988). The Nigerian Schist belts occur as prominent N-S trending features in the Nigerian Basement Complex. Lithologically, the schist belt consists of metamorphosed pelitic to semi-pelitic rocks, quartzites, calc-silicates rocks, metaconglomerates and pebbly schists; amphibolites and metavolcanic rocks. On the basis of lithology, metamorphism, structure, geochemical characteristics such as the tholeitic affinities of the amphibolites, and economic potentials, the schist belts show similarities to typical Archaean greenstone belts of the world (Wright and McCurry, 1970; Hubbard, 1975; Elueze, 1977; Klemm et al, 1979, 1984).

However, certain differences exist between these schist belts and typical greenstone belts. Though the schist belts of Nigeria have the sedimentary and ultramafic rock groups as defined by Anhaeusser et al, (1969), the so-called, "greenstone group" comprising serpentinites, crystalline limestones, rhyolites, banded ironstones of chemical origin and massive carbonated "greenstones" are either absent or less conspicuous. Also the ratio of metasediments to metavolcanics is much higher in the Schists belts of Nigeria than in the typical Archaean greenstone belts (Wright and McCurry, 1970). Mineralization is also not strongly developed in the schist's belts as in well known greenstone belts of the Canadian, Indian, Australian, and South African Precambrian shield areas.

#### **3. Location, geomorphology and relief of study area**

The area of study is located in the southern part of Ilesa and is geographically enclosed within Latitude 70 30`N to 7036` N and Longitude 40 38`E to 40 50`E. It covers an area of about 1200 square kilometers. There are a good number of major and minor roads that link up the towns and villages in the study area. There are also main paths and footpaths linking the communities. These make the entire study area fairly accessible. The landscape of the area of study can be generally described as undulating, rising gently to steeply, but in some areas is punctuated by hilly ridges. The ridges are formed by quartz-schist or quartzite that rises abruptly from the enveloping basins and trend in the North to South direction. On the other hand, hills which are probably products of fragments of coarse-grained batholitic granite or resistance gneisses have a positive relief and are covered up by vegetation. Dissected topography also develops over the easily eroded basic rocks which according to De Swardt (1953) reflect the erosion cycles that separately occur in the area.

#### **4. Research methodology**

72 Advances in Data, Methods, Models and Their Applications in Geoscience

zone that follows employed the Very – Low Frequency Electromagnetic (VLF – EM),

The Ilesa area, lies within the Southwest Nigerian Basement Complex (Schist Belt) which is of Precambrian age (De Swardt, 1953). De Swardt (1947) and Russ (1957) suggested that the Nigerian Basement Complex is Polycyclic. This was confirmed by Hurley (1966, 1970) who used radiometric method to determine the age of the rocks. The Nigerian basement is believed to have had structural complexity as a result of folding, igneous and metamorphic activities with five major rock units recognized within the Basement Complex by Rahaman

i. Slightly migmatized to unmigmatized paraschists and meta-igneous rocks which consists of pellitic schists, quartzites, amphibolites, talcose rocks, metaconglomerate,

Geochronological data on all these rock groups were summarized by Rahaman (1988). The

Fig. 1. Geological map of the study area (After Adebayo, 2008 and Adelusil, 2005)

iv. Unmetamorphosed acid-basic intrusives and hypabyssal rocks

geological map of Ilesa area is as shown in Figure 1.

Electrical resistivityand magnetic methods.

The migmatite-gneiss-quartzite complex

marble and calc-silicate rocks.

**2. Geologic setting** 

(1976). These are:

ii. Charnockitic rocks iii. Older Granites and

> Preliminary work in the survey area took the form of a reconnaissance geological mapping followed by the statistical analysis of geochemical data to delineate areas with geochemical anomalies indicative of possible mineralization (Ariyibi et. al. 2010). This was aimed at studying the geology and selecting geophysical traverses approximately normal to the strike of the geochemical anomaly. In some cases however, the dense vegetation necessitated the cutting of traverses, although most of the traverses used were along existing roads and footpaths. The field data acquisition involved ground magnetic, electrical resistivity and VLF – EM survey methods. Essentially, the magnetic and VLF - EM measurements were carried out simultaneously on the chosen traverses located on the delineated area using topographical and geochemical anomaly maps.

Integrated Geochemical and Geophysical Approach to

of the geochemical data.

**5.1.1.1 Statistical results** 

standardized variable.

their qualitative and quantitative distinctions.

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 75

As with all geochemical surveys, the first step in approaching an operational problem is to conduct an orientation survey. Such a survey normally consists of a series of preliminary experiments aimed at determining the existence and characteristics of anomalies associated with mineralization. This information may then be used in selecting adequate prospecting techniques and in determining the factors and criteria that have a bearing on interpretation

Although the orientation study will provide the necessary technical information upon which to base operational procedures, the final choice of methods to be used must also take into account other factors, such as cost of operation, availability of personnel, and the market value of the expected ore discoveries. The nature of the overburden, whether it is residual or is of glacial, alluvial, or wind-borne origin, is the first question that must be answered by the orientation survey. Sometimes it is surprisingly difficult to discriminate between residual and transported soil. The safest method therefore, is to make critical and careful examination of complete sections of the overburden at the start of every new field survey. If road-cut exposures are not available, the soil should be examined by pitting or auguring. Previous orientation studies carried out by Olorunfemi (1977) and Adewunmi (1984) in parts of southern Ilesa established that the C horizon is the preferredhorizon for sampling. Details of laboratory procedures and analysis of the samples were reported by Ariyibi et al. (2010)

The multivariate technique, has proven to be viable and credible when applied on geochemical data as reported by Grunfeld (2003). The Principal Component Analysis (PCA) which isa multivariate technique, describep observable random variables x1, x2, ….,xp in terms of the joint variation of a fewer number, k (<p) variables. The purpose of PCA is to determine factors (i. e. principal components) in order to explain as much of the total variation in the data as possible with as few of these factors as possible. This will uncover

Table1 shows the descriptive statistics of the data. The data are not widely dispersed from the average when values of standard deviation are compared with the raw data. The measured values of Fe in the samples are quite large and so account for the large value of standard deviation (5. 0903) as seen in the table. The covariance matrix is shown in Table 2 and the corresponding correlation coefficients are shown in Table 3 and this was used to obtain the coefficients of the principal component using MATLAB as shown in Table 4 from

Observation elements are on the rows of Table 4. For example, Pb is denoted by X1 and Fe by X2 and so on. U1, ………,U8 are the principal components. The loadings or coefficients of the principal components are on the vertical columns. The magnitude of loadings greater than or equal to 0. 5 is to be considered for interpretation (Dillon and Goldstein,1984) as this will give the element with higher association ratio. On the last two rows of Table 4 is the eigenvalues of covariance matrix of the data and the Hotelling's T2 statistic which gives a measure of the multivariate distance of each observation from the centre of the data set. A

The three principal components with elements having loadings of 0. 5 and above (for which also the variability is greater than 10%) are: U1, U2and U3 and these combined, account for 85. 34 % variability in the data. In U1 are the elements : Fe and Mn in association (i. e. Fe-Mn)

plot of the variability (in %) and the Principal component is as shown in Figure 2.

The magnetometer used for this work is the GEM – 8 Proton magneto-meter which measures the Earth`s total field. The potable VLF-EM equipment used for this work was the GEONICS-EM16 (with GBR station) and on frequency of 16 kHz and it measures the real and imaginary part of the signal. The ABEM Terrameter was used for the electrical resistivity measurement.

#### **5. Geoscientific methods used, data analysis and results**

#### **5.1 General**

The geoscientific methods that can be used in mineral prospecting include, magnetic, gravity, electrical, electromagnetic, radiometric, geothermal and seismic methods. However, the choice of method (s) would depend basically upon their resolution with respect to problems encountered or conditions sought after within a given locality. More often, consideration is given to the cost, time, portability and reliability of instruments used in small scale surveys (Adewusi, 1988). The methods considered in this work include the geochemical, electrical resistivity, VLF – EM and magnetic methods.

#### **5.1.1 The geochemical data, analysis and results**

Geochemical methods of exploration should be viewed as an integral component of the variety of weapons available to the modern prospector. As the goal of every exploration method is, of course the same – to find clues that will help in locating hidden ore, the geochemical prospecting for minerals, as defined by common usage, includes any method of mineral exploration based on systematic measurement of one or more chemical properties of a naturally occurring material (Suh, 1993). The chemical property measured is most commonly the trace content of some element or group of elements; the naturally occurring material may be rock, soil, gossan, glacial debris, vegetation, stream sediment or water. The purpose of the measurements is the discovery of abnormal chemical patterns, or geochemical anomalies, related to mineralization.

Sampling and analysis of residual soil is by far the most widely used of all the geochemical methods. The popularity of residual-soil surveying as an exploration method is a simple reflection of the reliability of soil anomalies as ore guides (Gill, 1997). Practical experiences in many climates and in many types of geological environments has shown that where the parent rock is mineralized, some kind of chemical pattern can be found in the residual soil that results from the weathering of that rock. Where residual soil anomalies are not found over known ore in the bedrock, further examination usuallyshows either that the material sampled was not truly residual or that an unsuitable horizon or size fractionof the soil was sampled, or possibly that an inadequate extraction method was used. In other words, when properly used, the method is exceptionally reliable in comparison with most other exploration methods.

By definition, an anomaly is a deviation from the norm. A geochemical anomaly, more specifically, is a departure from the geochemical patterns that are normal for a given area or geochemical landscape. Strictly speaking, an ore deposit being a relatively rare or abnormal phenomenon is itself a geochemical anomaly. Similarly, the geochemical patterns that are related either to the genesis or to the erosion of an ore deposit are anomalies (Hawkes and Webb,1962). Anomalies that are related to ore and that can be used as guides in exploration are termed significant anomalies. Anomalies that are superficially similar to significant anomalies but are unrelated to ore are known as non-significant anomalies.

As with all geochemical surveys, the first step in approaching an operational problem is to conduct an orientation survey. Such a survey normally consists of a series of preliminary experiments aimed at determining the existence and characteristics of anomalies associated with mineralization. This information may then be used in selecting adequate prospecting techniques and in determining the factors and criteria that have a bearing on interpretation of the geochemical data.

Although the orientation study will provide the necessary technical information upon which to base operational procedures, the final choice of methods to be used must also take into account other factors, such as cost of operation, availability of personnel, and the market value of the expected ore discoveries. The nature of the overburden, whether it is residual or is of glacial, alluvial, or wind-borne origin, is the first question that must be answered by the orientation survey. Sometimes it is surprisingly difficult to discriminate between residual and transported soil. The safest method therefore, is to make critical and careful examination of complete sections of the overburden at the start of every new field survey. If road-cut exposures are not available, the soil should be examined by pitting or auguring. Previous orientation studies carried out by Olorunfemi (1977) and Adewunmi (1984) in parts of southern Ilesa established that the C horizon is the preferredhorizon for sampling. Details of laboratory procedures and analysis of the samples were reported by Ariyibi et al. (2010)

#### **5.1.1.1 Statistical results**

74 Advances in Data, Methods, Models and Their Applications in Geoscience

The magnetometer used for this work is the GEM – 8 Proton magneto-meter which measures the Earth`s total field. The potable VLF-EM equipment used for this work was the GEONICS-EM16 (with GBR station) and on frequency of 16 kHz and it measures the real and imaginary part of the signal. The ABEM Terrameter was used for the electrical

The geoscientific methods that can be used in mineral prospecting include, magnetic, gravity, electrical, electromagnetic, radiometric, geothermal and seismic methods. However, the choice of method (s) would depend basically upon their resolution with respect to problems encountered or conditions sought after within a given locality. More often, consideration is given to the cost, time, portability and reliability of instruments used in small scale surveys (Adewusi, 1988). The methods considered in this work include the

Geochemical methods of exploration should be viewed as an integral component of the variety of weapons available to the modern prospector. As the goal of every exploration method is, of course the same – to find clues that will help in locating hidden ore, the geochemical prospecting for minerals, as defined by common usage, includes any method of mineral exploration based on systematic measurement of one or more chemical properties of a naturally occurring material (Suh, 1993). The chemical property measured is most commonly the trace content of some element or group of elements; the naturally occurring material may be rock, soil, gossan, glacial debris, vegetation, stream sediment or water. The purpose of the measurements is the discovery of abnormal chemical patterns, or

Sampling and analysis of residual soil is by far the most widely used of all the geochemical methods. The popularity of residual-soil surveying as an exploration method is a simple reflection of the reliability of soil anomalies as ore guides (Gill, 1997). Practical experiences in many climates and in many types of geological environments has shown that where the parent rock is mineralized, some kind of chemical pattern can be found in the residual soil that results from the weathering of that rock. Where residual soil anomalies are not found over known ore in the bedrock, further examination usuallyshows either that the material sampled was not truly residual or that an unsuitable horizon or size fractionof the soil was sampled, or possibly that an inadequate extraction method was used. In other words, when properly used, the method is exceptionally reliable in comparison with most other

By definition, an anomaly is a deviation from the norm. A geochemical anomaly, more specifically, is a departure from the geochemical patterns that are normal for a given area or geochemical landscape. Strictly speaking, an ore deposit being a relatively rare or abnormal phenomenon is itself a geochemical anomaly. Similarly, the geochemical patterns that are related either to the genesis or to the erosion of an ore deposit are anomalies (Hawkes and Webb,1962). Anomalies that are related to ore and that can be used as guides in exploration are termed significant anomalies. Anomalies that are superficially similar to significant

anomalies but are unrelated to ore are known as non-significant anomalies.

**5. Geoscientific methods used, data analysis and results** 

geochemical, electrical resistivity, VLF – EM and magnetic methods.

**5.1.1 The geochemical data, analysis and results** 

geochemical anomalies, related to mineralization.

exploration methods.

resistivity measurement.

**5.1 General** 

The multivariate technique, has proven to be viable and credible when applied on geochemical data as reported by Grunfeld (2003). The Principal Component Analysis (PCA) which isa multivariate technique, describep observable random variables x1, x2, ….,xp in terms of the joint variation of a fewer number, k (<p) variables. The purpose of PCA is to determine factors (i. e. principal components) in order to explain as much of the total variation in the data as possible with as few of these factors as possible. This will uncover their qualitative and quantitative distinctions.

Table1 shows the descriptive statistics of the data. The data are not widely dispersed from the average when values of standard deviation are compared with the raw data. The measured values of Fe in the samples are quite large and so account for the large value of standard deviation (5. 0903) as seen in the table. The covariance matrix is shown in Table 2 and the corresponding correlation coefficients are shown in Table 3 and this was used to obtain the coefficients of the principal component using MATLAB as shown in Table 4 from standardized variable.

Observation elements are on the rows of Table 4. For example, Pb is denoted by X1 and Fe by X2 and so on. U1, ………,U8 are the principal components. The loadings or coefficients of the principal components are on the vertical columns. The magnitude of loadings greater than or equal to 0. 5 is to be considered for interpretation (Dillon and Goldstein,1984) as this will give the element with higher association ratio. On the last two rows of Table 4 is the eigenvalues of covariance matrix of the data and the Hotelling's T2 statistic which gives a measure of the multivariate distance of each observation from the centre of the data set. A plot of the variability (in %) and the Principal component is as shown in Figure 2.

The three principal components with elements having loadings of 0. 5 and above (for which also the variability is greater than 10%) are: U1, U2and U3 and these combined, account for 85. 34 % variability in the data. In U1 are the elements : Fe and Mn in association (i. e. Fe-Mn)

Integrated Geochemical and Geophysical Approach to

Cd 0. 12 0. 22 0. 37 1. 00

Table 3. Correlation coefficients of the elements

U2 (27. . 65)

proportion of total variance in %) of the elements

Iperindo are surrounded by lower and moderate values.

Cr -0. 05 0. 03 0. 22 0. 17 1. 00

Cu 0. 15 0. 01 0. 01 -0. 03 0. 08 1. 00

U3 (16. 58)

Zn 0. 33 0. 04 0. 14 0. 37 0. 11 0. 40 1. 00

Mn 0. 29 0. 94 0. 44 0. 27 0. 09 0. 09 0. 03 1. 00

U4 (8. 31)

Pb X1 -0. 0022 0. 5905 -0. 1851 -0. 4640 0. 3429 -0. 1434 -0. 2725 0. 4351 Fe X2 -0. 5046 0. 2445 0. 0376 0. 0729 -0. 1184 0. 3095 0. 6589 0. 3674 Ni X3 -0. 3897 -0. 3036 -0. 1220 0. 5128 0. 5782 -0. 0440 -0. 2619 0. 2707 Cd X4 -0. 1052 -0. 3599 -0. 6629 -0. 1409 -0. 4200 -0. 3702 0. 0425 0. 2912 Cr X5 0. 0880 -0. 5187 0. 4400 -0. 3967 -0. 0550 0. 2898 -0. 1527 0. 5118 Cu X6 0. 4073 0. 2412 0. 2444 0. 5520 -0. 3130 -0. 2636 -0. 0585 0. 4905 Zn X7 0. 4034 0. 0405 -0. 5018 0. 1695 0. 0080 0. 7336 -0. 0911 0. 0929 Mn X8 -0. 5001 0. 2024 0. 0696 0. 0757 -0. 565 0. 2304 -0. 6214 -0. 0809

Matrix 3. 2890 2. 2120 1. 3262 0. 6653 0. 3033 0. 2008 0. 0034 0. 0000 T2 6. 1250 6. 1250 6. 1250 6. 1250 6. 1250 6. 1250 6. 1250 6. 1250 Table 4. Coefficients of the Principal component transformation (Numbers in Bracket are the

The principal components U4, U5, U6, U7 and U8 have smaller variability and have respective eigenvalues of 0. 6653, 0. 3033, 0. 2008, 0. 0034 and 0. 0000. These when compared to the first three components are very small which is an indication of their relative decrease in

Results of a previous regional geochemical survey carried out by Ajayi and Suh (1993) using the factor analysis statistical techniquerevealed the existence of : Zn – Co – Cd, Ni – Cr, Fe – Mn and Cu – Pb as relevant associations mainly in the Amphibolites rocks. The results from the present study compare favourably well to these earlier results obtained from factor analysis but the association region extends to the quartz-schist rocks as can be seen in Figures 3, 4 and 5. Figure 3 shows the association ratio of Fe – Mn. The range of values is shown by the coloured circles. Values are classified as low (in purple circles) with concentration less than 20ppm, moderate (in yellow circles) with concentration range of 21 – 40ppmand high (in blue circles) with concentration greater than 41ppm. It can be seen that higher values are clustered at the central part of the figure which is on the Amphibolite, Schist and Epidiorite Complex and also on the Quartzite/Quartz Schist. At other parts, the values are distributed between moderate and lower values, though, with some isolated higher values probably due to rock intrusions. For examples, the higher values near

significance in the data. So any association suggested by them cannot be realistic.

U5 (3. 79) U6 (2. 51) U7 (0. 04%) U8 (0%)

Pb 1. 00

Eig. of Cov.

Fe 0. 35 1. 00

% U1 (41. 11)

Ni 0. 01 0. 48 1. 00

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 77

Element Pb Fe Ni Cd Cr Cu Zn Mn

Fig. 2. A plot of the variability of the Principal Component, with five components accounting for 97. 44%.

accounting for 41. 11%. In U2 the elements,Pb and Cr (i. e. Pb – Cr) accounting for 27. 65%and U3 the elementsCd and Zn in association (i. e. Cd-Zn) with 16. 58 %.


Table 1. Descriptive statistics of the elements


Table 2. Covariance Matrix of the elements


Table 3. Correlation coefficients of the elements

Fig. 2. A plot of the variability of the Principal Component, with five components

65%and U3 the elementsCd and Zn in association (i. e. Cd-Zn) with 16. 58 %.

Range (ppm)

accounting for 41. 11%. In U2 the elements,Pb and Cr (i. e. Pb – Cr) accounting for 27.

Pb 4. 50 3. 00 – 8. 00 1. 10 0. 0512 Fe 400. 00 50. 00 – 1750. 00 346. 00 5. 0903 Ni 5. 00 1. 50 – 7. 00 4. 00 0. 2121 Cd 0. 80 0. 03 – 1. 70 0. 50 0. 3043 Cr 0. 40 0. 01 – 1. 00 0. 30 0. 3512 Cu 0. 04 0. 01 – 0. 90 0. 03 0. 0090 Zn 0. 20 0. 01 – 0. 40 0. 14 0. 0113 Mn 10. 00 0. 20 – 26. 0 7. 30 1. 2015

Element Pb Fe Ni Cd Cr Cu Zn Mn Pb 6. 41 438. 90 -0. 02 0. 08 -0. 05 0. 01 0. 08 4. 73 Fe 438. 90 281721. 80 339. 80 50. 00 3. 26 0. 14 2. 32 3602. 40 Ni -0. 02 339. 8 1. 81 0. 21 0. 06 0. 01 0. 02 4. 26 Cd 0. 08 50. 00 0. 21 0. 18 0. 02 -0. 01 0. 02 0. 81 Cr -0. 05 3. 26 0. 06 0. 02 0. 05 0. 01 0. 01 0. 15 Cu 0. 01 0. 14 0. 01 -0. 01 0. 01 0. 01 0. 01 0. 02 Zn 0. 08 2. 32 0. 02 0. 02 0. 01 0. 01 0. 01 0. 03 Mn 4. 73 3602. 4 4. 26 0. 81 0. 02 0. 02 0. 03 52. 41

Geometric Mean

Std. dev.

(ppm)

accounting for 97. 44%.

Element Threshold

(ppm)

Table 1. Descriptive statistics of the elements

Table 2. Covariance Matrix of the elements


Table 4. Coefficients of the Principal component transformation (Numbers in Bracket are the proportion of total variance in %) of the elements

The principal components U4, U5, U6, U7 and U8 have smaller variability and have respective eigenvalues of 0. 6653, 0. 3033, 0. 2008, 0. 0034 and 0. 0000. These when compared to the first three components are very small which is an indication of their relative decrease in significance in the data. So any association suggested by them cannot be realistic.

Results of a previous regional geochemical survey carried out by Ajayi and Suh (1993) using the factor analysis statistical techniquerevealed the existence of : Zn – Co – Cd, Ni – Cr, Fe – Mn and Cu – Pb as relevant associations mainly in the Amphibolites rocks. The results from the present study compare favourably well to these earlier results obtained from factor analysis but the association region extends to the quartz-schist rocks as can be seen in Figures 3, 4 and 5. Figure 3 shows the association ratio of Fe – Mn. The range of values is shown by the coloured circles. Values are classified as low (in purple circles) with concentration less than 20ppm, moderate (in yellow circles) with concentration range of 21 – 40ppmand high (in blue circles) with concentration greater than 41ppm. It can be seen that higher values are clustered at the central part of the figure which is on the Amphibolite, Schist and Epidiorite Complex and also on the Quartzite/Quartz Schist. At other parts, the values are distributed between moderate and lower values, though, with some isolated higher values probably due to rock intrusions. For examples, the higher values near Iperindo are surrounded by lower and moderate values.

Integrated Geochemical and Geophysical Approach to

Fig. 4. Map showing the association ratio of Pb – Cr in the study area.

Electrical methods are generally referred to as "resistivity surveys". Metallic minerals are relatively good conductors of electricity. In contrast, common rock forming minerals are generally poor conductors. This fact is the basis for geophysical exploration methods which measure conductivity to evaluate the metal content of rocks. The methods also provide some limited information about the geometry of the subsurface metallic mineralization. Surface electrical methods are limited to shallow depths (<200m), but the electrical properties of rocks can be measured at much greater depths by using electrical borehole instruments sent down deep drill holes. The location of the seven (7) VES data points are as shown in Figure 6. They are located so as to provide subsurface geological information including, layer resistivity, thickness and depth to the bedrock which will be useful in the geophysical modeling that will follow in the subsequent section. The Wenner configuration was used with electrode separation (a) varying from 1 - 96m. VES curves were interpreted using the partial curve matching technique followed with computer iteration procedure on the WinGLink computer software version 1. 62. 08. On this software, computed curves are compared with observed field curves. Where a good fit (i. e. 95 % correlation and above) was obtained between the two curves, the interpretation results was considered satisfactory; otherwise the geoelectric parameters were modified as appropriate and the procedure repeated until a satisfactory fit was obtained. The result from the computer iteration is as

**5.2 The electrical resistivity data, analysis and results** 

summarized with their geoelectric parameters in Table 5.

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 79

Fig. 3. Map showing the association ratio of Fe – Mn in the study area.

The association ratio of Pb – Cr are as shown in Figure 4. The higher values with concentration greater than 21ppm are more widely distributed than the Fe – Mn association ratio. However, most of the higher values are still concentrated on the Amphibolite, Quartzite/Quartz Schist and Schist Epidiorite Complex, though, with some moderate and lower values in between them. The association ratio of Cd – Zn is shown in Figure 5. The values are seen to be more widely distributed for most part of the figure. This shows the spread of the association over the basement rocks. Cd is known universally to associate with Zn. It actually reflects the strong lithologic influence related to the mafic minerals with which Zn is associated. It can thus be seen, that for the plotted concentration ratios, higher values of the metallic association are distributed largely towards the centre of the study area. This partly corresponds to the suggested mineralized areas by previous geological and geophysical studies of Ako (1980) and Ajayi (1988). Similar studies (such as the present one) were carried out on the Elura Deposit in the Cobar Mining district of Central New South Wales, Australia. The study identified high grade Zn – Pb - Agsulphide mineralization and this was later followed by extensive geophysical surveys to map the siliceous, pyriticand the pyrrhotitic ores (Palacky, 1988). A combined map of Figures 3, 4 and 5 is as shown in Figure 6. This gives the combined map for the geochemical anomaly over the study area. The Fe – Mn ratio is represented in red circles, the Pb – Cr ratio is represented in green circles while the Cd – Zn ratio is represented in blue circles. The anomaly is seen to be widely distributed over the delineated area. Also shown on the map are the geophysical locations and traverses to investigate the anomaly.

Fig. 3. Map showing the association ratio of Fe – Mn in the study area.

to investigate the anomaly.

The association ratio of Pb – Cr are as shown in Figure 4. The higher values with concentration greater than 21ppm are more widely distributed than the Fe – Mn association ratio. However, most of the higher values are still concentrated on the Amphibolite, Quartzite/Quartz Schist and Schist Epidiorite Complex, though, with some moderate and lower values in between them. The association ratio of Cd – Zn is shown in Figure 5. The values are seen to be more widely distributed for most part of the figure. This shows the spread of the association over the basement rocks. Cd is known universally to associate with Zn. It actually reflects the strong lithologic influence related to the mafic minerals with which Zn is associated. It can thus be seen, that for the plotted concentration ratios, higher values of the metallic association are distributed largely towards the centre of the study area. This partly corresponds to the suggested mineralized areas by previous geological and geophysical studies of Ako (1980) and Ajayi (1988). Similar studies (such as the present one) were carried out on the Elura Deposit in the Cobar Mining district of Central New South Wales, Australia. The study identified high grade Zn – Pb - Agsulphide mineralization and this was later followed by extensive geophysical surveys to map the siliceous, pyriticand the pyrrhotitic ores (Palacky, 1988). A combined map of Figures 3, 4 and 5 is as shown in Figure 6. This gives the combined map for the geochemical anomaly over the study area. The Fe – Mn ratio is represented in red circles, the Pb – Cr ratio is represented in green circles while the Cd – Zn ratio is represented in blue circles. The anomaly is seen to be widely distributed over the delineated area. Also shown on the map are the geophysical locations and traverses

Fig. 4. Map showing the association ratio of Pb – Cr in the study area.

#### **5.2 The electrical resistivity data, analysis and results**

Electrical methods are generally referred to as "resistivity surveys". Metallic minerals are relatively good conductors of electricity. In contrast, common rock forming minerals are generally poor conductors. This fact is the basis for geophysical exploration methods which measure conductivity to evaluate the metal content of rocks. The methods also provide some limited information about the geometry of the subsurface metallic mineralization. Surface electrical methods are limited to shallow depths (<200m), but the electrical properties of rocks can be measured at much greater depths by using electrical borehole instruments sent down deep drill holes. The location of the seven (7) VES data points are as shown in Figure 6. They are located so as to provide subsurface geological information including, layer resistivity, thickness and depth to the bedrock which will be useful in the geophysical modeling that will follow in the subsequent section. The Wenner configuration was used with electrode separation (a) varying from 1 - 96m. VES curves were interpreted using the partial curve matching technique followed with computer iteration procedure on the WinGLink computer software version 1. 62. 08. On this software, computed curves are compared with observed field curves. Where a good fit (i. e. 95 % correlation and above) was obtained between the two curves, the interpretation results was considered satisfactory; otherwise the geoelectric parameters were modified as appropriate and the procedure repeated until a satisfactory fit was obtained. The result from the computer iteration is as summarized with their geoelectric parameters in Table 5.

Integrated Geochemical and Geophysical Approach to

host rock is resistive and the overburden is thin.

ellipticity *(e)* as:

1 231

2 127

3 795

4 407

5 350

6 550

7 330

VES No Layer Resistivity (Ω –m)

> 368 892 233

> 439 104 324

202 455 3065

257 49 320

177 445 238

1195 1804 186

455 2212 319

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 81

conductive overburden seriously suppresses response from basement conductors, andrelatively small variations in overburden conductivity or thickness can themselves generate significant VLF anomalies. For this reason, VLF is more effective in areas where the

In the VLF method, two orthogonal components of the magnetic field were measured, and normally the tilt angle, α, and ellipticity, *e*, of the vertical magnetic polarization ellipse are derived. Real (in-phase) and imaginary (quadrature) are used in the Karous – Hjelt Fraser filter (KHFFILT) programme. These components are based on the tilt angle, (α) and

Layer thickness

(m)

3. 77 6. 01 13. 50 -

0. 59 2. 23 13. 28 -

1. 03 11. 45 7. 68 -

0. 60 2. 11 4. 87 -

1. 13 1. 80 36. 43 -

0. 50 6. 28 25. 03 -

1. 26 6. 16 22. 82

\*AMP = AmphiboliteGMU = Gneiss and Migmatite Undifferentiated QQS = Quartzite/Quartz Schist SEC= Schist and Epidiorite Complex

Table 5. Geoelectric layer parameters of the study area

Re =tan (α) 100% and Im = e 100%. (1)

Curve type Remark

AK AMP\*

KH AMP

HA AMP

QH GMU

HK GMU

AK SEC

AK QQS

Fig. 5. Map showing the association ratio of Cd – Zn in the study area.

#### **5.3 VLF– EM data, analysis and results**

The Very Low Frequency (VLF) electromagnetic method uses powerful remote radio transmitters set up in different parts of the world for military communications (Klein and Lajoie, 1980). In radio communications terminology, VLF means very low frequency, of about 15 to 25 kHz. Relative to frequencies generally used in geophysical exploration, these are actually very high frequencies. The radiated field from a remote VLF transmitter, propagating over a uniform or horizontally layered earth and measured on the earth's surface, consists of a vertical electric field component and a horizontal magnetic field component each perpendicular to the direction of propagation.

These radio transmitters are very powerful and induce electric currents in conductive bodies thousands of kilometers away. Under normal conditions, the fields produced are relatively uniform in the far field at a large distance (hundreds of kilometers) from the transmitters. The induced currents produce secondary magnetic fields that can be detected at the surface through deviation of the normal radiated field. The VLF method uses relatively simple instruments and can be a useful reconnaissance tool. Potential targets include tabular conductors in a resistive host rock such as faults in limestone or igneous terrain. The depth of exploration is limited to about 60% to 70% of the skin depth of the surrounding rock or soil. Therefore, the high frequency of the VLF transmitters means that in more conductive environments, the exploration depth is quite shallow; for example, the depth of exploration might be 10 to 12 m in 25-Ωm material (Milsom, 1989). Additionally, the presence of

Fig. 5. Map showing the association ratio of Cd – Zn in the study area.

component each perpendicular to the direction of propagation.

The Very Low Frequency (VLF) electromagnetic method uses powerful remote radio transmitters set up in different parts of the world for military communications (Klein and Lajoie, 1980). In radio communications terminology, VLF means very low frequency, of about 15 to 25 kHz. Relative to frequencies generally used in geophysical exploration, these are actually very high frequencies. The radiated field from a remote VLF transmitter, propagating over a uniform or horizontally layered earth and measured on the earth's surface, consists of a vertical electric field component and a horizontal magnetic field

These radio transmitters are very powerful and induce electric currents in conductive bodies thousands of kilometers away. Under normal conditions, the fields produced are relatively uniform in the far field at a large distance (hundreds of kilometers) from the transmitters. The induced currents produce secondary magnetic fields that can be detected at the surface through deviation of the normal radiated field. The VLF method uses relatively simple instruments and can be a useful reconnaissance tool. Potential targets include tabular conductors in a resistive host rock such as faults in limestone or igneous terrain. The depth of exploration is limited to about 60% to 70% of the skin depth of the surrounding rock or soil. Therefore, the high frequency of the VLF transmitters means that in more conductive environments, the exploration depth is quite shallow; for example, the depth of exploration might be 10 to 12 m in 25-Ωm material (Milsom, 1989). Additionally, the presence of

**5.3 VLF– EM data, analysis and results** 

conductive overburden seriously suppresses response from basement conductors, andrelatively small variations in overburden conductivity or thickness can themselves generate significant VLF anomalies. For this reason, VLF is more effective in areas where the host rock is resistive and the overburden is thin.

In the VLF method, two orthogonal components of the magnetic field were measured, and normally the tilt angle, α, and ellipticity, *e*, of the vertical magnetic polarization ellipse are derived. Real (in-phase) and imaginary (quadrature) are used in the Karous – Hjelt Fraser filter (KHFFILT) programme. These components are based on the tilt angle, (α) and ellipticity *(e)* as:


Re =tan (α) 100% and Im = e 100%. (1)

\*AMP = AmphiboliteGMU = Gneiss and Migmatite Undifferentiated

QQS = Quartzite/Quartz Schist SEC= Schist and Epidiorite Complex

Table 5. Geoelectric layer parameters of the study area

Integrated Geochemical and Geophysical Approach to

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 83

Fig. 7. The VLF – EM filtered real profiles for the four West – East traverses

Fig. 6. The geochemical anomalous zone is enclosed by the rectangle with dashed lines on the geological map (a) and the geophysical traverses and locations on the zone (b).

The real and imaginary data values were first plotted using the Microsoft Excel. Next was the plot using the KHFFILT programme (Pirttijarvi, 2004) to obtain the Fraser - filtered plot and the Karous – Hjelt filtered pseudo-section.

The Fraser and Karous – Hjelt filtering are the two methods widely used in processing VLF –EM data (Fraser, 1969: Karous and Hjelt, 1983). The Fraser filter transforms the zerocrossing points into positive peaks which indicate conductive structures. The Karous – Hjelt filter is also used to obtain relative current density pseudo-sections, in which lower values of relative current density correspond to higher values of resistivity (Benson et al., 1997). The areas of high current density (represented in red colour) flow correspond to positive values and low current density (in blue colour) flow to negative values on the accompanying colour scale (for example see Figure 8).

#### **5.3.1 The four west – east VLF (EM) profiles**

The filtered response for the four West – East profiles are presented as in Figure 7 based on their respective locations in Figure 6 to correlate and describe the fractures across the area with the geochemical anomaly. The magnitude of the filtered response is varied along the four profiles due to the nature of the conductivity of the underlying materials. It is clear that the response along Olorombo to Ibode (7a) differs from those along Gada to Iwikun, Okeipa to Eyinta and that of Itagunmodi to Aiyetoro which are similar (Figures (7 b– d)).

The positive peaks labeled F1 is seen to occur across the three profiles in Figures 7 b,7c and 7d. It occurs at about station 1000m along each profile on the Amphibolite. This shows that the linear feature, interpreted as mineralized fracture is consistent in occurrence in the Amphibolite. The positive peaks labeled F2 and F3 are observed to cut across the three profiles also on the Amphibolite as shown in Figures 7 c and 7 d. The linear feature labeled F4 is observed to be consistent in occurrence in Figures 7c and 7d and actually lie near the boundaries of the amphibolites and gneiss/migmatite Undifferentiated rocks (Figure 7c) and amphibolites and quartzite/quartz schist rocks (Figure 7d). The linear feature labeled F4 is not visible in Figure 7b due largely to the nature of the material hosted by the gneiss/migmatite Undifferentiated and the schist/epidiorite complex rocks along this profile.

Fig. 6. The geochemical anomalous zone is enclosed by the rectangle with dashed lines on the geological map (a) and the geophysical traverses and locations on the zone (b).

and the Karous – Hjelt filtered pseudo-section.

accompanying colour scale (for example see Figure 8).

**5.3.1 The four west – east VLF (EM) profiles** 

The real and imaginary data values were first plotted using the Microsoft Excel. Next was the plot using the KHFFILT programme (Pirttijarvi, 2004) to obtain the Fraser - filtered plot

The Fraser and Karous – Hjelt filtering are the two methods widely used in processing VLF –EM data (Fraser, 1969: Karous and Hjelt, 1983). The Fraser filter transforms the zerocrossing points into positive peaks which indicate conductive structures. The Karous – Hjelt filter is also used to obtain relative current density pseudo-sections, in which lower values of relative current density correspond to higher values of resistivity (Benson et al., 1997). The areas of high current density (represented in red colour) flow correspond to positive values and low current density (in blue colour) flow to negative values on the

The filtered response for the four West – East profiles are presented as in Figure 7 based on their respective locations in Figure 6 to correlate and describe the fractures across the area with the geochemical anomaly. The magnitude of the filtered response is varied along the four profiles due to the nature of the conductivity of the underlying materials. It is clear that the response along Olorombo to Ibode (7a) differs from those along Gada to Iwikun, Okeipa

The positive peaks labeled F1 is seen to occur across the three profiles in Figures 7 b,7c and 7d. It occurs at about station 1000m along each profile on the Amphibolite. This shows that the linear feature, interpreted as mineralized fracture is consistent in occurrence in the Amphibolite. The positive peaks labeled F2 and F3 are observed to cut across the three profiles also on the Amphibolite as shown in Figures 7 c and 7 d. The linear feature labeled F4 is observed to be consistent in occurrence in Figures 7c and 7d and actually lie near the boundaries of the amphibolites and gneiss/migmatite Undifferentiated rocks (Figure 7c) and amphibolites and quartzite/quartz schist rocks (Figure 7d). The linear feature labeled F4 is not visible in Figure 7b due largely to the nature of the material hosted by the gneiss/migmatite

to Eyinta and that of Itagunmodi to Aiyetoro which are similar (Figures (7 b– d)).

Undifferentiated and the schist/epidiorite complex rocks along this profile.

Fig. 7. The VLF – EM filtered real profiles for the four West – East traverses

Integrated Geochemical and Geophysical Approach to

Fig. 8. The VLF – EM pseudosection for the four West – East traverses

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 85

Figure 8 is the pseudosections for the four West – East profiles. The figure shows the character of the labeled linear features earlier discussed. The linear feature labeled F1 is observed to be dipping conductors (as are observed on the Amphiboliteat about station 1000m) in all the three traverses of Gada to Iwikun, Okeipa to Eyinta and Itagunmodi to Aiyetoro. These are seen to have values thatrange between 15% and 70%. The occurrence of these dipping fractures from near the surface to depth of 100m and approximately along the N – S direction suggest that it is one and the same linear feature which cuts across the study area. The other fractures (F2 and F3) also on the amphibolites which are almost vertical and at between stations 3000m and 4000m occur at a depth range of 20 -70m are also one and the same linear features which cut across along N – S direction in the Amphibolite. Vertical conductive structures are also observed in the schist/epidiorite Complex and inthe quartzite/quartz schist rocks. The occurrence of these linear features in the study area has implications for mineralization, geotechnical and groundwater studies (Palacky,1988). Minerals that are structurally controlled such as lateritic nickel, gold, talc and clay deposits can be prospected along the identified linear features.

#### **5.4 The magnetic data, analysis and results**

Magnetism has been studied for a very long time in human history. Early Greek philosophers knew about the attraction of iron to a magnet. The first magnets consisted of a naturally occurring rock called lodestone, a variety of massive magnetite (almost pure iron oxide). Magnetite is the only naturally occurring mineral with distinctly obvious magnetic properties. Only a few other minerals have any detectable magnetism. However, extremely sensitive magnetometers can detect trace magnetism in many different minerals. Iron, because of its atomic structure, has the greatest tendency to become magnetized. Other elements, such as cobalt and nickel, have fewer tendencies to become magnetic. Any mineral or rock which contains any of these elements is likely be more magnetic.

The Earth possesses a magnetic field caused primarily by sources in the core. The form of the field is roughly the same as would be caused by a dipole or bar magnet located near the Earth's center and aligned sub-parallel to the geographic axis. The intensity of the Earth's field is customarily expressed in S. I. units as nanotesla (nT) or in an older unit, gamma (γ):1 γ = 1 nT = 10-3 μT. Except for local perturbations, the intensity of the Earth's field can vary between about 25 and 80 μT. Many rocks and minerals are weakly magnetic or are magnetized by induction in the Earth's field, and cause spatial perturbations or "anomalies" in the Earth's main field. Man-made objects containing iron or steel are often highly magnetized and locally can cause large anomalies up to several thousands of nT. Magnetic methods are generally used to map the location and size of objects that have magnetic properties.

In order to produce a magnetic anomaly map of a region, the data have to be corrected to take into account the effect of latitude and, to a lesser extent, longitude (Reynolds, 1997). As the Earth's magnetic field strength varies from 25000nT at the magnetic equator to 69000nT at the poles, the increase in magnitude with latitude needs to be taken into account. Survey data at any given location can be corrected by subtracting the theoretical field value Fth, obtained from the International Geomagnetic Reference Field, from the measured value, Fobs. Regional latitudinal (φ) and longitudinal (θ) gradients can be determined for areas concerned and tied to a base value, Fo. Gradients northwards (δF/δφ) and westwards

Figure 8 is the pseudosections for the four West – East profiles. The figure shows the character of the labeled linear features earlier discussed. The linear feature labeled F1 is observed to be dipping conductors (as are observed on the Amphiboliteat about station 1000m) in all the three traverses of Gada to Iwikun, Okeipa to Eyinta and Itagunmodi to Aiyetoro. These are seen to have values thatrange between 15% and 70%. The occurrence of these dipping fractures from near the surface to depth of 100m and approximately along the N – S direction suggest that it is one and the same linear feature which cuts across the study area. The other fractures (F2 and F3) also on the amphibolites which are almost vertical and at between stations 3000m and 4000m occur at a depth range of 20 -70m are also one and the same linear features which cut across along N – S direction in the Amphibolite. Vertical conductive structures are also observed in the schist/epidiorite Complex and inthe quartzite/quartz schist rocks. The occurrence of these linear features in the study area has implications for mineralization, geotechnical and groundwater studies (Palacky,1988). Minerals that are structurally controlled such as lateritic nickel, gold, talc and clay deposits

Magnetism has been studied for a very long time in human history. Early Greek philosophers knew about the attraction of iron to a magnet. The first magnets consisted of a naturally occurring rock called lodestone, a variety of massive magnetite (almost pure iron oxide). Magnetite is the only naturally occurring mineral with distinctly obvious magnetic properties. Only a few other minerals have any detectable magnetism. However, extremely sensitive magnetometers can detect trace magnetism in many different minerals. Iron, because of its atomic structure, has the greatest tendency to become magnetized. Other elements, such as cobalt and nickel, have fewer tendencies to become magnetic. Any mineral

The Earth possesses a magnetic field caused primarily by sources in the core. The form of the field is roughly the same as would be caused by a dipole or bar magnet located near the Earth's center and aligned sub-parallel to the geographic axis. The intensity of the Earth's field is customarily expressed in S. I. units as nanotesla (nT) or in an older unit, gamma (γ):1 γ = 1 nT = 10-3 μT. Except for local perturbations, the intensity of the Earth's field can vary between about 25 and 80 μT. Many rocks and minerals are weakly magnetic or are magnetized by induction in the Earth's field, and cause spatial perturbations or "anomalies" in the Earth's main field. Man-made objects containing iron or steel are often highly magnetized and locally can cause large anomalies up to several thousands of nT. Magnetic methods are generally used to map the location and size of objects that have magnetic

In order to produce a magnetic anomaly map of a region, the data have to be corrected to take into account the effect of latitude and, to a lesser extent, longitude (Reynolds, 1997). As the Earth's magnetic field strength varies from 25000nT at the magnetic equator to 69000nT at the poles, the increase in magnitude with latitude needs to be taken into account. Survey data at any given location can be corrected by subtracting the theoretical field value Fth, obtained from the International Geomagnetic Reference Field, from the measured value, Fobs. Regional latitudinal (φ) and longitudinal (θ) gradients can be determined for areas concerned and tied to a base value, Fo. Gradients northwards (δF/δφ) and westwards

or rock which contains any of these elements is likely be more magnetic.

can be prospected along the identified linear features.

**5.4 The magnetic data, analysis and results** 

properties.

Fig. 8. The VLF – EM pseudosection for the four West – East traverses

Integrated Geochemical and Geophysical Approach to

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 87

Fig. 9. The observed and calculated magnetic profile along Olorombo to Ibode

rock at station 400m.

composition of the basement rocks across the profile.

basement blocks. The contact between bodies represents structural or lithological contacts. The model lithological contacts when correlated with the known geology show afair correlation. The model result suggests a westward shift in the geological boundary. The model also revealed the existence of a Quartz vein (s = 35 SI Unit) sandwiched between the Amphibolite and the Gneiss/Migmatite Undifferentiated rocks at stations between 2400 – 2600m along the profile. The model reveals the outcropping of the Schist Epidiorite Complex at stations 4100m and 5500m. The overburden is deepest (48m) in the Amphibolite

Figure 11A shows the observed and the calculated anomaly for the magneticprofile along Okepa to Eyinta and the corresponding geologic section in Figure 11B which is on the central part of the delineated area. Three model bodies are involved in the computation and these include the Amphibolite (s = 200 SI unit), Gneiss/Migmatite Undifferentiated (s = 100 SI unit) and Schist Epidiorite Complex (s = 300 SI unit) together with the overburden (s= 5 SI unit) and a dyke body (s=40 SI unit). The contact between bodies represents structural or lithological contacts. The model lithological contacts do not correlate with the known geology probably due to the "masking" effect of the overburden. The model reveals the existence of a dyke body (s = 400 SI unit) in the Quartzite/Quartz Schist rock just before station 6400m. Observed also are the five fractures in the Amphibolite at stations 200, 1400, 1600, 2300 and 3000m along the profile. The modeled basement blocks magnetic susceptibility contrast ranges between 100 – 300 SI units and reflects the variation in the

(δF/δθ) are expressed in nT/km. Consequently the anomalous value of the total field (δF) can be calculated from

$$
\delta \mathbf{F} = \mathbf{F}\_{\text{obs}} - (\mathbf{F}\_o - \frac{\delta \mathbf{F}}{\rho} \Big\langle \delta \boldsymbol{\phi} + \frac{\delta \mathbf{F}}{\delta \boldsymbol{\theta}} \Big\rangle \tag{2}
\tag{2}
$$

Geophysical (Magnetic) traverses over the delineated area are as shown in Figure 6b. In this survey, the total magnetic field was measured. The data reduction involved removing the regional field, reduction to the pole and vertical continuation before the plot of profile along the traverse. Removing the regional field helps to emphasize the magnetic anomaly of interest and this was done by subtracting the known regional field from the measured value. The reduction to the pole helps to change the actual inclination to the vertical. It was performed by convolving the magnetic field with a filter whose wave number response is the product of a polarization-orientation factor and the field –orientation factor (Baranov, 1957; Gunn, 1975; Spector and Grant, 1985). Also the field upward continuation attenuates anomalies caused by local, near – surface sources relative to anomalies caused by deeper more profound sources.

#### **5.4.1 The magnetic models**

Information available from the magnetic profiles along the four West – East traverses, VLF – EM, VES data and the geochemical anomaly are used in the modeling of magnetic data to confirm the existence of the linear features, basement depth (and topography) and the basement tectonic framework which are revealed in the area. The magnetic profiles were modeled using the 2. 5D modeling algorithm of the WingLink software programme (version 1. 62. 08). The profiles which are along the West – East include: Olorombo to Ibode, Gada to Iwikun, Okeipa to Eyinta and Itagunmodi to Aiyetoro. The modelling of these profiles shows very reasonable fit between the observed and the calculated magnetic profiles.

Figure 9A shows the observed and the calculated anomaly for the magnetic profile along Olorombo to Ibode and the corresponding geologic section in Figure 9B. Three model bodies are involved in the computation and these include the Amphibolite (s = 280 SI unit), Gneiss/Migmatite Undifferentiated (s = 300 SI unit) and Schist Epidiorite Complex (s = 100 SI unit) together with the overburden (s= 5 SI unit). The contact between the rock types may represent structural or lithological contacts especially in the area of basement outcrops (El-Shayeb, Personal communication). The model lithological contacts when correlated with the known geology shows that the contact between the Amphibolite and the Gneiss/Migmatite Undifferentiated partly correlated but the contact between the Gneiss/Migmatite Undifferentiated and the Schist Epidiorite does not correlate with the known geology. An overburden thickness of 2m is observed on theGneiss/Migmatite Undifferentiated rock at station 750m while the thickness is 1. 5m in the Schist Epidiorite Complex rock. The overburden is deepest (14m) in the Gneiss/Migmatite Undifferentiated rock at station 1350m.

Figure 10A shows the observed and the calculated anomaly for the magneticprofile along Gada to Iwikun and the corresponding geologic section in Figure 10B which is on the central part of the delineated area. Three model bodies are involved in the computation and these include the Amphibolite (s = 250 SI unit), Gneiss/Migmatite Undifferentiated (s = 130 SI unit) and Schist Epidiorite Complex (s = 150 SI unit) together with the overburden (s= 10 SI unit) and a Quartz vein (s=35 SI unit). The model has three bodies representing the three

(δF/δθ) are expressed in nT/km. Consequently the anomalous value of the total field (δF)

Geophysical (Magnetic) traverses over the delineated area are as shown in Figure 6b. In this survey, the total magnetic field was measured. The data reduction involved removing the regional field, reduction to the pole and vertical continuation before the plot of profile along the traverse. Removing the regional field helps to emphasize the magnetic anomaly of interest and this was done by subtracting the known regional field from the measured value. The reduction to the pole helps to change the actual inclination to the vertical. It was performed by convolving the magnetic field with a filter whose wave number response is the product of a polarization-orientation factor and the field –orientation factor (Baranov, 1957; Gunn, 1975; Spector and Grant, 1985). Also the field upward continuation attenuates anomalies caused by local, near – surface sources relative to anomalies caused by deeper

Information available from the magnetic profiles along the four West – East traverses, VLF – EM, VES data and the geochemical anomaly are used in the modeling of magnetic data to confirm the existence of the linear features, basement depth (and topography) and the basement tectonic framework which are revealed in the area. The magnetic profiles were modeled using the 2. 5D modeling algorithm of the WingLink software programme (version 1. 62. 08). The profiles which are along the West – East include: Olorombo to Ibode, Gada to Iwikun, Okeipa to Eyinta and Itagunmodi to Aiyetoro. The modelling of these profiles shows very reasonable fit between the observed and the calculated magnetic profiles. Figure 9A shows the observed and the calculated anomaly for the magnetic profile along Olorombo to Ibode and the corresponding geologic section in Figure 9B. Three model bodies are involved in the computation and these include the Amphibolite (s = 280 SI unit), Gneiss/Migmatite Undifferentiated (s = 300 SI unit) and Schist Epidiorite Complex (s = 100 SI unit) together with the overburden (s= 5 SI unit). The contact between the rock types may represent structural or lithological contacts especially in the area of basement outcrops (El-Shayeb, Personal communication). The model lithological contacts when correlated with the known geology shows that the contact between the Amphibolite and the Gneiss/Migmatite Undifferentiated partly correlated but the contact between the Gneiss/Migmatite Undifferentiated and the Schist Epidiorite does not correlate with the known geology. An overburden thickness of 2m is observed on theGneiss/Migmatite Undifferentiated rock at station 750m while the thickness is 1. 5m in the Schist Epidiorite Complex rock. The overburden is deepest (14m) in the Gneiss/Migmatite Undifferentiated rock at station

Figure 10A shows the observed and the calculated anomaly for the magneticprofile along Gada to Iwikun and the corresponding geologic section in Figure 10B which is on the central part of the delineated area. Three model bodies are involved in the computation and these include the Amphibolite (s = 250 SI unit), Gneiss/Migmatite Undifferentiated (s = 130 SI unit) and Schist Epidiorite Complex (s = 150 SI unit) together with the overburden (s= 10 SI unit) and a Quartz vein (s=35 SI unit). The model has three bodies representing the three

 

 

(nT) (2)

obs o F F (F F F )

can be calculated from

more profound sources.

1350m.

**5.4.1 The magnetic models** 

Fig. 9. The observed and calculated magnetic profile along Olorombo to Ibode

basement blocks. The contact between bodies represents structural or lithological contacts. The model lithological contacts when correlated with the known geology show afair correlation. The model result suggests a westward shift in the geological boundary. The model also revealed the existence of a Quartz vein (s = 35 SI Unit) sandwiched between the Amphibolite and the Gneiss/Migmatite Undifferentiated rocks at stations between 2400 – 2600m along the profile. The model reveals the outcropping of the Schist Epidiorite Complex at stations 4100m and 5500m. The overburden is deepest (48m) in the Amphibolite rock at station 400m.

Figure 11A shows the observed and the calculated anomaly for the magneticprofile along Okepa to Eyinta and the corresponding geologic section in Figure 11B which is on the central part of the delineated area. Three model bodies are involved in the computation and these include the Amphibolite (s = 200 SI unit), Gneiss/Migmatite Undifferentiated (s = 100 SI unit) and Schist Epidiorite Complex (s = 300 SI unit) together with the overburden (s= 5 SI unit) and a dyke body (s=40 SI unit). The contact between bodies represents structural or lithological contacts. The model lithological contacts do not correlate with the known geology probably due to the "masking" effect of the overburden. The model reveals the existence of a dyke body (s = 400 SI unit) in the Quartzite/Quartz Schist rock just before station 6400m. Observed also are the five fractures in the Amphibolite at stations 200, 1400, 1600, 2300 and 3000m along the profile. The modeled basement blocks magnetic susceptibility contrast ranges between 100 – 300 SI units and reflects the variation in the composition of the basement rocks across the profile.

Integrated Geochemical and Geophysical Approach to

contrast ranges between 280 – 400 SI units.

**6. Discussion and conclusions** 

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 89

Figure 12A shows the observed and the calculated anomaly for the magneticprofile along Itagunmodi to Aiyetoro and the corresponding geologic section in Figure 12B which is on the southern part of the delineated area. Two model bodies are involved in the computation and these include the Amphibolite (s = 280 SI unit), Quartzite/Quartz Schist (s = 400 SI unit) together with the overburden (s= 10 SI unit). The contact between bodies represents structural or lithological contacts. The model lithological contact when correlated with the known geology shows a good correlation. Observed also are many fractures/faults in the Amphibolite along the profile. The modeled basement blocks magnetic susceptibility

Fig. 12. The observed and calculated magnetic profile along Itagunmodi to Aiyetoro

The geochemical data shows an anomaly with elemental association of Fe – Mn, Pb – Cr, and Cd – Zn and trends approximately along the North – South direction. The VLF-EM data revealed the existence of linear features which are interpreted as mineralized fractures, faults and veins. These linear features are consistent across the study area and run approximately in the N – S direction. These structures exist from near the surface to a depth of up to 100m. The magnetic data also mapped the linear features, magnetized bodies (interpreted as dykes) and the geological contacts. The coincidence of electromagnetic (VLF) and magnetic anomalies and their correlation with the geochemical anomaly, especially on the amphibolites, is an indication of the occurrence of sulphide deposits rich in Zn-Pb-Cralong the identified linear features . The geophysical methods engaged have helped to map the structural complexity such as evidence of faulting, mineralized fractures, joints and dykes in the study area. In addition, it is now evident that mineralization is not limited to

Fig. 10. The observed and calculated magnetic profile along Gada to Iwukun

Fig. 11. The observed and calculated magnetic profile along Okepa to Eyinta

Fig. 10. The observed and calculated magnetic profile along Gada to Iwukun

Fig. 11. The observed and calculated magnetic profile along Okepa to Eyinta

Figure 12A shows the observed and the calculated anomaly for the magneticprofile along Itagunmodi to Aiyetoro and the corresponding geologic section in Figure 12B which is on the southern part of the delineated area. Two model bodies are involved in the computation and these include the Amphibolite (s = 280 SI unit), Quartzite/Quartz Schist (s = 400 SI unit) together with the overburden (s= 10 SI unit). The contact between bodies represents structural or lithological contacts. The model lithological contact when correlated with the known geology shows a good correlation. Observed also are many fractures/faults in the Amphibolite along the profile. The modeled basement blocks magnetic susceptibility contrast ranges between 280 – 400 SI units.

Fig. 12. The observed and calculated magnetic profile along Itagunmodi to Aiyetoro

### **6. Discussion and conclusions**

The geochemical data shows an anomaly with elemental association of Fe – Mn, Pb – Cr, and Cd – Zn and trends approximately along the North – South direction. The VLF-EM data revealed the existence of linear features which are interpreted as mineralized fractures, faults and veins. These linear features are consistent across the study area and run approximately in the N – S direction. These structures exist from near the surface to a depth of up to 100m. The magnetic data also mapped the linear features, magnetized bodies (interpreted as dykes) and the geological contacts. The coincidence of electromagnetic (VLF) and magnetic anomalies and their correlation with the geochemical anomaly, especially on the amphibolites, is an indication of the occurrence of sulphide deposits rich in Zn-Pb-Cralong the identified linear features . The geophysical methods engaged have helped to map the structural complexity such as evidence of faulting, mineralized fractures, joints and dykes in the study area. In addition, it is now evident that mineralization is not limited to

Integrated Geochemical and Geophysical Approach to

1007/s12517-010-0175-5

Annu. Rep., pp 14-19.

desert, Egypt 19p

582-589

637.

239 -290

Nigeria Bulletin 23 ; 55p.

Longman Limited. 110p.

*Prospecting* 31, 782–794.

– 86.

Mineral Prospecting – A Case Study on the Basement Complex of Ilesa Area, Nigeria 91

Anhaeusser, C. R., Mason, R., Viljoen, M. J. and Viljoen, R. P. (1969). A reappraisal of some aspects of Precambrian shield Geology. Bull. Geol. Soc. Amer. Vol. 80, 2175-2200 Ariyibi, E. A., Folami S. L., Ako B. D., Ajayi, T. R. and Adelusi, A. O. (2010). Application of

Baranov, V., (1957). A new method for interpretation of aeromagnetic maps: Error analysis

Benson, A. K., Payne, K. L. and Stubben, M. A. (1997). Mapping groundwater contamination

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Mining and groundwater geophysics. Published by The Geological Survey of

within the amphibolites, but also exist in the other rock types. There is an improved delineation of the rock contacts which has hitherto been difficult to map as a result ofdearth of outcrops and the presence of overburden.

Based on the combined geological, geochemical and geophysical data which are available (and the modeled results) and interpreted over the delineated area, a new geological map is proposed for the area. Figure 13 shows the disposition of the prominent linear features, dykes and the inferred mineralized zone found in the area. The fractures are seen to trend approximately in the N – S direction. The frequency of fracturing is a function of rock elastic properties, structure and tectonic history. The rock with high fracture frequency is known to be highly brittle and prone to fracturing. From this study the occurrence of fractures on the Amphibolite is high and so also that on the Quartzite/Quartz Schist and Gneiss/Migmatite Undifferentiated rocks are moderately high. The Quartzites/Quartz Schist isalso strongly magneticprobably due to the occurrence of iron oxides as described by Ajayi (1988).

#### **7. Acknowledgments**

The chapter contribution to the Geoscience Text was done while the author was on Associateship visit to ICTP, Trieste, Italy. The financial and material support by ICTP that ensured the successful completion of the work is greatly acknowledged.

#### **8. References**


within the amphibolites, but also exist in the other rock types. There is an improved delineation of the rock contacts which has hitherto been difficult to map as a result ofdearth

Based on the combined geological, geochemical and geophysical data which are available (and the modeled results) and interpreted over the delineated area, a new geological map is proposed for the area. Figure 13 shows the disposition of the prominent linear features, dykes and the inferred mineralized zone found in the area. The fractures are seen to trend approximately in the N – S direction. The frequency of fracturing is a function of rock elastic properties, structure and tectonic history. The rock with high fracture frequency is known to be highly brittle and prone to fracturing. From this study the occurrence of fractures on the Amphibolite is high and so also that on the Quartzite/Quartz Schist and Gneiss/Migmatite Undifferentiated rocks are moderately high. The Quartzites/Quartz Schist isalso strongly

magneticprobably due to the occurrence of iron oxides as described by Ajayi (1988).

ensured the successful completion of the work is greatly acknowledged.

The chapter contribution to the Geoscience Text was done while the author was on Associateship visit to ICTP, Trieste, Italy. The financial and material support by ICTP that

Adebayo, A. B. (2006). Physico-chemical characteristics of groundwater in two mining areas

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Ajibade, A. C. (1976). Provisional classification and correlation of the Schist Belts

Ako, B. D. Ajayi, T. R. and Alabi, A. O. (1978). A geoelectrical study of the Ifewara area.

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C. A. Kogbe (ed) Geology of Nigeria, Elizabethan Publishing Co. Lagos, pp85 -90.

Department of Geology, Obafemi Awolowo University, Ile- Ife, 80p. Adelusi, A. O. (2005). Multi-method geophysical investigation for groundwater study in

of contrasting lithologies in the Ife-Ilesa Schist Belt. Unpubl. B. Sc. Thesis,

southeastern part of Ilesa area, Osun state Southwestern Nigeria. Ph. D Thesis, Department of Applied Geophysics, Federal University of Technology, Akure. 289p

water samples in ilesa Area and their probable relationships to thesurrounding rock types. M. Sc. Thesis, Department of Geology, Obafemi Awolowo University,

M. Sc. Thesis, Department of Geology, Obafemi Awolowo University, Ile-Ife . 247p

Ilesa Goldfield. Ph. D Thesis. Obafemi Awolowo University, Ile - Ife, Nigeria,

of outcrops and the presence of overburden.

**7. Acknowledgments** 

Ile-Ife . 185p.

ofNorthwestern Nigeria (In)

*Journal of Mining and Geology* 15 (2) p84-89

PhD Thesis, University of Ife, Ile-Ife. 371p

459pp.

**8. References** 


**5** 

*1Algeria 2France* 

**Regularity Analysis of Airborne Natural** 

*1University of Sciences and Technology Houari Boumediene, Algiers, 2Laboratoire Géosciences- University Montpellier 2- CNRS, Montpellier,* 

The airborne Gamma Ray (GR) measurements have been used since decades in geophysical research. The airborne measurement of gamma radiation emitted by naturally occurring elements finds applications in: geological mapping (Graham and Bonham-Carter, 1993; Jaques *et al.*, 1997; Doll *et al.*, 2000, Aydin *et al.,* 2006; Sulekha Rao *et al.*, 2009), regolith and soil mapping (Cook *et al.*, 1996; Wilford *et al.*, 1997; Bierwirth and Welsh, 2000), mineral exploration (Brown *et al.*, 2000), and hydrocarbon research (Matolín and Stráník, 2006). Potassium (K), Uranium (U) and Thorium (Th) are the three most abundant, naturally occurring radioactive elements. The K element is the main component of mineral deposits, while Uranium and Thorium are present in trace amounts, as mobile and immobile elements, respectively. The concentration of these different radioelements varies between different rock types, thus the information provided by a gamma-ray spectrometer can be exploited for needs of the rocks cartography. The obtained maps allow to localize

radioelement anomalies corresponding to zones disrupted by a mineralizing system.

measurements recorded over the Hoggar area (Algeria).

and some information about heterogeneities is lost.

The approach presented in this chapter deepens the results derived from the conventional study. It consists on a mono(two)-dimensional fractal analysis of natural radioactivity

The natural radioactivity measurements, like other geophysical signals, contain a deterministic and a stochastic components. The former part holds information related to the regional aspect, while the latter reflects the local heterogeneities. As the raw spectrometric data need to be processed before any exploitation, the stochastic component can be altered

Here, we show first the fractal behavior of the analyzed GR measurements. In addition, it is demonstrated that this behavior is not affected by all the pre-processing operations (spectrometric corrections and 2D-interpolations). The corrections are not then necessary. Since the analyzed data exhibit a fractal exponent varying with the spatial position, they are modeled as paths of multifractional Brownian motions (mBms) (Peltier and Lévy-Véhel,

**1. Introduction** 

1995).

**Gamma Ray Data Measured in** 

**the Hoggar Area (Algeria)** 

and Mohamed Hamoudi1

Saïd Gaci1, Naïma Zaourar1, Louis Briqueu2

Nigeria. Presented at the Conference on African geology, University of Ibadan July 1978.


Wing Link Integrated Geosystem software version 1. 62. 08 – 20030519. Microsoft Corp. 23p

Wright, J. B. and McCurry, P. (1970). A reappraisal of some aspects of the Precambrian shield geology. A discussion. *Bulletin of Geological Society of America*, 81: 3491 – 3492.

## **Regularity Analysis of Airborne Natural Gamma Ray Data Measured in the Hoggar Area (Algeria)**

Saïd Gaci1, Naïma Zaourar1, Louis Briqueu2 and Mohamed Hamoudi1

*1University of Sciences and Technology Houari Boumediene, Algiers, 2Laboratoire Géosciences- University Montpellier 2- CNRS, Montpellier, 1Algeria 2France* 

#### **1. Introduction**

92 Advances in Data, Methods, Models and Their Applications in Geoscience

Klemm, D. D., Schneider, W. and Wagner, B., (1984). Precambrian metavolcano –

Mazzullo, J. (1996). Investigations into Physical geology, A laboratory manual. Saunders

Northern Nigeria – A review, in C. A. Kogbe (ed) Geology of Nigeria. Elizabethan pub. Co.,

Olorunfemi, B. N. (1977). A geochemical soil survey in the Ife-Ifewara- Ogudu Area of Oyo State, Nigeria. M. Sc. Thesis, Department of Geology, University of Ife99pp. Oyawoye, M. O. (1964). Geology of the Nigerian Basement Complex – A survey of our

Palacky, G. J., (1988). Resistivity characteristics of geologic targets. Electromagnetic Methods

Pirttijärvi, M., (2004). Karous–Hjelt and Fraser filtering of VL measurements. Manual of the

Rahaman, M. A. (1976). Review of the basement Geology of southwesternNigeria. Geology

Rahaman, M. A. (1988). Recent advances in the study of the Basement Complex of Nigeria.

Reynolds, J. M. (1997). An introduction to applied and environmental geophysics. John

Spector, A., and F. S. Grant. (1985). Statistical models for interpreting magnetic data,

Suh, C. E. (1993). Primary metal dispersion patterns for gold exploration in the

Wing Link Integrated Geosystem software version 1. 62. 08 – 20030519. Microsoft Corp. 23p Wright, J. B. and McCurry, P. (1970). A reappraisal of some aspects of the Precambrian

Amphibolites of Ife – Ilesa schist belt. M. Sc. Thesis. Department of Geology,

shield geology. A discussion. *Bulletin of Geological Society of America*, 81: 3491 – 3492.

present knowledge of them. Journal of Mining Geology and Metal vol. 1 no 2pp87

McCurry, P. (1976). The geology of the Precambrian to lower Paleozoic rocks of

Milsom, J. (1989). Field Geophysics: Milton Keynes: Open university press. 172p

in Applied Geophysics, vol. 1. SEG, Tulsa, OK, pp. 106–121.

Russ, P. (1957). Airborne electromagnetics in review. *Geophysics*, 22 691-713

Kogbe, C. A.; (Ed). Elizabethan Publ. Co., Lagos, Nigeria. 41-58.

Precambrian Geology of Nigeria. Pp 11 - 39

Obafemi Awolowo University, Ile -Ife. 145p

*Journal of African Earth Sciences*, 2 (2) : 161 – 176.

College Publishing 361p.

KHFFILT Program. 26p

Wiley and sons. 796p.

*Geophysics*, 35, 293- 302,

Lagos, pp 15- 40.

1978.

– 103.

of Nigeria,

Nigeria. Presented at the Conference on African geology, University of Ibadan July

sedimentary sequence east of Ife and Ilesa, S. W. Nigeria – A Nigerian Schist belt?

The airborne Gamma Ray (GR) measurements have been used since decades in geophysical research. The airborne measurement of gamma radiation emitted by naturally occurring elements finds applications in: geological mapping (Graham and Bonham-Carter, 1993; Jaques *et al.*, 1997; Doll *et al.*, 2000, Aydin *et al.,* 2006; Sulekha Rao *et al.*, 2009), regolith and soil mapping (Cook *et al.*, 1996; Wilford *et al.*, 1997; Bierwirth and Welsh, 2000), mineral exploration (Brown *et al.*, 2000), and hydrocarbon research (Matolín and Stráník, 2006).

Potassium (K), Uranium (U) and Thorium (Th) are the three most abundant, naturally occurring radioactive elements. The K element is the main component of mineral deposits, while Uranium and Thorium are present in trace amounts, as mobile and immobile elements, respectively. The concentration of these different radioelements varies between different rock types, thus the information provided by a gamma-ray spectrometer can be exploited for needs of the rocks cartography. The obtained maps allow to localize radioelement anomalies corresponding to zones disrupted by a mineralizing system.

The approach presented in this chapter deepens the results derived from the conventional study. It consists on a mono(two)-dimensional fractal analysis of natural radioactivity measurements recorded over the Hoggar area (Algeria).

The natural radioactivity measurements, like other geophysical signals, contain a deterministic and a stochastic components. The former part holds information related to the regional aspect, while the latter reflects the local heterogeneities. As the raw spectrometric data need to be processed before any exploitation, the stochastic component can be altered and some information about heterogeneities is lost.

Here, we show first the fractal behavior of the analyzed GR measurements. In addition, it is demonstrated that this behavior is not affected by all the pre-processing operations (spectrometric corrections and 2D-interpolations). The corrections are not then necessary. Since the analyzed data exhibit a fractal exponent varying with the spatial position, they are modeled as paths of multifractional Brownian motions (mBms) (Peltier and Lévy-Véhel, 1995).

Regularity Analysis of Airborne Natural

 Two types of planes : Douglas DC-3. Aero Commander.

**3. Overview on the analyzed GR measurements** 

research and the regional geological mapping. The technical characteristics of the survey are:

Navigation System: Doppler type A DRA-12

Camera with a continuous 35 mm-film

magnetic tapes of 1/2".

Two types of magnetometers:

(Th) and Potassium (K).

Background corrections

spectrometry),

formulae:

average it is about two kilometers.

Compton) effect and height effect (IAEA, 2003).

There are three components of the background correction:

atoms and molecules in the upper atmosphere.

Magnetic Compass of type Sperry CL 2, with a resolution of 1°.

magnetic and spectrometric profiles respectively.

Magnetometer Flow-gate of a resolution of 0.5 NT.

resolution of 0.02 NT (nano Tesla).

Radar altimeter with an accuracy of 30 feet (type Honeywell Minneapolis).

Gamma Ray Data Measured in the Hoggar Area (Algeria) 95

The analyzed GR measurements are recorded during a magneto-spectrometric survey accomplished, between 1971 and 1974 over the Hoggar, for the purpose of the mining

Acquisition system of data (type Lancer) for the recording of the numerical data on

Two types of graphic recorders: with 2 and 6 channels for the graphic monitoring of the

NaI(Tl) spectrometer with four (04) channels: Total Count (TC), Uranium (U), Thorium

The distance between lines varies from 2 to 5 kilometers according to the areas, but on

The measurements acquired during an airborne spectrometric survey can not be exploited in a raw state, but need to be corrected mainly from aircraft background, stripping (or

The instrument background (called ''aircraft background'' in airborne gamma

The cosmic background arisen from the reaction of primary cosmic radiation with

 The effect of atmospheric radon. In portable or car-borne gamma ray surveys, the background component is usually small relative to the signal from the ground. The observed count rates in the four channels: Total Count (TC), Potassium (K), Uranium (U) and Thorium (Th), are corrected for the background effects using the following

The parameters of airborne spectrometric survey carried out over the Hoggar area are:

The distance between the observation points is approximately 46.2 m (152 feet).

 The average of the flight height is fixed at 500 feet (approximately 150 m). The direction of the profiles: perpendicular to the geological structures.

**4. Corrections of the airborne natural activity measurements** 

Magnetometer with optical pumping with the Cesium (model VARIAN) of

The local Hölder exponent (or local regularity) maps obtained from the GR data recorded in the K, Th and U channels, using a multiple filter technique that we generalize to a 2D-case, exhibit almost an identical image. Besides, they allow to locate the faults affecting the studied zone.

#### **2. Regional geology**

The Hoggar is a large shield area covering approximately 550,000 km2. It includes an important surface of the Tergui shield, prolonged in South-east, in Mali, by the solid mass of Iforas and in the East, in Niger, by the solid mass of Aïr (Fig. 1).

The Hoggar belongs to the Trans-Saharan pan-African chain (Cahen *et al.*, 1984, Liégeois *et al*., 1994). It is crossed by two major submeridian faults, located at longitudes 4°50' and 8°30', which delimit three longitudinal compartments (Eastern, Central and Western), with different structural and lithological characteristics. This geological configuration resulted by an extreme E-W compression, during the pan-African (600 My), of the Touareg shield by two rigid plates: the Western African craton and the Eastern African craton (Bertrand and Caby, 1978; Black *et al.*, 1979).

**1** - Archaean granulites; **2** - Gneiss and metasediments, series of Arechchoum (Pr1); **3** - Gneiss with facies amphibole, series of Aleskod (Pr2); **4** - Indif. gneiss (Pr3); **5** - Pharusian Greywackes; **6** - Arkoses and conglomerates, series of Tiririne (Pr4); **7** - Volcano-sediments of Tafassasset (Pr4); **8** - Molasses (purple series) of Cambrian; **9** – Pan-African syn-orogenic granites; **10** - Pan-African Granites; **11** - Pan-African post-orogenic granites; **12** - Granites of Eastern Hoggar; **13** - Late pan-African Granites; **14** - Basalts and recent volcanism; **15** - Paleozoic cover; **16** - Fault.

Fig. 1. A simplified geological map of the Hoggar (Caby *et al.*, 1981, modified)

### **3. Overview on the analyzed GR measurements**

The analyzed GR measurements are recorded during a magneto-spectrometric survey accomplished, between 1971 and 1974 over the Hoggar, for the purpose of the mining research and the regional geological mapping.

The technical characteristics of the survey are:

Two types of planes :

94 Advances in Data, Methods, Models and Their Applications in Geoscience

The local Hölder exponent (or local regularity) maps obtained from the GR data recorded in the K, Th and U channels, using a multiple filter technique that we generalize to a 2D-case, exhibit almost an identical image. Besides, they allow to locate the faults affecting the

The Hoggar is a large shield area covering approximately 550,000 km2. It includes an important surface of the Tergui shield, prolonged in South-east, in Mali, by the solid mass of

The Hoggar belongs to the Trans-Saharan pan-African chain (Cahen *et al.*, 1984, Liégeois *et al*., 1994). It is crossed by two major submeridian faults, located at longitudes 4°50' and 8°30', which delimit three longitudinal compartments (Eastern, Central and Western), with different structural and lithological characteristics. This geological configuration resulted by an extreme E-W compression, during the pan-African (600 My), of the Touareg shield by two rigid plates: the Western African craton and the Eastern African craton (Bertrand and

**Central Hoggar** 

**Eastern Hoggar** 

**1** - Archaean granulites; **2** - Gneiss and metasediments, series of Arechchoum (Pr1); **3** - Gneiss with facies amphibole, series of Aleskod (Pr2); **4** - Indif. gneiss (Pr3); **5** - Pharusian Greywackes; **6** - Arkoses and conglomerates, series of Tiririne (Pr4); **7** - Volcano-sediments of Tafassasset (Pr4); **8** - Molasses (purple series) of Cambrian; **9** – Pan-African syn-orogenic granites; **10** - Pan-African Granites; **11** - Pan-African post-orogenic granites; **12** - Granites of Eastern Hoggar; **13** - Late pan-African Granites;

Fig. 1. A simplified geological map of the Hoggar (Caby *et al.*, 1981, modified)

**14** - Basalts and recent volcanism; **15** - Paleozoic cover; **16** - Fault.

Iforas and in the East, in Niger, by the solid mass of Aïr (Fig. 1).

**Western Hoggar** 

studied zone.

**2. Regional geology** 

Caby, 1978; Black *et al.*, 1979).

	- Magnetometer with optical pumping with the Cesium (model VARIAN) of resolution of 0.02 NT (nano Tesla).
	- Magnetometer Flow-gate of a resolution of 0.5 NT.

The parameters of airborne spectrometric survey carried out over the Hoggar area are:


#### **4. Corrections of the airborne natural activity measurements**

The measurements acquired during an airborne spectrometric survey can not be exploited in a raw state, but need to be corrected mainly from aircraft background, stripping (or Compton) effect and height effect (IAEA, 2003).

Background corrections

There are three components of the background correction:


The observed count rates in the four channels: Total Count (TC), Potassium (K), Uranium (U) and Thorium (Th), are corrected for the background effects using the following formulae:

$$\begin{aligned} \text{TC}\_{corr} &= \text{TC}\_{obs} - \text{BC}\_{TC} \\ \text{K}\_{corr} &= \text{K}\_{obs} - \text{BC}\_{K} \\ \text{LI}\_{corr} &= \text{II}\_{obs} - \text{BC}\_{II} \\ \text{Th}\_{corr} &= \text{Th}\_{obs} - \text{BC}\_{Th} \end{aligned} \tag{1}$$

Regularity Analysis of Airborne Natural

**gamma ray measurements** 

local regularity analysis.

for each data profile.

the increment process:

Gamma Ray Data Measured in the Hoggar Area (Algeria) 97

Once all the corrections are applied, the corrected measurements grid is regrided using twodimensional interpolation algorithms to get a regular sampled grid which is processed by a

The set of operations (corrections and interpolations) affects the stochastic component of the raw airborne spectrometric measurements, which holds information about heterogeneities.

In the first stage, we have obtained the ''corrected'' and the ''corrected and interpolated'' data grids from the ''raw'' grid data corresponding to the measurements of the three channels: K, Th and U. The 2D-interpolation algorithms used in this study are: the trianglebased linear, the triangle-based cubic and the nearest neighbor interpolation algorithms. Since the results obtained by the different interpolation methods are close, only those related

First, five vertical profiles are extracted from the three considered grids (''raw'', ''corrected'' and ''corrected and interpolated '' grids) from the measurements of the three channels (Fig.2). The Fourier amplitude spectrum and the local Hölder exponent *H*(*x*) are computed

Fig. 2. Position of the five profiles extracted from the GR measurements (in red).

Regarding the computation of *H*(*x*), we need a sequence *Sk,n*(*i*) defined by the local growth of

1

, *1<k<n* (4)

**2 3 4 5** 

Profile

 2 2

*j i k ,i k <sup>m</sup> S i <sup>X</sup> <sup>j</sup> <sup>X</sup> <sup>j</sup>*

*n*

(The geological map of the Hoggar, from Caby *et al.*, 1981).

**<sup>1</sup>**(1) western branch (pharusian chain)

(2) central branch (pharusian chain) (3) In-ouzzal mole (Western Hoggar) (4) Issalane mole (Eastern Hoggar)

Major accident Suture zone Palaeozoic cover

1 *k ,n*

Therefore the fractal properties of the raw data may be changed.

to the triangle-based linear algorithm are presented.

**5. Impact of the pre-processings on the fractal properties of the airborne** 

where all these values are expressed in counts per second (cps). *TCcorr*, *Kcorr*, *Ucorr* and *Thcorr* : Values of the corrected count rates in the four channels, *TCobs*, *Kobs*, *Uobs* and *Thobs* : Values of the observed count rates in the four channels, *BCTC*, *BCK*, *BCU* and *BCTh* : Values of the background correction in the four channels. In this case, the estimated values are (Groune, 2009): *BCTC* = 250 cps, *BCK* = 72 cps, *BCU* = 17 cps and *BCTh* = 5 cps.

#### Stripping correction

This correction, also known as the channel interaction correction, consists of removing ('strips') count rates from each of the K, U and Th for gamma rays not originating from the radioelement or decay series being monitored. For example, Th series gamma rays appear in both the U and K channels, and U series gamma rays appear in the K channel. The corrections are given by:

$$\begin{aligned} \mathsf{U}I\_{corr} &= \mathsf{U}\_{obs} - \alpha \, \mathsf{T}\mathfrak{h}\_{obs} \\ \mathsf{K}\_{corr} &= \mathsf{K}\_{obs} - \beta \, \mathsf{T}\mathfrak{H}\_{obs} - \gamma \, \mathsf{U}I\_{obs} \end{aligned} \tag{2}$$

*Kcorr* and *Ucorr* : Values of the corrected count rates in the K and U channels respectively. *Kobs*, *Uobs* and *Thobs* : Values of the observed count rates in the K, U and Th channels respectively.

 *,* and : Stripping coefficients. The used coefficients in this application are (Aeroservice, 1975): 0 45 *.* , 0 59 *.* and 0 94 *. .*

#### Height correction

This correction is applied only on airborne gamma spectrometric measurements. The gamma radiation decreases exponentially with the elevation. Since the height of the aircraft changes continuously, the airborne Gamma Ray spectrometric data need to be corrected to a nominal survey height above the ground.

$$\begin{aligned} TC\_{corr} &= TC\_{obs} \exp\left[\mu\_{TC} \left(h - h\_0\right)\right] \\ K\_{corr} &= K\_{obs} \exp\left[\mu\_K \left(h - h\_0\right)\right] \\ L\_{corr} &= L\_{obs} \exp\left[\mu\_{U} \left(h - h\_0\right)\right] \\ Th\_{corr} &= Th\_{obs} \exp\left[\mu\_{Th} \left(h - h\_0\right)\right] \end{aligned} \tag{3}$$

*TCcorr*, *Kcorr*, *Ucorr* and *Thcorr* : Values of the corrected count rates in the four channels, *TCobs*, *Kobs*, *Uobs* and *Thobs* : Values of the observed count rates in the four channels, *h* : Real survey height ,

*h0* : Nominal survey height (*h0*=150 m),

*μTC*, *μK*, *μU* and *μTh* : Linear attenuation coefficients in the four channels. The estimated values of these coefficients are (Groune, 2009) : *μK* = 6.8617 10-3 m-1, *μU* = 6.3726 10-3 m-1 , and *μTh* = 5.2247 10-3 m-1 *.* The *μTC* is calculated as the approximate average of the three coefficients: *μTC* = 6.56 10-3 m-1 .

*corr obs TC corr obs K corr obs U corr obs Th*

(1)

(3)

 

*BCTC*, *BCK*, *BCU* and *BCTh* : Values of the background correction in the four channels. In this case, the estimated values are (Groune, 2009): *BCTC* = 250 cps, *BCK* = 72 cps, *BCU* = 17 cps and

This correction, also known as the channel interaction correction, consists of removing ('strips') count rates from each of the K, U and Th for gamma rays not originating from the radioelement or decay series being monitored. For example, Th series gamma rays appear in both the U and K channels, and U series gamma rays appear in the K channel. The

*corr obs obs*

*Kcorr* and *Ucorr* : Values of the corrected count rates in the K and U channels respectively. *Kobs*, *Uobs* and *Thobs* : Values of the observed count rates in the K, U and Th channels

*U U Th*

*corr obs obs obs*

*,* and : Stripping coefficients. The used coefficients in this application are (Aeroservice,

This correction is applied only on airborne gamma spectrometric measurements. The gamma radiation decreases exponentially with the elevation. Since the height of the aircraft changes continuously, the airborne Gamma Ray spectrometric data need to be corrected to a

exp

*μTC*, *μK*, *μU* and *μTh* : Linear attenuation coefficients in the four channels. The estimated values of these coefficients are (Groune, 2009) : *μK* = 6.8617 10-3 m-1, *μU* = 6.3726 10-3 m-1 , and *μTh* = 5.2247 10-3 m-1 *.* The *μTC* is calculated as the approximate average of the three

 

*TC TC h h K K hh U U hh Th Th h h*

exp exp exp

*corr obs K corr obs U corr obs Th*

*TCcorr*, *Kcorr*, *Ucorr* and *Thcorr* : Values of the corrected count rates in the four channels, *TCobs*, *Kobs*, *Uobs* and *Thobs* : Values of the observed count rates in the four channels,

*corr obs TC*

0

 

0 0 0

(2)

*K K Th U* 

*TC TC BC K K BC U U BC Th Th BC*

*TCcorr*, *Kcorr*, *Ucorr* and *Thcorr* : Values of the corrected count rates in the four channels, *TCobs*, *Kobs*, *Uobs* and *Thobs* : Values of the observed count rates in the four channels,

where all these values are expressed in counts per second (cps).

*BCTh* = 5 cps.

respectively.

Height correction

*h* : Real survey height ,

Stripping correction

corrections are given by:

1975): 0 45 *.* , 0 59 *.* and 0 94 *. .*

nominal survey height above the ground.

*h0* : Nominal survey height (*h0*=150 m),

coefficients: *μTC* = 6.56 10-3 m-1 .

#### **5. Impact of the pre-processings on the fractal properties of the airborne gamma ray measurements**

Once all the corrections are applied, the corrected measurements grid is regrided using twodimensional interpolation algorithms to get a regular sampled grid which is processed by a local regularity analysis.

The set of operations (corrections and interpolations) affects the stochastic component of the raw airborne spectrometric measurements, which holds information about heterogeneities. Therefore the fractal properties of the raw data may be changed.

In the first stage, we have obtained the ''corrected'' and the ''corrected and interpolated'' data grids from the ''raw'' grid data corresponding to the measurements of the three channels: K, Th and U. The 2D-interpolation algorithms used in this study are: the trianglebased linear, the triangle-based cubic and the nearest neighbor interpolation algorithms. Since the results obtained by the different interpolation methods are close, only those related to the triangle-based linear algorithm are presented.

First, five vertical profiles are extracted from the three considered grids (''raw'', ''corrected'' and ''corrected and interpolated '' grids) from the measurements of the three channels (Fig.2). The Fourier amplitude spectrum and the local Hölder exponent *H*(*x*) are computed for each data profile.

Fig. 2. Position of the five profiles extracted from the GR measurements (in red). (The geological map of the Hoggar, from Caby *et al.*, 1981).

Regarding the computation of *H*(*x*), we need a sequence *Sk,n*(*i*) defined by the local growth of the increment process:

$$S\_{k,n}(i) = \frac{m}{n-1} \sum\_{j \in \left[i-k/2, i+k/2\right]} \left| X(j+1) - X(j) \right|, 1 \prec k \prec n \tag{4}$$

where *n* is the signal *X* length, *k* is a fixed window size, and *m* is the largest integer not exceeding *n/k*.

The local Hölder function *H*(*x*) at point

$$\infty = \frac{i}{n-1} \tag{5}$$

Regularity Analysis of Airborne Natural

local Hölder function.

Gamma Ray Data Measured in the Hoggar Area (Algeria) 99

b)

c)

On the left, the measurements profile, in the middle the module of the amplitude spectrum of the measurements profile versus the wavenumber (rad/degree) in the log-log scale, and on the right, the

The raw data (blue), the corrected data (red) and the corrected and interpolated data (green). Fig. 3. Investigation of the impact of pre-processings on the fractal properties of the five

profiles of the airborne GR data recorded in the channel: (a) K, (b) Th, (c) U.

is given by (Peltier and Lévy-Véhél, 1994, 1995; Muniandy *et al.*, 2001 ; Li *et al.*, 2007, 2008; Gaci *et al.*, 2010):

$$\hat{H}(i) = -\frac{\log\left[\sqrt{\pi/2}\ S\_{k,n}(i)\right]}{\log\left(n-1\right)}\tag{6}$$

From figure 3, it can be seen that all the calculated amplitude spectra, represented in a loglog plan, decay algebraically, the analyzed data exhibit then a fractal behavior. Moreover, the latter is described by a Hölder exponent varying with the latitude of the measure. Hence the data can be considered as paths of multifractional Brownian motions (mBms) (Peltier and Lévy-Véhel, 1995; Gaci *et al.*, 2011).

A significant result deserves to be noted is the fact that the spectra obtained from the ''raw'', ''corrected'' and ''corrected and interpolated'' measurements display a similar form. That is the applied operations (corrections and interpolations) do not affect the fractal aspect of the raw data.

Fig. 3. (Continued)

where *n* is the signal *X* length, *k* is a fixed window size, and *m* is the largest integer not

is given by (Peltier and Lévy-Véhél, 1994, 1995; Muniandy *et al.*, 2001 ; Li *et al.*, 2007, 2008;

log 2

From figure 3, it can be seen that all the calculated amplitude spectra, represented in a loglog plan, decay algebraically, the analyzed data exhibit then a fractal behavior. Moreover, the latter is described by a Hölder exponent varying with the latitude of the measure. Hence the data can be considered as paths of multifractional Brownian motions (mBms) (Peltier

A significant result deserves to be noted is the fact that the spectra obtained from the ''raw'', ''corrected'' and ''corrected and interpolated'' measurements display a similar form. That is the applied operations (corrections and interpolations) do not affect the fractal aspect of the

a)

*S i k ,n H i*

*ˆ*

log 1

*n*

*x*

1 *i*

*<sup>n</sup>* (5)

(6)

exceeding *n/k*.

Gaci *et al.*, 2010):

raw data.

Fig. 3. (Continued)

The local Hölder function *H*(*x*) at point

and Lévy-Véhel, 1995; Gaci *et al.*, 2011).

On the left, the measurements profile, in the middle the module of the amplitude spectrum of the measurements profile versus the wavenumber (rad/degree) in the log-log scale, and on the right, the local Hölder function.

The raw data (blue), the corrected data (red) and the corrected and interpolated data (green).

Fig. 3. Investigation of the impact of pre-processings on the fractal properties of the five profiles of the airborne GR data recorded in the channel: (a) K, (b) Th, (c) U.

Regularity Analysis of Airborne Natural

Gamma Ray Data Measured in the Hoggar Area (Algeria) 101

Fig. 5. Interpolated Gamma Ray measurements (in cps) related to the Th channel.

Fig. 6. Interpolated Gamma Ray measurements (in cps) related to the U channel.

GR measurements recorded in the three channels (K, Th and U).

**6.2 Establishment of local regularity maps from interpolated spectrometric data**  Using a wavelet-based algorithm, we estimate Hölder exponent maps, from the interpolated

Moreover, the estimated Hölder functions obtained from the three types of measurements present very close values. Again, we confirm that the fractal properties of the raw data are not modified by both pre-processing operations. The implementation of the different 2Dinterpolation algorithms illustrates that the choice of the interpolation algorithm has a very slight effect on the estimated *H* value. An important result to be noted: the spectrometric corrections are not necessary for a fractal analysis which can be carried out directly on the raw measurements. By doing so, the stochastic component of the measurements is kept intact.

#### **6. Local regularity analysis of airborne spectrometric data**

In this section, we establish local two-dimensional regularity maps, from the interpolated raw GR data measured in the three channels: K, Th and U, using a wavelet-based algorithm via the two-dimensional Multiple Filter Technique (2D MFT). We obtained the latter technique by generalizing the mono-dimensional version (Dziewonski *et al.*, 1969; Li, 1997) to the 2D-case (Gaci, 2011).

#### **6.1 Spectrometric data interpolation**

Considering the limitations of the computer's processing capacity, we consider the GR measurements recorded, in the K, Th and U channels, over the zone whose geographical coordinates are defined by: longitude: 3° 13' 58''- 6°59' 26'' E, and latitude: 20° 27' 35''-25° 06' 37'' N.

The 2D-interpolation of the raw spectrometric data is performed owing to the kriging algorithm. The interpolated GR grids data related to the K, Th and U channels are illustrated respectively by figures 4, 5 and 6.

Fig. 4. Interpolated Gamma Ray measurements (in cps) related to the K channel .

Moreover, the estimated Hölder functions obtained from the three types of measurements present very close values. Again, we confirm that the fractal properties of the raw data are not modified by both pre-processing operations. The implementation of the different 2Dinterpolation algorithms illustrates that the choice of the interpolation algorithm has a very slight effect on the estimated *H* value. An important result to be noted: the spectrometric corrections are not necessary for a fractal analysis which can be carried out directly on the raw measurements. By doing so, the stochastic component of the measurements is kept

In this section, we establish local two-dimensional regularity maps, from the interpolated raw GR data measured in the three channels: K, Th and U, using a wavelet-based algorithm via the two-dimensional Multiple Filter Technique (2D MFT). We obtained the latter technique by generalizing the mono-dimensional version (Dziewonski *et al.*, 1969; Li, 1997)

Considering the limitations of the computer's processing capacity, we consider the GR measurements recorded, in the K, Th and U channels, over the zone whose geographical coordinates are defined by: longitude: 3° 13' 58''- 6°59' 26'' E, and latitude: 20° 27' 35''-25°

The 2D-interpolation of the raw spectrometric data is performed owing to the kriging algorithm. The interpolated GR grids data related to the K, Th and U channels are illustrated

Fig. 4. Interpolated Gamma Ray measurements (in cps) related to the K channel .

**6. Local regularity analysis of airborne spectrometric data** 

intact.

06' 37'' N.

to the 2D-case (Gaci, 2011).

**6.1 Spectrometric data interpolation** 

respectively by figures 4, 5 and 6.

Fig. 5. Interpolated Gamma Ray measurements (in cps) related to the Th channel.

Fig. 6. Interpolated Gamma Ray measurements (in cps) related to the U channel.

#### **6.2 Establishment of local regularity maps from interpolated spectrometric data**

Using a wavelet-based algorithm, we estimate Hölder exponent maps, from the interpolated GR measurements recorded in the three channels (K, Th and U).

Regularity Analysis of Airborne Natural

updated detailed geological maps.

using the equation (11).

Gamma Ray Data Measured in the Hoggar Area (Algeria) 103

is the local spectral exponent which is related to the local Hurst (or Hölder) exponent, *H x, y* . The spectral exponent *x,y* in each point *x,y* is computed as the slope of the scalogram versus the wavenumber in the log-log plan, the *H x, y* value is then derived

The implementation of the wavelet-based algorithm, using the generalized multiple filter technique, allows to establish regularity maps from the interpolated GR measurements recorded in the three channels (K, Th and U) (Fig. 7). In order to interpret the resulting maps

The results show that the *H* maps, derived from the measurements of all the channels, exhibit almost an identical image of the local regularity. By reporting the faults affecting the studied zone on the obtained regularity maps, we remark that the faults locations correspond to local minima of *H* values. The main accident (the 4°50' fault) is noticeable on almost all the regularity maps. However, the regularity maps present local minima of *H* values in some places, probably due to less important faults which have to be checked on

26°

20°

23°

(a) A geological map of the studied zone

**1** - Archaean granulites; **2** - Gneiss and metasediments, series of Arechchoum (Pr1); **3** - Gneiss with facies amphibole, series of Aleskod (Pr2); **4** - Indif. gneiss (Pr3); **5** - Pharusian Greywackes; **6** - Arkoses and conglomerates, series of Tiririne (Pr4); **7** - Volcano-sediments of Tafassasset (Pr4); **8** - Molasses (purple series) of Cambrian; **9** – Pan-African syn-orogenic granites; **10** - Pan-African Granites; **11** - Pan-African post-orogenic granites; **12** - Granites of Eastern Hoggar; **13** - Late pan-African Granites;

3° 7°

5°

**14** - Basalts and recent volcanism; **15** - Paleozoic cover; **16** - Fault.

Fig. 7. (Continued)

in terms of geology, a geological map of the studied zone is considered.

Recall that the two-dimensional continuous wavelet transform (2D- CWT) is given by a convolution product of a signal *s x, y* and an analyzing wavelet *gx,y* (Chui, 1992; Holschneider, 1995):

$$S(a, b\_{\times}, b\_{y}) = \frac{1}{\sqrt{a}} \int\_{-\infty}^{\infty} s(\infty, y) \, \mathrm{g}\left(\frac{x - b\_{\times}}{a}, \frac{y - b\_{y}}{a}\right) dx \, dy$$

where "*a*" is the scale parameter, "*bx* " and "*by*" are the respective translations according to Xaxis and Y-axis (the symbol " ― " denotes the complex conjugate). Alternatively, it can be computed via the Fast Fourier Transform:

$$S(a, b\_{\chi'} b\_{\underline{y}}) = FFT^{-1}\left(\hat{s}(\xi\_{\underline{\cdot}} \mathbf{v}).\sqrt{a}, \overline{\hat{\xi}}\left(a \xi\_{\underline{\cdot}} a \mathbf{v}\right)\right)$$

Here, we compute the wavelet coefficients via FFT using the two-dimensional multiple filter technique (2D MFT). The latter technique is obtained by generalizing the one-dimensional version (1D MFT), suggested by Dziewonski et *al.* (1969) and improved by Li (1997), to the two-dimensional case. It consists of filtering a two-dimensional signal using a Gaussian filter *G(k, , ) n m* given by (Gaci, 2011):

$$\begin{split} \mathbf{G}(k, \mathbb{X}\_{\boldsymbol{\mu}}, \mathbf{v}\_{m}) &= \mathbf{G}\_{1}(k, \mathbb{X}\_{\boldsymbol{\mu}}) \mathbf{G}\_{2}(k, \mathbf{v}\_{m}) \\ &= e^{-\alpha \left(\frac{k - \mathbb{X}\_{\boldsymbol{\mu}}}{\mathbb{X}\_{\boldsymbol{\mu}}}\right)^{2}} e^{-\alpha \left(\frac{k - \mathbb{V}\_{\boldsymbol{\mu}}}{\mathbb{V}\_{\boldsymbol{\mu}}}\right)^{2}} \end{split} \tag{7}$$

Where *n* and *m* are variable center angular frequencies (or wavenumbers) of the respective filters *G (k, )* <sup>1</sup> *<sup>n</sup>* and *G (k, )* <sup>2</sup> *<sup>m</sup>* . The bandwidths 1 *k* and 2 *k* of both filters are calculated as:

$$\begin{aligned} \Delta k\_1 &= \mathfrak{k}\_2 - \mathfrak{k}\_1 = \mathfrak{k}. L n(\mathfrak{k}\_n) \\ \Delta k\_2 &= \mathfrak{v}\_2 - \mathfrak{v}\_1 = \mathfrak{k}. L n(\mathfrak{v}\_m) \end{aligned} \tag{8}$$

Where is a constant, (*ξ1* , *ξ2*) and (*ν1* , *ν2*) are respectively the – 3 dB points of the Gaussian filters *G1* and *G2* , respectively.

A fractal surface *s x, y* verifies the self-affinity property (Mandelbrot, 1977, 1982; Feder, 1988) :

$$\text{s}(\text{\"\lambda x}, \text{\"\lambda y}) \cong \text{\"\lambda}^H.\text{s}(\text{x}, \text{y}) \,, \text{\"\text\'} \lambda > 0 \tag{9}$$

Where *H* is the Hurst exponent (or the self-affinity parameter). The symbol means the equality of all its finite-dimensional probability distributions.

For sufficiently large values of *k*, the scalogram, defined as the square of the amplitude spectrum: <sup>2</sup> *P k,x,y S(k,x,y)* , can be expressed as:

$$P(k, \mathbf{x}, y) = P'(\mathbf{x}, y).k^{-\Re(\mathbf{x}, y)} \propto k^{-\Re(\mathbf{x}, y)}\tag{10}$$

Where

$$\mathbb{B}(\mathbf{x}, y) = \mathbf{2} \, H(\mathbf{x}, y) + \mathbf{1} \tag{11}$$

Recall that the two-dimensional continuous wavelet transform (2D- CWT) is given by a convolution product of a signal *s x, y* and an analyzing wavelet *gx,y* (Chui, 1992;

> <sup>1</sup> *<sup>y</sup> <sup>x</sup> x y x b y b S(a, b ,b ) s(x,y) g , dx dy a a a*

where "*a*" is the scale parameter, "*bx* " and "*by*" are the respective translations according to X-

*x y S(a,b ,b ) FFT s( , ). a ˆ ˆg a ,a*

Here, we compute the wavelet coefficients via FFT using the two-dimensional multiple filter technique (2D MFT). The latter technique is obtained by generalizing the one-dimensional version (1D MFT), suggested by Dziewonski et *al.* (1969) and improved by Li (1997), to the two-dimensional case. It consists of filtering a two-dimensional signal using a Gaussian

<sup>1</sup>

2 2

*n m*

(8)

*<sup>H</sup> s( x, y) .s(x,y)* , 0 (9)

*(x,y) (x,y) P( k,x,y) P'(x,y).k k* (10)

*x,y H x,y* 2 1 (11)

(7)

*n n n n*

1 2

*nm n m k k*

*G(k, , ) G (k, )G (k, )*

*e e*

Where *n* and *m* are variable center angular frequencies (or wavenumbers) of the respective filters *G (k, )* <sup>1</sup> *<sup>n</sup>* and *G (k, )* <sup>2</sup> *<sup>m</sup>* . The bandwidths 1 *k* and 2 *k* of both filters are

> *k .Ln( ) k .Ln( )*

A fractal surface *s x, y* verifies the self-affinity property (Mandelbrot, 1977, 1982; Feder,

Where *H* is the Hurst exponent (or the self-affinity parameter). The symbol means the

For sufficiently large values of *k*, the scalogram, defined as the square of the amplitude

equality of all its finite-dimensional probability distributions.

spectrum: <sup>2</sup> *P k,x,y S(k,x,y)* , can be expressed as:

is a constant, (*ξ1* , *ξ2*) and (*ν1* , *ν2*) are respectively the – 3 dB points of the Gaussian

121 221

axis and Y-axis (the symbol " ― " denotes the complex conjugate). Alternatively, it can be computed via the Fast Fourier Transform:

filter *G(k, , ) n m* given by (Gaci, 2011):

Holschneider, 1995):

calculated as:

filters *G1* and *G2* , respectively.

Where 

1988) :

Where

is the local spectral exponent which is related to the local Hurst (or Hölder) exponent, *H x, y* . The spectral exponent *x,y* in each point *x,y* is computed as the slope of the scalogram versus the wavenumber in the log-log plan, the *H x, y* value is then derived using the equation (11).

The implementation of the wavelet-based algorithm, using the generalized multiple filter technique, allows to establish regularity maps from the interpolated GR measurements recorded in the three channels (K, Th and U) (Fig. 7). In order to interpret the resulting maps in terms of geology, a geological map of the studied zone is considered.

The results show that the *H* maps, derived from the measurements of all the channels, exhibit almost an identical image of the local regularity. By reporting the faults affecting the studied zone on the obtained regularity maps, we remark that the faults locations correspond to local minima of *H* values. The main accident (the 4°50' fault) is noticeable on almost all the regularity maps. However, the regularity maps present local minima of *H* values in some places, probably due to less important faults which have to be checked on updated detailed geological maps.

(a) A geological map of the studied zone

**1** - Archaean granulites; **2** - Gneiss and metasediments, series of Arechchoum (Pr1); **3** - Gneiss with facies amphibole, series of Aleskod (Pr2); **4** - Indif. gneiss (Pr3); **5** - Pharusian Greywackes; **6** - Arkoses and conglomerates, series of Tiririne (Pr4); **7** - Volcano-sediments of Tafassasset (Pr4); **8** - Molasses (purple series) of Cambrian; **9** – Pan-African syn-orogenic granites; **10** - Pan-African Granites; **11** - Pan-African post-orogenic granites; **12** - Granites of Eastern Hoggar; **13** - Late pan-African Granites; **14** - Basalts and recent volcanism; **15** - Paleozoic cover; **16** - Fault.

Fig. 7. (Continued)

Regularity Analysis of Airborne Natural

Gamma Ray Data Measured in the Hoggar Area (Algeria) 105

(d) Regularity map obtained from GR measured in the U channel

Fig. 7. Comparison of regularity maps obtained from GR measured in (b)K, (c)Th and

Now, we try to establish a correspondence between the obtained regularity maps and the geological map of the area. Since the obtained regularity maps are similar, we choose that estimated from the measurements recorded in the Th channel. Then, on the considered geological map and *H* map, we delimit in dotted lines the geological formations; the same color corresponds to the same geological facies (Fig. 8). These two maps show that a considered lithology is not characterized by the same value of the *H* coefficient. These obtained preliminary results reveal that the *H* value can not be used as an attribute to characterize lithology, while it could be used for the recognition and the establishment of

(d)U channel and the geological map of the studied zone (a). The faults affecting the studied area are projected on the *H* maps.

**4°50' Fault** 

the network faults.

Fig. 7. (Continued)

(b) Regularity map obtained from GR measured in the K channel

**4°50' Fault**

**4°50' Fault**

(c) Regularity map obtained from GR measured in the Th channel

Fig. 7. (Continued)

(d) Regularity map obtained from GR measured in the U channel

Fig. 7. Comparison of regularity maps obtained from GR measured in (b)K, (c)Th and (d)U channel and the geological map of the studied zone (a). The faults affecting the studied area are projected on the *H* maps.

Now, we try to establish a correspondence between the obtained regularity maps and the geological map of the area. Since the obtained regularity maps are similar, we choose that estimated from the measurements recorded in the Th channel. Then, on the considered geological map and *H* map, we delimit in dotted lines the geological formations; the same color corresponds to the same geological facies (Fig. 8). These two maps show that a considered lithology is not characterized by the same value of the *H* coefficient. These obtained preliminary results reveal that the *H* value can not be used as an attribute to characterize lithology, while it could be used for the recognition and the establishment of the network faults.

Regularity Analysis of Airborne Natural

carried out directly on the interpolated raw measurements.

does not allow to characterize the lithological facies.

3 volumes, Houston, Philadelphia.

of Rural Sciences, Kingston, Australia.

Tectonics, Elsevier, Amst. pp. 407-434.

Geophysics. Vol. 65, pp. 1372–1387.

Africa, Clarendon Press, Oxford., 512 pp. Chui, C.K. (1992) An introduction to wavelets. Academic Press.

Sciences, Vol. 47, 757–770.

No.1, pp. 183–194.

tectonics in west Africa, Nature, Vol. 278, pp. 223-227.

**7. Conclusion** 

**8. Acknowledgements** 

67, pp. 357-388.

787.

**9. References** 

Gamma Ray Data Measured in the Hoggar Area (Algeria) 107

This study presents a regularity analysis undertaken on the airborne spectrometric natural radioactivity measured, in three channels: K, Th and U, over the Hoggar area (Algeria). It reveals that the investigated data exhibit fractal properties depending on the spatial measurement location, thus can be modeled using multifractional Brownian motions. As the spectrometric corrections do not affect these properties, the regularity analysis can be

The Hölder exponent maps, obtained from the Gamma Ray measurements recorded in the three channels, show a similar local regularity. Besides, a strong correlation is derived between the *H* exponent values and the faults locations. Indeed, a fault corresponds to local minima *H* values, the *H* exponent value can then be used to identify the faults. However, it

This work was supported by the Algerian –French program CMEP—PHC Tassili N°09 MDU

Aeroservice Corporation (1975) Aero-magneto-spectrometric survey of Algeria. Final report,

Aydin, I.; Selman Aydoğan, M. ; Oksum, E. & Koçak, A. (2006) An attempt to use aerial gamma-

Bierwirth, P.N., & Welsh, W.D. (2000) Delineation of Recharge Beds in the Great Artesian

Black, R.; Caby, R. & Moussine-Pouchkine, A. (1979) Evidence for late Precambrian plate

Brown, W.M. ; Gedeon, T.D. ; Groves, D.I. & Barnes, R.G. (2000) Artificial neural networks: a

Caby, R.; Bertrand, J.M.L. & Black, R. (1981) Pan-African closure and continental collision in

Cahen, L., Snelling, N.J. ; Delhal, J. & Vail J.R. (1984) The geochronology and evolution of

Cook, S.E.; Corner, R.J.; Groves, P.R. & Grealish, G.J. (1996) Use of airborne gamma

Doll, W.E.; Nyquist, J.E.; Beard, L.P. & Gamey,T.J. (2000) Airborne geophysical surveying for

ray spectrometry results in petrochemical assessments of the volcanic and plutonic associations of Central Anatolia (Turkey). Geophys. J. Int. Vol. 167, pp. 1044–1052. Bertrand, J.M.L. & Caby, R. (1978) Geodynamic evolution of the pan-african orogenic belt: A

new interpretation of the Hoggar shield (Algerian Sahara), Geol. Rundschman, Vol.

Basin Using Airborne Gamma Radiometrics and Satellite Remote Sensing, Bureau

new method for mineral prospectivity mapping. Australian Journal of Earth

the Hoggar-Iforas segment, central Sahara. in Kroner A (ed) Precambrian Plate

radiometric data for soil mapping, Australian Journal of Soil Research. Vol. 34,

hazardous waste site characterization on the Oak Ridge Reservation, Tennessee,

**1** - Archaean granulites; **2** - Gneiss and metasediments, series of Arechchoum (Pr1); **3** - Gneiss with facies amphibole, series of Aleskod (Pr2); **4** - Indif. gneiss (Pr3); **5** - Pharusian Greywackes; **6** - Arkoses and conglomerates, series of Tiririne (Pr4); **7** - Volcano-sediments of Tafassasset (Pr4); **8** - Molasses (purple series) of Cambrian; **9** – Pan-African syn-orogenic granites; **10** - Pan-African Granites; **11** - Pan-African post-orogenic granites; **12** - Granites of Eastern Hoggar; **13** - Late pan-African Granites; **14** - Basalts and recent volcanism; **15** - Paleozoic cover; **16** - Fault.

Fig. 8. Correlation of the regularity map (b) obtained from the GR measurements recorded in the Th channel with the geological map of the studied zone (a). The ellipses in dotted lines delimit the geological formations: black (pan-African syn-orogenic granites), white (pan-African granites), simple blue line (basalts and recent volcanism), doubled blue line (gneiss with amphibole facies), brown (gneiss and metasediments).

### **7. Conclusion**

106 Advances in Data, Methods, Models and Their Applications in Geoscience

26°

20°

23°

b) **1** - Archaean granulites; **2** - Gneiss and metasediments, series of Arechchoum (Pr1); **3** - Gneiss with facies amphibole, series of Aleskod (Pr2); **4** - Indif. gneiss (Pr3); **5** - Pharusian Greywackes; **6** - Arkoses and conglomerates, series of Tiririne (Pr4); **7** - Volcano-sediments of Tafassasset (Pr4); **8** - Molasses (purple series) of Cambrian; **9** – Pan-African syn-orogenic granites; **10** - Pan-African Granites; **11** - Pan-African post-orogenic granites; **12** - Granites of Eastern Hoggar; **13** - Late pan-African Granites;

Fig. 8. Correlation of the regularity map (b) obtained from the GR measurements recorded in the Th channel with the geological map of the studied zone (a). The ellipses in dotted lines delimit the geological formations: black (pan-African syn-orogenic granites), white (pan-African granites), simple blue line (basalts and recent volcanism), doubled blue line

**14** - Basalts and recent volcanism; **15** - Paleozoic cover; **16** - Fault.

**4°50' Fault** 

3° 7°

5°

a)

(gneiss with amphibole facies), brown (gneiss and metasediments).

This study presents a regularity analysis undertaken on the airborne spectrometric natural radioactivity measured, in three channels: K, Th and U, over the Hoggar area (Algeria). It reveals that the investigated data exhibit fractal properties depending on the spatial measurement location, thus can be modeled using multifractional Brownian motions. As the spectrometric corrections do not affect these properties, the regularity analysis can be carried out directly on the interpolated raw measurements.

The Hölder exponent maps, obtained from the Gamma Ray measurements recorded in the three channels, show a similar local regularity. Besides, a strong correlation is derived between the *H* exponent values and the faults locations. Indeed, a fault corresponds to local minima *H* values, the *H* exponent value can then be used to identify the faults. However, it does not allow to characterize the lithological facies.

### **8. Acknowledgements**

This work was supported by the Algerian –French program CMEP—PHC Tassili N°09 MDU 787.

#### **9. References**


**6** 

 *Algeria* 

**Two-Dimensional Multifractional Brownian** 

A core sample is a cylindrical section obtained by driving a hollow tube into the undisturbed medium and withdrawing it with its content. In practice, the sample is pushed more or less unbroken into the tube. Once removed from the tube in the laboratory, it is analyzed by different techniques and equipment depending on the desired type of data. The hole made for the core sample is called the "core hole". A variety of core samplers exist to sample different media under diverse conditions. For instance, sediments or rocks are

A scientific coring has been used in the first time for sampling the ocean floor. Then, it is soon exploited to analyze lakes, ice, mud, soil and wood. Cores provide precious information about the evolution of climate, species and sedimentary composition during

In petroleum engineering, core analysis presents a way of measuring well conditions downhole by studying samples of reservoir rocks. It gives the most accurate estimations of porosity, permeability, fluid saturation and grain density. These measurements help to

In addition to the basic petrophysical properties estimated from the core, a special core analysis can be undertaken in order to determine permeability, wettability, capillary pressure, and electrical properties. Petrographic studies and sieve analysis can also be

In recent years, numerical analysis has been widely used for the investigation of images, since it yields results more objective and reliable than those obtained by conventional methods based on human observations. Fractal analysis has been introduced to examine images texture (Bourissou *et al.*, 1994; Lévy-Véhel and Mignot, 1994; Liu and Li, 1997; Lévy-Véhél, 1995, 1997, 1998; Pesquet-Popescu and Lévy-Véhel, 2002; Malladi *et al.*, 2003; Tahiri *et* 

In this study, we suggest to go beyond the conventional core analysis, and to perform a new approach to extract the maximum features from a core image using a fractal analysis. The conventional fractal model used previously in image processing, the two-dimensional fractional Brownian motion (2D- fBm), presents a constant Hölder function *H*, thus does not allow to explore the spatial evolution of the local regularity. To do so, we suggest to

**1. Introduction** 

geologic history.

*al.*, 2005).

carried out in such analysis.

sampled with a hollow steel tube called a core drill.

understand the conditions of the well and its potential productivity.

**Motion- Based Investigation of** 

Saïd Gaci and Naïma Zaourar

**Heterogeneities from a Core Image** 

*University of Sciences and Technology Houari Boumediene, Algiers,* 


## **Two-Dimensional Multifractional Brownian Motion- Based Investigation of Heterogeneities from a Core Image**

Saïd Gaci and Naïma Zaourar

*University of Sciences and Technology Houari Boumediene, Algiers, Algeria* 

#### **1. Introduction**

108 Advances in Data, Methods, Models and Their Applications in Geoscience

Dziewonski, A.; Bloch, S. & Landisman, M. (1969) A technique for the analysis of transient

Gaci, S.; Zaourar, N. ; Hamoudi, M. & Holschneider, M. (2010). Local regularity analysis of strata

Gaci, S.; Zaourar, N.; Briqueu, L. & Djeddi, M., (2011). Fractal characterization of natural

Graham, D.F. & Bonham-Carter, G.F. (1993) Airborne radiometric data: A tool for

Groune D. (2009) Magneto-spectrometric analysis of the airborne geophysical data of the

International Atomic Energy Agency (IAEA) (2003) Guidelines for radioelement mapping

Jaques, A.L.; Wellman, P.; Whitaker, A. & Wyborn, D. (1997) High-resolution geophysics in

Li, X-P (1997). Decomposition of vibroseis data by the multiple filter technique. *Geophysics*,

Li, M.; Lim, S.C. ; Hu, B-J. & Feng, H. (2007). Towards describing multi-fractality of traffic

Li, M.; Lim, S.C. & Zhao, W. (2008). Investigating multi-fractality of network traffic using local Hurst function, Advanced Studies in Theoretical Physics, Vol. 2, No. 10, pp. 479–490. Liégeois, J. P.; Black, R.; Navez, J. & Latouche, L. (1994) Early and late Pan-African orogenies

Mandelbrot, B.B. (1977). Fractals : Form, Chance and Dimensions. Freeman, San Francisco.

Matolín, M. & Stráník, Z. (2006) Radioactivity of sedimentary rocks over the Ždánice

Muniandy, S.V.; Lim, S.C. & Murugan, R. (2001). Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates, Physica A, Vol. 301, No. 1–4, pp. 407–428, 2001. Peltier, R.F. & Lévy-Véhel, J. (1994). A New Method for Estimating the Parameter of

Peltier, R.F. & Lévy-Véhel, J. (1995). Multifractional Brownian Motion: Definition and

Sulekha Rao, N. ; Sengupta, D. ; Guin, R. & Saha S. K. (2009) Natural radioactivity

Wilford, J.R.; Bierwirth, P.N. & Craig, M.A. (1997) Application of airborne gamma-ray

measurements in beach sand along southern coast of Orissa, eastern India. Environ

spectrometry in soil/regolith mapping and applied geomorphology, Journal of

Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. Freeman, San Francisco.

Fractional Brownian motion, Technical report, INRIA RR 2396.

Australian Geology and Geophysics, Vol. 17, No. 2, pp. 201–216.

preliminary results, Technical report, INRIA RR 2645.

hydrocarbon field. Geophys. J. Int., Vol. 167, pp. 1491–1500.

Holschneider, M. (1995). Wavelets: an Analysis Tool. Clarendon. Oxford, England.

using gamma ray spectrometry data. Vienna, Austria. 179 pp.

heterogeneities from sonic logs. *Nonlin. Processes Geophys.*, Vol. 17, pp. 455-466, http: www.nonlin-processes-geophys.net/17/455/2010/doi:10.5194/npg-17-455-2010 Gaci, S. (2011). Multifractional analysis of geophysical signals (*in French*). PhD thesis. Univ.

radioactivity measurements in the Hoggar region (Algeria), EGU Proceedings,

reconnaissance geological mapping using a GIS, Photogrammetric Engineering and

large Pharusian ditch (Western Hoggar). Msc thesis, University of Boumerdes.

modern geological mapping, AGSO Journal of Australian Geology and Geophysics.

using local Hurst function. *Lecture Notes in Computer Science*, Vol. 4488, pp. 1012-1020.

in the Aïr assembly of terranes (Tuareg shield, Niger), Precambrian Research, Vol.

seismic signals: *Bull. Seismol. Soc. Am.*, Vol. 59, pp. 427–444.

of Sciences and Technology Houari Boumdiene (Algeria).

Feder, J. (1988). Fractals, p. 283, Plenum (Ed.), New York.

Remote Sensing, Vol. 59, pp. 1243–1249.

Vienna, Austria.

Algeria (in French).

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Vol. 62, No. 3, pp. 980–991.

67, No. 1-2, pp.59-88.

Earth Sci. Vol. 59, pp. 593–601.

A core sample is a cylindrical section obtained by driving a hollow tube into the undisturbed medium and withdrawing it with its content. In practice, the sample is pushed more or less unbroken into the tube. Once removed from the tube in the laboratory, it is analyzed by different techniques and equipment depending on the desired type of data. The hole made for the core sample is called the "core hole". A variety of core samplers exist to sample different media under diverse conditions. For instance, sediments or rocks are sampled with a hollow steel tube called a core drill.

A scientific coring has been used in the first time for sampling the ocean floor. Then, it is soon exploited to analyze lakes, ice, mud, soil and wood. Cores provide precious information about the evolution of climate, species and sedimentary composition during geologic history.

In petroleum engineering, core analysis presents a way of measuring well conditions downhole by studying samples of reservoir rocks. It gives the most accurate estimations of porosity, permeability, fluid saturation and grain density. These measurements help to understand the conditions of the well and its potential productivity.

In addition to the basic petrophysical properties estimated from the core, a special core analysis can be undertaken in order to determine permeability, wettability, capillary pressure, and electrical properties. Petrographic studies and sieve analysis can also be carried out in such analysis.

In recent years, numerical analysis has been widely used for the investigation of images, since it yields results more objective and reliable than those obtained by conventional methods based on human observations. Fractal analysis has been introduced to examine images texture (Bourissou *et al.*, 1994; Lévy-Véhel and Mignot, 1994; Liu and Li, 1997; Lévy-Véhél, 1995, 1997, 1998; Pesquet-Popescu and Lévy-Véhel, 2002; Malladi *et al.*, 2003; Tahiri *et al.*, 2005).

In this study, we suggest to go beyond the conventional core analysis, and to perform a new approach to extract the maximum features from a core image using a fractal analysis. The conventional fractal model used previously in image processing, the two-dimensional fractional Brownian motion (2D- fBm), presents a constant Hölder function *H*, thus does not allow to explore the spatial evolution of the local regularity. To do so, we suggest to

Two-Dimensional Multifractional Brownian

**2.2 Multifractional Brownian motion** 

regularity.

*BH*

conjugate.

Motion- Based Investigation of Heterogeneities from a Core Image 111

Multifractional Brownian motion (mBm) was introduced by Peltier and Lévy-Véhél (1995), and Benassi *et al.* (1997) by allowing *H* to vary over time. Even if no longer stationary nor self-similar compared to the fBm, the mBm presents the advantage to be very flexible since the function *H*(*t*) can model phenomena whose sample paths display a time changing

For a continuous function <sup>2</sup> *Hx R R* : , the isotropic multifractional Brownian field

 *Hx Hy Hx H y Hx H y H x H y E W xW y x y x y*

Identically to the 2D-fBm, the local regularity of the 2D-mBm paths is measured by means of

The two-dimensional continuous wavelet transform (2D- CWT) of a signal *s x* ,*y* is given

where *gx*,*y* is the analyzing wavelet, "*a*" is the scale parameter, "*bx*" and "*by*" are the respective translations according to X-axis and Y-axis. The symbol "―" denotes the complex

> 

Let us define the function 0 0 , (,) *x y s x y* in each point 0 0 (,) *x y* by: 0 0 , 0 <sup>0</sup> (,) ( , ) (,) *x y s x y sx x y y s x y* . This function also satisfies the self-affine property

> 0 0 0 0 , , ( , ) (,) *<sup>H</sup> x y x y s x*

This property is reflected by the 2D-CWT provided that the analyzing wavelet decreases

 

0 0 <sup>1</sup> (,) <sup>2</sup>

 *<sup>x</sup> <sup>y</sup> Sa x b y b <sup>x</sup> <sup>y</sup>* ,

0 0 0 0 (, , ) (, , ) *Hx y*

<sup>1</sup> (, , ) (, ) , *<sup>y</sup> <sup>x</sup> x y x b y b Sa b b sxy g dx dy a a a*

described by (Mandelbrot, 1977, 1982; Feder, 1988; Vicsek 1989; Edgard, 1990) :

swiftly enough to zero and has enough vanishing moments (Holschneider, 1995):

 

Let *s x* ,*y* be a self-affine fractal surface. It satisfies then the relation:

( , ) .( , ) *<sup>H</sup> s x*

with the Hurst exponent *H* and a positive factor

*S ax b y b*

 

of the relation follow the same law.

the pointwise Hölder exponent. For a differentiable function *H*, the relation

 (3)

(4)

*y s x y* (5)

*y s x y* (6)

. If *s* is a stochastic process, the two sides

0 (7)

.

*WH x* is a centered Gaussian field with a covariance function

*x Hx* is demonstrated, almost surely, for all <sup>2</sup> *x R*

**3. Regularity analysis using the wavelet transform** 

**3.1 Two- dimensional continuous wavelet transform** 

by (Chui, 1992; Holschneider, 1995):

consider a generalized fractal model, the two–dimensional multifractional Brownian motion (2D-mBm), which presents a regularity varying in space.

The mBm model, initially proposed by Peltier and Lévy-Véhél (1995), and Benassi *et al.*  (1997), is used in many disciplines: images processing (Bicego and Trudda, 2010), traffic phenomena (Li *et al.*, 2007), geophysics (Wanliss, 2005; Wanliss and Cersosimo, 2006; Cersosimo and Wanliss, 2007; Gaci *et al.*, 2010; Gaci and Zaourar, 2010, 2011). For the estimation of the mBm processes' local regularity, we propose three algorithms based on the two-dimensional continuous wavelet transform (2D- CWT). The wavelet coefficients are calculated by Fast Fourier Transform (FFT) using the Morlet wavelet and the Mexican hat for the first and the second algorithms, respectively. However for the third algorithm, the coefficients estimation is carried out using the multiple filter technique (2D MFT) that we generalized to two dimensions (Gaci, 2011), from the one-dimensional case (1D MFT) (Li, 1997; Gaci *et al.*, 2011).

This chapter is organized as follows. First, we give a brief theory on 2D-mBm model and the wavelet-based estimators of the local regularity. The potential of the suggested algorithms is then demonstrated on synthetic 2D-mBm paths. The results showed that the 2D MFT algorithm yields the best Hölder exponent estimates. Next, the suggested regularity analysis is extended to digitalized image data of a core extracted from an Algerian borehole. It is shown that the data exhibit a fractal behavior. In addition, the derived regularity maps, obtained with the 2D MFT algorithm, show a strong correlation with the core heterogeneities.

#### **2. (Multi)fractional Brownian motion**

#### **2.1 Fractional Brownian motion**

Fractional Brownian motion (fBm) is one of the most popular stochastic fractal models for studying rough signals. It was introduced by Kolmogorov (1940) and studied by Mandelbrot and Van Ness (1968).

A fBm, denoted by *BH* (*t*), is the zero-mean Gaussian process with stationary increments. It is parameterized by a constant Hurst parameter *H*. The fBm is *H*-self affine, *i.e.*:

$$B\_H\left(\mathcal{X}t\right) \cong \mathcal{X}^H B\_H\left(t\right), \ \forall \; \mathcal{X} > 0 \tag{1}$$

Where means the equality of all its finite-dimensional probability distributions.

The bidimensional isotropic fractional Brownian motion, or Lévy Brownian fractional field, with Hurst parameter *H* is a centered Gaussian field *BH* with an autocorrelation function (Kamont, 1996):

$$\mathbb{E}\left(B\left(\vec{\mathbf{x}}\right)B\left(\vec{y}\right)\right) \propto \left\|\vec{\mathbf{x}}\right\|^{2H} + \left\|\vec{y}\right\|^{2H} - \left\|\vec{\mathbf{x}} - \vec{y}\right\|^{2H}, \text{ with } 0 < H < 1\tag{2}$$

where <sup>2</sup> *<sup>x</sup>*, *<sup>y</sup><sup>R</sup>* and . is the usual Euclidian norm.

For *H*=1/2, the fractional Brownian motion is reduced to a Wiener process.

The regularity of the 2D-fBm is measured by the pointwise Hölder exponent *BH x* . Indeed, it is shown that almost surely: *BH x H* . Therefore, the higher the *H* value, the smoother the 2D-fBm paths.

#### **2.2 Multifractional Brownian motion**

110 Advances in Data, Methods, Models and Their Applications in Geoscience

consider a generalized fractal model, the two–dimensional multifractional Brownian motion

The mBm model, initially proposed by Peltier and Lévy-Véhél (1995), and Benassi *et al.*  (1997), is used in many disciplines: images processing (Bicego and Trudda, 2010), traffic phenomena (Li *et al.*, 2007), geophysics (Wanliss, 2005; Wanliss and Cersosimo, 2006; Cersosimo and Wanliss, 2007; Gaci *et al.*, 2010; Gaci and Zaourar, 2010, 2011). For the estimation of the mBm processes' local regularity, we propose three algorithms based on the two-dimensional continuous wavelet transform (2D- CWT). The wavelet coefficients are calculated by Fast Fourier Transform (FFT) using the Morlet wavelet and the Mexican hat for the first and the second algorithms, respectively. However for the third algorithm, the coefficients estimation is carried out using the multiple filter technique (2D MFT) that we generalized to two dimensions (Gaci, 2011), from the one-dimensional case (1D MFT) (Li,

This chapter is organized as follows. First, we give a brief theory on 2D-mBm model and the wavelet-based estimators of the local regularity. The potential of the suggested algorithms is then demonstrated on synthetic 2D-mBm paths. The results showed that the 2D MFT algorithm yields the best Hölder exponent estimates. Next, the suggested regularity analysis is extended to digitalized image data of a core extracted from an Algerian borehole. It is shown that the data exhibit a fractal behavior. In addition, the derived regularity maps, obtained with the 2D MFT algorithm, show a strong correlation with the core

Fractional Brownian motion (fBm) is one of the most popular stochastic fractal models for studying rough signals. It was introduced by Kolmogorov (1940) and studied by

A fBm, denoted by *BH* (*t*), is the zero-mean Gaussian process with stationary increments. It is

The bidimensional isotropic fractional Brownian motion, or Lévy Brownian fractional field, with Hurst parameter *H* is a centered Gaussian field *BH* with an autocorrelation function

The regularity of the 2D-fBm is measured by the pointwise Hölder exponent *BH*

<sup>2</sup>*<sup>H</sup>* 2 2 *H H E BxBy x y x y* , with 0 1 *<sup>H</sup>* (2)

*x H* . Therefore, the higher the *H* value, the

0(1)

 *x* .

parameterized by a constant Hurst parameter *H*. The fBm is *H*-self affine, *i.e.*:

For *H*=1/2, the fractional Brownian motion is reduced to a Wiener process.

 *<sup>H</sup> B t Bt H H* ,

Where means the equality of all its finite-dimensional probability distributions.

(2D-mBm), which presents a regularity varying in space.

1997; Gaci *et al.*, 2011).

heterogeneities.

(Kamont, 1996):

**2. (Multi)fractional Brownian motion** 

where <sup>2</sup> *<sup>x</sup>*, *<sup>y</sup><sup>R</sup>* and . is the usual Euclidian norm.

Indeed, it is shown that almost surely: *BH*

smoother the 2D-fBm paths.

**2.1 Fractional Brownian motion** 

Mandelbrot and Van Ness (1968).

Multifractional Brownian motion (mBm) was introduced by Peltier and Lévy-Véhél (1995), and Benassi *et al.* (1997) by allowing *H* to vary over time. Even if no longer stationary nor self-similar compared to the fBm, the mBm presents the advantage to be very flexible since the function *H*(*t*) can model phenomena whose sample paths display a time changing regularity.

For a continuous function <sup>2</sup> *Hx R R* : , the isotropic multifractional Brownian field *WH x* is a centered Gaussian field with a covariance function

$$E\left(\mathcal{W}\_{H(\vec{x})}\left(\vec{x}\right)\mathcal{W}\_{H(\vec{y})}\left(\vec{y}\right)\right) \propto \left\|\vec{x}\right\|^{H(\vec{x}) + H(\vec{y})} + \left\|\vec{y}\right\|^{H(\vec{x}) + H(\vec{y})} - \left\|\vec{x} - \vec{y}\right\|^{H(\vec{x}) + H(\vec{y})} \tag{3}$$

Identically to the 2D-fBm, the local regularity of the 2D-mBm paths is measured by means of the pointwise Hölder exponent. For a differentiable function *H*, the relation *BH x Hx* is demonstrated, almost surely, for all <sup>2</sup> *x R* .

#### **3. Regularity analysis using the wavelet transform**

#### **3.1 Two- dimensional continuous wavelet transform**

The two-dimensional continuous wavelet transform (2D- CWT) of a signal *s x* ,*y* is given by (Chui, 1992; Holschneider, 1995):

$$S(a, b\_x, b\_y) = \frac{1}{\sqrt{a}} \int\_{-\infty}^{a} s(x, y) g\left(\frac{x - b\_x}{a}, \frac{y - b\_y}{a}\right) dx \, dy \tag{4}$$

where *gx*,*y* is the analyzing wavelet, "*a*" is the scale parameter, "*bx*" and "*by*" are the respective translations according to X-axis and Y-axis. The symbol "―" denotes the complex conjugate.

Let *s x* ,*y* be a self-affine fractal surface. It satisfies then the relation:

$$\mathbf{s}(\mathcal{X}\mathbf{x}, \mathcal{X}y) \cong \mathcal{X}^H . \mathbf{s}(\mathbf{x}, \mathbf{y}) \tag{5}$$

with the Hurst exponent *H* and a positive factor . If *s* is a stochastic process, the two sides of the relation follow the same law.

Let us define the function 0 0 , (,) *x y s x y* in each point 0 0 (,) *x y* by: 0 0 , 0 <sup>0</sup> (,) ( , ) (,) *x y s x y sx x y y s x y* . This function also satisfies the self-affine property described by (Mandelbrot, 1977, 1982; Feder, 1988; Vicsek 1989; Edgard, 1990) :

$$s\_{x\_0, y\_0}(\mathcal{A}\mathbf{x}, \mathcal{A}y) \cong \mathcal{A}^H s\_{x\_0, y\_0}(\mathbf{x}, y) \tag{6}$$

This property is reflected by the 2D-CWT provided that the analyzing wavelet decreases swiftly enough to zero and has enough vanishing moments (Holschneider, 1995):

$$S(\mathcal{A}, a, \mathbf{x}\_0 + \mathcal{A}b\_{\mathbf{x}}, y\_0 + \mathcal{A}b\_y) \cong \mathcal{A}^{H(\mathbf{x}\_0, y\_0) + \frac{1}{2}} S(a, \mathbf{x}\_0 + b\_{\mathbf{x}}, y\_0 + b\_y), \mathcal{A} > 0 \tag{7}$$

Two-Dimensional Multifractional Brownian

Fig. 1. Used bidimensional analyzing wavelets:

Spatial representation (d)

decomposition using a Gaussian filter:

is a shaping parameter of the filter.

*0x=0y=5.).*  Spatial representation: (a) real part (b) imaginary part

Fourier transform representation (c)

Fourier transform representation (e)

**3.3.2 Generalized two-dimensional multiple filter technique** 

The 1D MFT was initially suggested by Dziewonski et *al.* (1969). It consists on carrying out a

(, )

is a constant, *k1* and *k2* are the – 3 dB points of the Gaussian filter.

*<sup>k</sup> Gkk e <sup>n</sup>*

where *nk* is a variable center angular frequency (or wavenumber) of the filter (, ) *Gkkn* , and

In order to overcome the poor ''time'' and ''low-frequency'' domains resolution toward the low frequencies, Li (1997) suggests a varying quality factor *Q* and a varying bandwidth *Δk*:

> 2 1 .() *<sup>n</sup> k k k Ln k*

2

(13)

(14)

*n n k k*

Morlet wavelet *(*

Mexican hat.

Where 

Motion- Based Investigation of Heterogeneities from a Core Image 113

*(a) (b) (c)* 

*(d) (e)* 

By taking the scale "*a*" inversely proportional to the wavenumber *k*: *a k* 1 , the wavelet coefficients will be expressed in (*k*, *bx*, *by*) plane.

The scalogram can be defined as the square of the amplitude spectrum: <sup>2</sup> *Pkx*,, (,,) *y Skx y* . For large values of *k*, it can be expressed as:

$$P(k, \mathbf{x}, y) = P'(\mathbf{x}, y) \, k^{-\beta(\mathbf{x}, y)} \propto k^{-\beta(\mathbf{x}, y)} \tag{8}$$

Where

$$\mathcal{A}\left(\mathbf{x}, y\right) = 2\,\mathrm{H}\left(\mathbf{x}, y\right) + 1\tag{9}$$

is the local spectral exponent which is related to the local Hurst (or Hölder) exponent, *H x* ,*y* . The spectral exponent *x*,*y* in each point *x*,*y* is computed as the slope of the scalogram versus the wavenumber in the log-log plan, the *H x* ,*y* value is then derived using the equation (9).

#### **3.2 Used analyzing wavelets**

The analyzing wavelets used in this application are the Morlet wavelet and the Mexican hat (Fig. 1). This choice is motivated by their adequate properties for the regularity analysis.


$$\hat{\mathbf{g}}\left(\mathbf{x},\mathbf{y}\right) = e^{-i\left(a\_{0x}\mathbf{x} + a\_{0y}\mathbf{y}\right)} \cdot e^{-\frac{1}{2}\left(\mathbf{x}^{2} + \mathbf{y}^{2}\right)}$$

$$\hat{\mathbf{g}}\left(\xi,\nu\right) = e^{-\frac{1}{2}\left[\left(\xi - a\_{0x}\right)^{2} + \left(\nu - a\_{0y}\right)^{2}\right]}; \quad \text{with } \left(a\_{0x}^{2} + a\_{0y}^{2}\right)^{1/2} \ge 5 \tag{10}$$


$$\log \left( \mathbf{x}, y \right) = \left( 2 - \mathbf{x}^2 - y^2 \right) e^{-\left( \mathbf{x}^2 + y^2 \right) \left| \frac{2}{\mathbf{x}} \right|} ; \hat{\mathbf{g}} \left( \boldsymbol{\xi}, \nu \right) = \left( \boldsymbol{\xi}^2 + \nu^2 \right) e^{-\left( \boldsymbol{\xi}^2 + \nu^2 \right) \left| \frac{2}{\mathbf{x}} \right|} \tag{11}$$

#### **3.3 Wavelet-based estimators of the local regularity**

As explained earlier, the computation of the local Hölder exponents *H*(*x*,*y*) requires to calculate the two-dimensional wavelet continuous transform. Here, we suggest three algorithms for the implementation of the 2D- CWT, which are:

#### **3.3.1 FFT-based algorithms**

These algorithms are based on the property that wavelet coefficients, expressed by the equation (4), can be performed via the Fourier transform using the Morlet wavelet and the Mexican hat:

$$S(a, b\_{x'} b\_y) = FFT^{-1}\left(\hat{\mathfrak{s}}(\xi, \nu). \sqrt{a}, \overline{\hat{\mathfrak{s}}}\left(a \,\xi, a\nu\right)\right) \tag{12}$$

These algorithms are accurate but slow, and the signal length must be a power of 2.

By taking the scale "*a*" inversely proportional to the wavenumber *k*: *a k* 1 , the wavelet

The scalogram can be defined as the square of the amplitude spectrum:

(,) (,) ( , , ) '( , ). *<sup>x</sup> <sup>y</sup> <sup>x</sup> <sup>y</sup> Pkxy P xy k k* 

is the local spectral exponent which is related to the local Hurst (or Hölder) exponent,

scalogram versus the wavenumber in the log-log plan, the *H x* ,*y* value is then derived

The analyzing wavelets used in this application are the Morlet wavelet and the Mexican hat (Fig. 1). This choice is motivated by their adequate properties for the regularity analysis.

> 

 <sup>2</sup> <sup>2</sup> 0 0

 

1 <sup>2</sup> ˆ(,) *x y*

2 2 <sup>2</sup> 2 2 , 2 *x y*

algorithms for the implementation of the 2D- CWT, which are:

**3.3 Wavelet-based estimators of the local regularity** 

*g e*

  *gxy e e*

; with

*gxy x y e* 2 2 <sup>2</sup> 2 2 ;, . *g e* <sup>ˆ</sup>

As explained earlier, the computation of the local Hölder exponents *H*(*x*,*y*) requires to calculate the two-dimensional wavelet continuous transform. Here, we suggest three

These algorithms are based on the property that wavelet coefficients, expressed by the equation (4), can be performed via the Fourier transform using the Morlet wavelet and the

> 

These algorithms are accurate but slow, and the signal length must be a power of 2.

0 0

<sup>2</sup> , . *x y ix y <sup>x</sup> <sup>y</sup>*

 

(8)

*xy H xy* ,2,1 (9)

*x*,*y* in each point *x*,*y* is computed as the slope of the

2 2

1 2 2 2 0 0 5

> 

*x y* (10)

(11)

1

 

> 

 <sup>1</sup> ( , , ) ( , ). , ˆ ˆ *S a b b FFT s a g a a x y* (12)

coefficients will be expressed in (*k*, *bx*, *by*) plane.

*H x* ,*y* . The spectral exponent

**3.2 Used analyzing wavelets** 

using the equation (9).



**3.3.1 FFT-based algorithms** 

Mexican hat:

Where

<sup>2</sup> *Pkx*,, (,,) *y Skx y* . For large values of *k*, it can be expressed as:

Fig. 1. Used bidimensional analyzing wavelets:

 Morlet wavelet *(0x=0y=5.).* 

 Spatial representation: (a) real part (b) imaginary part Fourier transform representation (c) Mexican hat.

 Spatial representation (d) Fourier transform representation (e)

#### **3.3.2 Generalized two-dimensional multiple filter technique**

The 1D MFT was initially suggested by Dziewonski et *al.* (1969). It consists on carrying out a decomposition using a Gaussian filter:

$$\mathbf{G}(k\_{\prime}k\_{\boldsymbol{n}}) = e^{-a\left(\frac{k-k\_{\boldsymbol{n}}}{k\_{\boldsymbol{n}}}\right)^{2}}\tag{13}$$

where *nk* is a variable center angular frequency (or wavenumber) of the filter (, ) *Gkkn* , and is a shaping parameter of the filter.

In order to overcome the poor ''time'' and ''low-frequency'' domains resolution toward the low frequencies, Li (1997) suggests a varying quality factor *Q* and a varying bandwidth *Δk*:

$$
\Delta k = k\_2 - k\_1 = \beta. \text{Lv(k\_n)}\tag{14}
$$

Where is a constant, *k1* and *k2* are the – 3 dB points of the Gaussian filter.

Two-Dimensional Multifractional Brownian

logistic (middle) and periodic (bottom).

Fig. 3. (Continued)

*(a)* 

Motion- Based Investigation of Heterogeneities from a Core Image 115

*H function Simulated 2D-mBm path*

Fig. 2. A 3D-view representation and a XY-plan projection of the theoretical *H* function and the corresponding simulated 2D-mBm path, for the three types of *H* functions. Bilinear (top),

Here, we propose to extend the 1D MFT enhanced by Li (1997) to 2 dimensions. The idea consists on decomposing the two-dimensional signal using a Gaussian filter (, , ) *G k n m*defined as:

$$\begin{split} \mathbf{G}\{k\_{\prime}\xi\_{n},\nu\_{m}\} &= \mathbf{G}\_{1}(k\_{\prime}\xi\_{n})\mathbf{G}\_{2}(k\_{\prime}\nu\_{m}) \\ &= e^{-\alpha\left(\frac{k-\xi\_{n}}{\xi\_{n}}\right)^{2}}e^{-\alpha\left(\frac{k-\nu\_{n}}{\nu\_{n}}\right)^{2}} \end{split} \tag{15}$$

Where *<sup>n</sup>* and *<sup>m</sup>* are variable center angular frequencies (or wavenumbers) of the respective filters 1(, ) *G k <sup>n</sup>* and 2 *G k*(, ) *<sup>m</sup>* . The bandwidths 1 *k* and 2 *k* of both filters are calculated as above (Eq. 14).

#### **4. Application to simulated 2D-mBm paths**

In this section, the suggested estimators of the local regularity are tested on synthetic 2DmBm paths whose lengths are 256 x 256, generated using the kriging method (Barrière, 2007). Three types of Hölder function *H* are chosen:

$$\text{bilinear}: \ H\_1(\mathbf{x}\_1, \mathbf{x}\_2) = 0.8 - 0.6 \,\mathbf{x}\_1 \,\mathbf{x}\_2$$

$$\text{logistic} : H\_2(\mathbf{x}\_1, \mathbf{x}\_2) = 0.7 - \frac{0.4}{1 + \exp\left(-20(\mathbf{x}\_2 - 0.5)\right)}$$

$$\text{periodic}: \ H\_3(\mathbf{x}\_1, \mathbf{x}\_2) = 0.5 + 0.3 \sin \left( 2 \pi \,\mathbf{x}\_1 \right) \cos \left( \frac{3}{2} \pi \,\mathbf{x}\_2 \right)$$

The regularity functions and the simulated 2D-mBm paths corresponding to the three theoretical *H* functions are presented in Figure 2. The larger *H* value, the smoother the modeled surface.

Using the three algorithms, we have estimated *H* maps. For the first wavelet-based algorithm, we use the Morlet wavelet with *0x=0y=*8.9443, while for 2D MFT, the selected parameters for the two-dimensional Gaussian filters are:


The *H* maps obtained by the three estimators, presented in Figure 3, show that the regularity estimated by the first wavelet-based algorithm using the Morlet wavelet are better than that calculated by the second algorithm with the Mexican hat. In addition, the suggested 2D MFT provides the best estimations of the regularity maps with the least errors. For this reason, we retain only this estimator in the following. It can be also remarked that all the used algorithms yield large absolute values of the estimation error in the limits of the analyzed 2D-mBms.

Here, we propose to extend the 1D MFT enhanced by Li (1997) to 2 dimensions. The idea consists on decomposing the two-dimensional signal using a Gaussian filter

1 2 (, , ) (, ) (, )

*Gk G k G k*

 

and 2 *G k*(, )

*H xx*

*H xx*



In this section, the suggested estimators of the local regularity are tested on synthetic 2DmBm paths whose lengths are 256 x 256, generated using the kriging method (Barrière,

bilinear : 112 1 2 *H xx*, 0.8 0.6 *x x*

logistic : 2 12

periodic : 3 12 <sup>1</sup> <sup>2</sup>

The regularity functions and the simulated 2D-mBm paths corresponding to the three theoretical *H* functions are presented in Figure 2. The larger *H* value, the smoother the

Using the three algorithms, we have estimated *H* maps. For the first wavelet-based

The *H* maps obtained by the three estimators, presented in Figure 3, show that the regularity estimated by the first wavelet-based algorithm using the Morlet wavelet are better than that calculated by the second algorithm with the Mexican hat. In addition, the suggested 2D MFT provides the best estimations of the regularity maps with the least errors. For this reason, we retain only this estimator in the following. It can be also remarked that all the used algorithms yield large absolute values of the estimation error in the limits of the analyzed

*0x=*

0.4 , 0.7 1 exp 20 0.5

<sup>3</sup> , 0.5 0.3sin 2 cos <sup>2</sup>

*<sup>x</sup>*

*nm n m k k*

*e e* 

2 2

 

*<sup>m</sup>* . The bandwidths 1 *k* and 2 *k* of both filters are

2

 *x x*

*0y=*8.9443, while for 2D MFT, the selected

(15)

 

*n n n n*

*<sup>m</sup>* are variable center angular frequencies (or wavenumbers) of the

 

 

(, , ) *G k n m*

Where *<sup>n</sup>* and

modeled surface.

2D-mBms.


defined as:

**4. Application to simulated 2D-mBm paths** 

2007). Three types of Hölder function *H* are chosen:

algorithm, we use the Morlet wavelet with

*=*40,


parameters for the two-dimensional Gaussian filters are:

respective filters 1(, ) *G k <sup>n</sup>*

calculated as above (Eq. 14).

Fig. 2. A 3D-view representation and a XY-plan projection of the theoretical *H* function and the corresponding simulated 2D-mBm path, for the three types of *H* functions. Bilinear (top), logistic (middle) and periodic (bottom).

Two-Dimensional Multifractional Brownian

sub-parallel to F1 but less important.

with a sampling rate Δ*x*=Δ*y*=0.0121 cm.

0.2175 m, 0.3142 m and 0.4109 m.

1

2

3

4

5

and five vertical profiles as shown in Figure 5.

Fig. 4. Core image.

**5. Application to digitalized core image data** 

main geological features of the studied region (Fig.4).

Motion- Based Investigation of Heterogeneities from a Core Image 117

Here, the local regularity analysis is performed on digitalized core image data. The analyzed core is extracted from a well drilled in an Algerian basin. It is chosen since it represents the

The core presents medium to fine quartzitic sandstone, clay and quartz cemented cross stratifications underlined by mud films. The formation is affected by a main fracture F1 with a high angle dip (≈75°) filled with quartz. It is also noted the presence of another fracture F2

Mud films Break F1 F2

The processing of the core image requires first its digitalization. The core image is digitalized and codified in gray levels with integer values ranged between 0 and 255. The obtained digitalized core image, illustrated by figure 5, corresponds to a matrix of 3642 x 996

First, the fractal behavior of the digitalized core image data is inspected on five horizontal

1 2 3 4 5

Fig. 5. Positions of the horizontal and the vertical profiles on the digitalized core image. The horizontal profiles numbered from 1 to 5 (in blue) correspond to the respective

positions *y* = 0.0120 m, 0.0361 m, 0.0603 m, 0.0845 m and 0.1087 m, while the vertical profiles numbered from 1 to 5 (in red) correspond to the respective positions *x* = 0.0241 m, 0.1208 m,

Fig. 3. Regularity functions obtained by the three algorithms from the 2D-mBm paths, represented in Fig.2, simulated with three types of *H* function: (a) bilinear (b) logistic (c) periodic

Line 1: theoretical *H* function; Lines 2 & 3: regularity functions estimated using FFT-based algorithms with, respectively, the Morlet wavelet and the Mexican hat; Line 4: regularity function estimated using 2D MFT (=40).

The columns from left to right represent: (1) the estimated *H* function , (2) the estimation error , calculated as the difference between the estimated *H* function and the theoretical *H* function.

### **5. Application to digitalized core image data**

Here, the local regularity analysis is performed on digitalized core image data. The analyzed core is extracted from a well drilled in an Algerian basin. It is chosen since it represents the main geological features of the studied region (Fig.4).

The core presents medium to fine quartzitic sandstone, clay and quartz cemented cross stratifications underlined by mud films. The formation is affected by a main fracture F1 with a high angle dip (≈75°) filled with quartz. It is also noted the presence of another fracture F2 sub-parallel to F1 but less important.

Fig. 4. Core image.

116 Advances in Data, Methods, Models and Their Applications in Geoscience

Fig. 3. Regularity functions obtained by the three algorithms from the 2D-mBm paths, represented in Fig.2, simulated with three types of *H* function: (a) bilinear (b) logistic (c)

Line 1: theoretical *H* function; Lines 2 & 3: regularity functions estimated using FFT-based algorithms with, respectively, the Morlet wavelet and the Mexican hat; Line 4: regularity

The columns from left to right represent: (1) the estimated *H* function , (2) the estimation error , calculated as the difference between the estimated *H* function and the theoretical *H* function.

periodic

function estimated using 2D MFT (=40).

The processing of the core image requires first its digitalization. The core image is digitalized and codified in gray levels with integer values ranged between 0 and 255. The obtained digitalized core image, illustrated by figure 5, corresponds to a matrix of 3642 x 996 with a sampling rate Δ*x*=Δ*y*=0.0121 cm.

First, the fractal behavior of the digitalized core image data is inspected on five horizontal and five vertical profiles as shown in Figure 5.

Fig. 5. Positions of the horizontal and the vertical profiles on the digitalized core image. The horizontal profiles numbered from 1 to 5 (in blue) correspond to the respective positions *y* = 0.0120 m, 0.0361 m, 0.0603 m, 0.0845 m and 0.1087 m, while the vertical profiles numbered from 1 to 5 (in red) correspond to the respective positions *x* = 0.0241 m, 0.1208 m, 0.2175 m, 0.3142 m and 0.4109 m.

Two-Dimensional Multifractional Brownian

Motion- Based Investigation of Heterogeneities from a Core Image 119

(a) Horizontal profiles

Fig. 6. Investigation of the fractal properties of the five horizontal (a) and vertical (b) profiles extracted from the digitalized core image. The five lines in (a) (resp. (b)), from top to bottom, correspond to the respective horizontal (resp. vertical) profiles numbered from 1 to 5. Left: the profile of the digitalized core image data, middle: the amplitude spectrum module of the data with respect to the wavenumber in the log-log scale, right: the local *H* exponent.

(b) Vertical profiles

For each profile, the Fourier amplitude spectrum is computed and represented in a double logarithmic scale. Then, we estimate the local Hölder function *H*(*x*) using an algorithm based on the local growth of the increment process *Sk,n*(*i*) (Peltier and Lévy-Véhél, 1994, 1995; Muniandy *et al.*, 2001; Li *et al.*, 2008; Gaci *et al.*, 2010):

$$S\_{k,n}(i) = \frac{m}{n-1} \sum\_{j \in \left[i-k/2, i+k/2\right]} \left| X(j+1) - X(j) \right|, \text{ 1\lessapprox} \tag{16}$$

where *n* is the signal *X* length, *k* is a fixed window size, and *m* is the largest integer not exceeding *n/k*.

The local Hölder function *H*(*x*) at point

$$\infty = \frac{i}{n-1} \tag{17}$$

is given by

$$\hat{H}(i) = -\frac{\log\left[\sqrt{\pi/2}\ S\_{k,n}(i)\right]}{\log\left(n-1\right)}\tag{18}$$

The obtained results corresponding to the horizontal profiles and the vertical profiles are respectively exposed in figures 6a and 6b.

It can be noted that all the resulted amplitude spectra exhibit an algebraic decay; that illustrates the fractal properties of the digitalized data. Besides, the analyzed profiles present a varying regularity with the position according to X- and Y-axis. They can be then regarded as paths of multifractional Brownian motions (mBms) (Peltier and Lévy-Véhel, 1995). The variation of *H* exponent value is related to the local lithological changes of the core composition.

The next step consists on establishing regularity maps from the digitalized data using the 2D MFT algorithm. The implementation of the latter algorithm requires the ''reconditioning'' of the data so that the matrix dimensions corresponding to the digitalized data are a power of 2. For the purpose of processing the digitalized data, and considering the limitations of the available computer's capacities, we have splited the obtained matrix (3642 x 996) into two overlapping sub-matrixes whose size is 2048 x 1024. The sub-matrixes are padded by zeros so that their dimensions following *Y*-axis, initially equal to 996, reach 1024.

The parameters selected for the 2D MFT are as follow:


$$
\xi\_{\text{max}} = \nu\_{\text{max}} = 2\pi/(2\text{ }\Delta\text{x}) \approx 25964 \text{ rad/m};
$$

The other parameters (and *N*) are similar to those used in the previous section.

The final regularity map is constructed from the *H* sub-maps related to the two sub-matrixes (Fig. 7). The *H* values in the overlapping zone are calculated as the average of the *H* values corresponding to the *H* values in the sub-maps.

For each profile, the Fourier amplitude spectrum is computed and represented in a double logarithmic scale. Then, we estimate the local Hölder function *H*(*x*) using an algorithm based on the local growth of the increment process *Sk,n*(*i*) (Peltier and Lévy-Véhél, 1994,

1

, *1<k<n* (16)

*<sup>n</sup>* (17)

(18)

2, 2

*x*

where *n* is the signal *X* length, *k* is a fixed window size, and *m* is the largest integer not

1 *i*

log 1

*n*

The obtained results corresponding to the horizontal profiles and the vertical profiles are

It can be noted that all the resulted amplitude spectra exhibit an algebraic decay; that illustrates the fractal properties of the digitalized data. Besides, the analyzed profiles present a varying regularity with the position according to X- and Y-axis. They can be then regarded as paths of multifractional Brownian motions (mBms) (Peltier and Lévy-Véhel, 1995). The variation of *H* exponent value is related to the local lithological changes of the core

The next step consists on establishing regularity maps from the digitalized data using the 2D MFT algorithm. The implementation of the latter algorithm requires the ''reconditioning'' of the data so that the matrix dimensions corresponding to the digitalized data are a power of 2. For the purpose of processing the digitalized data, and considering the limitations of the available computer's capacities, we have splited the obtained matrix (3642 x 996) into two overlapping sub-matrixes whose size is 2048 x 1024. The sub-matrixes are padded by zeros

*ξmax=νmax =* 2/(2 Δx)≈ 25964 rad/m;

The final regularity map is constructed from the *H* sub-maps related to the two sub-matrixes (Fig. 7). The *H* values in the overlapping zone are calculated as the average of the *H* values

and *N*) are similar to those used in the previous section.

so that their dimensions following *Y*-axis, initially equal to 996, reach 1024.


The parameters selected for the 2D MFT are as follow:


corresponding to the *H* values in the sub-maps.

, log 2 <sup>ˆ</sup>

*S i k n H i*

 

*j ik ik <sup>m</sup> S i Xj Xj*

1995; Muniandy *et al.*, 2001; Li *et al.*, 2008; Gaci *et al.*, 2010):

1 *k n*

The local Hölder function *H*(*x*) at point

respectively exposed in figures 6a and 6b.

exceeding *n/k*.

is given by

composition.

The other parameters (

,

*n*

(a) Horizontal profiles

Fig. 6. Investigation of the fractal properties of the five horizontal (a) and vertical (b) profiles extracted from the digitalized core image. The five lines in (a) (resp. (b)), from top to bottom, correspond to the respective horizontal (resp. vertical) profiles numbered from 1 to 5. Left: the profile of the digitalized core image data, middle: the amplitude spectrum module of the data with respect to the wavenumber in the log-log scale, right: the local *H* exponent.

Two-Dimensional Multifractional Brownian

characterizing the surrounding medium.

and class 6 = 235, 255 .

Motion- Based Investigation of Heterogeneities from a Core Image 121

trajectory of a 2D-mBm. The obtained *H* maps highlight well the main fault F1, the break and the mud films. However, the minor fault F2 is locally noticeable. We note that these lithological changes are marked by local maxima of *H* values which are higher than those

Now, we aim to establish a correspondence between the digitalized data values, which are the gray levels values representing the geological facies, and the *H* value via a statistical analysis. In order to avoid the abnormally high values of *H* due to the limits effects, we consider the digitalized data corresponding to a central zone extracted from the core image (X: 10.8671- 43.5047cm; Y: 0.9550- 10.2627 cm). Thereafter, six classes are determined by fitting the results yielded by the application of the k-means method on the selected data. The six classes of the gray levels resulted from this classification are: class 1 = 0, 62 , class 2 = 62,80 , class 3 = 80,160 , class 4 = 160, 210 , class 5 = 210, 235

From figure 8, it can be seen that the histograms of *H* values calculated by 2D MFT follow a normal distribution. For each class, the statistical parameters (mean and standard-deviation) are estimated from the histograms of the gray level values, and the corresponding *H* values (Table 1). It is worth noting that for the six classes, the statistical parameters of *H* values, estimated from the histograms, present very close values. These results show that the Hölder exponent value can not characterize a geological facies represented by the gray level,

whereas its local variation reflects local lithological changes as explained earlier.

Fig. 8. Histograms of the digitalized data values extracted from the core image, and the corresponding *H* values estimated by 2D MFT, for the six classes. The six columns from left

to right correspond respectively to the classes 1 to 6.

Fig. 7. A regularity map (b) obtained by 2D MFT from the digitalized core image data (a). The regularity map (b), corresponding to the data of the whole core, is obtained from the regularity maps (c) and (d), related to the two ''sub- zones'' of the core image.

From Figure 7, it can be seen that the analyzed data present a varying regularity in the XY plan. It is again confirmed that the digitalized core image data can be modeled as a

Fig. 7. A regularity map (b) obtained by 2D MFT from the digitalized core image data (a). The regularity map (b), corresponding to the data of the whole core, is obtained from the

From Figure 7, it can be seen that the analyzed data present a varying regularity in the XY plan. It is again confirmed that the digitalized core image data can be modeled as a

regularity maps (c) and (d), related to the two ''sub- zones'' of the core image.

trajectory of a 2D-mBm. The obtained *H* maps highlight well the main fault F1, the break and the mud films. However, the minor fault F2 is locally noticeable. We note that these lithological changes are marked by local maxima of *H* values which are higher than those characterizing the surrounding medium.

Now, we aim to establish a correspondence between the digitalized data values, which are the gray levels values representing the geological facies, and the *H* value via a statistical analysis. In order to avoid the abnormally high values of *H* due to the limits effects, we consider the digitalized data corresponding to a central zone extracted from the core image (X: 10.8671- 43.5047cm; Y: 0.9550- 10.2627 cm). Thereafter, six classes are determined by fitting the results yielded by the application of the k-means method on the selected data. The six classes of the gray levels resulted from this classification are: class 1 = 0, 62 , class 2 = 62,80 , class 3 = 80,160 , class 4 = 160, 210 , class 5 = 210, 235 and class 6 = 235, 255 .

From figure 8, it can be seen that the histograms of *H* values calculated by 2D MFT follow a normal distribution. For each class, the statistical parameters (mean and standard-deviation) are estimated from the histograms of the gray level values, and the corresponding *H* values (Table 1). It is worth noting that for the six classes, the statistical parameters of *H* values, estimated from the histograms, present very close values. These results show that the Hölder exponent value can not characterize a geological facies represented by the gray level, whereas its local variation reflects local lithological changes as explained earlier.

Fig. 8. Histograms of the digitalized data values extracted from the core image, and the corresponding *H* values estimated by 2D MFT, for the six classes. The six columns from left to right correspond respectively to the classes 1 to 6.

Two-Dimensional Multifractional Brownian

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Table 1. Statistical parameters estimated from the histograms (gray level and corresponding *H* values) related to the six classes.

#### **6. Conclusion**

In this study, the 2D-mBm has been successfully used for a local Hölder regularity-based modeling of the core image. We have presented three methods for estimating the local regularity. The first and the second ones are FFT-based algorithms using, respectively, the Morlet wavelet and the Mexican hat, while the third method is obtained by extending the one-dimensional multiple filter technique to 2 dimensions (2D MFT). The application of these methods on synthetic 2D-mBm paths showed that the 2D MFT yields the best estimations of the *H* functions.

The analysis of profiles extracted from the digitalized core image data reveals a fractal behavior. Furthermore, the regularity maps obtained by 2D MFT from the digitalized data can characterize heterogeneities from the analyzed core. Although a Hölder exponent value does not describe a specific geological facies, its local variation reflects the lithological changes (faults, breaks, stratifications, etc.). The presented analysis must be undertaken on a large number of cores in order to establish a relation between a geological facies, the corresponding gray level and *H* values.

#### **7. Acknowledgements**

I would like to thank Mr. Tenkhi for his comments and suggestions.

#### **8. References**


*H* value Mean 0,218 0,222 0,192 0,181 0,172 0,163

Table 1. Statistical parameters estimated from the histograms (gray level and corresponding

In this study, the 2D-mBm has been successfully used for a local Hölder regularity-based modeling of the core image. We have presented three methods for estimating the local regularity. The first and the second ones are FFT-based algorithms using, respectively, the Morlet wavelet and the Mexican hat, while the third method is obtained by extending the one-dimensional multiple filter technique to 2 dimensions (2D MFT). The application of these methods on synthetic 2D-mBm paths showed that the 2D MFT yields the best

The analysis of profiles extracted from the digitalized core image data reveals a fractal behavior. Furthermore, the regularity maps obtained by 2D MFT from the digitalized data can characterize heterogeneities from the analyzed core. Although a Hölder exponent value does not describe a specific geological facies, its local variation reflects the lithological changes (faults, breaks, stratifications, etc.). The presented analysis must be undertaken on a large number of cores in order to establish a relation between a geological facies, the

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Characterization and Classification on SAR Images; *International Geoscience and Remote Sensing Symposium (IGARSS)*, Vol. 3, pp. 1609–1611. doi :

Class 3 80,160

Mean 40,811 72,093 93,054 198,517 227,367 245,087

deviation 9,761 4,432 11,085 4,945 4,626 5,558

Class 4 160, 210

0,090 0,107 0,095 0,071 0,070 0,070

Class 5 210, 235 Class 6 235, 255

Class 2 62,80

Class 1

Standard-

Standarddeviation

*H* values) related to the six classes.

estimations of the *H* functions.

**7. Acknowledgements** 

**8. References** 

corresponding gray level and *H* values.

I would like to thank Mr. Tenkhi for his comments and suggestions.

*Iberoamericana*, Vol. 13, No.1, pp. 19–90.

10.1109/IGARSS.1994.399514. August 8-12, 1994.

Digitalized data

**6. Conclusion** 

0, 62


**7** 

*China* 

**3D Seismic Sedimentology of Nearshore** 

The nearshore subaqueous fan, also known as the steep bank sublacustrine fan (Zhao, 2000), or submarine fan (Catuneanu et al., 2002; Richard & Bowman, 1998; Takahiro & Makoto, 2002), is the fan-shaped sedimentary accumulation of sand–conglomerate body located in the footwall of major fault in rift basins (Zhang, J.L & Shen, 1991; Zhang, M. & Tian, 1999), and commonly composed by three sub- facies including a root sub-fan, a mid sub-fan and a marginal sub-fan. Its formation and development are controlled by basin boundary conditions, paleotopography, tectonic evolution, the nature of the provenance, paleoclimate, paleocurrent and other factors (Lu, 2008; Xie et al., 2004; Yan et al., 2005). In the Bohai Bay Basin, eastern China, a nearshore subaqueous fan system of Paleogene age is widely developed in the lower Es4 Formation in Paleogene in the northern Dongying Depression (Fig.1). Analyses found that the mid sub-fan is the main part of the fan, characterized by the pebbly sandstones, conglomerates and block sandstones in the braided channel microfacies, intra-channel microfacies and leafy sandbody microfacies (Gao et al., 2008; Song, 2004; Yan et al., 2005). Oil and gas exploration in the Dongying Depression has demonstrated that the sand–conglomerate developed in the mid sub-fan is the effective oil and gas reservoir. Due to a deep burial (>3500m), multi staged sub-fan development, and small seismic impedance differences, however, to describe and predict the distribution of the effective sand– conglomerate reservoir in the nearshore subaqueous fan is difficult. Studies have also found that conventional 3D seismic data with industry-standard and seismic acoustic impedance inversion data from ac+den loggings could not distinguish the effective sand–conglomerate

Seismic sedimentology is the use of seismic data to study sedimentary rocks and processes by which they form (Zeng et al., 2001, 2004). Since its first introduction in 1998 (Zeng et al., 1998), the concept has been applied in the identification of paleorivers, the sedimentary facies and sedimentary environment evolutions of carbonate platform and the slope fans with many good results (Carter, 2003; Chen.& Meng, 2004; Crumeyrolle et al., 2007; Darmad et al., 2007; Gee & Gawthorpe, 2007; Handford & Baria, 2007; Ling et al., 2005; Lin et al.,

reservoir from sand–conglomerate sedimentary body (Song, 2004).

**1. Introduction** 

**Subaqueous Fans – A Case Study from** 

**Dongying Depression, Eastern China** 

*1School of Ocean and Earth Science, Tongji University, Shanghai,* 

Yang Fengli1,\*, Zhao Wenfang1, Sun Zhuan1,

*2Jiangsu Oilfield, SINOPEC, Yangzhou, Jiangsu, 3Chengdu University of Technology, Chengdu, Sichuan,* 

Cheng Haisheng2 and Peng Yunxin3


## **3D Seismic Sedimentology of Nearshore Subaqueous Fans – A Case Study from Dongying Depression, Eastern China**

Yang Fengli1,\*, Zhao Wenfang1, Sun Zhuan1, Cheng Haisheng2 and Peng Yunxin3 *1School of Ocean and Earth Science, Tongji University, Shanghai, 2Jiangsu Oilfield, SINOPEC, Yangzhou, Jiangsu, 3Chengdu University of Technology, Chengdu, Sichuan, China* 

#### **1. Introduction**

124 Advances in Data, Methods, Models and Their Applications in Geoscience

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Hölder regularity analysis of the sparse code; *IEEE Int. Geosci. Remote Sens. Symp.*,

Malaysian foreign currency exchange rates, Physica A, Vol. 301, No. 1–4, pp. 407–

The nearshore subaqueous fan, also known as the steep bank sublacustrine fan (Zhao, 2000), or submarine fan (Catuneanu et al., 2002; Richard & Bowman, 1998; Takahiro & Makoto, 2002), is the fan-shaped sedimentary accumulation of sand–conglomerate body located in the footwall of major fault in rift basins (Zhang, J.L & Shen, 1991; Zhang, M. & Tian, 1999), and commonly composed by three sub- facies including a root sub-fan, a mid sub-fan and a marginal sub-fan. Its formation and development are controlled by basin boundary conditions, paleotopography, tectonic evolution, the nature of the provenance, paleoclimate, paleocurrent and other factors (Lu, 2008; Xie et al., 2004; Yan et al., 2005). In the Bohai Bay Basin, eastern China, a nearshore subaqueous fan system of Paleogene age is widely developed in the lower Es4 Formation in Paleogene in the northern Dongying Depression (Fig.1). Analyses found that the mid sub-fan is the main part of the fan, characterized by the pebbly sandstones, conglomerates and block sandstones in the braided channel microfacies, intra-channel microfacies and leafy sandbody microfacies (Gao et al., 2008; Song, 2004; Yan et al., 2005). Oil and gas exploration in the Dongying Depression has demonstrated that the sand–conglomerate developed in the mid sub-fan is the effective oil and gas reservoir. Due to a deep burial (>3500m), multi staged sub-fan development, and small seismic impedance differences, however, to describe and predict the distribution of the effective sand– conglomerate reservoir in the nearshore subaqueous fan is difficult. Studies have also found that conventional 3D seismic data with industry-standard and seismic acoustic impedance inversion data from ac+den loggings could not distinguish the effective sand–conglomerate reservoir from sand–conglomerate sedimentary body (Song, 2004).

Seismic sedimentology is the use of seismic data to study sedimentary rocks and processes by which they form (Zeng et al., 2001, 2004). Since its first introduction in 1998 (Zeng et al., 1998), the concept has been applied in the identification of paleorivers, the sedimentary facies and sedimentary environment evolutions of carbonate platform and the slope fans with many good results (Carter, 2003; Chen.& Meng, 2004; Crumeyrolle et al., 2007; Darmad et al., 2007; Gee & Gawthorpe, 2007; Handford & Baria, 2007; Ling et al., 2005; Lin et al.,

3D Seismic Sedimentology of Nearshore Subaqueous Fans –

burial depth of these subaqueous fans now reaches more than 3500m.

A Case Study from Dongying Depression, Eastern China 127

characterized by a structural style of half-graben with a northern faulting and southward overlaping. The Depression can be divided in to three structural belts: a northern steep belt (NSB), a middle sag belt (MSB) and a southern slope belt (SSB) (Fig.1c). During the lower Es4 Formation in the early Paleogene, under the controlling of the northern Chenjiazhuang boundary extensional fault, many nearshore subaqueous fans developed in the footwall of the Chenjiazhuang major fault along the northern steep belt and extending into the deep and semi-deep lacustrine facies of the middle sag belt (Fig.1d) with sources mainly from the northern Chenjiazhuang Uplift (Gao et al., 2008; Xie et al., 2004; Yan et al., 2005) (Fig. 1). The

Facies analyses shows that the Dongying nearshore subaqueous fan consists of three subfacies including a root sub-fan, a mid sub -fan and a marginal sub -fan (Gao et al., 2008; Song, 2004; Yan et al., 2005). The root sub-fan is composed by one or more major channel

Fig. 2. The single-well facies analysis of well f8 shows that the 4th member of the lower Es4 Formation is a nearshore subaqueous fans with three sub-facies (modified from Gao et al.,

2008; Song, 2004; Yan et al., 2005).

2007; Liu, B.G. & Liu, L.H., 2008; Nordfjord et al., 2005; Posamentier & Killa, 2003; Prather, 2003; Sullivan et al., 2007; Schwab et al., 2007; Wang et al , 2004; Wu et al, 2005; Zeng et al., 2003, 2004, 2007; Zhang et al., 2007), but rarely used to study nearshore subaqueous fans. In this paper, we took the nearshore subaqueous fan in the Dongying Depression as a case, and used the pseudo-acoustic 3D seismic inversion method on characteristic logs to reconstruct 3D seismic sedimentological structures of the nearshore subaqueous fans including the distribution of the effective sand-conglomerate reservoirs and the temporospatial evolution of individual nearshore subaqueous fan system.

Over the years, six exploratory wells were drilled into the lower Es4 Formation in the northern Dongying Depression and four of them encountered commercial oil and gas. The logging data from all six wells yield good coverage with 0.125 m or 0.25 m sampling spacing. An industry- standard 3D seismic data of 600 km2 acquired in 2005 was processed using high-fidelity prestack time migration technique with 25m × 25m track spacing, 1ms sampling interval, 25HZ dominant frequency and 10-60Hz effective frequency bandwidth in the target formation.

#### **2. Characteristics of the nearshore subaqueous fan in the northern Dongying Depression**

The Dongying Depression is a typical sub-structural unit in the Bohai Bay Basin, Eastern China, surrounded by a series of uplifts, including the Luxi Massif in the south, Chenjiazhuang Uplift in the north, Qingtuozi Uplift in the east, Binxian Uplift and Qingcheng Uplift in the west (Fig.1). As a rift basin, the Dongying Depression is

Fig. 1. Location and distribution of sedimentary facies of the lower Es4 Formation in the northern Dongying Depression, Bohai Bay Basin, Eastern China. 3D seismic area is marked by Red box.

2007; Liu, B.G. & Liu, L.H., 2008; Nordfjord et al., 2005; Posamentier & Killa, 2003; Prather, 2003; Sullivan et al., 2007; Schwab et al., 2007; Wang et al , 2004; Wu et al, 2005; Zeng et al., 2003, 2004, 2007; Zhang et al., 2007), but rarely used to study nearshore subaqueous fans. In this paper, we took the nearshore subaqueous fan in the Dongying Depression as a case, and used the pseudo-acoustic 3D seismic inversion method on characteristic logs to reconstruct 3D seismic sedimentological structures of the nearshore subaqueous fans including the distribution of the effective sand-conglomerate reservoirs and the temporospatial evolution

Over the years, six exploratory wells were drilled into the lower Es4 Formation in the northern Dongying Depression and four of them encountered commercial oil and gas. The logging data from all six wells yield good coverage with 0.125 m or 0.25 m sampling spacing. An industry- standard 3D seismic data of 600 km2 acquired in 2005 was processed using high-fidelity prestack time migration technique with 25m × 25m track spacing, 1ms sampling interval, 25HZ dominant frequency and 10-60Hz effective frequency bandwidth in

**2. Characteristics of the nearshore subaqueous fan in the northern Dongying** 

The Dongying Depression is a typical sub-structural unit in the Bohai Bay Basin, Eastern China, surrounded by a series of uplifts, including the Luxi Massif in the south, Chenjiazhuang Uplift in the north, Qingtuozi Uplift in the east, Binxian Uplift and Qingcheng Uplift in the west (Fig.1). As a rift basin, the Dongying Depression is

Fig. 1. Location and distribution of sedimentary facies of the lower Es4 Formation in the northern Dongying Depression, Bohai Bay Basin, Eastern China. 3D seismic area is marked

of individual nearshore subaqueous fan system.

the target formation.

**Depression** 

by Red box.

characterized by a structural style of half-graben with a northern faulting and southward overlaping. The Depression can be divided in to three structural belts: a northern steep belt (NSB), a middle sag belt (MSB) and a southern slope belt (SSB) (Fig.1c). During the lower Es4 Formation in the early Paleogene, under the controlling of the northern Chenjiazhuang boundary extensional fault, many nearshore subaqueous fans developed in the footwall of the Chenjiazhuang major fault along the northern steep belt and extending into the deep and semi-deep lacustrine facies of the middle sag belt (Fig.1d) with sources mainly from the northern Chenjiazhuang Uplift (Gao et al., 2008; Xie et al., 2004; Yan et al., 2005) (Fig. 1). The burial depth of these subaqueous fans now reaches more than 3500m.

Facies analyses shows that the Dongying nearshore subaqueous fan consists of three subfacies including a root sub-fan, a mid sub -fan and a marginal sub -fan (Gao et al., 2008; Song, 2004; Yan et al., 2005). The root sub-fan is composed by one or more major channel

Fig. 2. The single-well facies analysis of well f8 shows that the 4th member of the lower Es4 Formation is a nearshore subaqueous fans with three sub-facies (modified from Gao et al., 2008; Song, 2004; Yan et al., 2005).

3D Seismic Sedimentology of Nearshore Subaqueous Fans –

**3.1 Methodology** 

A Case Study from Dongying Depression, Eastern China 129

**3. The pseudo-acoustic 3D seismic inversion based on Logs reconstruction** 

The pseudo-acoustic 3D seismic inversion method different from the conventional 3D seismic impedance inversion method not only in working through logs reconstruction, inversion, interpolation and extrapolation, but also adding or replacing characteristic curves to the density logs or, more commonly, velocity logs in order to achieve the ability to identify the reservoir from the surrounding rock in the case of small impedance difference (Shen & Yang, 2006; Zhang et al., 2005). The potential reservoir may show no direct relationship with the

The velocity and the time-depth relationship after logs reconstruction may change so deviations between seismic reflection horizon and synthetic seismogram calibration's horizon should be established to reflect these changes (Luo et al., 2006). The pseudo-acoustic seismic inversion results based on logs reconstruction may be not accurately reveals the corresponding lithological changes of the target layers. To solve this problem, the zero Mean-Based logs reconstruction techniques, which keeps the original time-depth relationship unchanged, can be applied. The principle is to set the characteristic curves or logs involved in seismic inversion to a mean of 0, that is ΣAi = 0 (Ai is characteristic curve sample values of target layers). Adding or subtracting the normalized curve and acoustic characteristics curve, then properly magnifying the normalized characteristics curve in

As the characteristic curves keep the information of the target layer, and the velocity curves of the upper and lower target layers are kept unchanged, so the original time-depth

The implementation process of this method includes the following: ①selection of the characteristic curves; ②standardization of the characteristic curves; ③normalization and reconstruction of the pseudo-acoustic curve; ④seismic wavelet extraction and the

To select the characteristic curves of the target layers, quantitative and semi-quantitative correlations through statistical analysis are established between different lithologyies (such as the conglomerate in the fan-root, sand–conglomerate in the mid-fan, mudstone, gypsumsalt rock in the marginal-fan), effective reservoir (such as gas sand–conglomerate in the midfan), logs (such as acoustic time (ac), natural gamma (gr), neutron porosity (cnl), spontaneous potential (sp), and logging parameters that correspond to different lithology

The results show that single logs parameter cannot identify the different lithologies in different fans, but combinations of any two of logging parameters (ac, gr or sp) can effectively indentify them to some extent. Further analysis also show that any two logs parameter's combinations between ac, gr, and sp could distinguish the effective and ineffective sand –conglomerate reservoir with a thicknesses greater than 6 m (Fig.4). Therefore, we can use any two logs combination between ac, gr, and sp as the characteristic

seismic reflection but can be distinguished from different lithological changes.

order to highlight lithology information. This process can be expressed as:

establishment of the initial model; ⑤ pseudo-acoustic seismic inversion.

**3.2 The pseudo-acoustic 3D seismic inversion based on logs reconstruction** 

pseudo-acoustic curve = acoustic logs ± characteristic curves × K,

while K stands for the curve amplification factor.

1. Selection of the characteristic curves

types in different fans.

curves.

relationship will remaine unchange (Luo et al., 2006).

sediments and the main lithology includes gray matrix-supported conglomerates, sandy conglomerates and black shales. The mid sub-fan, which is the main part of the nearshore subaqueous fan and forms the effective reservoir in the study area, is characterized by braided channels with braided channel microfacies, intra-channel microfacies and leafy sandbody microfacies. The main lithology of the mid sub-fan includes pebbly sandstones, conglomerate and block sandstones, with thickness varying between 1 and 55 m. The marginal sub-fan consists of siltstones, muddy siltstones and mudstone interbedding rocks (Fig.2). According to well stratigraphic cyclicities and 3D seismic reflection features, the lower Es4 Formation can be divided further into 5 members, standing for 5 individual nearshore subaqueous fans with several sub-facies (Fig. 2).

In general, 3D seismic reflection profiles of the nearshore subaqueous fan are characterized by wedge-shaped, mound-shaped or lenticular-shaped systems, and sub-fans can be further identified. On the synthetic seismograms record calibration, the root sub-fan is characterized by weak reflection, non-reflection or chaotic reflection, the mid sub-fan is characterized by weak to moderate intensity amplitudes, sub-parallel, weak continuous reflection, and the marginal sub-fan is characterized by continuous medium frequency, moderate to low intensity amplitudes. The deep lacustrine facies in the sag belt is characterized by either weak reflection or non- reflection. However, to identify the sub-facies of the nearshore subaqueous fan using the 3D seismic section is difficult (Fig.3).

Fig. 3. 3D seismic reflection characteristics of the nearshore subaqueous fans along line B'B (see Line location in Fig.1)

### **3. The pseudo-acoustic 3D seismic inversion based on Logs reconstruction**

#### **3.1 Methodology**

128 Advances in Data, Methods, Models and Their Applications in Geoscience

sediments and the main lithology includes gray matrix-supported conglomerates, sandy conglomerates and black shales. The mid sub-fan, which is the main part of the nearshore subaqueous fan and forms the effective reservoir in the study area, is characterized by braided channels with braided channel microfacies, intra-channel microfacies and leafy sandbody microfacies. The main lithology of the mid sub-fan includes pebbly sandstones, conglomerate and block sandstones, with thickness varying between 1 and 55 m. The marginal sub-fan consists of siltstones, muddy siltstones and mudstone interbedding rocks (Fig.2). According to well stratigraphic cyclicities and 3D seismic reflection features, the lower Es4 Formation can be divided further into 5 members, standing for 5 individual

In general, 3D seismic reflection profiles of the nearshore subaqueous fan are characterized by wedge-shaped, mound-shaped or lenticular-shaped systems, and sub-fans can be further identified. On the synthetic seismograms record calibration, the root sub-fan is characterized by weak reflection, non-reflection or chaotic reflection, the mid sub-fan is characterized by weak to moderate intensity amplitudes, sub-parallel, weak continuous reflection, and the marginal sub-fan is characterized by continuous medium frequency, moderate to low intensity amplitudes. The deep lacustrine facies in the sag belt is characterized by either weak reflection or non- reflection. However, to identify the sub-facies of the nearshore

nearshore subaqueous fans with several sub-facies (Fig. 2).

subaqueous fan using the 3D seismic section is difficult (Fig.3).

Fig. 3. 3D seismic reflection characteristics of the nearshore subaqueous fans along

line B'B (see Line location in Fig.1)

The pseudo-acoustic 3D seismic inversion method different from the conventional 3D seismic impedance inversion method not only in working through logs reconstruction, inversion, interpolation and extrapolation, but also adding or replacing characteristic curves to the density logs or, more commonly, velocity logs in order to achieve the ability to identify the reservoir from the surrounding rock in the case of small impedance difference (Shen & Yang, 2006; Zhang et al., 2005). The potential reservoir may show no direct relationship with the seismic reflection but can be distinguished from different lithological changes.

The velocity and the time-depth relationship after logs reconstruction may change so deviations between seismic reflection horizon and synthetic seismogram calibration's horizon should be established to reflect these changes (Luo et al., 2006). The pseudo-acoustic seismic inversion results based on logs reconstruction may be not accurately reveals the corresponding lithological changes of the target layers. To solve this problem, the zero Mean-Based logs reconstruction techniques, which keeps the original time-depth relationship unchanged, can be applied. The principle is to set the characteristic curves or logs involved in seismic inversion to a mean of 0, that is ΣAi = 0 (Ai is characteristic curve sample values of target layers). Adding or subtracting the normalized curve and acoustic characteristics curve, then properly magnifying the normalized characteristics curve in order to highlight lithology information. This process can be expressed as:

pseudo-acoustic curve = acoustic logs ± characteristic curves × K,

while K stands for the curve amplification factor.

As the characteristic curves keep the information of the target layer, and the velocity curves of the upper and lower target layers are kept unchanged, so the original time-depth relationship will remaine unchange (Luo et al., 2006).

The implementation process of this method includes the following: ①selection of the characteristic curves; ②standardization of the characteristic curves; ③normalization and reconstruction of the pseudo-acoustic curve; ④seismic wavelet extraction and the establishment of the initial model; ⑤ pseudo-acoustic seismic inversion.

#### **3.2 The pseudo-acoustic 3D seismic inversion based on logs reconstruction**

#### 1. Selection of the characteristic curves

To select the characteristic curves of the target layers, quantitative and semi-quantitative correlations through statistical analysis are established between different lithologyies (such as the conglomerate in the fan-root, sand–conglomerate in the mid-fan, mudstone, gypsumsalt rock in the marginal-fan), effective reservoir (such as gas sand–conglomerate in the midfan), logs (such as acoustic time (ac), natural gamma (gr), neutron porosity (cnl), spontaneous potential (sp), and logging parameters that correspond to different lithology types in different fans.

The results show that single logs parameter cannot identify the different lithologies in different fans, but combinations of any two of logging parameters (ac, gr or sp) can effectively indentify them to some extent. Further analysis also show that any two logs parameter's combinations between ac, gr, and sp could distinguish the effective and ineffective sand –conglomerate reservoir with a thicknesses greater than 6 m (Fig.4). Therefore, we can use any two logs combination between ac, gr, and sp as the characteristic curves.

3D Seismic Sedimentology of Nearshore Subaqueous Fans –

A Case Study from Dongying Depression, Eastern China 131

Fig. 5. Comparison between results using different 3D seismic inversion parameters. a. Conventional 3D seismic inversion data using ac+den loggings; b. Pseudo-acoustic (GS)

3D seismic inversion data based on gr + sp Logs reconstruction

Fig. 4. Statistical analysis between the different lithology, logging parameters of gr and sp and effective reservoir with a thicknesses of > 6 m in wells f1,f2,f3,f8.

2. The standardization of the characteristic curve

In order to eliminate the systematic error caused by different measuring apparatuses and time, the characteristic curves need to be standardized by depth correction, environment correction, mudstone baseline correction, outliers removal, wave filtering and so on.

3. Normalization and the creation of the pseudo-acoustic curve

In order to avoid the systematic error caused by differences in dimension and value range, the characteristic curves need to be normalized before creating the pseudo-acoustic curve. Firstly, the natural gamma (gr) and spontaneous potential (sp) logs will be normalized by regulating the numerical range to the [0 ,1] ,and conducting the [0 ,100] amplification process before summing them for a GS (gr+sp) curve. Then, the asonic logging curve (ac) is processed for the treatment filter values that exceed 100 in order to remain the lowfrequency information and eliminate high-frequency information of ac. Finally, the pseudoacoustic curve GS is obtained by adding the characteristic curve (GS) to the filtered ac. It is clear that the pseudo-acoustic curve GS contain not only the high frequency information of both gr and sp, but also the low frequency information of ac, thus the ability to identify lithologies and strata is greatly improved.

Fig. 4. Statistical analysis between the different lithology, logging parameters of gr and sp

In order to eliminate the systematic error caused by different measuring apparatuses and time, the characteristic curves need to be standardized by depth correction, environment

In order to avoid the systematic error caused by differences in dimension and value range, the characteristic curves need to be normalized before creating the pseudo-acoustic curve. Firstly, the natural gamma (gr) and spontaneous potential (sp) logs will be normalized by regulating the numerical range to the [0 ,1] ,and conducting the [0 ,100] amplification process before summing them for a GS (gr+sp) curve. Then, the asonic logging curve (ac) is processed for the treatment filter values that exceed 100 in order to remain the lowfrequency information and eliminate high-frequency information of ac. Finally, the pseudoacoustic curve GS is obtained by adding the characteristic curve (GS) to the filtered ac. It is clear that the pseudo-acoustic curve GS contain not only the high frequency information of both gr and sp, but also the low frequency information of ac, thus the ability to identify

correction, mudstone baseline correction, outliers removal, wave filtering and so on.

and effective reservoir with a thicknesses of > 6 m in wells f1,f2,f3,f8.

3. Normalization and the creation of the pseudo-acoustic curve

2. The standardization of the characteristic curve

lithologies and strata is greatly improved.

Fig. 5. Comparison between results using different 3D seismic inversion parameters. a. Conventional 3D seismic inversion data using ac+den loggings; b. Pseudo-acoustic (GS) 3D seismic inversion data based on gr + sp Logs reconstruction

3D Seismic Sedimentology of Nearshore Subaqueous Fans –

evolution stages of sub-facies in the nearshore subaqueous fan system.

A Case Study from Dongying Depression, Eastern China 133

of 2-5 sub-facies (Fig.6). The time for high frequent sub-facies development is during deposition of the 4th member of the lower Es4 Formation, which includes at least 5 subfacies. Fig.7 shows the instantaneous frequency level slices of sub-layers' bottom boundary of the lower Es4 Formation as characterized by a low frequency in the main channel in the fan-root, a middle-low frequency in the mid-fan and a high frequency in the marginal-fan. These results clearly reveal the paleogeographic characteristics and different temporospatial

Fig. 7. The instantaneous frequency level slices of sub-layers' bottom boundary of the lower Es4 Formation reflect the paleogeographic characteristics and space-time evolution of

different sub-layers

4. Seismic wavelet extraction and initial model creation

Establishing a reasonable initial geological model is the key for getting a good pseudoacoustic seismic inversion. In fact it is a process of deciphering interpolation and extrapolation of well data under the constraints of the geological concept; the quality of the seismic inversion results are largely dependant on the initial model, which is decided by previous geological knowledge. In order to acquire a good model of impedance inversion, we not only replace the sonic logging curve (ac) by the GS logging curve and by extract Ricker wavelet from the target layer, but also combine the available well information based on the synthetic seismograms calibration and test runs repeatedly.

5. Pseudo-acoustic 3D seismic inversion

On the Strata5.2 inversion software platform, the GS, the GS pseudo-acoustic 3D seismic inversion data are obtained by calculation after importing the GS. The results show that 3D seismic inversion data based on gr+sp logs reconstruction is better than the conventional 3D seismic inversion using ac+den loggings to distinguish the internal structure of the nearshore subagueous fans (Figs. 5, 6)

Fig. 6. 3D seismic reflection characteristics of the internal structure in the nearshore subaqueous fans based on GS 3D seismic inversion data along line B'B (see Line L location in Fig.1)

#### **4. 3D seismic sedimentology analysis of nearshore subaqueous fans**

#### **4.1 Evolution characteristics of seismic palaeogeomorphology of nearshore subaqueous fans**

By using the GS pseudo-acoustic 3D seismic inversion data coupled with calibration of the synthetic seismograms, the internal sub-facies in each member of the lower Es4 Formation can be identified and the temporospatial evolution of the nearshore subaqueous fans can be extrapolated (Fig.6). The analysis finds that each member of the lower Es4 generally consists

Establishing a reasonable initial geological model is the key for getting a good pseudoacoustic seismic inversion. In fact it is a process of deciphering interpolation and extrapolation of well data under the constraints of the geological concept; the quality of the seismic inversion results are largely dependant on the initial model, which is decided by previous geological knowledge. In order to acquire a good model of impedance inversion, we not only replace the sonic logging curve (ac) by the GS logging curve and by extract Ricker wavelet from the target layer, but also combine the available well information based

On the Strata5.2 inversion software platform, the GS, the GS pseudo-acoustic 3D seismic inversion data are obtained by calculation after importing the GS. The results show that 3D seismic inversion data based on gr+sp logs reconstruction is better than the conventional 3D seismic inversion using ac+den loggings to distinguish the internal structure of the

Fig. 6. 3D seismic reflection characteristics of the internal structure in the nearshore subaqueous

By using the GS pseudo-acoustic 3D seismic inversion data coupled with calibration of the synthetic seismograms, the internal sub-facies in each member of the lower Es4 Formation can be identified and the temporospatial evolution of the nearshore subaqueous fans can be extrapolated (Fig.6). The analysis finds that each member of the lower Es4 generally consists

fans based on GS 3D seismic inversion data along line B'B (see Line L location in Fig.1)

**4. 3D seismic sedimentology analysis of nearshore subaqueous fans 4.1 Evolution characteristics of seismic palaeogeomorphology of nearshore** 

4. Seismic wavelet extraction and initial model creation

on the synthetic seismograms calibration and test runs repeatedly.

5. Pseudo-acoustic 3D seismic inversion

nearshore subagueous fans (Figs. 5, 6)

**subaqueous fans** 

of 2-5 sub-facies (Fig.6). The time for high frequent sub-facies development is during deposition of the 4th member of the lower Es4 Formation, which includes at least 5 subfacies. Fig.7 shows the instantaneous frequency level slices of sub-layers' bottom boundary of the lower Es4 Formation as characterized by a low frequency in the main channel in the fan-root, a middle-low frequency in the mid-fan and a high frequency in the marginal-fan. These results clearly reveal the paleogeographic characteristics and different temporospatial evolution stages of sub-facies in the nearshore subaqueous fan system.

Fig. 7. The instantaneous frequency level slices of sub-layers' bottom boundary of the lower Es4 Formation reflect the paleogeographic characteristics and space-time evolution of different sub-layers

3D Seismic Sedimentology of Nearshore Subaqueous Fans –

impedance inversion.

pp.909–934, ISSN 0149-1423

2004), pp.33-36, ISSN 1000-1441

pp.198-200, ISSN 1000-0747

**6. References** 

A Case Study from Dongying Depression, Eastern China 135

3. Compared with the conventional 3D seismic inversion, the pseudo-acoustic 3D seismic inversion based on characteristic logs reconstruction greatly improves the ability to identify internal seismic sub-facies. Several internal sub-facies in each member of the

4. The pseudo-acoustic 3D seismic inversion technique based on logs reconstruction reveals the 3D seismic sedimentological characteristics of nearshore subaqueous fans including the internal sub-facies structure and various temporospatial evolution stages in different sub-facies. The distribution of the effective sand-conglomerate reservoirs can be better quantified by using this method than the conventional 3D seismic

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nearshore subaqueous fan in the lower Es4 Formation have been identified.

**4.2 The distribution characteristics of effective reservoir in nearshore subaqueous fan**  The synthetic seismogram calibration results show significantly higher dimension values of 12000-15500 in the GS pseudo-acoustic 3D seismic inversion for the effective sandconglomerate reservoir but lower dimension values<12,000 for the ineffective reservoir in the lower Es4 Formation (Fig.8). Accordingly, quantifying the thickness and the distribution of the effective sand-conglomerate reservoir in the lower Es4 Formation can be relatively easy (Fig.8).

Fig. 8. The effective reservoirs range of values in the GS 3D seismic inversion data for the blue zone (see location in Fig.5b)

### **5. Conclusions**


#### **6. References**

134 Advances in Data, Methods, Models and Their Applications in Geoscience

**4.2 The distribution characteristics of effective reservoir in nearshore subaqueous fan**  The synthetic seismogram calibration results show significantly higher dimension values of 12000-15500 in the GS pseudo-acoustic 3D seismic inversion for the effective sandconglomerate reservoir but lower dimension values<12,000 for the ineffective reservoir in the lower Es4 Formation (Fig.8). Accordingly, quantifying the thickness and the distribution of the effective sand-conglomerate reservoir in the lower Es4 Formation can be relatively

Fig. 8. The effective reservoirs range of values in the GS 3D seismic inversion data for the

1. Nearshore subaqueous fans of Paleogene age are well developed in the lower Es4 Formation of the Dongying Depression, in the Bohai Bay Basin, eastern China. Research and oil and gas exploration in the northern Dongying Depression have demonstrated that the sand–conglomerate in the mid sub-fan is not only the main part of the nearshore subaqueous fan, but also the effective oil and gas reservoir in the region. 2. Statistical analyses on different lithology and effective reservoir and logging parameters show that the acoustic (ac), natural gamma (gr), spontaneous potential (sp) can be used as characteristic curves for seismic inversion calculation. Any combinations of two logs can distinguish the effective from the ineffective sand –conglomerate reservoirs with a

easy (Fig.8).

blue zone (see location in Fig.5b)

thicknesses greater than 6 m.

**5. Conclusions** 


3D Seismic Sedimentology of Nearshore Subaqueous Fans –

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the nearshore submerged fan taking the hird member of the Shahejie Formation in Well C913 and C916 area on the northern zone of the Zhanhua Depression as example (in Chinese with English abstract).*Journal of Chengdu University of* 

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**8** 

Ahmad Bilal

 *Syria* 

*Damascus University,* 

**Mapping and Analyzing the Volcano-Petrology** 

**and Tectono-Seismicity Characteristics Along** 

The European and African continents are crossed by several N-S-trending rifts, all together major structural features at world scale. They include, from North to South, firstly the Oslo Permian rift (Norway), continued by the Neogene fracture system of Central-Southern Germany (Eifel, Rhine Graben), then the rift system of French massif Central and Rhone

These major crustal fractures, extending down in the underlying mantle, have been active at different times, while always keeping the same approximate N-S direction. Periods of major activity are marked by extensive volcanism, with a distinct tendency to show younger ages southwards: Permian in Norway, Neogene in Germany, Neogene to subactual in France, actual (present-day) in Africa. These ages correspond mainly to the initial stage of riftforming, whereas more ancient accidents (e.g. Norway) could repeatedly play again, at each

In direct continuity with the Dead Sea Fault, the Syrian rift links the rigid Arabian plate to the mobile ophiolite belt of Cyprus and Southern Turkey (Juteau 1974, Parrot 1977). It plays a very important role in the regional geodynamic structure. Its exact position, as well as the related fracture system, has been documented from the analysis of complete aerial photo

Many partial works on the different aspects of this area: tectonics, geodynamics, volcanism, crustal and mantle rocks, and seismicity have been done. But a global synthetic on these aspects are given in this research, using new data in field and laboratory. The results either of my team at Damascus university, or either those of the scientific cooperation projects, from 1998 till now, with the teams of colleagues from the French universities: professors Jean Chorowicz, and Albert Jambon, from Pierre and Marie Curie university; professor Phillipe Huchon, from Ecole Normal Superior of Paris; professor Jacques Touret, from Ecole des Mines of Paris, and professor Jean Ives Cottin from the university Jean Monnet of Saint-Etienne. In addition to international works indicated in the references list. While the global work, at the macro- scale, has been achieved, it still more works to do at the micro –scale: the detailed composition variations of the volcanic rocks, and their geologic process indication; the liaison between the different tectonic unities, and theirs liaison with the

coverage of the whole Syrian territory (Bilal and Ammar 2004).

regional geotectonic; and the micro- seismic zonation in the country.

valley, ending finally with the great African rift, the major structure of this continent.

**1. Introduction** 

phase of crustal extension.

**the Syrian Rift – NW the Arabian Plate** 


## **Mapping and Analyzing the Volcano-Petrology and Tectono-Seismicity Characteristics Along the Syrian Rift – NW the Arabian Plate**

Ahmad Bilal *Damascus University, Syria* 

#### **1. Introduction**

138 Advances in Data, Methods, Models and Their Applications in Geoscience

Zeng, H.L. & Kerans, C. (2003). Seismic frequency control on carbonate seismic stratigraphy:

Zeng, H.L. & Hentz, T. (2004). High-frequency sequence stratigraphy from seismic

Zeng, H.L.; Loucks, R. & Frank B. (2007). Mapping sediment- dispersal patterns and

Zhao, C.L. (2000). *Sedimentation-reservoir geologic essays* (in Chinese)*,* Petroleum Industry

Zhang, R.H.; Yu, S.Y. & Wu J.H. (1997). The effect of sediments supply condiction on

No.2 (February 2003), pp.273-293, ISSN 0149-1423

No.7, (July 2007), pp.981–1003, ISSN 0149-1423

No.2, (March 1997), pp.139-144, ISSN 1000-2383

Press, ISBN 7-5021-3006-3, Beijing, China

1423

A case study of the Kingdom Abo sequence, west Texas.*AAPG Bulletin,* Vol..87,

sedimentology: Applied to Miocene, Vermilion Block 50, Tiger schoal area,offshore Louisiana. *AAPG Bulletin,* Vol..88, No.2, (February 2004 ), pp.153-174, ISSN 0149-

associated systems tracts in fourth- and fifth-order sequences using seismic sedimentology: Example from Corpus Christi Bay, Texas. *AAPG Bulletin,* Vol.91,

sequence stratigraphy analysis in continental lacustrine basins (in Chinese with English abstract). *Earth Science-journal of China University of Geosciences,* Vol. 22,

> The European and African continents are crossed by several N-S-trending rifts, all together major structural features at world scale. They include, from North to South, firstly the Oslo Permian rift (Norway), continued by the Neogene fracture system of Central-Southern Germany (Eifel, Rhine Graben), then the rift system of French massif Central and Rhone valley, ending finally with the great African rift, the major structure of this continent.

> These major crustal fractures, extending down in the underlying mantle, have been active at different times, while always keeping the same approximate N-S direction. Periods of major activity are marked by extensive volcanism, with a distinct tendency to show younger ages southwards: Permian in Norway, Neogene in Germany, Neogene to subactual in France, actual (present-day) in Africa. These ages correspond mainly to the initial stage of riftforming, whereas more ancient accidents (e.g. Norway) could repeatedly play again, at each phase of crustal extension.

> In direct continuity with the Dead Sea Fault, the Syrian rift links the rigid Arabian plate to the mobile ophiolite belt of Cyprus and Southern Turkey (Juteau 1974, Parrot 1977). It plays a very important role in the regional geodynamic structure. Its exact position, as well as the related fracture system, has been documented from the analysis of complete aerial photo coverage of the whole Syrian territory (Bilal and Ammar 2004).

> Many partial works on the different aspects of this area: tectonics, geodynamics, volcanism, crustal and mantle rocks, and seismicity have been done. But a global synthetic on these aspects are given in this research, using new data in field and laboratory. The results either of my team at Damascus university, or either those of the scientific cooperation projects, from 1998 till now, with the teams of colleagues from the French universities: professors Jean Chorowicz, and Albert Jambon, from Pierre and Marie Curie university; professor Phillipe Huchon, from Ecole Normal Superior of Paris; professor Jacques Touret, from Ecole des Mines of Paris, and professor Jean Ives Cottin from the university Jean Monnet of Saint-Etienne. In addition to international works indicated in the references list. While the global work, at the macro- scale, has been achieved, it still more works to do at the micro –scale: the detailed composition variations of the volcanic rocks, and their geologic process indication; the liaison between the different tectonic unities, and theirs liaison with the regional geotectonic; and the micro- seismic zonation in the country.

Mapping and Analyzing the Volcano-Petrology and Tectono -

**3. Interplate volcanism along the Syrian rift** 

et al.1998, Rojay et al 2001,Yurtmen et al 2002).

faults of Owen (Arabia-India),to the East (Barrier et al.2004).

plate(Cetin et al.2003).

are summarized below:

**3.1 Volcanism** 

zone.

C, D),(Bosworth et al.2005)

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 141



The territory of syria corresponds to the NW corner of the Arabian plate. It is bordered by the Zagros Taurus collision zone, to the North, and the oceanic expansion zone, to the South. In the Western part of Syria, the rift structure, which corresponds to the northern part of the Dead Sea Fault Zone(DSFZ), is named the Levant fault, in continuity with the Red Sea rift

The Syrian rift is marked by an active interplate volcanism, occurring from Jurassic to present (Ponikarov 1967, Laws and Wilson 1997, Giannerini et al.1998). Volcanoes bring to the surface a number of mantle xenoliths, which provide essential information on the nature and composition of the underlying lithospheric mantle (Stein and Hofman 1992, Stein et al 1993, Sharkov et al.1993, Bilal and Touret 2001, Bilal and Sheleh 2004). Most important data

The occurrence of volcanic activity in its geotectonic context shows that this activity covers an important part of the surface of the Arabian plate: in Syria; in Jordan; and in Saudi Arabia (Fig.2). This volcanism covers the Mesozoic and Cenozoic times, but the major eruption is recent. It is distributed over three distinct regions (Mor 1993): (1) the Harrat Ash Shaam plateau; (2) the region from the Homs basalts to the Karasu valley; (3) the Arabian

The Harrat Ash Shaam basalt eruption occurred in three episodes: at 26-22 Ma.;18- 13Ma.;and 7to <0,5Ma.(Mor 1993, Ilani et al 2001).The Homs basalts are dated at 6,5- 2,0Ma.(Mouty et al.1992,Sharkovet al.1994,1998,Butler et al.1997, Butler and Spencer 1999).In the Ghab basin area and east of it ,the age ranges from 2.0 to 1,1 Ma (Heiman et al 1998). In the Karasu valley and vicinity, the age vary from 1, 6 to 0, 05 Ma. (Capan et al.1987,Heiman

Summarizing, volcanism in Syria, started during Lias with magmatism associated to the ophiolites in the north of the territory (in the Baer et Bassit region),at the same time of volcanism in the southern of Turkey (Antalya et Hatay ),or in the Mamonia complex in Cyprus (Robertson et al.1991).This volcanism is related to subvertical tension fractures caused by transcurent movement along the Syrian part (the Syrian rift)of the Dead Sea Fault Zone(DSFZ).It can be hypothetized that these fractures induced adiabatic partial melting in the lithosphere (Polat et al.1997,Adiyaman and Chorowwicz 2002,Chorowicz et al.2005). The volcanic emission extends over about 10% of the whole surface area of Syria (Fig. 3).Volcanism is related to the movement of the Arabian plate towards the Eurasian plate, at a velocity of 18±2mma-1, in a NNW direction (McClusky et al2000). Eruptions, flooding cover significant areas, where the Cenozoic basaltic lavas may be up to 500 M thick and are

platform and the Southern part of the Bitlis belt (e.g.karacadage volcano).

covered by Tertiary and Quaternary sediments (Al Mishwat and Nasir 2004).

Aurasia-Arabia, as well as the Anatolian fault at the north-west end of the Arabian

### **2. Geodynamic setting**

The Arabian plate has a roughly polygonal shape, inserted between the major African plate (including Nubian and Somalian ),to the East, and Eurasiatic and Indian plates, to the North. It is delimitated by the Red Sea in the South-West, the Aden gulf in the South, and the Za**g**ros and Taurus chains in the North and North-East, respectively.

Geophysical investigations confirms the typical continental nature of this plate, with an average crust thickness of 40 Km, which changes, at the level of the Red Sea , to less than 15 Km., on a distance of about 250Km.(Al Damegh et al.2005).

The Arabian plate shows three types of active borders (Fig.1):

Fig. 1. Geodynamic framework of the Arab plate (Barrier et al. 2004).



The territory of syria corresponds to the NW corner of the Arabian plate. It is bordered by the Zagros Taurus collision zone, to the North, and the oceanic expansion zone, to the South. In the Western part of Syria, the rift structure, which corresponds to the northern part of the Dead Sea Fault Zone(DSFZ), is named the Levant fault, in continuity with the Red Sea rift zone.

#### **3. Interplate volcanism along the Syrian rift**

The Syrian rift is marked by an active interplate volcanism, occurring from Jurassic to present (Ponikarov 1967, Laws and Wilson 1997, Giannerini et al.1998). Volcanoes bring to the surface a number of mantle xenoliths, which provide essential information on the nature and composition of the underlying lithospheric mantle (Stein and Hofman 1992, Stein et al 1993, Sharkov et al.1993, Bilal and Touret 2001, Bilal and Sheleh 2004). Most important data are summarized below:

#### **3.1 Volcanism**

140 Advances in Data, Methods, Models and Their Applications in Geoscience

The Arabian plate has a roughly polygonal shape, inserted between the major African plate (including Nubian and Somalian ),to the East, and Eurasiatic and Indian plates, to the North. It is delimitated by the Red Sea in the South-West, the Aden gulf in the South, and the

Geophysical investigations confirms the typical continental nature of this plate, with an average crust thickness of 40 Km, which changes, at the level of the Red Sea , to less than 15

Za**g**ros and Taurus chains in the North and North-East, respectively.

Fig. 1. Geodynamic framework of the Arab plate (Barrier et al. 2004).


Km., on a distance of about 250Km.(Al Damegh et al.2005). The Arabian plate shows three types of active borders (Fig.1):

**2. Geodynamic setting** 

The occurrence of volcanic activity in its geotectonic context shows that this activity covers an important part of the surface of the Arabian plate: in Syria; in Jordan; and in Saudi Arabia (Fig.2). This volcanism covers the Mesozoic and Cenozoic times, but the major eruption is recent. It is distributed over three distinct regions (Mor 1993): (1) the Harrat Ash Shaam plateau; (2) the region from the Homs basalts to the Karasu valley; (3) the Arabian platform and the Southern part of the Bitlis belt (e.g.karacadage volcano).

The Harrat Ash Shaam basalt eruption occurred in three episodes: at 26-22 Ma.;18- 13Ma.;and 7to <0,5Ma.(Mor 1993, Ilani et al 2001).The Homs basalts are dated at 6,5- 2,0Ma.(Mouty et al.1992,Sharkovet al.1994,1998,Butler et al.1997, Butler and Spencer 1999).In the Ghab basin area and east of it ,the age ranges from 2.0 to 1,1 Ma (Heiman et al 1998). In the Karasu valley and vicinity, the age vary from 1, 6 to 0, 05 Ma. (Capan et al.1987,Heiman et al.1998, Rojay et al 2001,Yurtmen et al 2002).

Summarizing, volcanism in Syria, started during Lias with magmatism associated to the ophiolites in the north of the territory (in the Baer et Bassit region),at the same time of volcanism in the southern of Turkey (Antalya et Hatay ),or in the Mamonia complex in Cyprus (Robertson et al.1991).This volcanism is related to subvertical tension fractures caused by transcurent movement along the Syrian part (the Syrian rift)of the Dead Sea Fault Zone(DSFZ).It can be hypothetized that these fractures induced adiabatic partial melting in the lithosphere (Polat et al.1997,Adiyaman and Chorowwicz 2002,Chorowicz et al.2005).

The volcanic emission extends over about 10% of the whole surface area of Syria (Fig. 3).Volcanism is related to the movement of the Arabian plate towards the Eurasian plate, at a velocity of 18±2mma-1, in a NNW direction (McClusky et al2000). Eruptions, flooding cover significant areas, where the Cenozoic basaltic lavas may be up to 500 M thick and are covered by Tertiary and Quaternary sediments (Al Mishwat and Nasir 2004).

Mapping and Analyzing the Volcano-Petrology and Tectono -

Fig. 3. The volcano-tectonics map of Syria.

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 143

Fig. 2. The Arabian interplatplate volcanism occurrence in its tectonics context. (Adiyaman and Chorowicz, 2002 ).

Fig. 2. The Arabian interplatplate volcanism occurrence in its tectonics context. (Adiyaman

and Chorowicz, 2002 ).

Fig. 3. The volcano-tectonics map of Syria.

Mapping and Analyzing the Volcano-Petrology and Tectono -

basalt around intergrain boundaries (Fig.5, A, B, C).

peridotite( Bilal and Touret 2001,Bilal et al.2011).

orthopyroxene in solid solution)+Co2.

(Bilal and Sheleh 2004).

**3.3 Fluid inclusions** 

**3.2 Composition of the lithospheric mantle** 

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 145

A number of volcanoes along the rift contain a number of ultrasiques xenoliths, notably lherzolites, harzburgites and pyroxenites(Bilal and Touret 2001).Major rock -forming minerals are Olivine (Ol), Ortho- and Clinopyroxene (Opx and Cpx),with as common accessories spinel and amphibole. Microstructure varies from coarse-grained, coarsegrained-tabular to rare porphyroclastic (Ismail et al.2008).Most mantle peridotites are very well preserved with however a small variable possibility of local melting by the enclosing

Most abundant rock types are harzburgites (Ol+Opx),which from their mineral composition and geochemistry can be divided into three groups (Ismail et al 2008): Group I, issued from a residual, depleted mantle, Groups II and III which correspond to a refertilized mantle, caused by the percolation of undifferentiated basaltic melt or ephemeral carbonate magmas through the residual lithosphere. Both groups correspond to a different degree of melting of the mantle peridotite (large for Group II, small for Group III).They are characterized by undispread mantle metasomatism with a carbonatite signature (Frezzotti et al 2002, Gregoir et al 2000), as notably indicated by the composition of clinopyroxene in some pyroxenites

Rare garnet-bearing varieties have also been observed in the middle and south domains (Mheilbeh,Tel Thenoun) including few grenatites. These correspond most probably to lower crustal granulites, even if the occurrence of some high-pressure basaltic derivates cannot be excluded (Bilal and Touret 2001). The possible occurrence of xenoliths corresponding to lower crustal granulites is further indicated by the occurrence of sapphirine in some garnet and/or spinel-bearing websterites (Opx and Cpx-bearing pyroxenites, Fig. 5 D ,E) (Bilal 2009b, Bilal et al.2011). These basalts result from a complex polybaric melting process, first starting in the garnet peridotite stability field, then proceeding within the field of spinel

A great of pure CO2-bearing fluid inclusions have been found in olivine and pyroxenes from xenoliths, and in phenocrysts from enclosing basalts (Bilal and Touret 2001).This type of inclusions occur in virtually all mantle xenoliths in basalts worldwide(Roedder 1984),but in the present case some features confirm the occurrence of mantle metasomatism seen above in group II and III.The CO2 density in inclusions is very variable ,most commonly around or lower the critical point(about 0,4 g/Cm3).Fluid pressure at trapping conditions ,for a reference temperature of about 1000C,correspond to a depth of about 5 Km, namely the last magma chamber prior to eruption .But some primary inclusions contain fluid of much higher density recording deeper episode of the rock evolution. Highest fluid densities (up to 1, 15 g/cm2) are found in pyroxenites, notably in clinopyroxene. Fig 5 (F , G, H, I) show primary inclusions, of tubular shape, aligned along orthopyroxene or plagioclase exsolution lamellae within the clinopyroxene host .It is belived that these fluids are formed

Olivin+Carbonate (from the Carbonatite)→Clinopyroxene (with plagioclase and

P-T conditions of mineral equilibration in the xenoliths can are deduced from the pyroxene mineral assemblage (pyroxene thermometry) for the temperature (Wells 1977, Bertrand and Mercier 1986,Brey and Kohler 1990, Kohler and Brey 1990),and from the maximum fluid

by a reaction illustrating the mantle metasomatism carbonatite connection:

The volcanism is divided into two periods: upper Jurassic-lower Cretaceous, a period corresponding to a phase of extension of the Arabian plate margin, it corresponds to the Bhannes-Tayasir area of Syria sequence, constitutes isolated lavas or covered by the Neogene eruption, especially in the south of the country (west of Damascus), and in the center (Nabi Mata region) (Dubertret 1962,Ponikarov 1967,Laws and Wilson 1997).More recent Neogene-Quaternary eruptions are related to the formation of the Red Sea (24-16Ma), and Dead Sea rifts (8-0,4 Ma) (Ponikarov 1967, Bohanon et al.1989,Camp et Roobol 1989,Baker et al 1997,Chorowicz et al 2005). A number of eruptions have been identified from 17 Ma to present. The last volcanic eruption took place in the South of the country, about 10000 years ago, as the end of the last eruption (<1Ma) (Dubertret 1933, Baker et al 1997).

Erupted lavas are in general very basic.rock compositions , cover the basalt-, picrobasalt-, and basanites fields on the diagram of Le Bas et al.(1986), (Fig.4),corresponding to a low differentiated magma(Ismail et al.2008). Major and trace elements data show overall similarities between recent and ancient ones, with however a more distinct alkaline trend and stronger variations of LILE-elements for recent lavas. These data involve small volume melt fractions.

Fig. 4. Total alkalis-silica diagram of Le Bas et al (1986) for the basaltic rocks along the Syrian rift (Bilal and Touret 2001).

#### **3.2 Composition of the lithospheric mantle**

144 Advances in Data, Methods, Models and Their Applications in Geoscience

The volcanism is divided into two periods: upper Jurassic-lower Cretaceous, a period corresponding to a phase of extension of the Arabian plate margin, it corresponds to the Bhannes-Tayasir area of Syria sequence, constitutes isolated lavas or covered by the Neogene eruption, especially in the south of the country (west of Damascus), and in the center (Nabi Mata region) (Dubertret 1962,Ponikarov 1967,Laws and Wilson 1997).More recent Neogene-Quaternary eruptions are related to the formation of the Red Sea (24-16Ma), and Dead Sea rifts (8-0,4 Ma) (Ponikarov 1967, Bohanon et al.1989,Camp et Roobol 1989,Baker et al 1997,Chorowicz et al 2005). A number of eruptions have been identified from 17 Ma to present. The last volcanic eruption took place in the South of the country, about 10000 years ago, as the end of the last eruption (<1Ma) (Dubertret 1933, Baker et al

Erupted lavas are in general very basic.rock compositions , cover the basalt-, picrobasalt-, and basanites fields on the diagram of Le Bas et al.(1986), (Fig.4),corresponding to a low differentiated magma(Ismail et al.2008). Major and trace elements data show overall similarities between recent and ancient ones, with however a more distinct alkaline trend and stronger variations of LILE-elements for recent lavas. These data involve small volume

Fig. 4. Total alkalis-silica diagram of Le Bas et al (1986) for the basaltic rocks along the Syrian

1997).

melt fractions.

rift (Bilal and Touret 2001).

A number of volcanoes along the rift contain a number of ultrasiques xenoliths, notably lherzolites, harzburgites and pyroxenites(Bilal and Touret 2001).Major rock -forming minerals are Olivine (Ol), Ortho- and Clinopyroxene (Opx and Cpx),with as common accessories spinel and amphibole. Microstructure varies from coarse-grained, coarsegrained-tabular to rare porphyroclastic (Ismail et al.2008).Most mantle peridotites are very well preserved with however a small variable possibility of local melting by the enclosing basalt around intergrain boundaries (Fig.5, A, B, C).

Most abundant rock types are harzburgites (Ol+Opx),which from their mineral composition and geochemistry can be divided into three groups (Ismail et al 2008): Group I, issued from a residual, depleted mantle, Groups II and III which correspond to a refertilized mantle, caused by the percolation of undifferentiated basaltic melt or ephemeral carbonate magmas through the residual lithosphere. Both groups correspond to a different degree of melting of the mantle peridotite (large for Group II, small for Group III).They are characterized by undispread mantle metasomatism with a carbonatite signature (Frezzotti et al 2002, Gregoir et al 2000), as notably indicated by the composition of clinopyroxene in some pyroxenites (Bilal and Sheleh 2004).

Rare garnet-bearing varieties have also been observed in the middle and south domains (Mheilbeh,Tel Thenoun) including few grenatites. These correspond most probably to lower crustal granulites, even if the occurrence of some high-pressure basaltic derivates cannot be excluded (Bilal and Touret 2001). The possible occurrence of xenoliths corresponding to lower crustal granulites is further indicated by the occurrence of sapphirine in some garnet and/or spinel-bearing websterites (Opx and Cpx-bearing pyroxenites, Fig. 5 D ,E) (Bilal 2009b, Bilal et al.2011). These basalts result from a complex polybaric melting process, first starting in the garnet peridotite stability field, then proceeding within the field of spinel peridotite( Bilal and Touret 2001,Bilal et al.2011).

#### **3.3 Fluid inclusions**

A great of pure CO2-bearing fluid inclusions have been found in olivine and pyroxenes from xenoliths, and in phenocrysts from enclosing basalts (Bilal and Touret 2001).This type of inclusions occur in virtually all mantle xenoliths in basalts worldwide(Roedder 1984),but in the present case some features confirm the occurrence of mantle metasomatism seen above in group II and III.The CO2 density in inclusions is very variable ,most commonly around or lower the critical point(about 0,4 g/Cm3).Fluid pressure at trapping conditions ,for a reference temperature of about 1000C,correspond to a depth of about 5 Km, namely the last magma chamber prior to eruption .But some primary inclusions contain fluid of much higher density recording deeper episode of the rock evolution. Highest fluid densities (up to 1, 15 g/cm2) are found in pyroxenites, notably in clinopyroxene. Fig 5 (F , G, H, I) show primary inclusions, of tubular shape, aligned along orthopyroxene or plagioclase exsolution lamellae within the clinopyroxene host .It is belived that these fluids are formed by a reaction illustrating the mantle metasomatism carbonatite connection:

Olivin+Carbonate (from the Carbonatite)→Clinopyroxene (with plagioclase and orthopyroxene in solid solution)+Co2.

P-T conditions of mineral equilibration in the xenoliths can are deduced from the pyroxene mineral assemblage (pyroxene thermometry) for the temperature (Wells 1977, Bertrand and Mercier 1986,Brey and Kohler 1990, Kohler and Brey 1990),and from the maximum fluid

Mapping and Analyzing the Volcano-Petrology and Tectono -

about 1100-1300C for the temperature, 10-13 Kb for the pressure.

type) lithospheric mantle (Bilal and Touret 2001,Bilal and Sheleh 2004).

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 147

density in primary carbonic inclusions, for the pressure (Bilal et Touret 2001,Bilal et Sheleh 2004).Using theses parameters the figure (6),show the obtained Results, which correspond to

In conclusion it is suggested that the volcanic activity along the Syrian rift is due to the presence under the Arabic plate of a mantle plume(Stein and Katz 1989,Stein and Hofman 1992 ,Stein et al 1993), active since Cretaceous times, locally refertilizing a residual (oceanic-

Fig. 6. Tthermparometric conditions (P, T), of Syrian mantle xenoliths (Bilal and Touret 2001, Bilal and Sheleh 2004).Th: homogenization temperature of CO2 fluid inclusions; d: density

The tectono- seismicity characteristics are deducted from the satellite imagery, the field survey, the seismic observatories data, the odometric measurements, and the analyzing of

of CO2 liquid.

**4. Tectono-seismicity characteristics** 

ancient and recent earthquakes.

Fig. 5. Photomicrographs of petrographic features of mantle xenoliths , and fluid carbonic inclusions.

A: Coarse-grained microstructure harzburgit (sample37Th ,Tel Thenoun)-large Olivine (Ol) and Clinopyroxene(OPX) crystals shown a dark melt zone(M) at the intergranular boundary containing white veinlet filled with secondary minerals(opal, carbonate),and trail of secondary ,low density ,carbonic inclusions(FI), issued from M, and disposed along the OPX cleavage plan. B: Coarse-grainedtubular microstructure spinel lherzolite (sample 34Th,Tel Thenoun)-large pyroxenite crystals, subordinate olivine(Ol),and large spinel crystals surrounded by a dark reaction zone.Primary CO2 inclusions(FI) are disposed in the core of some clinopyroxene crystals. C:Coarse-grained microstructure in harzburgite (sample 43Th,Tel Thenoun).D:composite BSE image section(sample Th12,Tel Thenoun).The submillimitric coronitic feature correspond to spinel (light grey core) rimmed by sapphirine(dark grey).Scale bar 2mm.E: More clear of coronitic spinel of figure D,where the sapphirine corona(dark grey) is continuous.A thin rim of symplectite is hardly visible between sapphirine and clinopyroxene.F:Carbonic (pure CO2) fluid inclusions(black circles) in exsolution features in the butterfly-wing structure, in pyroxenite(sample 135Th,Tel Thenoun).Scale bar50 micron m. G:Tubular carbonic inclusions in pyroxene (sample135Th,Tel Thenoun),Scale 20 micron m.H:Details of the butterfly-wing structure around inclusion in olivine(sample 11Th,Tel Thenoun).Scale20 micronm. I, J: Carbonic inclusions in clinopyroxene .X and Y supercritical CO2 (homogenization temperature =15 C),(sample 135Th,Tel Thenoun).bar 20 micronm.

Fig. 5. Photomicrographs of petrographic features of mantle xenoliths , and fluid carbonic

A: Coarse-grained microstructure harzburgit (sample37Th ,Tel Thenoun)-large Olivine (Ol) and Clinopyroxene(OPX) crystals shown a dark melt zone(M) at the intergranular boundary containing white veinlet filled with secondary minerals(opal, carbonate),and trail of secondary ,low density ,carbonic inclusions(FI), issued from M, and disposed along the OPX cleavage plan. B: Coarse-grainedtubular microstructure spinel lherzolite (sample 34Th,Tel Thenoun)-large pyroxenite crystals, subordinate olivine(Ol),and large spinel crystals surrounded by a dark reaction zone.Primary CO2 inclusions(FI) are disposed in the core of some clinopyroxene crystals. C:Coarse-grained microstructure

in harzburgite (sample 43Th,Tel Thenoun).D:composite BSE image section(sample Th12,Tel Thenoun).The submillimitric coronitic feature correspond to spinel (light grey core) rimmed by sapphirine(dark grey).Scale bar 2mm.E: More clear of coronitic spinel of figure D,where the sapphirine corona(dark grey) is continuous.A thin rim of symplectite is hardly visible between sapphirine and clinopyroxene.F:Carbonic (pure CO2) fluid inclusions(black circles) in exsolution features in the butterfly-wing structure, in pyroxenite(sample 135Th,Tel Thenoun).Scale bar50 micron m. G:Tubular carbonic inclusions in pyroxene (sample135Th,Tel Thenoun),Scale 20 micron m.H:Details of the butterfly-wing structure around inclusion in olivine(sample 11Th,Tel Thenoun).Scale20 micronm. I, J: Carbonic inclusions in clinopyroxene .X and Y supercritical CO2 (homogenization temperature =15

C),(sample 135Th,Tel Thenoun).bar 20 micronm.

inclusions.

density in primary carbonic inclusions, for the pressure (Bilal et Touret 2001,Bilal et Sheleh 2004).Using theses parameters the figure (6),show the obtained Results, which correspond to about 1100-1300C for the temperature, 10-13 Kb for the pressure.

In conclusion it is suggested that the volcanic activity along the Syrian rift is due to the presence under the Arabic plate of a mantle plume(Stein and Katz 1989,Stein and Hofman 1992 ,Stein et al 1993), active since Cretaceous times, locally refertilizing a residual (oceanictype) lithospheric mantle (Bilal and Touret 2001,Bilal and Sheleh 2004).

Fig. 6. Tthermparometric conditions (P, T), of Syrian mantle xenoliths (Bilal and Touret 2001, Bilal and Sheleh 2004).Th: homogenization temperature of CO2 fluid inclusions; d: density of CO2 liquid.

#### **4. Tectono-seismicity characteristics**

The tectono- seismicity characteristics are deducted from the satellite imagery, the field survey, the seismic observatories data, the odometric measurements, and the analyzing of ancient and recent earthquakes.

Mapping and Analyzing the Volcano-Petrology and Tectono -

2001), successively through Lebanon, Syria and Turkey.

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 149

reaches the Africa-Arabia-Eurasia triple junction near Maras(Khair et al 2000,Meghraoui et

Thus, the Syrian rift is an active seismic zone oriented North-South.It could be identified either by a satellite image or in the field (Fig.8). It cross the middle east through more 1200Km., from the Aqaba gulf in the South, to the Turkey in the North (Bilal and Touret

Fig. 8. Structure of the Syrian rift from the satellite image, Landsat 2005, and epicenters of

the seisms in 2005 – 2006 after the Syrian seismic centre

al.2003), confirmed by recent field studies (Chorowicz et al.2005,Bilal 2009a,b).

#### **4.1 Tectonics**

The Syria platform is constituted from several structural units, which have been formed at different periods since the Permo-Trias. The map of figure (7), shows these principles units: The Palmyrides in the center; the graben of Euphrates and the Djebel Abdelaziz in the East; the Afrin region and the Aleppo plateau in the North-West; and the Coastal chain at the west of the Levant fault ( Al Abdalla 2008).

The West of Syria is occupied by an important structure, locally named the Syrian rift, and worldly known the Levant fault, corresponding to the northern part of the Dead Sea fault zone (DSFZ), which forms the boundary between the African and Arabian plates. The tectonic activity along its northern part, the Yammouneh fault and northward continuation is still a subject of controversy. Between those who maintained that this segment is poorly active(Girdler 1990,Butler et al1997,1998,Butler and Spencer 1999),and others who concluded ,from the earthquakes study ,that this segment would then be active until it

Fig. 7. Principles structural units of Syria, northwest of the Arabian plate (Al Abdalla 2008)

The Syria platform is constituted from several structural units, which have been formed at different periods since the Permo-Trias. The map of figure (7), shows these principles units: The Palmyrides in the center; the graben of Euphrates and the Djebel Abdelaziz in the East; the Afrin region and the Aleppo plateau in the North-West; and the Coastal chain at the

The West of Syria is occupied by an important structure, locally named the Syrian rift, and worldly known the Levant fault, corresponding to the northern part of the Dead Sea fault zone (DSFZ), which forms the boundary between the African and Arabian plates. The tectonic activity along its northern part, the Yammouneh fault and northward continuation is still a subject of controversy. Between those who maintained that this segment is poorly active(Girdler 1990,Butler et al1997,1998,Butler and Spencer 1999),and others who concluded ,from the earthquakes study ,that this segment would then be active until it

Fig. 7. Principles structural units of Syria, northwest of the Arabian plate (Al Abdalla 2008)

**4.1 Tectonics** 

west of the Levant fault ( Al Abdalla 2008).

reaches the Africa-Arabia-Eurasia triple junction near Maras(Khair et al 2000,Meghraoui et al.2003), confirmed by recent field studies (Chorowicz et al.2005,Bilal 2009a,b).

Thus, the Syrian rift is an active seismic zone oriented North-South.It could be identified either by a satellite image or in the field (Fig.8). It cross the middle east through more 1200Km., from the Aqaba gulf in the South, to the Turkey in the North (Bilal and Touret 2001), successively through Lebanon, Syria and Turkey.

Fig. 8. Structure of the Syrian rift from the satellite image, Landsat 2005, and epicenters of the seisms in 2005 – 2006 after the Syrian seismic centre

Mapping and Analyzing the Volcano-Petrology and Tectono -

2009 b, Tab.1).

basalt.

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 151

al.1998). The overall displacement along the fault since the time of eruption, in other words the total length of pull-apart, could be estimated from the displacement of the famous "Krak des Chevaliers" in respect to the main Shine volcano (Fig.9). This gives 16 km, significantly less than other estimates (20 Km, Chorowicz et al 2005). This would give an average displacement rate of 2,7 – 3,3 mm/year, in line with estimates along the Wadi Araba fault, in the northern part of the Levant fault (4,6 +/- 2 mm/year, with a decreasing value of 2,3 mm/year for the last 12 ka , Le Beon 2008). In Syria, the displacement rate in the region of Homs corresponds to a maximum value. The movement rate, estimated by different methods, decreases significantly in the others regions. It is: 1-1.5 mm/yr in the region of Palmyra, less than 1 mm/yr in the Eastern and North Eastern parts of the country (Bilal

Region Movement rate /mm.Yr. Method

Table 1. Movement rate in different regions estimated by different methods

El Ghab, the Syria rift 2, 7-3, 3 Basaltic displacement Palmyra chain 1, 5 Monuments cracks Eastern Syria, Russafeh 1-1, 5 Monuments cracks Afrin region 1 Field measurements Northern east Syria < 1 Field measurement

Fig. 9. Movement rate estimate, from field observation and satellite imagery analysis (Landsat TM 1995). ab: displacement, estimated at 16Km during 6 My, the age of the Homs

In Syria, the Levant fault continues towards the North, between Damascus and Tartous, by the Yammouneh fault. This last structure marks an important transition to the Palmyra chain, making a sort of hinge between the northern and southern parts of the rift. The rift continues to the north through the El Ghab basin, and it disappears in the Taurus zone, in Turkey, in the Maras's triple junction point which relays Africa-Arabia-Eurasia. Many arguments, from structural analysis and field observation, in addition to satellite imagery data, and geomorphologic analysis, point to a recent, up to present day tectonic activity along this structure, e.g. mylonites and fine-grained shear zones, filling of pull-apart basins, deformed small active ravines and formation of scarps.

The Syrian rift corresponds to a transform fault, with lateral displacements decreasing from more than100 Km, to the South, to less than 30 Km, to the North, at the level of the Yammouneh fault (Walley 1988).The secondary faults and fractures deduced by the satellite images (Bilal1994 a,b) ,and detected in the field (Lovelock 1984,Sawaf et al. 1993),support this results, but more studies are needed to more explore others factors.

Many faults, as shown by the structural analysis and field observation, in addition to satellite imagery data and geomorphologic analysis, attest that have recently been or are still active along the Syrian rift. This is notably indicated by several phenomena: 1) the local transformation of basaltic rocks into mylonites and fine-grained shear zones. Carbonate basement rocks may also be deformed; they are more mylonitic because more easily fragmented than basalts. 2) The occurrence of pull-apart basins filled with quaternary sediments. 3) The deformation of small active ravines, with the formation of scarps (Chorowicz et al.2005, Bilal 2009a, b).

#### **4.2 Seismology**

Syria, the northern part of the Dead Sea Fault Zone (DSFZ), has a long record of active seismicity (Taher 1979, Al Tarazi 1999). Field observations, physical effects on ancient building structures and movement analysis show that tectonic is still active at present time (Khair et al.2000, Meghraoui et al2003, Chorowicz et al 2005).

Most major seisms in Syria occur in two regions: Either within or close to the rift zone, along a North – South direction, or SW – NE oriented, along the Damascus Palmyra mountain chain. This last domain does not contain any volcanic activity. Earthquakes in this region can only be caused by superficial deformation of the sedimentary cover.

Many of seisms take place within the litohsphere, in response to active fault displacement (Lay and Wallace1995,Yeats et al.1997) ,but others could also originate when the crust is subducted into the mantle, or along rifts in response to an ascending hot spot (plume) (Yeats et al.1997,Bilal and Sheleh 2004).This is precisely what may happen in Syria. The study of volcanic xenoliths has identified a hot spot under the Arabic plate (Stein and Hofman 1992, Sharkov et al.1993), starting during Cretaceous and ascending continuously until present time (Bilal and Touret 2002, Bilal and Sheleh 2004). This part aims to analyzing the seismicity distribution in the Syrian territory, using tectonic activity, laboratory measurements, and historic and recent earthquakes records. It will also attempt to compare these data with volcanic parameters.

#### **4.2.1 Seismic parameters**

The movement rate-displacement along a given fault could be estimated in the region of Homs, where important basaltic eruptions took place 6 Ma ago (Sharkov et al.1994, Butler et

In Syria, the Levant fault continues towards the North, between Damascus and Tartous, by the Yammouneh fault. This last structure marks an important transition to the Palmyra chain, making a sort of hinge between the northern and southern parts of the rift. The rift continues to the north through the El Ghab basin, and it disappears in the Taurus zone, in Turkey, in the Maras's triple junction point which relays Africa-Arabia-Eurasia. Many arguments, from structural analysis and field observation, in addition to satellite imagery data, and geomorphologic analysis, point to a recent, up to present day tectonic activity along this structure, e.g. mylonites and fine-grained shear zones, filling of pull-apart basins,

The Syrian rift corresponds to a transform fault, with lateral displacements decreasing from more than100 Km, to the South, to less than 30 Km, to the North, at the level of the Yammouneh fault (Walley 1988).The secondary faults and fractures deduced by the satellite images (Bilal1994 a,b) ,and detected in the field (Lovelock 1984,Sawaf et al. 1993),support

Many faults, as shown by the structural analysis and field observation, in addition to satellite imagery data and geomorphologic analysis, attest that have recently been or are still active along the Syrian rift. This is notably indicated by several phenomena: 1) the local transformation of basaltic rocks into mylonites and fine-grained shear zones. Carbonate basement rocks may also be deformed; they are more mylonitic because more easily fragmented than basalts. 2) The occurrence of pull-apart basins filled with quaternary sediments. 3) The deformation of small active ravines, with the formation of scarps

Syria, the northern part of the Dead Sea Fault Zone (DSFZ), has a long record of active seismicity (Taher 1979, Al Tarazi 1999). Field observations, physical effects on ancient building structures and movement analysis show that tectonic is still active at present time

Most major seisms in Syria occur in two regions: Either within or close to the rift zone, along a North – South direction, or SW – NE oriented, along the Damascus Palmyra mountain chain. This last domain does not contain any volcanic activity. Earthquakes in this region

Many of seisms take place within the litohsphere, in response to active fault displacement (Lay and Wallace1995,Yeats et al.1997) ,but others could also originate when the crust is subducted into the mantle, or along rifts in response to an ascending hot spot (plume) (Yeats et al.1997,Bilal and Sheleh 2004).This is precisely what may happen in Syria. The study of volcanic xenoliths has identified a hot spot under the Arabic plate (Stein and Hofman 1992, Sharkov et al.1993), starting during Cretaceous and ascending continuously until present time (Bilal and Touret 2002, Bilal and Sheleh 2004). This part aims to analyzing the seismicity distribution in the Syrian territory, using tectonic activity, laboratory measurements, and historic and recent earthquakes records. It will also attempt to compare

The movement rate-displacement along a given fault could be estimated in the region of Homs, where important basaltic eruptions took place 6 Ma ago (Sharkov et al.1994, Butler et

deformed small active ravines and formation of scarps.

(Chorowicz et al.2005, Bilal 2009a, b).

these data with volcanic parameters.

**4.2.1 Seismic parameters** 

**4.2 Seismology** 

this results, but more studies are needed to more explore others factors.

(Khair et al.2000, Meghraoui et al2003, Chorowicz et al 2005).

can only be caused by superficial deformation of the sedimentary cover.

al.1998). The overall displacement along the fault since the time of eruption, in other words the total length of pull-apart, could be estimated from the displacement of the famous "Krak des Chevaliers" in respect to the main Shine volcano (Fig.9). This gives 16 km, significantly less than other estimates (20 Km, Chorowicz et al 2005). This would give an average displacement rate of 2,7 – 3,3 mm/year, in line with estimates along the Wadi Araba fault, in the northern part of the Levant fault (4,6 +/- 2 mm/year, with a decreasing value of 2,3 mm/year for the last 12 ka , Le Beon 2008). In Syria, the displacement rate in the region of Homs corresponds to a maximum value. The movement rate, estimated by different methods, decreases significantly in the others regions. It is: 1-1.5 mm/yr in the region of Palmyra, less than 1 mm/yr in the Eastern and North Eastern parts of the country (Bilal 2009 b, Tab.1).


Table 1. Movement rate in different regions estimated by different methods

Fig. 9. Movement rate estimate, from field observation and satellite imagery analysis (Landsat TM 1995). ab: displacement, estimated at 16Km during 6 My, the age of the Homs basalt.

Mapping and Analyzing the Volcano-Petrology and Tectono -

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 153

Fig. 10. Histogram of the seismicity evolution in time, after their magnitude and age.

**4.2.3 Seismic hazard zoning map of Syria and Arab plate** 

East South and East North (low) in line with the rate movement, and

seismic acceleration coefficient evolution (Fig.12B).

country and in the off shore.

For recent seisms, we have collected good data, especially from the physical effects on the structures and the station seismic net (Fig.11). They are distributed in the whole of the

In order to evaluate the seismic hazards on the whole territory of Syria, and to examine their effect on building structures, odometric experiments on the more representative soil types occur in the country, have been performed in laboratory. Using scale of magnitude intensity of 7, 7.5, 8, and 8.5 respectively, the elasticity modulus (E = power/surface = Kilo Newton / m2), and the Poisson ratio (P=executed displacement / original displacement = deformation %), have been determined. They allow the determination of the soil rigidity and the behavior of building during a seism (interaction soil-seism for a given building). The experiments have been measured on more than 80 litho- logical samples. Measurements were analyzed using the SAP Software (computer and structures Inc. USA, Bilal and Mahmoud 1997). Results are given in terms of relative unity response to seismic hazard, namely relative damage, the result of seism-soil effect on building, estimated from low to strong. It is maximal along the rift (moderate), and decreases gradually towards the East,

These results are confirmed by physical effects on the building structures in the region (field measurement on houses, measurement by Bilal and Ammar 2004, unpublished data). They can be taken as an average value for the movement rate repartition in the whole territory.

For an earthquake of a given intensity, defined by the value of the Magnitude (in Richter), the action on a builded structure, which result in the greatest number of casualties, depends from two sets of parameters: the characteristics of the structure itself and the nature of the ground on which it is built. Several equations are proposed to relate all these variables (Bojoroque and DeRoeck 2007, Ozkan 1998). The Syrian code (2004), used in this work is based on the following equations:

$$\mathbf{Z} = \mathbf{V} / \text{IKCSW} \tag{1}$$

$$\mathbf{C} = \mathbf{1}/\mathbf{T} \tag{2}$$

$$\mathbf{T} \sim \mathbf{0}, \mathbf{1} \mathbf{N} \tag{3}$$

Where V is the horizontal shear force, I correspond to the type and geometry of the structure (bridges, tunnels, towers, dams, etc.), K the inelasticity coefficient of the structure, C the dynamic coefficient, linked to the nodes propagation period (T), and the number of stages (N), S a coefficient relative to the soil, and finally, W the total weight.

This seismic acceleration coefficient (Z) is a critical parameter. Estimated in cm /s2, it describes the reaction of an object -structure in a limited zone -to an earthquake of a given intensity. Its value changes from region to other after the upon seismic parameters, and so in the same region according to the estimated parameters values, from 0 to a variable value, reaching 1, 5 cm /s2 (Bojoroque and DeRoeck 2007).

For the dams Z is estimated, in Japan, at 0, 1- 0, 12 for weak earthquake zones, and 0, 15 for strong zones. It is taken between 0, 05 and 0, 20 in Turkey, and between 0, 03 and 0, 24 in India (Bilal 2009). A coefficient of 0, 1 indicates that a building is designed so that 0, 1 of its weight can be applied horizontally during an earthquake

In Syria Z ranges between 0 and 0,25, depending on the region.It is 0,25 in Al Ghab region, 0,12 in Palmyra, and 0,05 – 0,1 in Deir Zour, in the East.

#### **4.2.2 Seismicity-time analysis**

The repetition of an earthquake (frequency return period of an earthquake in the same locality), namely the seismic cycle is controversial (King 2004, Maderiaga 2004). However if an earthquake is unique for a given locality, the distruction of earthquake activity with time is of major importance.

Therefore, the historical record of ancient earthquakes has been investigated. Only were used these verified by different sources (Taher 1979, Al Tarazi 1999). Available historical data covers a wide period with variable magnitude: Ancient time between 750 and 1800,with magnitude estimated at 7.5-6.5 (Meghraoui 2003), it becomes 6 - 5 between 1800 - 2000 (UNISCO 1983,Stiro1992,Sbeinati and Darawcheh 1992,Al Tarazi1999),less than 5 for the period of 1960 to 2000 and between 4,9-4 at present (USGS 1999). The results are represented by the histogram of figure (10).They show that the seismic intensity tends to decreases with time, in agreement with recent estimates on the movement rate (Le Beon 2008).

These results are confirmed by physical effects on the building structures in the region (field measurement on houses, measurement by Bilal and Ammar 2004, unpublished data). They can be taken as an average value for the movement rate repartition in the

For an earthquake of a given intensity, defined by the value of the Magnitude (in Richter), the action on a builded structure, which result in the greatest number of casualties, depends from two sets of parameters: the characteristics of the structure itself and the nature of the ground on which it is built. Several equations are proposed to relate all these variables (Bojoroque and DeRoeck 2007, Ozkan 1998). The Syrian code (2004), used in this work is

Where V is the horizontal shear force, I correspond to the type and geometry of the structure (bridges, tunnels, towers, dams, etc.), K the inelasticity coefficient of the structure, C the dynamic coefficient, linked to the nodes propagation period (T), and the number of stages

This seismic acceleration coefficient (Z) is a critical parameter. Estimated in cm /s2, it describes the reaction of an object -structure in a limited zone -to an earthquake of a given intensity. Its value changes from region to other after the upon seismic parameters, and so in the same region according to the estimated parameters values, from 0 to a variable value,

For the dams Z is estimated, in Japan, at 0, 1- 0, 12 for weak earthquake zones, and 0, 15 for strong zones. It is taken between 0, 05 and 0, 20 in Turkey, and between 0, 03 and 0, 24 in India (Bilal 2009). A coefficient of 0, 1 indicates that a building is designed so that 0, 1 of its

In Syria Z ranges between 0 and 0,25, depending on the region.It is 0,25 in Al Ghab region,

The repetition of an earthquake (frequency return period of an earthquake in the same locality), namely the seismic cycle is controversial (King 2004, Maderiaga 2004). However if an earthquake is unique for a given locality, the distruction of earthquake activity with time

Therefore, the historical record of ancient earthquakes has been investigated. Only were used these verified by different sources (Taher 1979, Al Tarazi 1999). Available historical data covers a wide period with variable magnitude: Ancient time between 750 and 1800,with magnitude estimated at 7.5-6.5 (Meghraoui 2003), it becomes 6 - 5 between 1800 - 2000 (UNISCO 1983,Stiro1992,Sbeinati and Darawcheh 1992,Al Tarazi1999),less than 5 for the period of 1960 to 2000 and between 4,9-4 at present (USGS 1999). The results are represented by the histogram of figure (10).They show that the seismic intensity tends to decreases with time, in agreement with recent estimates on the movement rate (Le Beon

(N), S a coefficient relative to the soil, and finally, W the total weight.

reaching 1, 5 cm /s2 (Bojoroque and DeRoeck 2007).

weight can be applied horizontally during an earthquake

0,12 in Palmyra, and 0,05 – 0,1 in Deir Zour, in the East.

**4.2.2 Seismicity-time analysis** 

is of major importance.

2008).

Z= V/ IKCSW (1)

C=1/T (2)

T ~ 0, 1N (3)

whole territory.

based on the following equations:

Fig. 10. Histogram of the seismicity evolution in time, after their magnitude and age.

For recent seisms, we have collected good data, especially from the physical effects on the structures and the station seismic net (Fig.11). They are distributed in the whole of the country and in the off shore.

#### **4.2.3 Seismic hazard zoning map of Syria and Arab plate**

In order to evaluate the seismic hazards on the whole territory of Syria, and to examine their effect on building structures, odometric experiments on the more representative soil types occur in the country, have been performed in laboratory. Using scale of magnitude intensity of 7, 7.5, 8, and 8.5 respectively, the elasticity modulus (E = power/surface = Kilo Newton / m2), and the Poisson ratio (P=executed displacement / original displacement = deformation %), have been determined. They allow the determination of the soil rigidity and the behavior of building during a seism (interaction soil-seism for a given building). The experiments have been measured on more than 80 litho- logical samples. Measurements were analyzed using the SAP Software (computer and structures Inc. USA, Bilal and Mahmoud 1997). Results are given in terms of relative unity response to seismic hazard, namely relative damage, the result of seism-soil effect on building, estimated from low to strong. It is maximal along the rift (moderate), and decreases gradually towards the East, East South and East North (low) in line with the rate movement, and seismic acceleration coefficient evolution (Fig.12B).

Mapping and Analyzing the Volcano-Petrology and Tectono -

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 155

Fig. 12. Seismic map of Syria, showing the five seismic zones, and distribution of the

indicate the relative damage(B).

and corresponding seismic intensity (Tab.2).

damage for the constructions, while zone five has the lowest one.

earthquakes which their magnitude more than 4; white square: M> 6 ; black circle: 5< M < 6; black square: M< 5 ;white; circle: M=4,9 – 4(A), and odometric result where the black part

According to the movement rate, estimated in the field between <1mm/yr and 2, 7 -3, 3 mm/yr, the Z value estimated at 0-0.25 cm/S2, the relative seismic intensity measured in laboratory (Bilal and Mahmoud 1997), the analysis of recent seismicity documented by the seismic network, and finally historical record, we have identified a number of seismic zones

These zones are represented on a seismic map of Syria (Fig.12A), established here for the first time. This map divides Syria into five zones, each of which corresponds to a given seismic intensity value. Zone one has the highest seismic intensity risk, with most potential

On the same figure (12A) , the earthquake epicenters with a magnitude higher than 4 are projected. They occur in the whole territory but mostly in zones 1 and 2, associated with volcanism, or along the Damascus-Palmyra mountain chain. Only some earthquakes had a

Fig. 11. Occurrence of the recent seismicity in Syria: a-Sbeinati and Darawcheh for the XX century (1992),b-USGS for the period of 1961-1983,(in Stiro 1992);c-USGS for the last years(Monitor,vol.5,1,1995).

Fig. 11. Occurrence of the recent seismicity in Syria: a-Sbeinati and Darawcheh for the XX century (1992),b-USGS for the period of 1961-1983,(in Stiro 1992);c-USGS for the last

years(Monitor,vol.5,1,1995).

Fig. 12. Seismic map of Syria, showing the five seismic zones, and distribution of the earthquakes which their magnitude more than 4; white square: M> 6 ; black circle: 5< M < 6; black square: M< 5 ;white; circle: M=4,9 – 4(A), and odometric result where the black part indicate the relative damage(B).

According to the movement rate, estimated in the field between <1mm/yr and 2, 7 -3, 3 mm/yr, the Z value estimated at 0-0.25 cm/S2, the relative seismic intensity measured in laboratory (Bilal and Mahmoud 1997), the analysis of recent seismicity documented by the seismic network, and finally historical record, we have identified a number of seismic zones and corresponding seismic intensity (Tab.2).

These zones are represented on a seismic map of Syria (Fig.12A), established here for the first time. This map divides Syria into five zones, each of which corresponds to a given seismic intensity value. Zone one has the highest seismic intensity risk, with most potential damage for the constructions, while zone five has the lowest one.

On the same figure (12A) , the earthquake epicenters with a magnitude higher than 4 are projected. They occur in the whole territory but mostly in zones 1 and 2, associated with volcanism, or along the Damascus-Palmyra mountain chain. Only some earthquakes had a

Mapping and Analyzing the Volcano-Petrology and Tectono -

Seismicity Characteristics Along the Syrian Rift –NW the Arabian Plate 157

Using data obtained by deferments sources ( UNESCO 1983,Barrier et al 2004,Al Damegh et al 2005,Le Beon 2008,Bilal 2009b), and the seismo-tectonic parameters, an extrapolated seismic zoning map for the Arab plate is established(Fig.13).It distinguishes between three seismic zones: zone 1 ,the highest seismic zone intensity with major damage risk; zone 3,zone of low seismic intensity with lowest potential risk ,and zone 3,the intermediary zone with intermediary potential risk. These results need to more verification by a qualified team.

Fig. 14. Regional tectonic map of Syria showing the rift structure, volcanism and the

distribution of earthquakes epicenters (in black circles), with the highest magnitude (>5 -7, 5).


Table 2. Calculated seismic parameters, corresponding seismic zones and their intensity.

magnitude higher than 7, 5- 6, 5, even if this remains controversial. Most recorded earthquakes in the twentieth century have a magnitude less than 6. Out of hundred earthquakes in the region and off shore, 25% have a magnitude between 6-5, and most of them have a magnitude less than 5. All together, the whole Syria shows moderate seismicity, compared to the north, Taurus-Zagros fault zone, or to the south, under the Indian Ocean expansion.

Fig. 13. An extrapolated seismic zoning map of the Arab plate . Zone 1, the highest seismic intensity zon;zone 2,the intermediary one and zone 3,the lowest one.

magnitude higher than 7, 5- 6, 5, even if this remains controversial. Most recorded earthquakes in the twentieth century have a magnitude less than 6. Out of hundred earthquakes in the region and off shore, 25% have a magnitude between 6-5, and most of them have a magnitude less than 5. All together, the whole Syria shows moderate seismicity, compared to the north, Taurus-Zagros fault zone, or to the south, under the

Fig. 13. An extrapolated seismic zoning map of the Arab plate . Zone 1, the highest seismic

intensity zon;zone 2,the intermediary one and zone 3,the lowest one.

Indian Ocean expansion.

MR mm/yr. Z cm/S2 Seismic zone Seismic intensity 0 0 0 none <1 0.05 0-1 very low 1 01 1 -2A 1.5 0.15 2A middle-low 2 0.2 2B middle 2.5 0.25 2C moderate Table 2. Calculated seismic parameters, corresponding seismic zones and their intensity. Using data obtained by deferments sources ( UNESCO 1983,Barrier et al 2004,Al Damegh et al 2005,Le Beon 2008,Bilal 2009b), and the seismo-tectonic parameters, an extrapolated seismic zoning map for the Arab plate is established(Fig.13).It distinguishes between three seismic zones: zone 1 ,the highest seismic zone intensity with major damage risk; zone 3,zone of low seismic intensity with lowest potential risk ,and zone 3,the intermediary zone with intermediary potential risk. These results need to more verification by a qualified team.

Fig. 14. Regional tectonic map of Syria showing the rift structure, volcanism and the distribution of earthquakes epicenters (in black circles), with the highest magnitude (>5 -7, 5).

Mapping and Analyzing the Volcano-Petrology and Tectono -

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#### **5. Conclusion**

The Syrian rift is a world structure, and constitute the north part of the Dead Sea Fault Zone (DSFZ).Structural analysis using variable techniques attest that many faults have recently or are still active to occuresent along the Syrian rift. This is notably indicated by two phenomena: volcanism and seismicity.

The composition of the underlying lithospheric mantle points to a complex history involving polybaric partial melting at various degrees, starting in the garnet - and proceeding in the spinel stability field. Some clinopyroxenes at least record mantle metasomatism, caused by ephemeral carbonate magmas or percolating basalting melts issued from a mantle plume under the Arabic plate.

Most major seisms in Syria occur in two zones (Fig.14): with the rift zone, in a North – South direction, but not exactly along the fractures. Most epicenters occur westward along the coast or in the sea. The other zone is SW – NE oriented, along the Damascus Palmyra mountain chain. It does not seem to be related to any volcanic activity, but corresponds namely to superficial deformation of the sedimentary cover.

For volcanic-related seismicity, Petrological data from volcanic xenoliths have identified the existence of a hot spot (plume), under the Syrian rift. In the earliest period of volcanic activity (Cretaceous), this plume started at the level of mantel garnet peridotite, leading to a marked explosive volcanism. It may be hypothesized that this type of volcanism did correspond to major seismicity. In more recent time, the plume head tends to rise, while at the same time migrating towards the West. This was accompanied by a more effusive type of volcanism, associated to the moderate seismicity, presently shown. The last eruption (10.000 y) occurred in the large volcanic massif at the South (Djebel Al Arab). With one exception, no major seism relates to this last eruption. This recent massif, by far the larger in Syria, seems to distantiate from the rift zone, at the difference, notably, of older Cretaceous volcanism.

At the scale of the human observation, the seismicity does not seem to be directly related to present-day volcanic activity.Either reminiscence of ancient volcanism, or consequence of superficial deformation. Both phenomena tend to fade out with time, in line with the decrease of major seismic intensity which has occurred during the last millennium.

#### **6. References**


The Syrian rift is a world structure, and constitute the north part of the Dead Sea Fault Zone (DSFZ).Structural analysis using variable techniques attest that many faults have recently or are still active to occuresent along the Syrian rift. This is notably indicated by two

The composition of the underlying lithospheric mantle points to a complex history involving polybaric partial melting at various degrees, starting in the garnet - and proceeding in the spinel stability field. Some clinopyroxenes at least record mantle metasomatism, caused by ephemeral carbonate magmas or percolating basalting melts

Most major seisms in Syria occur in two zones (Fig.14): with the rift zone, in a North – South direction, but not exactly along the fractures. Most epicenters occur westward along the coast or in the sea. The other zone is SW – NE oriented, along the Damascus Palmyra mountain chain. It does not seem to be related to any volcanic activity, but corresponds

For volcanic-related seismicity, Petrological data from volcanic xenoliths have identified the existence of a hot spot (plume), under the Syrian rift. In the earliest period of volcanic activity (Cretaceous), this plume started at the level of mantel garnet peridotite, leading to a marked explosive volcanism. It may be hypothesized that this type of volcanism did correspond to major seismicity. In more recent time, the plume head tends to rise, while at the same time migrating towards the West. This was accompanied by a more effusive type of volcanism, associated to the moderate seismicity, presently shown. The last eruption (10.000 y) occurred in the large volcanic massif at the South (Djebel Al Arab). With one exception, no major seism relates to this last eruption. This recent massif, by far the larger in Syria, seems to distantiate from the rift zone, at the difference, notably, of older Cretaceous

At the scale of the human observation, the seismicity does not seem to be directly related to present-day volcanic activity.Either reminiscence of ancient volcanism, or consequence of superficial deformation. Both phenomena tend to fade out with time, in line with the

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plate kinematics during transperssion evolution of the Lebanese restraining bend of the Dead Sea Transform.In: *Continental Transpressional and Transtensionbal Tectonics*.

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Quaternary volcanism in :Karasu valley(Hatay).N. *end of Dead Sea Rift zone in SE Turkey*. Yerbilimleri Bulletin of Earth. Sciences, Hacettepe University, Ankara, 14,

Pliocene Homs Basalts (Syria) and implications for the Dead Sea Fault Zone

fluid inclusions in mantel xenoliths from Tenerif, Canary Islands: a story of trapping,

intraplaques et volcanisme associe :exemple de la plaque arabique au Cenozoique.

and partitioning in mantle xenoliths metasomatized by alkaline and carbonate-rich

zone, northern continuation of Dead Sea Transform in Anatolia (Turkey).In: *Third* 

Ash Shaam volcanic field in Jordan: Implications for the span and duration of the upper-mantle upwelling beneath the western Arabian plate. *Geological Society of* 

and geochemical constraints on the composition of the lithospheric mantle beneath the Syrian rift, northern part of the arabian polate. In Coltorti M and Grégoire M (eds) Metasomatism in Oceanic and Continental Lithospheric Mantle. *Geol Soc* 


**9** 

*France* 

**Water-Rock Interaction Mechanisms** 

*2Ecole des Ponts ParisTech – CERMES, Now at Schlumberger, EPRC,* 

The microstructures of geomaterials and their evolution under the effects of applied loading and/or environmental conditions can affect the integrity of the solid skeletons and eventually change the mechanical behaviours of the materials at the macroscopic scale. Analyses of geomaterial microstructure and its 'ageing' are therefore critical to the understanding of their

This process of progressive ageing of the microstructure is mainly related to the interaction between the solid skeleton and the fluids that partially or completely saturate the porous network. Water/rock interaction mechanisms and ageing processes in geomaterials are often slow, leading to structural and textural changes that are generally imperceptible to the naked eye but which can significantly affect matrix integrity and cause sudden collapse. This is a particularly well-known phenomenon in shallow abandoned chalk mines, such as those found in France, where the chalk may remain stable over many tens of years but then suddenly break down, leading to collapse of the openings and the ground above them and

In this chapter we present results from a research program (led by Institut National de l'Environnement Industriel et des Risques (INERIS), France, in collaboration with Ecole des Ponts ParisTech – CERMES, France) that was carried out to evaluate the mechanical behaviour of chalk in the shallow underground mine of Estreux, located in northern France.

iii. microscopic scale (electron scanning environmental microscope (ESEM) observations

In situ characteristics of the Estreux mine are first described, including mine geometry, excavation method, overburden lithology, pillar monitoring, and in situ measurements. Then, petrophysical properties, microstructural characterisation, retention properties, and mechanical behaviour of the chalk investigated at laboratory scale (oedometric and triaxial

A microstructural analysis of the Estreux chalk is also presented. This part of the study was conducted using an ESEM, a recent technology that allows the observation of

mechanical behaviour and performance in engineering environments.

subsidence at a macroscopic scale (Sorgi, C. & Watelet, J., 2007).

The study was conducted at three different scales:

ii. laboratory scale (standard core testing)

i. site scale (stability analysis)

and micro-testing)

tests) are presented.

**1. Introduction** 

**and Ageing Processes in Chalk** 

*1INERIS, Verneuil-en-Halatte, Now at Schlumberger, EPRC,* 

Claudia Sorgi1 and Vincenzo De Gennaro2


SYRIAN ENGENEERING SYNDICAT, (2004)- *The Syrian seismicity code*. Damascus, Syria.


## **Water-Rock Interaction Mechanisms and Ageing Processes in Chalk**

Claudia Sorgi1 and Vincenzo De Gennaro2 *1INERIS, Verneuil-en-Halatte, Now at Schlumberger, EPRC, 2Ecole des Ponts ParisTech – CERMES, Now at Schlumberger, EPRC, France* 

#### **1. Introduction**

162 Advances in Data, Methods, Models and Their Applications in Geoscience

Roedder, E. (1984) - Reviews in mineralogy, vol.12, fluid inclusions. *Mineralogical Society of* 

Rojay, B; Heimann, A. and Toprak, V. (2001)-Neotectonic and volcanic charactiristics of the

Transform and the East Anatolian fault zone.*Geodynamica Acta*, 14, 197-212. Sawaf, T; Al Saad, D; Gebran, A; Barazangi, M; Best, JA. and Chaimove, T. (1993)- Structure

Sbeinati, M. and Darawcheh, R. (1992)- seismological bulletin for earthquakes in and around

Sharkov, YE.V; Lazko, YE.YE. and Hanna, S. (1993)- Plutonic xenoliths from the Nabi Matta explosive center, Northwest Syria. *Geochemistry international*, 30, (4). 23–24. Sharkov, YE.V; Shernyshev, I.V; Devyatkine, V. and al. (1994)- Geochronology of Late

Sharkov, YE.V; Chernyshev, I.V. and Devyatken E.V. et al. (1998)-New data on the

Sheleh, F. (2001)- Étude des enclaves mantéliques associées au rift syrien; Composition et

Sosson, M; Rolland, Y; Corsini, M; Danelian, T; Stephan, J-F; Avagyan, A; Melkonian,

Stein, M; Garfunkel, Z.and Jagoutz, E. (1993) Chronometry of peridotite, pyroxenite

Stiro, S. (1992)- Epicenters of earthquakes from 1961-1983, after *USGS.Workshop*, Damascus, 32-36 SYRIAN ENGENEERING SYNDICAT, (2004)- *The Syrian seismicity code*. Damascus, Syria. Taher, M.A. (1979)- Documents historiques des tremblements de terre en Syrie depuis l'Islam jusqu'à XII siècle "hygerique".*Thèse Université*, Paris 1, 300 P. UNESCO (1983)- Assessement and mitigation of earthquakes risk in the Arab region.

U.S. Geological Survey (1999)- Special Report:The Hector Mine Earthquake 10/16/99(1999),

Walley, C.D. (1998)-Some outstanding issues in the geology of Lebanon and their importance in the tectonic evolution of the Levantine region.*Tectonophysics*, 298, 37-62. Wells, P.R.A. (1977)-Pyroxene thermometry in simple and complex systems.

motion on the Amanos Fault(Karasu valley, southern Turkey) constrained by Kr-Ar dating and geochemical analysis of Quaternary basalts.*Tectonophysics*, 344, 207-246.

Yeats, R.S; Sieh, K. and Allen, C.R. (1997)- *The geology of earthquakes*. Oxford Univ. Press. Yurtmen, S; Guillou, H; Westaway, R; Rowbotham, G. and Tatar, O. (2002)-Rate of strik-slip

(see *http//Www.Socal*.*W.Usgs.Gov/Hector/Report/Html* )

régionales. *Thèse de doctorat* (en Arabe), Université de Damas, 180p.

Karasu fault zone (Anatolia, Turkey):The transition between the Dead Sea

and stratigraphy of eastern Syria across the Euphrate depression. *Tectonophysics*,

geochronology of upper Cenozoic plateau basalts from the northeastern periphery of the Red Sea rift area(Northern Syria). *Doklady Earth Sciences*, 358, (1), 19-22. Shaw, J.E. Baker, J.A. R; Kent, A.J. R; Ibrahim, K.M. and Menzies, M.A. (2007)- The

geochemistry of the Arabian lithospheric mantle -a source for intraplate volcanism?

évolution du manteau supérieur en Syrie-Implications géodynamiques et

R;Jrbashyan, R; Melikian, L. and Galoin, G. (2005)-Tectonic evolution of the Lesser Caucasus (Armenia) revisited in the light of new structural and stratigraphical results.European Geosciences Union. *Geophysical Research Abstracts,* V 7, 06224. Stein, M. and Hofman, A. (1992)- Fossil plume head beneath the Arabian lithosphere?, *Earth* 

xenoliths: implications for the thermal evolution of the arabian plate. *Geochim* 

*America.* 645p.

220: 267-281.

Syria.*Report international, SAES,* Damascus.

*Journal of petrology*, Vol.48, no 8, 1495-1512.

*Planet. Sci. Let*, n 114, 193– 209.

*Cosmochim Acta*, 57: 1325-1337.

Contr.Mineral.Petrol., 62, 129-139.

*UNESCO/ AFESD/ IDP*.

Cenozoic basalts in Western Syria.*Petrology*, 2(4), 439-448.

The microstructures of geomaterials and their evolution under the effects of applied loading and/or environmental conditions can affect the integrity of the solid skeletons and eventually change the mechanical behaviours of the materials at the macroscopic scale. Analyses of geomaterial microstructure and its 'ageing' are therefore critical to the understanding of their mechanical behaviour and performance in engineering environments.

This process of progressive ageing of the microstructure is mainly related to the interaction between the solid skeleton and the fluids that partially or completely saturate the porous network. Water/rock interaction mechanisms and ageing processes in geomaterials are often slow, leading to structural and textural changes that are generally imperceptible to the naked eye but which can significantly affect matrix integrity and cause sudden collapse. This is a particularly well-known phenomenon in shallow abandoned chalk mines, such as those found in France, where the chalk may remain stable over many tens of years but then suddenly break down, leading to collapse of the openings and the ground above them and subsidence at a macroscopic scale (Sorgi, C. & Watelet, J., 2007).

In this chapter we present results from a research program (led by Institut National de l'Environnement Industriel et des Risques (INERIS), France, in collaboration with Ecole des Ponts ParisTech – CERMES, France) that was carried out to evaluate the mechanical behaviour of chalk in the shallow underground mine of Estreux, located in northern France. The study was conducted at three different scales:


In situ characteristics of the Estreux mine are first described, including mine geometry, excavation method, overburden lithology, pillar monitoring, and in situ measurements.

Then, petrophysical properties, microstructural characterisation, retention properties, and mechanical behaviour of the chalk investigated at laboratory scale (oedometric and triaxial tests) are presented.

A microstructural analysis of the Estreux chalk is also presented. This part of the study was conducted using an ESEM, a recent technology that allows the observation of

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 165



Data were recorded from February 2004 to February 2008, and the following were observed:






3) and lateral extension (swelling) of the pillar (Fig. 5)

Fig. 1. Diagram of the full instrumentation employed in the Estreux mine

core of the pillar (Figs. 3 and 4 respectively)


within the pillar

overall decreasing trend (Fig. 2)

points within the pillar (15 cm, 35 cm, and 70 cm from the surface)

microstructural changes in geomaterials in their natural state, under controlled conditions of temperature and pressure.

Some other aspects of this technology are discussed, along with suggestions for potential development of this tool for further geomechanical applications and analyses of the Estreux chalk.

#### **2. Site scale: Stability analysis**

The study was carried out on Estreux abandoned underground chalk mine in Northern France, which is located 10 km east of the city of Valenciennes. The Estreux chalk formation is of the Late Cretaceous geological period (89 to 94 Ma years ago).

The Estreux mine, which was principally dug for blocks for dimension stone (for buildings and masonry) at the end of the 18th century, covers an area of 10 hectares. The chalk was excavated at a depth of 20 metres using the pillar-and-stall method, where networks of galleries were dug from access shafts, leaving large pillars in place to support the weight of the roof. This prevents the openings caving in, at least during excavation. The width of the galleries in the Estreux mine vary from 2 to 3 metres, and the pillars measure on average between 1.5 and 4.5 metres square. The excavation ratio (relation between the area exploited and the total area) is around 78%.

#### **2.1 Lithology**

The lithostratigraphic section of the Estreux mine overburden comprises, from top to bottom:


In 1980, Raffoux and Ervel conducted geomechanics laboratory tests on over one hundred core samples from this mine. The mechanical properties obtained are shown in Table 1. From these characteristics and the mining geometry, they estimated a stability factor close to 1 in several zones of the mine. As the mine is not stable in the long term, site monitoring was deemed necessary, and four convergence meters were subsequently installed in a weak zone of the mine.


Table 1. Mechanical characteristics of the Estreux chalk (Raffoux & Ervel, 1980)

Since August 2003, new instrumentation has been installed (Fig. 1) to analyse geomechanics phenomena of the rock mass over time. The galleries were monitored and a pillar of 1.4 m square and 1.8 m high was instrumented. The instrumentation comprises:


microstructural changes in geomaterials in their natural state, under controlled conditions of

Some other aspects of this technology are discussed, along with suggestions for potential development of this tool for further geomechanical applications and analyses of the Estreux

The study was carried out on Estreux abandoned underground chalk mine in Northern France, which is located 10 km east of the city of Valenciennes. The Estreux chalk formation

The Estreux mine, which was principally dug for blocks for dimension stone (for buildings and masonry) at the end of the 18th century, covers an area of 10 hectares. The chalk was excavated at a depth of 20 metres using the pillar-and-stall method, where networks of galleries were dug from access shafts, leaving large pillars in place to support the weight of the roof. This prevents the openings caving in, at least during excavation. The width of the galleries in the Estreux mine vary from 2 to 3 metres, and the pillars measure on average between 1.5 and 4.5 metres square. The excavation ratio (relation between the area exploited

The lithostratigraphic section of the Estreux mine overburden comprises, from top to bottom:

In 1980, Raffoux and Ervel conducted geomechanics laboratory tests on over one hundred core samples from this mine. The mechanical properties obtained are shown in Table 1. From these characteristics and the mining geometry, they estimated a stability factor close to 1 in several zones of the mine. As the mine is not stable in the long term, site monitoring was deemed necessary, and four convergence meters were subsequently installed in a weak zone

> **Young's Modulus, GPa**

**Poisson's Ratio** 

**Breaking limit, Mpa** 

Table 1. Mechanical characteristics of the Estreux chalk (Raffoux & Ervel, 1980)

square and 1.8 m high was instrumented. The instrumentation comprises:

Dry 9 10.3 2.83 0.3 Saturated 4.6 5.3 1.61 0.3

Since August 2003, new instrumentation has been installed (Fig. 1) to analyse geomechanics phenomena of the rock mass over time. The galleries were monitored and a pillar of 1.4 m

is of the Late Cretaceous geological period (89 to 94 Ma years ago).

temperature and pressure.

**2. Site scale: Stability analysis** 

and the total area) is around 78%.



**State Elastic Limit,** 


**Mpa** 


**2.1 Lithology** 

of the mine.


chalk.


Data were recorded from February 2004 to February 2008, and the following were observed:


Fig. 1. Diagram of the full instrumentation employed in the Estreux mine

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 167

Fig. 5. Changes over time in lateral extension at two points within the pillar

Fig. 6. Convergence over time between the mine wall and roof

as does the pillar's ability to sustain the stability of the rock mass.

considerably to the degradation of the pillars over time.

In a mine where the water-level shows a generally decreasing trend, the influence of ambient hygrometry can have a major impact on the evolution of the pillars. This has been observed in some gypsum mines (Auvray et al., 2004), where scanning electron microscopy analysis of rock sections from different distances from the surface of the pillar has shown extensive traces of dissolution at the surface of the pillar, reducing towards the centre. This dissolution can induce rock matrix degradation that can lead to progressive spalling (flakeoff) of the pillar (Fig. 7). As a direct consequence, the section of the pillar reduces over time,

The instrumentation of the underground mine in Estreux shows significant seasonal changes in the water level and ambient hygrometry. These changes induce variations in pore pressure, leading to alternating cycles of saturation/desaturation that can contribute

To study the consequences of this type of phenomenon on the rock matrix in detail, laboratory tests were carried out reproducing the environmental conditions in the mine.

Fig. 2. Evolution of the water level over time

Fig. 3. Evolution of pore pressure at different points within the pillar

Fig. 4. Changes in rock temperature over time at different points within the pillar and ambient temperature

Fig. 2. Evolution of the water level over time

ambient temperature

Fig. 3. Evolution of pore pressure at different points within the pillar

Fig. 4. Changes in rock temperature over time at different points within the pillar and

Fig. 5. Changes over time in lateral extension at two points within the pillar

Fig. 6. Convergence over time between the mine wall and roof

In a mine where the water-level shows a generally decreasing trend, the influence of ambient hygrometry can have a major impact on the evolution of the pillars. This has been observed in some gypsum mines (Auvray et al., 2004), where scanning electron microscopy analysis of rock sections from different distances from the surface of the pillar has shown extensive traces of dissolution at the surface of the pillar, reducing towards the centre. This dissolution can induce rock matrix degradation that can lead to progressive spalling (flakeoff) of the pillar (Fig. 7). As a direct consequence, the section of the pillar reduces over time, as does the pillar's ability to sustain the stability of the rock mass.

The instrumentation of the underground mine in Estreux shows significant seasonal changes in the water level and ambient hygrometry. These changes induce variations in pore pressure, leading to alternating cycles of saturation/desaturation that can contribute considerably to the degradation of the pillars over time.

To study the consequences of this type of phenomenon on the rock matrix in detail, laboratory tests were carried out reproducing the environmental conditions in the mine.

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 169

It is well known that any change in total suction induces a change in the degree of water saturation, *Srw*, which can be quantified via the water retention curve (WRC) of the material. The WRC of Estreux chalk is presented in Fig. 8 (De Gennaro et al., 2006). As it can be observed, significant changes in *Srw* occur when suction varies between 1 and 2 MPa,

Hr = 83.5% ( s = 24.9 MPa)

Hr = 97% ( s = 4.2 MPa)

The slight differences observed between the drying and wetting paths denote a moderate hysteresis effect, also observed in other chalks (Priol, 2005). A possible effect of the glauconite fraction in reducing the hysteresis effect is suspected, although a clear explanation of the slight hysteresis is not straightforward. The drying curve shows that the air entry value of Estreux chalk can be estimated at approximately 1.5 MPa. Following the drying path, the degree of saturation exhibits a dramatic reduction, with a value as low as 30% at 2.5 MPa. At the highest suction (*s* = 24.9 MPa, *hr* = 83.5%) the degree of saturation is as low as 2% to 5%, showing that the chalk is nearly completely desaturated. Based on the water retention curve, the suction of a dry sample can be estimated at 30 MPa. The shape of the water-retention curve of Estreux chalk and the sudden decrease in saturation above 1.5 MPa show that changing values of the ambient relative humidity in the mine (between 80% and 100%) can definitely lead to significantly unsaturated states, at least at the surface of the pillar, directly in contact with the ambient relative humidity. As a consequence, the mechanical properties of the chalk in unsaturated states have to be considered when addressing the long-term stability of the pillars. As a first step, the compressibility

Dry path Wetting path Initial state

0 0.2 0.4 0.6 0.8 1 DEGREE OF SATURATION, Srw

Hr = 98.2% ( s = 2.5 MPa)

Hr = 99.8% ( s = 1.5 MPa)

Oedometer tests involve uniaxial compression of samples that are prevented from expanding laterally. The two independent stress variables commonly used in the

properties of the chalk under various controlled suctions are investigated.

causing near-total desaturation.

Fig. 8. Water retention curve of Estreux chalk

0.001

0.01

0.1

SUCTION, s :MPa

1

10

100

**3.2 Oedometer tests** 

Fig. 7. Progressive spalling of a pillar in a gypsum mine. From left to right, photos from 1996, 2000, and 2004 (Sorgi & Watelet, 2007)

#### **3. Laboratory scale: Core testing**

Estreux chalk is a glauconite-rich chalk. Glauconite is an alumino-silicate of iron, potassium, and sodium. Its mineral composition is close to that of illite, although glauconite is not hydrated, with the additional presence of sodium and strong isomorphism by substitution of aluminium atoms with Fe2+ and Fe3+ iron atoms. Glauconite is often present in chalk deposits in northern France (Masson, 1973).

The porosity of Estreux chalk is about 37%, its specific gravity is *Gs* = 2.74, and the average water content is equal to 20.7% when the rock is water-saturated. At the microstructural level, the solid matrix is made up of micrometric grains that are principally fragments of coccolithes. Sometimes intact coccolithes also occur. The chalk is then principally made up of calcite (calcium carbonate, CaCO3), which often also constitutes the cementing agent at the intergranular contacts. Microfossils and mineral impurities are also frequently observed.

#### **3.1 Retention properties of Estreux chalk**

The Estreux chalk samples were completely saturated when extracted; the mine temperature was 11°C and the relative humidity, *hr*, was 100% (with 2% accuracy of the hygrometry resistive sensors). Based on Kelvin's law, the change in relative humidity modifies the total air/water suction, *ts* , the difference between the water vapour pressure (assumed equal to the atmospheric pressure, *pa*), and the water pressure, *p*w, according to the following relation:

$$s\_t = p\_a - p\_w = -\frac{\rho\_w}{M\_v} RT \ln \frac{p\_v}{p\_{vs}} \tag{1}$$

where w is the water density, *Mv* the molar mass of the water vapour, *R* the universal constant of an ideal gas (8.314 Jmol-1K-1), *T* the absolute temperature, *pv* the vapour pressure and *pvs* the pressure of the saturating vapour at temperature *T* (*hr* = *pv/pvs*).

Fig. 7. Progressive spalling of a pillar in a gypsum mine. From left to right, photos from

Estreux chalk is a glauconite-rich chalk. Glauconite is an alumino-silicate of iron, potassium, and sodium. Its mineral composition is close to that of illite, although glauconite is not hydrated, with the additional presence of sodium and strong isomorphism by substitution of aluminium atoms with Fe2+ and Fe3+ iron atoms. Glauconite is often present in chalk

The porosity of Estreux chalk is about 37%, its specific gravity is *Gs* = 2.74, and the average water content is equal to 20.7% when the rock is water-saturated. At the microstructural level, the solid matrix is made up of micrometric grains that are principally fragments of coccolithes. Sometimes intact coccolithes also occur. The chalk is then principally made up of calcite (calcium carbonate, CaCO3), which often also constitutes the cementing agent at the intergranular contacts. Microfossils and mineral impurities are also frequently observed.

The Estreux chalk samples were completely saturated when extracted; the mine temperature was 11°C and the relative humidity, *hr*, was 100% (with 2% accuracy of the hygrometry resistive sensors). Based on Kelvin's law, the change in relative humidity modifies the total air/water suction, *ts* , the difference between the water vapour pressure (assumed equal to the atmospheric pressure, *pa*), and the water pressure, *p*w, according to the following

*<sup>w</sup> <sup>v</sup> t aw*

*<sup>p</sup> s p p RT M p*

where w is the water density, *Mv* the molar mass of the water vapour, *R* the universal constant of an ideal gas (8.314 Jmol-1K-1), *T* the absolute temperature, *pv* the vapour

pressure and *pvs* the pressure of the saturating vapour at temperature *T* (*hr* = *pv/pvs*).

*v vs*

ln (1)

1996, 2000, and 2004 (Sorgi & Watelet, 2007)

deposits in northern France (Masson, 1973).

**3.1 Retention properties of Estreux chalk** 

relation:

**3. Laboratory scale: Core testing** 

It is well known that any change in total suction induces a change in the degree of water saturation, *Srw*, which can be quantified via the water retention curve (WRC) of the material. The WRC of Estreux chalk is presented in Fig. 8 (De Gennaro et al., 2006). As it can be observed, significant changes in *Srw* occur when suction varies between 1 and 2 MPa, causing near-total desaturation.

Fig. 8. Water retention curve of Estreux chalk

The slight differences observed between the drying and wetting paths denote a moderate hysteresis effect, also observed in other chalks (Priol, 2005). A possible effect of the glauconite fraction in reducing the hysteresis effect is suspected, although a clear explanation of the slight hysteresis is not straightforward. The drying curve shows that the air entry value of Estreux chalk can be estimated at approximately 1.5 MPa. Following the drying path, the degree of saturation exhibits a dramatic reduction, with a value as low as 30% at 2.5 MPa. At the highest suction (*s* = 24.9 MPa, *hr* = 83.5%) the degree of saturation is as low as 2% to 5%, showing that the chalk is nearly completely desaturated. Based on the water retention curve, the suction of a dry sample can be estimated at 30 MPa. The shape of the water-retention curve of Estreux chalk and the sudden decrease in saturation above 1.5 MPa show that changing values of the ambient relative humidity in the mine (between 80% and 100%) can definitely lead to significantly unsaturated states, at least at the surface of the pillar, directly in contact with the ambient relative humidity. As a consequence, the mechanical properties of the chalk in unsaturated states have to be considered when addressing the long-term stability of the pillars. As a first step, the compressibility properties of the chalk under various controlled suctions are investigated.

#### **3.2 Oedometer tests**

Oedometer tests involve uniaxial compression of samples that are prevented from expanding laterally. The two independent stress variables commonly used in the

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 171

Dry (T1) 0.0022 0.1082 16.0 Dry (T2) 0.0055 0.0940 13.5

The values of the mechanical parameters are given in Table 2. These illustrate the sensitivity of the mechanical response of the Estreux chalk to changes in suction. They are in good agreement with the water-weakening effects described by Matthews and Clayton (1993), and with earlier observations on reservoir chalks (with water and oil as pore fluids) by De

Influence of water sensitivity is also denoted by the swelling observed in test T1 (during water injection under 441 kPa of applied vertical load) and by the collapse observed in test T2 under water injection at 29.28 MPa of applied vertical stress. The increase in compressibility and decrease in yield stress with increased degree of saturation (decreased

> 100 1000 10000 100000 VERTICAL STRESS, v: kPa

 WATER INJECTION

COLLAPSE

suction) are two other manifestations of the water-weakening effect.

Fig. 10. Compressibility curves obtained with oedometers

T1 (dry) T2 (dry) T3 (s = 4.2 MPa) T4 (saturated)

0.35

0.4

0.45

0.5

 WATER INJECTION

SWELLING

VOID RATIO, e

0.55

0.6

0.65

Suction Controlled (T3) 0.0095 0.1137 1.4 Saturated (T4) 0.0039 0.1350 7.5 Table 2. Compressibility and yield stress of Estreux chalk derived from oedometer tests.

Gennaro et al. (2004) and Priol (2005).

**State Compressibility Yield Stress, MPa Elastic Plastic** 

investigation of the mechanical behaviour of unsaturated soils are the suction, *s* = *ua – uw* (where *ua* and *uw* are the air and water pressure respectively), and mean net stress, *pnet* = *p – ua* (where *p* is the total mean stress).

The loading paths followed during the oedometric tests are presented in Fig. 9. The resulting compressibility curves in the [log *<sup>v</sup>* : *e*] diagrams are presented in Fig. 10, where *e* is the void ratio (*e = Vv/Vs*, where *Vv* is the volume of void and *Vs* is the volume of solid skeleton).

The testing program comprises four compression tests carried out as follows:


Fig. 9. Loading paths

The compressibility curves in Fig. 10 show some responses typical of unsaturated soils:


investigation of the mechanical behaviour of unsaturated soils are the suction, *s* = *ua – uw* (where *ua* and *uw* are the air and water pressure respectively), and mean net stress, *pnet* = *p –*

The loading paths followed during the oedometric tests are presented in Fig. 9. The

is the void ratio (*e = Vv/Vs*, where *Vv* is the volume of void and *Vs* is the volume of solid




Dry, s = 30 MPa

s = 4.2 MPa

The compressibility curves in Fig. 10 show some responses typical of unsaturated soils:

100 1000 10000 100000 VERTICAL STRESS, v: kPa

saturated, s = 0 MPa



injection) is close to the saturated compression curves of tests T1 and T4

*<sup>v</sup>* : *e*] diagrams are presented in Fig. 10, where *e*

The testing program comprises four compression tests carried out as follows:

 *ua* (where *p* is the total mean stress).

and reload at 40.76 MPa.

SUCTION, s

Fig. 9. Loading paths

skeleton).

resulting compressibility curves in the [log

MPa, reload to 29.28 MPa, and water injection.

down to 8.82 MPa, and reload to 39.7 MPa.

T1

T2

T3

T4




Table 2. Compressibility and yield stress of Estreux chalk derived from oedometer tests.

The values of the mechanical parameters are given in Table 2. These illustrate the sensitivity of the mechanical response of the Estreux chalk to changes in suction. They are in good agreement with the water-weakening effects described by Matthews and Clayton (1993), and with earlier observations on reservoir chalks (with water and oil as pore fluids) by De Gennaro et al. (2004) and Priol (2005).

Influence of water sensitivity is also denoted by the swelling observed in test T1 (during water injection under 441 kPa of applied vertical load) and by the collapse observed in test T2 under water injection at 29.28 MPa of applied vertical stress. The increase in compressibility and decrease in yield stress with increased degree of saturation (decreased suction) are two other manifestations of the water-weakening effect.

Fig. 10. Compressibility curves obtained with oedometers

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 173

of the pressure in the observation chamber was used to define the level of hygrometry, *hr*,

The changes in microstructure under wetting when passing from *hr* = 97% (chalk in its natural state at sampling with *w* = 20.7%) to *hr* = 100% are evident when comparing Figs. 12a and 12b. A reference network has been superposed to the micrograph and the boundary of one characteristic pore has been plotted. Since conditions in the chamber correspond to *hr* = 100% (*p* = 705 Pa, *T* = 2°C), hydration takes place as time passes. In Fig. 12b, the same pore is visualised after the in-situ hydration. As is seen from the two images, hydration produced a progressive enlargement of the pore boundaries due probably, but not exclusively, to the loss of capillary bridges between the grains. Progressive saturation of smaller pores is also observed on the left side of the photo in Fig. 12b. This observation still remains rather qualitative, though it provides an initial picture of the ongoing phenomena. It should be emphasised that pore enlargement is certainly amplified by the specific condition reproduced in the ESEM environment, namely the absence of any external loading and the observation of the external surface of the sample. It is expected that the extent of this phenomenon could be less for the inner non-visible pores. It is worth mentioning that the occurrence of pore enlargement during saturation at zero external applied load is consistent with the swelling

shown in Fig. 10 for test T1 during water injection under low applied vertical stress.

a) b)

intermediate state before complete saturation

**4.3 Saturation/desaturation cycles with ESEM** 

Fig. 12. Modifications of the porous network in chalk during wetting: a) initial state, b)

A series of tests was carried out on samples submitted to saturation/desaturation cycles following the path indicated in Fig. 11. During these tests a constant temperature condition was chosen (*T* = 2°C). Relative humidity was then modified, changing the level of vacuum inside the chamber between 705 Pa and 346 Pa, corresponding to an *hr* varying between 100% and 50% (path A-B-C-D in Fig. 11). Observations were conducted at 1500

based on the state diagram of water (Fig. 11).

**4.2 Microstructural changes under wetting** 

#### **4. Microscopic scale: Electron Scanning Environmental Microscope (ESEM) observations and micro-testing**

The electron scanning environmental microscope (ESEM) allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Unlike the traditional scanning electron microscopy (SEM), ESEM technology does not require any preliminary treatment of the observed samples (such as dehydration or conductive coating). This has undeniable advantages in the analysis of the microstructure of geomaterials. In this study, a FEI Quanta 400® ESEM equipped with a Deben® microtesting facility has been used as a tool for the microstructural and micromechanical characterisation of Estreux chalk.

Changes in *Srw* were reproduced by controlling sample temperature and pressure following the state diagram of water (Fig. 11), being simultaneously correlated to the corresponding microstructural evolutions. A further step of the analysis involved the investigation of the microstructure while the material was subjected to a micromechanical loading, under constant or variable relative humidity, by means of ESEM micromechanical in situ tests.

Fig. 11. State diagram of water and imposed changes during observation (ii)

Three types of observations were conducted: (i) changes in microstructure under wetting, (ii) samples submitted to saturation/de-saturation cycles starting from their natural state of saturation (path Fig. 11), and (iii) samples submitted to unconfined axial compression microtests under variable states of water saturation (Sorgi & De Gennaro, 2007).

#### **4.1 Sample preparation**

Sub-samples were extracted from available blocks of Estreux chalk retrieved from the underground mine, and these were sealed and stored in a thermo-regulated chamber to ensure the preservation of in situ conditions in terms of water content.

Observations (i) and (ii) were conducted on sub-samples having a square section (about 10 mm/side) and a thickness varying from 2 mm to 4 mm. These were fixed on the observation plate inside the ESEM chamber using a carbon conductive glue. Reduced plug thicknesses ensured a more uniform temperature distribution within the samples, and temperature was controlled using a thermo-electric cooler (based on Peltier's effect). The corresponding value of the pressure in the observation chamber was used to define the level of hygrometry, *hr*, based on the state diagram of water (Fig. 11).

#### **4.2 Microstructural changes under wetting**

172 Advances in Data, Methods, Models and Their Applications in Geoscience

**4. Microscopic scale: Electron Scanning Environmental Microscope (ESEM)** 

The electron scanning environmental microscope (ESEM) allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Unlike the traditional scanning electron microscopy (SEM), ESEM technology does not require any preliminary treatment of the observed samples (such as dehydration or conductive coating). This has undeniable advantages in the analysis of the microstructure of geomaterials. In this study, a FEI Quanta 400® ESEM equipped with a Deben® microtesting facility has been used as a tool for the microstructural and

Changes in *Srw* were reproduced by controlling sample temperature and pressure following the state diagram of water (Fig. 11), being simultaneously correlated to the corresponding microstructural evolutions. A further step of the analysis involved the investigation of the microstructure while the material was subjected to a micromechanical loading, under constant or variable relative humidity, by means of ESEM micromechanical in situ tests.

> hr = 100 % 95 % 85%

> > 60% 50%

Fig. 11. State diagram of water and imposed changes during observation (ii)

 **C** GAS

microtests under variable states of water saturation (Sorgi & De Gennaro, 2007).

ensure the preservation of in situ conditions in terms of water content.

Three types of observations were conducted: (i) changes in microstructure under wetting, (ii) samples submitted to saturation/de-saturation cycles starting from their natural state of saturation (path Fig. 11), and (iii) samples submitted to unconfined axial compression

0 2 4 6 8 10 12 14 TEMPERATURE (°C)

Sub-samples were extracted from available blocks of Estreux chalk retrieved from the underground mine, and these were sealed and stored in a thermo-regulated chamber to

Observations (i) and (ii) were conducted on sub-samples having a square section (about 10 mm/side) and a thickness varying from 2 mm to 4 mm. These were fixed on the observation plate inside the ESEM chamber using a carbon conductive glue. Reduced plug thicknesses ensured a more uniform temperature distribution within the samples, and temperature was controlled using a thermo-electric cooler (based on Peltier's effect). The corresponding value

**observations and micro-testing** 

**4.1 Sample preparation** 

PRESSURE (P

a)

micromechanical characterisation of Estreux chalk.

 **A D**

LIQUID

 **B**

The changes in microstructure under wetting when passing from *hr* = 97% (chalk in its natural state at sampling with *w* = 20.7%) to *hr* = 100% are evident when comparing Figs. 12a and 12b. A reference network has been superposed to the micrograph and the boundary of one characteristic pore has been plotted. Since conditions in the chamber correspond to *hr* = 100% (*p* = 705 Pa, *T* = 2°C), hydration takes place as time passes. In Fig. 12b, the same pore is visualised after the in-situ hydration. As is seen from the two images, hydration produced a progressive enlargement of the pore boundaries due probably, but not exclusively, to the loss of capillary bridges between the grains. Progressive saturation of smaller pores is also observed on the left side of the photo in Fig. 12b. This observation still remains rather qualitative, though it provides an initial picture of the ongoing phenomena. It should be emphasised that pore enlargement is certainly amplified by the specific condition reproduced in the ESEM environment, namely the absence of any external loading and the observation of the external surface of the sample. It is expected that the extent of this phenomenon could be less for the inner non-visible pores. It is worth mentioning that the occurrence of pore enlargement during saturation at zero external applied load is consistent with the swelling shown in Fig. 10 for test T1 during water injection under low applied vertical stress.

Fig. 12. Modifications of the porous network in chalk during wetting: a) initial state, b) intermediate state before complete saturation

#### **4.3 Saturation/desaturation cycles with ESEM**

A series of tests was carried out on samples submitted to saturation/desaturation cycles following the path indicated in Fig. 11. During these tests a constant temperature condition was chosen (*T* = 2°C). Relative humidity was then modified, changing the level of vacuum inside the chamber between 705 Pa and 346 Pa, corresponding to an *hr* varying between 100% and 50% (path A-B-C-D in Fig. 11). Observations were conducted at 1500

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 175

a) b)

c) d)

allow the quantification of the Young's modulus. The latter is clearly influenced by the various states of saturation that follow; Young's modulus for dry chalk was *Edry* = 1.1 GPa, as compared with that of saturated chalk, where *Esat* = 0.71 GPa. The ratio *Edry / Esat* = 1.6 is of the same order as that obtained by other researchers by means of standard laboratory unconfined compression tests (e.g. Raffoux & Ervel, 1980). At a suction level, *so*, of 4.2 MPa

In relation to material strength, the comparison between the unconfined compression strength (UCS) values obtained at saturated and dry states gives a ratio UCSdry/UCSsat 2 in

Fig. 13. a) and b) fracture opening in chalk specimen during drying, c) and d) fracture

the value of Young's modulus, *Eo*, is between *Edry* and *Esat,* with a value of 0.78 GPa.

closing following the second saturation

magnifications starting from the saturated state (*hr* = 100%). During the pressure changes, images were captured every 2 minutes and later mounted as a video clip. The observed zone was characterised by the presence of a rigid inclusion (crystal) embedded in the chalk porous matrix (Fig. 13a). The analysed cycles included:


During the first phase of saturation (Phase 1), the initial condition corresponding to full water saturation was reproduced inside the samples (Fig. 13a). The successive drying process (Phase 2) induced a fracture opening at the contact between the crystal and the chalk matrix (indicated by an arrow in Fig. 13b). This fracture was not evident at the beginning of the test (Fig. 13a), and its creation would seem to be associated with the changes in suction induced by wetting and drying cycles, athough it is recognised that capillary effects could also be a cause of this microstructural modification (swelling/shrinkage of the material).

In other words, wetting would have brought on fracture closing whereas drying would cause chalk matrix shrinkage around the crystal, inducing fracture opening. Fracture opening could then be the consequence of increasing capillary bridges (hence air/water interfaces) inside the chalk matrix during drying. In contrast, wetting would decrease the number of air/water menisci between the chalk matrix and the crystal, leading to a progressive fracture sealing (Figs. 13c, 13d). If related to material ageing, the evolution of this phenomenon with time following consecutive wetting and drying cycles could contribute to microstructral features associated with material degradation. The observations made here could also be supplemented and improved by advanced techniques of 2D and 3D image analysis, allowing for a more quantitative characterisation of the morphological modifications induced by changes in water saturation (see Sorgi & De Gennaro, 2007).

#### **4.4 Micromechanical in situ testing**

The combined use of the ESEM technique with unconfined compression tests was achieved using a micromechanical testing apparatus.

A Deben MICROTEST® loading module allowed the application of a maximal compression load of 5000 N at a constant strain rate of 1x10-5 s-1. A specific setup was developed to carry out micromechanical tests under controlled total suction (controlling the level of relative humidity during the tests). Cylindrical samples of about 8 mm in diameter and 15 mm in height were used. Samples were obtained by means of high-precision coring. End-face parallelism was ensured by means of a high-precision slicer having accuracy of the order of 1 µm. A series of preliminary micromechanical tests was conducted on saturated, partially saturated, and dry samples in order to verify the agreement between the micromechanical test results and the earlier laboratory test results performed on samples with larger (standard) dimensions.

The preliminary results from the unconfined compression microtests are presented in Fig. 14. It can be seen from the test results for the dry samples that there was good reproducibility. The linear slopes of the compression curves after a first tightening phase

magnifications starting from the saturated state (*hr* = 100%). During the pressure changes, images were captured every 2 minutes and later mounted as a video clip. The observed zone was characterised by the presence of a rigid inclusion (crystal) embedded in the chalk




The combined use of the ESEM technique with unconfined compression tests was achieved

A Deben MICROTEST® loading module allowed the application of a maximal compression load of 5000 N at a constant strain rate of 1x10-5 s-1. A specific setup was developed to carry out micromechanical tests under controlled total suction (controlling the level of relative humidity during the tests). Cylindrical samples of about 8 mm in diameter and 15 mm in height were used. Samples were obtained by means of high-precision coring. End-face parallelism was ensured by means of a high-precision slicer having accuracy of the order of 1 µm. A series of preliminary micromechanical tests was conducted on saturated, partially saturated, and dry samples in order to verify the agreement between the micromechanical test results and the earlier laboratory test results performed on samples with larger

The preliminary results from the unconfined compression microtests are presented in Fig. 14. It can be seen from the test results for the dry samples that there was good reproducibility. The linear slopes of the compression curves after a first tightening phase

path A-B-C in Fig. 11). Sample is left to stabilise for 60 minutes.

porous matrix (Fig. 13a). The analysed cycles included:

elapsed time.

**4.4 Micromechanical in situ testing** 

(standard) dimensions.

using a micromechanical testing apparatus.

Fig. 13. a) and b) fracture opening in chalk specimen during drying, c) and d) fracture closing following the second saturation

allow the quantification of the Young's modulus. The latter is clearly influenced by the various states of saturation that follow; Young's modulus for dry chalk was *Edry* = 1.1 GPa, as compared with that of saturated chalk, where *Esat* = 0.71 GPa. The ratio *Edry / Esat* = 1.6 is of the same order as that obtained by other researchers by means of standard laboratory unconfined compression tests (e.g. Raffoux & Ervel, 1980). At a suction level, *so*, of 4.2 MPa the value of Young's modulus, *Eo*, is between *Edry* and *Esat,* with a value of 0.78 GPa.

In relation to material strength, the comparison between the unconfined compression strength (UCS) values obtained at saturated and dry states gives a ratio UCSdry/UCSsat 2 in

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 177

possible developments, like Digital Image Correlation (DIC) (e.g. Vales et al., 2008), might also be considered in order to obtain a quantitative characterisation of the local deformation

Fig. 15. ESEM failure pattern during ESEM in situ unconfined compression test on water

A preliminary investigation of the behaviour of chalk samples retrieved from the pillars of the abandoned Estreux mine (northern France), conducted as part of an assessment of the stability of underground chalk mines, has been presented. Due to environmental changes occurring within the mine (such as hygrometry and water table), the pillars are regularly subjected to variations in the degree of water saturation. The potential impact of the evolution of the water saturation on the mechanical behaviour of the chalk has been assessed based on the methods and concepts of the mechanics of unsaturated soils at

At site scale, observations conducted during a four-year period (from February 2004 to February 2008) have highlighted that relative humidity in the mine can vary between 85% and 100%. The seasonal changes in the water table have been of reduced extent during the monitoring period, showing a general tendency towards decreasing water table level. However, as the water table rose, both pillar expansion and roof convergence were observed. Pressure and temperature measurements inside the chalk pillars have shown that both parameters vary on a seasonal basis, causing alternating states of saturation/desaturation. As expected, both pressure and temperature are not constant

different scales: site scale, laboratory scale, and microstructural scale.

saturated chalk

**5. Conclusion** 

at microstructural (few hundreds of µm) and mesostructural (some mm) levels.

agreement with available data on northern French chalk (e.g. Bonvallet, 1979). Results from the sample tested under constant suction equal to 4.2 MPa (*Sr* 97%, Fig. 10) show that higher suctions strengthen the rock. This is likely to be associated with additional bonding due to capillary effects. The observed behaviour during unconfined compression microtests seems in good agreement with the general behavioural features observed for this chalk in oedometric compression tests under controlled suction conditions (Nguyen et al., 2008).

Fig. 14. ESEM in situ unconfined compression tests on dry and water saturated chalk

Note that Nguyen et al. (2008) also found a ratio of 2.1 between the yield stress in oedometric tests in dry and saturated conditions, close to the ratio UCSdry/UCSsat 2 found during the ESEM micro-testing performed here. The ratio between the yield stress at a suction level of 4.2 MPa and that at saturated and dry state was 1.5 and 0.7, respectively. Similar ratios obtained by micromechanical testing using ESEM were equal to 1.5 and 0.75, showing a notable agreement with the oedometric test results.

Finally, Fig. 15 shows some preliminary results of ESEM in situ testing with simultaneous visualisation of the deformation pattern and the failure mode. The direction of compression is vertical, as indicated on the ESEM image (A). At peak strength (image B), the sample surface is still apparently unchanged. At about 0.9% axial strain, in the softening regime, a pseudo-vertical fracture is visible (image C), followed by a progressive opening in the postpeak phase (images D and E).

The aim of these preliminary tests was to explore the possibility of obtaining a characterisation of the local strain field during hydro-mechanical loading using ESEM. Some possible developments, like Digital Image Correlation (DIC) (e.g. Vales et al., 2008), might also be considered in order to obtain a quantitative characterisation of the local deformation at microstructural (few hundreds of µm) and mesostructural (some mm) levels.

Fig. 15. ESEM failure pattern during ESEM in situ unconfined compression test on water saturated chalk

### **5. Conclusion**

176 Advances in Data, Methods, Models and Their Applications in Geoscience

agreement with available data on northern French chalk (e.g. Bonvallet, 1979). Results from the sample tested under constant suction equal to 4.2 MPa (*Sr* 97%, Fig. 10) show that higher suctions strengthen the rock. This is likely to be associated with additional bonding due to capillary effects. The observed behaviour during unconfined compression microtests seems in good agreement with the general behavioural features observed for this chalk in oedometric compression tests under controlled suction conditions (Nguyen et al., 2008).

Fig. 14. ESEM in situ unconfined compression tests on dry and water saturated chalk

showing a notable agreement with the oedometric test results.

peak phase (images D and E).

Note that Nguyen et al. (2008) also found a ratio of 2.1 between the yield stress in oedometric tests in dry and saturated conditions, close to the ratio UCSdry/UCSsat 2 found during the ESEM micro-testing performed here. The ratio between the yield stress at a suction level of 4.2 MPa and that at saturated and dry state was 1.5 and 0.7, respectively. Similar ratios obtained by micromechanical testing using ESEM were equal to 1.5 and 0.75,

Finally, Fig. 15 shows some preliminary results of ESEM in situ testing with simultaneous visualisation of the deformation pattern and the failure mode. The direction of compression is vertical, as indicated on the ESEM image (A). At peak strength (image B), the sample surface is still apparently unchanged. At about 0.9% axial strain, in the softening regime, a pseudo-vertical fracture is visible (image C), followed by a progressive opening in the post-

The aim of these preliminary tests was to explore the possibility of obtaining a characterisation of the local strain field during hydro-mechanical loading using ESEM. Some A preliminary investigation of the behaviour of chalk samples retrieved from the pillars of the abandoned Estreux mine (northern France), conducted as part of an assessment of the stability of underground chalk mines, has been presented. Due to environmental changes occurring within the mine (such as hygrometry and water table), the pillars are regularly subjected to variations in the degree of water saturation. The potential impact of the evolution of the water saturation on the mechanical behaviour of the chalk has been assessed based on the methods and concepts of the mechanics of unsaturated soils at different scales: site scale, laboratory scale, and microstructural scale.

At site scale, observations conducted during a four-year period (from February 2004 to February 2008) have highlighted that relative humidity in the mine can vary between 85% and 100%. The seasonal changes in the water table have been of reduced extent during the monitoring period, showing a general tendency towards decreasing water table level. However, as the water table rose, both pillar expansion and roof convergence were observed. Pressure and temperature measurements inside the chalk pillars have shown that both parameters vary on a seasonal basis, causing alternating states of saturation/desaturation. As expected, both pressure and temperature are not constant

Water-Rock Interaction Mechanisms and Ageing Processes in Chalk 179

The work presented here has been undertaken within the French National Project BCRD coordinated by INERIS (2005-2008). The financial support of INERIS is gratefully acknowledged. The authors are also indebted to P. Delage, H. D. Nguyen and P. Delalain for their fruitful discussions on a range of issues related to the mechanical behaviour of chalk. The technical support of E. De Laure and J. Thiriat in designing the experimental

Auvray, C., Homand, F., & Sorgi, C. (2004). The aging of gypsum in underground mines.

Bonvallet, J. (1979). Une classification géotechnique des craies du nord utilisée pour l'étude

De Gennaro, V., Delag,e P., Cui, Y.J., Schroeder, Ch., & Collin, F. 2003. Time-dependent

De Gennaro, V., Delage, P., Priol, G., Collin, F., & Cui, Y.J. 2004. On the collapse behaviour

De Gennaro, V., Sorgi, C., & Delage P. (2006). Water retention properties of a mine chalk.

Masson, M. (1973). Pétrophysique de la craie. *La craie, Bulletin des Laboratories des Ponts et* 

Matthews, M.C. & Clayton, C.R.I (1993). Influence of intact porosity on the engineering

Nguyen, H. D., De Gennaro, V., Delage, P., & Sorgi C. (2008). Retention and

Nguyen, H.D. (2009). Water-rock interaction and long term behaviour of shallow cavities in

Priol, G. (2005). Comportement mécanique d'une craie pétrolifèrecomportement différé et

Raffoux, J. F. & Ervel, C. (1980). Stabilitt ggabilit de la carria c souterraine d'Estreux. Rapport

Sorgi C. (2004). Contribution méthodologique et expérimentale à l'étude de la diminution de

Sorgi, C. & Watelet, J. (2007). Fenomeni di degrade e rischio di crollo nelle cave di gesso

*evaporitiche*, Patron Editore, Bergamo, Italy, September 2007, pp. 41-59.

la résistance des massifs rocheux par veillissement. BCRD Rapport Final (2001-

abbandonate: l'esperienza francese. *Proceedings Dissesti indotti dall'alterazione di rocce* 

of oil reservoir chalk. *Géotechnique,* Vol. 54, No. 6, pp. 415 - 420

de stabilité des carrières souterraines. *Revue Française de Géotechnique* Vol. 8,

behaviour of oil reservoir chalk: a multiphase approach. *Soils and Foundations*, Vol.

*Proceedings of the 4th International Conference on Unsaturated Soils (UNSAT 2006),*

properties of a weak rock. *Proceedings of the conference on geotechnical engineering of* 

compressibility properties of a partially saturated mine chalk. *Proceedings of the 1st European Conference, E-UNSAT 2008*, Durham, United Kingdom, July 2008,

**6. Acknowledgment** 

**7. References** 

pp. 5-15

pp. 283–289

01111) INERIS-DRS: 132 pp

43, No. 4, pp. 131-148

apparatuses presented is also greatfully acknowledged.

*Engineering Geology,* Vol. 74, No. 3-4, pp. 183 – 196

Phoenix, Arizona, USA, April 2006, pp. 1371-1381

chalks. Doctoral thesis, Ecole des Ponts ParisTech, Paris

CERCHAR rapport C CTO-CE/JS 80-76-2510/01: 8

mouillabilité. Doctoral Thesis, Ecole des Ponts ParisTech, Paris

*Chaussées*, Special Volume, pp. 23-48.

*hard soils - soft rocks,* Vol. 1, pp. 693-702.

inside the pillars, but rather depends on the position of the point considered (altitude and distance from the pillar surface), on the liquid water inflow at the base of the pillar (which depends on the water table level), and on the evaporation rate at the surface of the pillar. It has been shown that, moving inwards from the free surface to the core of the pillar, both pressure and temperature decrease. The observations at site scale confirmed that water saturation in the chalk, controlled by the evolution of relative humidity and water table, influences the deformation of mine pillars and roof.

At laboratory scale, a detailed experimental program was carried out to better quantify the influence of water saturation on the mechanical behaviour of the Estreux chalk. A significant phenomena identified by the water retention properties is that significant desaturation occurs when the suction increases from 1 to 2.5 MPa, corresponding to a change in relative humidity from 99.3% to 98.2%. In such situations, water saturation decreases from almost full saturation (higher than 90%) down to *Srw* = 12%. The degree of water saturation of the chalk at equilibrium under a relative humidity of 83.5% (suction of 24.9 MPa) was about 7%. Considering that conditions of relative humidity, *hr*, of around 80% can occur in the mine, and that for this situation *Srw* at equilibrium is as low as 5%, the significance of the chalk behaviour in unsaturated conditions is confirmed. Similarly to what has been shown in oil reservoir chalks (De Gennaro et al., 2003, 2004), the methods and concepts of unsaturated soils have been successfully adapted to Estreux chalk. Controlled suction oedometer tests provided more details on the water-weakening effects in chalk, showing increasing compaction during water injection (pore collapse). As observed in unsaturated soils, the yield stress determined in the oedometer increases when suction is increased (i.e. when the degree of saturation is decreased), confirming in more detail the suction-hardening effect as is observed in unsaturated soils.

For the microstructural scale, some applications of the ESEM for the microstructural characterisation of the partially saturated chalk have been presented. ESEM allows the observation of microstructural changes of geomaterials in their natural state under controlled conditions of temperature and pressure. Change in saturation can be easily reproduced in the observation chamber by means of a thermo-electric cooler based on the Peltier effect. This provided a preliminary analysis of the microstructural modifications of the Estreux chalk induced by the saturation/desaturation cycles in the absence of mechanical loading. Suction-controlled micromechanical in situ tests are also feasible. The validation of a specific experimental technique has been presented and results from micromechanical uniaxial unconfined compression tests have been compared with available results from laboratory-scale tests in terms of isotropic Young's moduli and UCS values. Good agreement has been observed between the different tests, confirming the reliability of this technique for further investigation of the micromechanical behaviour of geometerials under controlled saturation states (controlled suction).

Further developments using the ESEM are expected to all quantitatively characterise the effects of the mechanical and physico-chemical processes associated with the water-rock interaction. In the specific case of carbonate rocks these developments could provide a better understanding of some fundamental processes, such as dissolution, precipitation, crystallisation, and solid transport under stress, that lie at the onset and cause the degradation mechanisms of these rocks under the effect of environmental and mechanical agents.

#### **6. Acknowledgment**

178 Advances in Data, Methods, Models and Their Applications in Geoscience

inside the pillars, but rather depends on the position of the point considered (altitude and distance from the pillar surface), on the liquid water inflow at the base of the pillar (which depends on the water table level), and on the evaporation rate at the surface of the pillar. It has been shown that, moving inwards from the free surface to the core of the pillar, both pressure and temperature decrease. The observations at site scale confirmed that water saturation in the chalk, controlled by the evolution of relative humidity and water table,

At laboratory scale, a detailed experimental program was carried out to better quantify the influence of water saturation on the mechanical behaviour of the Estreux chalk. A significant phenomena identified by the water retention properties is that significant desaturation occurs when the suction increases from 1 to 2.5 MPa, corresponding to a change in relative humidity from 99.3% to 98.2%. In such situations, water saturation decreases from almost full saturation (higher than 90%) down to *Srw* = 12%. The degree of water saturation of the chalk at equilibrium under a relative humidity of 83.5% (suction of 24.9 MPa) was about 7%. Considering that conditions of relative humidity, *hr*, of around 80% can occur in the mine, and that for this situation *Srw* at equilibrium is as low as 5%, the significance of the chalk behaviour in unsaturated conditions is confirmed. Similarly to what has been shown in oil reservoir chalks (De Gennaro et al., 2003, 2004), the methods and concepts of unsaturated soils have been successfully adapted to Estreux chalk. Controlled suction oedometer tests provided more details on the water-weakening effects in chalk, showing increasing compaction during water injection (pore collapse). As observed in unsaturated soils, the yield stress determined in the oedometer increases when suction is increased (i.e. when the degree of saturation is decreased), confirming in more detail the suction-hardening effect as

For the microstructural scale, some applications of the ESEM for the microstructural characterisation of the partially saturated chalk have been presented. ESEM allows the observation of microstructural changes of geomaterials in their natural state under controlled conditions of temperature and pressure. Change in saturation can be easily reproduced in the observation chamber by means of a thermo-electric cooler based on the Peltier effect. This provided a preliminary analysis of the microstructural modifications of the Estreux chalk induced by the saturation/desaturation cycles in the absence of mechanical loading. Suction-controlled micromechanical in situ tests are also feasible. The validation of a specific experimental technique has been presented and results from micromechanical uniaxial unconfined compression tests have been compared with available results from laboratory-scale tests in terms of isotropic Young's moduli and UCS values. Good agreement has been observed between the different tests, confirming the reliability of this technique for further investigation of the micromechanical behaviour of geometerials

Further developments using the ESEM are expected to all quantitatively characterise the effects of the mechanical and physico-chemical processes associated with the water-rock interaction. In the specific case of carbonate rocks these developments could provide a better understanding of some fundamental processes, such as dissolution, precipitation, crystallisation, and solid transport under stress, that lie at the onset and cause the degradation mechanisms of these rocks under the effect of environmental and mechanical

influences the deformation of mine pillars and roof.

is observed in unsaturated soils.

agents.

under controlled saturation states (controlled suction).

The work presented here has been undertaken within the French National Project BCRD coordinated by INERIS (2005-2008). The financial support of INERIS is gratefully acknowledged. The authors are also indebted to P. Delage, H. D. Nguyen and P. Delalain for their fruitful discussions on a range of issues related to the mechanical behaviour of chalk. The technical support of E. De Laure and J. Thiriat in designing the experimental apparatuses presented is also greatfully acknowledged.

#### **7. References**


**10** 

**New Identity of the Kimberlite Melt:** 

Vadim S. Kamenetsky, Maya B. Kamenetsky and Roland Maas

Kimberlite magmas are in many aspects unusual compared to other terrestrial magmatic liquids. They are very rare and occur in small volumes, but their intimate relationships with diamonds make them invaluable to the scientific and exploration communities. The association of kimberlite rocks with diamonds and deep-seated mantle xenoliths links the origin of parental kimberlite magmas to the highest known depths (> 150 km) of magma derivation (e.g. Dawson, 1980; Eggler, 1989; Girnis & Ryabchikov, 2005; Mitchell, 1986; Mitchell, 1995; Pasteris, 1984). Kimberlite magmas would have one of the lowest viscosities and highest buoyancies that enable exceptionally rapid transport from the source region (Canil & Fedortchouk, 1999; Eggler, 1989; Haggerty, 1999; Kelley & Wartho, 2000; Sparks et

Despite significant research efforts, there is still uncertainty about the true chemical identity of kimberlite parental melts and their derivates. Kimberlite magmas are always contaminated by large quantities of lithic fragments and crystals, unrelated to the evolution of the parental melt. In most cases kimberlites are severely modified by syn- and postmagmatic changes that have altered the original alkali and volatile element abundances. These problems are reflected in the definition of the kimberlite rock as "*both a contaminated and altered sample of its parent melt*" (Pasteris, 1984). Numerous other definitions of the kimberlite commonly reflect on ultramafic compositions and enrichment in volatiles (CO2 and H2O; Clement et al., 1984; Kjarsgaard et al., 2009; Kopylova et al., 2007; Mitchell, 1986; Mitchell, 2008; Patterson et al., 2009; Skinner & Clement, 1979) which are supposedly

The physical properties of a kimberlite magma directly, and occurrence of diamonds indirectly, relate to the enrichment in carbonate components which are represented in common kimberlites by calcite and dolomite. The abundant carbonate component in kimberlite rocks is counter-balanced by a more abundant olivine (ultramafic) component, represented by olivine fragments and crystals that are commonly affected by serpentinisation. The ultramafic silicate compositions of kimberlites are ascribed to

**1. Introduction** 

al., 2006) and preservation of diamonds.

inherited from parental magmas.

**Constraints from Unaltered** 

**Diamondiferous Udachnaya –**

**East Pipe Kimberlite, Russia** 

*University of Tasmania, University of Melbourne,* 

*Australia* 

Sorgi C. & De Gennaro V. (2007). ESEM analysis of chalk microstructure submitted to hydromechanical loading. *C.R. Géosciences* Vol. 339., No. 7, pp. 468-481.Valès F., Bornert M., Gharbi H., Nguyen, M. D., & Eytard, J.C. (2007). Micromechanical investigations of the hydro-mechanical behaviour of argillite rocks by means of optical full field strain measurement and acoustic emission techniques. *Proceedings of the 11th International Society for Rock Mechanics Congress*, Lisbon, July 2007

## **New Identity of the Kimberlite Melt: Constraints from Unaltered Diamondiferous Udachnaya – East Pipe Kimberlite, Russia**

Vadim S. Kamenetsky, Maya B. Kamenetsky and Roland Maas *University of Tasmania, University of Melbourne, Australia* 

#### **1. Introduction**

180 Advances in Data, Methods, Models and Their Applications in Geoscience

Sorgi C. & De Gennaro V. (2007). ESEM analysis of chalk microstructure submitted to

*of the 11th International Society for Rock Mechanics Congress*, Lisbon, July 2007

hydromechanical loading. *C.R. Géosciences* Vol. 339., No. 7, pp. 468-481.Valès F., Bornert M., Gharbi H., Nguyen, M. D., & Eytard, J.C. (2007). Micromechanical investigations of the hydro-mechanical behaviour of argillite rocks by means of optical full field strain measurement and acoustic emission techniques. *Proceedings* 

> Kimberlite magmas are in many aspects unusual compared to other terrestrial magmatic liquids. They are very rare and occur in small volumes, but their intimate relationships with diamonds make them invaluable to the scientific and exploration communities. The association of kimberlite rocks with diamonds and deep-seated mantle xenoliths links the origin of parental kimberlite magmas to the highest known depths (> 150 km) of magma derivation (e.g. Dawson, 1980; Eggler, 1989; Girnis & Ryabchikov, 2005; Mitchell, 1986; Mitchell, 1995; Pasteris, 1984). Kimberlite magmas would have one of the lowest viscosities and highest buoyancies that enable exceptionally rapid transport from the source region (Canil & Fedortchouk, 1999; Eggler, 1989; Haggerty, 1999; Kelley & Wartho, 2000; Sparks et al., 2006) and preservation of diamonds.

> Despite significant research efforts, there is still uncertainty about the true chemical identity of kimberlite parental melts and their derivates. Kimberlite magmas are always contaminated by large quantities of lithic fragments and crystals, unrelated to the evolution of the parental melt. In most cases kimberlites are severely modified by syn- and postmagmatic changes that have altered the original alkali and volatile element abundances. These problems are reflected in the definition of the kimberlite rock as "*both a contaminated and altered sample of its parent melt*" (Pasteris, 1984). Numerous other definitions of the kimberlite commonly reflect on ultramafic compositions and enrichment in volatiles (CO2 and H2O; Clement et al., 1984; Kjarsgaard et al., 2009; Kopylova et al., 2007; Mitchell, 1986; Mitchell, 2008; Patterson et al., 2009; Skinner & Clement, 1979) which are supposedly inherited from parental magmas.

> The physical properties of a kimberlite magma directly, and occurrence of diamonds indirectly, relate to the enrichment in carbonate components which are represented in common kimberlites by calcite and dolomite. The abundant carbonate component in kimberlite rocks is counter-balanced by a more abundant olivine (ultramafic) component, represented by olivine fragments and crystals that are commonly affected by serpentinisation. The ultramafic silicate compositions of kimberlites are ascribed to

New Identity of the Kimberlite Melt: Constraints from

Taimyr Fold Belt

**Norilsk**

70oN

(1995).

depths of the mine.

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 183

**Laptev Sea**

**Anabar**

**Udachnaya**

80oE 140oE

Baikal Fold Belt

Fig. 1. Map of the Siberian Platform showing the major kimberlite fields after Pearson et al.

et al., 1976). At deeper levels (> 400 m) of the kimberlite body the amount of serpentine in the groundmass gradually decreases and the amount of carbonate in the groundmass increases. Intensive mining of the Udachnaya pipe revealed widespread chloride minerals (mostly halite) as dispersed masses in the groundmass and massive multi-mineral segregations of halite, serpentine, anhydrite, carbonates and hydrous iron oxides (Pavlov & Ilupin, 1973). The amount of chloride minerals in the groundmass increases with depth, and recently a large number of chloride-carbonate "nodules" were recovered from ~470-500 m

The studies Udachnaya-East kimberlites are dark massive rocks with porphyroclastic fragmental textures. They are exceptionally olivine-rich (Fig. 2, 12a), a feature shared by the majority of known kimberlites, excluding rare aphanitic kimberlites, such as those from Kimberley, South Africa (Edgar et al., 1988; Edgar & Charbonneau, 1993; le Roex et al., 2003; Shee, 1986) and Jericho, Canada (Price et al., 2000). The large abundance of olivine (45-60 vol%) is reflected in the high MgO content of the bulk rock compositions (28-36 wt%). Olivine is set in a fine-grained matrix of carbonates (Fig. 2, calcite, shortite Na2Ca2(CO3)3 and

**Yakutsk**

Verkhoyansk Fold Belt

**Aldan**

Russia

Kimberlite fields Archaean shields

abundant olivine macrocrysts and phenocrysts, whereas significant CO2 and H2O contents are attributed respectively to carbonate minerals (calcite and dolomite) and serpentine (+ other H2O-bearing magnesian silicates). Unfortunately, the masking effects of deuteric and post-magmatic alteration do not permit routine recognition of olivine generations, and so the olivine component originally dissolved in the kimberlite parental melt remains controversial (Brett et al., 2009; Francis & Patterson, 2009; Mitchell & Tappe, 2010; Patterson et al., 2009). Similarly, the original magmatic abundances of volatile and fluid-mobile alkali elements are disturbed by syn- and post-emplacement modifications, thus complicating complicating quantification of the parental melt composition if inferred from bulk kimberlite analyses.

The existing dogma about correspondence between compositions of whole rock kimberlites and their parental melt has been recently challenged by the newcomers to the kimberlite scientific community (e.g., Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Kamenetsky et al., 2007b; Kamenetsky et al., 2008; Kamenetsky et al., 2009a; Kamenetsky et al., 2009b; Kamenetsky et al., 2009c; Maas et al., 2005). A breakthrough into understanding of the kimberlite magma chemical and physical characteristics was made possible by detailed studies of the diamondiferous Udachnaya-East kimberlite pipe in Siberia. Unlike other kimberlites worldwide, severely modified by syn- and post-magmatic changes, the Udachnaya-East kimberlite is the only known fresh rock of this type, and thus it is invaluable source of information on the composition and temperature of primary melt, its mantle source, rheological properties of ascending kimberlite magma. This kimberlite preserved unequivocal evidence for olivine populations, olivine paragenetic assemblages and olivine-hosted melt inclusions, and the role of mantle-derived alkali carbonate and alkali chloride components in the parental melt.

#### **2. Udachnaya-East kimberlite: Location and samples**

The Udachnaya diamondiferous kimberlite pipe is located in the Daldyn-Alakit region of the Siberian diamondiferous kimberlite province (Fig. 1). Most Siberian pipes are tuffbreccias essentially devoid of unaltered olivine, but some contain large blocks of massive fresh kimberlite. A remarkable characteristic of this region is that it contains more pipes with fresh, unaltered olivine than any other kimberlite region within the Siberian province. About 10% of the intrusions exhibit either two adjacent channelways or repeated intrusion of magma through the same chimney. The Udachnaya pipe, the best known example of these twin diatremes, is located in the northwest part of the Daldyn field (Fig. 1). At the surface it consists of two adjacent bodies (East and West) that are separated at depth >250- 270 m. Based on stratigraphic relationships both intrusions formed at the Devonian-Carboniferous boundary (~350 Ma), and the age estimates vary from 389 to 335 Ma (Burgess et al., 1992; Kamenetsky et al., 2009c; Kinny et al., 1997; Maas et al., 2005; Maslovskaja et al., 1983). The eastern and western bodies of the Udachnaya kimberlite pipe are different from each other in terms of mineralogy, petrography, composition, and degree of alteration. As the alteration of the western pipe can be considered typical of this rock type, the rocks of the Udachnaya-East are unique in having lesser alteration, and in some places they are completely unaltered.

At depths greater than 350 m a particularly fresh porphyritic kimberlite has been found. These rocks are described as dark-grey massive kimberlite, characterized by unaltered euhedral-subhedral olivine phenocrysts set in a dominantly carbonate matrix (Marshintsev

abundant olivine macrocrysts and phenocrysts, whereas significant CO2 and H2O contents are attributed respectively to carbonate minerals (calcite and dolomite) and serpentine (+ other H2O-bearing magnesian silicates). Unfortunately, the masking effects of deuteric and post-magmatic alteration do not permit routine recognition of olivine generations, and so the olivine component originally dissolved in the kimberlite parental melt remains controversial (Brett et al., 2009; Francis & Patterson, 2009; Mitchell & Tappe, 2010; Patterson et al., 2009). Similarly, the original magmatic abundances of volatile and fluid-mobile alkali elements are disturbed by syn- and post-emplacement modifications, thus complicating complicating quantification of the parental melt composition if inferred from bulk

The existing dogma about correspondence between compositions of whole rock kimberlites and their parental melt has been recently challenged by the newcomers to the kimberlite scientific community (e.g., Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Kamenetsky et al., 2007b; Kamenetsky et al., 2008; Kamenetsky et al., 2009a; Kamenetsky et al., 2009b; Kamenetsky et al., 2009c; Maas et al., 2005). A breakthrough into understanding of the kimberlite magma chemical and physical characteristics was made possible by detailed studies of the diamondiferous Udachnaya-East kimberlite pipe in Siberia. Unlike other kimberlites worldwide, severely modified by syn- and post-magmatic changes, the Udachnaya-East kimberlite is the only known fresh rock of this type, and thus it is invaluable source of information on the composition and temperature of primary melt, its mantle source, rheological properties of ascending kimberlite magma. This kimberlite preserved unequivocal evidence for olivine populations, olivine paragenetic assemblages and olivine-hosted melt inclusions, and the role of mantle-derived alkali carbonate and

The Udachnaya diamondiferous kimberlite pipe is located in the Daldyn-Alakit region of the Siberian diamondiferous kimberlite province (Fig. 1). Most Siberian pipes are tuffbreccias essentially devoid of unaltered olivine, but some contain large blocks of massive fresh kimberlite. A remarkable characteristic of this region is that it contains more pipes with fresh, unaltered olivine than any other kimberlite region within the Siberian province. About 10% of the intrusions exhibit either two adjacent channelways or repeated intrusion of magma through the same chimney. The Udachnaya pipe, the best known example of these twin diatremes, is located in the northwest part of the Daldyn field (Fig. 1). At the surface it consists of two adjacent bodies (East and West) that are separated at depth >250- 270 m. Based on stratigraphic relationships both intrusions formed at the Devonian-Carboniferous boundary (~350 Ma), and the age estimates vary from 389 to 335 Ma (Burgess et al., 1992; Kamenetsky et al., 2009c; Kinny et al., 1997; Maas et al., 2005; Maslovskaja et al., 1983). The eastern and western bodies of the Udachnaya kimberlite pipe are different from each other in terms of mineralogy, petrography, composition, and degree of alteration. As the alteration of the western pipe can be considered typical of this rock type, the rocks of the Udachnaya-East are unique in having lesser alteration, and in some places they are

At depths greater than 350 m a particularly fresh porphyritic kimberlite has been found. These rocks are described as dark-grey massive kimberlite, characterized by unaltered euhedral-subhedral olivine phenocrysts set in a dominantly carbonate matrix (Marshintsev

kimberlite analyses.

completely unaltered.

alkali chloride components in the parental melt.

**2. Udachnaya-East kimberlite: Location and samples** 

Fig. 1. Map of the Siberian Platform showing the major kimberlite fields after Pearson et al. (1995).

et al., 1976). At deeper levels (> 400 m) of the kimberlite body the amount of serpentine in the groundmass gradually decreases and the amount of carbonate in the groundmass increases. Intensive mining of the Udachnaya pipe revealed widespread chloride minerals (mostly halite) as dispersed masses in the groundmass and massive multi-mineral segregations of halite, serpentine, anhydrite, carbonates and hydrous iron oxides (Pavlov & Ilupin, 1973). The amount of chloride minerals in the groundmass increases with depth, and recently a large number of chloride-carbonate "nodules" were recovered from ~470-500 m depths of the mine.

The studies Udachnaya-East kimberlites are dark massive rocks with porphyroclastic fragmental textures. They are exceptionally olivine-rich (Fig. 2, 12a), a feature shared by the majority of known kimberlites, excluding rare aphanitic kimberlites, such as those from Kimberley, South Africa (Edgar et al., 1988; Edgar & Charbonneau, 1993; le Roex et al., 2003; Shee, 1986) and Jericho, Canada (Price et al., 2000). The large abundance of olivine (45-60 vol%) is reflected in the high MgO content of the bulk rock compositions (28-36 wt%). Olivine is set in a fine-grained matrix of carbonates (Fig. 2, calcite, shortite Na2Ca2(CO3)3 and

New Identity of the Kimberlite Melt: Constraints from

(c)

carbonate-chloride melt inclusions.

**3. Kimberlite olivine: Morphology and composition** 

overlap in terms of composition, and possibly origin.

(a)

alteration that affected most kimberlites worldwide.

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 185

indicate that two of the inferred key characteristics of kimberlitic magmas - low sodium and high water contents (Fig. 5; Kjarsgaard et al., 2009) – unambiguously relate to postmagmatic

(b)

0.5 mm

(d)

Fig. 3. Photomicrographs in plane-polarised light of individual crystals of olivine-I (a, b) and olivine-II (c, d) showing networks of magmatic inclusions, including crystal, fluid and

Two populations of olivine in the Udachnaya-East kimberlite can be recognised based on size, colour, morphology, and entrapped inclusions. Consistent with many other studies of kimberlitic olivine (e.g., Boyd & Clement, 1977; Emeleus & Andrews, 1975; Hunter & Taylor, 1984; Mitchell, 1973; Mitchell, 1978; Nielsen & Jensen, 2005; Sobolev et al., 1989) the populations are represented by olivine-I (interpreted by different workers as cognate phenocrysts or xenocrysts) and groundmass olivine-II. However, as it follows from Arndt et al. (2010), Brett et al. (2009) and Kamenetsky et al. (2008) both populations significantly

0.1 mm 0.1 mm

0.5 mm

zemkorite (Na, K)2Ca(CO3)2), chlorides (halite and sylvite), and minor phlogopite and opaque minerals (e.g. spinel group minerals, perovskite, Fe±(Ni,Cu,K) sulphides) (Golovin et al., 2007; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Sharygin et al., 2003; Sobolev et al., 1989). Groundmass olivine is very abundant (up to 40 vol%), completely unaltered, and contains crystal, fluid and melt inclusions (Fig. 3; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Kamenetsky et al., 2008; Kamenetsky et al., 2009a).

Fig. 2. Backscattered electron image and X-ray element maps showing intimate association of euhedral zoned olivine, Na–K chlorides, alkali carbonates, calcite, and sodalite in the groundmass of Udachnaya-East kimberlite

The bulk rock compositions are also characterised by low Al2O3 (1.2-2.3 wt%), but high CaO (8.4-18.2 wt%) and CO2 (4-14 wt%) contents. Trace element compositions are similar to those of other kimberlites, having incompatible element enrichment and depletion in heavy rareearth elements and Y (Fig. 4). The radiogenic isotope data (87Sr/86Srt ≈ 0.7047, �Nd ≈ +4, 206Pb/204Pbt ≈ 18.7, 207Pb/204Pbt = 15.53, 208Pb/204Pbt = 35.5–38.9, t = 367 Ma; Maas et al., 2005) fall within the field defined by most group-I kimberlites (Fraser et al., 1985; Smith, 1983; Weis & Demaiffe, 1985). The overall petrographic, mineralogical and chemical characteristics of the Udachnaya-East kimberlites suggest that they are common type-I (Mitchell, 1989) or group-I (Clement & Skinner, 1985; Smith, 1983) kimberlite.

However, the studied Udachnaya-East samples are distinctly different from other kimberlites in that they have high abundances of alkali elements (up to 6 wt% Na2O), strong enrichment in chlorine (up to 6 wt%), and extraordinary depletion in H2O (< 0.5 wt%) correlated with absence of primary or secondary serpentine. Thus unusual for kimberlites low H2O abundances coupled with extraordinary enrichment in Na2O and Cl (Fig. 5) may

zemkorite (Na, K)2Ca(CO3)2), chlorides (halite and sylvite), and minor phlogopite and opaque minerals (e.g. spinel group minerals, perovskite, Fe±(Ni,Cu,K) sulphides) (Golovin et al., 2007; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Sharygin et al., 2003; Sobolev et al., 1989). Groundmass olivine is very abundant (up to 40 vol%), completely unaltered, and contains crystal, fluid and melt inclusions (Fig. 3; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Kamenetsky et al., 2008;

**100m**

**Na**

Fig. 2. Backscattered electron image and X-ray element maps showing intimate association of euhedral zoned olivine, Na–K chlorides, alkali carbonates, calcite, and sodalite in the

The bulk rock compositions are also characterised by low Al2O3 (1.2-2.3 wt%), but high CaO (8.4-18.2 wt%) and CO2 (4-14 wt%) contents. Trace element compositions are similar to those of other kimberlites, having incompatible element enrichment and depletion in heavy rareearth elements and Y (Fig. 4). The radiogenic isotope data (87Sr/86Srt ≈ 0.7047, �Nd ≈ +4, 206Pb/204Pbt ≈ 18.7, 207Pb/204Pbt = 15.53, 208Pb/204Pbt = 35.5–38.9, t = 367 Ma; Maas et al., 2005) fall within the field defined by most group-I kimberlites (Fraser et al., 1985; Smith, 1983; Weis & Demaiffe, 1985). The overall petrographic, mineralogical and chemical characteristics of the Udachnaya-East kimberlites suggest that they are common type-I

However, the studied Udachnaya-East samples are distinctly different from other kimberlites in that they have high abundances of alkali elements (up to 6 wt% Na2O), strong enrichment in chlorine (up to 6 wt%), and extraordinary depletion in H2O (< 0.5 wt%) correlated with absence of primary or secondary serpentine. Thus unusual for kimberlites low H2O abundances coupled with extraordinary enrichment in Na2O and Cl (Fig. 5) may

(Mitchell, 1989) or group-I (Clement & Skinner, 1985; Smith, 1983) kimberlite.

**Mg Ca**

**Cl**

Kamenetsky et al., 2009a).

groundmass of Udachnaya-East kimberlite

indicate that two of the inferred key characteristics of kimberlitic magmas - low sodium and high water contents (Fig. 5; Kjarsgaard et al., 2009) – unambiguously relate to postmagmatic alteration that affected most kimberlites worldwide.

Fig. 3. Photomicrographs in plane-polarised light of individual crystals of olivine-I (a, b) and olivine-II (c, d) showing networks of magmatic inclusions, including crystal, fluid and carbonate-chloride melt inclusions.

### **3. Kimberlite olivine: Morphology and composition**

Two populations of olivine in the Udachnaya-East kimberlite can be recognised based on size, colour, morphology, and entrapped inclusions. Consistent with many other studies of kimberlitic olivine (e.g., Boyd & Clement, 1977; Emeleus & Andrews, 1975; Hunter & Taylor, 1984; Mitchell, 1973; Mitchell, 1978; Nielsen & Jensen, 2005; Sobolev et al., 1989) the populations are represented by olivine-I (interpreted by different workers as cognate phenocrysts or xenocrysts) and groundmass olivine-II. However, as it follows from Arndt et al. (2010), Brett et al. (2009) and Kamenetsky et al. (2008) both populations significantly overlap in terms of composition, and possibly origin.

New Identity of the Kimberlite Melt: Constraints from

85 87 89 91 93 95

85 87 89 91 93 95

NiO, wt% NiO, wt%

**3.1 Olivine-I** 

N

5

0.1

than the size of the symbols.

**3.2 Olivine-II: Morphology and zoning** 

0.2

0.3

0.4

0.5

15

25

35

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 187

Light-green or light-yellow olivine-I is present as rounded and oval crystals, or more often as angular fragments with smooth edges Fig. 3a, b). Angular olivine-I is characteristically transparent and large (0.5 to 7-8 mm), whereas ovoid grains are smaller (0.7-2 mm) and often 'dusted' with inclusions (Fig. 3a, b). Melt and fluid inclusions occur in angular olivine-I and some round crystals only in "secondary" trails along healed fractures (Fig. 3a, b). Olivine-I is characterised by variable forsterite content (Fo) from 85 to 94 mol%, although most grains are Fo>91 (Fig. 6a). Most grains appear to be homogeneous, at least in terms of their Fo content, except outermost rims and around healed fractures. Abundances of trace elements Ca, Ni, Cr and Mn in olivine-I vary strongly with Fo (Fig. 6a). The trace element composition trends resembling fractionation can be seen for NiO decreasing (0.43-0.13 wt%) and MnO increasing (0.07-0.17 wt%) as the Fo value decreases (Fig. 6a). However, it should

2

Fo, mol% Fo, mol%

0.1

Fig. 6. Forsterite and trace element compositions of olivine-I (a) and olivine-II, 0.3-0.5mm size (b). Grey and black circles represent cores and rims of olivine-II, respectively. N, number of grains. The analytical error (1, equals 0.08% for Fo and 2% for NiO) is smaller

Olivine-II is represented by relatively small (0.05-0.8 mm) euhedral flattened grains (Fig. 3c,d). Crystals display a tabular habit (tablet shape), and crystal growth was preferentially developed in the {100} and {001} directions. Olivine-II is colourless or slightly greenish or

0.2

0.3

0.4

0.5

85 87 89 91 93 95

85 87 89 91 93 95

6

10

14

18

N

(a) (b)

be noted that NiO in the majority of olivine-I is almost constant (0.35-0.39 wt%).

Fig. 4. Trace element abundance patterns of the Udachnaya-East kimberlites (lines) and kimberlites worldwide (field). All compositions are normalised to the "Primitive Mantle" composition of Sun and McDonough (1989).

Fig. 5. Compositional co-variations of Na2O and H2O (in wt.%) in the Udachnaya-East kimberlites and "archetypal" rocks from South Africa, Greenland and Canada (field). The trend to low sodium and high water contents is considered to be caused by post-magmatic alteration.

#### **3.1 Olivine-I**

186 Advances in Data, Methods, Models and Their Applications in Geoscience

**Rb Ba Th U Nb Ta K La Ce Pb Pr Sr P NdSm Zr Hf Eu Ti Gd Tb Dy Y Ho Er TmYb Lu**

**Na2O, wt%**

Fig. 5. Compositional co-variations of Na2O and H2O (in wt.%) in the Udachnaya-East kimberlites and "archetypal" rocks from South Africa, Greenland and Canada (field). The trend to low sodium and high water contents is considered to be caused by post-magmatic

**0.01 0.1 1 10**

Fig. 4. Trace element abundance patterns of the Udachnaya-East kimberlites (lines) and kimberlites worldwide (field). All compositions are normalised to the "Primitive Mantle"

**0**

**H**

**2**

**1**

**10**

**0.1**

alteration.

**O, wt%**

composition of Sun and McDonough (1989).

**1**

**10**

sample/primitive mantle

**100**

**1000**

Light-green or light-yellow olivine-I is present as rounded and oval crystals, or more often as angular fragments with smooth edges Fig. 3a, b). Angular olivine-I is characteristically transparent and large (0.5 to 7-8 mm), whereas ovoid grains are smaller (0.7-2 mm) and often 'dusted' with inclusions (Fig. 3a, b). Melt and fluid inclusions occur in angular olivine-I and some round crystals only in "secondary" trails along healed fractures (Fig. 3a, b).

Olivine-I is characterised by variable forsterite content (Fo) from 85 to 94 mol%, although most grains are Fo>91 (Fig. 6a). Most grains appear to be homogeneous, at least in terms of their Fo content, except outermost rims and around healed fractures. Abundances of trace elements Ca, Ni, Cr and Mn in olivine-I vary strongly with Fo (Fig. 6a). The trace element composition trends resembling fractionation can be seen for NiO decreasing (0.43-0.13 wt%) and MnO increasing (0.07-0.17 wt%) as the Fo value decreases (Fig. 6a). However, it should be noted that NiO in the majority of olivine-I is almost constant (0.35-0.39 wt%).

Fig. 6. Forsterite and trace element compositions of olivine-I (a) and olivine-II, 0.3-0.5mm size (b). Grey and black circles represent cores and rims of olivine-II, respectively. N, number of grains. The analytical error (1, equals 0.08% for Fo and 2% for NiO) is smaller than the size of the symbols.

#### **3.2 Olivine-II: Morphology and zoning**

Olivine-II is represented by relatively small (0.05-0.8 mm) euhedral flattened grains (Fig. 3c,d). Crystals display a tabular habit (tablet shape), and crystal growth was preferentially developed in the {100} and {001} directions. Olivine-II is colourless or slightly greenish or

New Identity of the Kimberlite Melt: Constraints from

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

zoning and core and rim relationships. Scale bars represent 100 µm

Fo >89.5, and then gradually decrease in less magnesian olivine (Fig. 6b).

**3.3 Olivine-II: Compositional variation** 

Fig. 7. Back-scattered electron images of olivine-II crystals demonstrating different types of

The inner parts ("cores") of olivine-II are strongly variable in Fo content (85.5 - 93.5 mol%), although the compositions 90.5-93 mol% Fo are most common (69%, Fig. 6b). The cores display relatively wide range of NiO (0.13-0.44 wt%, Fig. 6b), CaO (0-0.08 wt%), MnO (0-0.15 wt%), and Cr2O3 (0-0.09 wt%) contents. NiO contents are the highest and almost constant at

The outer parts ("rims") of olivine-II, although representing significant volumes of this population, have very constant Fo content 89.0 ± 0.2 mol% (Fig. 6b). In contrast, the trace

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 189

brownish, and a large amount of various inclusions is responsible for weak transparency and "cloudy" appearance of their host crystals (Fig. 3c, d).

The BSE images of individual olivine-II grains demonstrate compositional variability in terms of Fe-Mg relationships (higher and lower Fo correspond to *darker* and *lighter* areas, respectively; Fig. 7). Nearly all groundmass olivine crystals, even the smallest, exhibit intragrain compositional variability (Fig. 7). The commonly used term "zoning" is not appropriate in the case of olivine-II, as evident from the description below. Five main types of olivine "structure" account for most typical Fo variations within single grains (Fig. 7):


All olivine-II show abrupt change to extremely Mg-rich (Fo96) compositions at the very edge of the grains (~5-10 µm thick) in contact with matrix carbonate.

The grains with a single core (types 1-3) are the most abundant (~80%); however, a single core of euhedral or subhedral shape (type 1) is very rare (5%). Some cores have almost perfect olivine crystal shapes, and as a rule the crystallographic outlines of inner cores are parallel to the whole grain outlines (Fig. 7 a, d-g). The majority of olivine grains have corroded core edges (Fig. 7 b-d, f, h), and the degree of irregularity varies even within a single core. In other words, some outlines of the core can be straight and parallel to the crystal's outer rims, whereas other boundaries of the same core appear highly diffuse. These are transitional between types 1 and 2, and are more abundant than type 1.

Type 2 grains have a single core of variable size (relatively to grain size) and degree of resorption. The majority of the type 2 crystals tend to have oval to very irregular outlines of cores (Fig. 7 b, c, f). Some cores exhibit linear features (e.g. cracks) along which the olivine composition changes.

Types 1 and 2 are additionally subdivided into subtypes with normal (Focore>Forim) and reverse (Focore<Forim) "zoning".

Type 3 grains with a single core are characterised by presence of a compositionally distinct layer, separating cores and rims (Fig. 7 a, e, f). These layers are variable in shape, continuity and width. Even within a single grain the "separating" layer shows significant variability in shape, width and composition. The composition of such layers in the grains with reverse "zoning" is always more Fo-rich than the composition of both cores and rims.

The crystals belonging to type 4 with two or three cores are relatively rare (14%), but can be very important for genetic interpretations. Typically type 4 is an intergrowth of two distinct grains, where the cores with different or similar Fo have the shape and orientation similar to those of the grain's edges (Fig. 7g). In grains with two or more cores of different compositions, the cores are usually separated from each other (Fig. 7h), although a few examples are noted where the cores coalesce. In some crystals, the core has layers of different compositions, manifesting a gradual or abrupt zoning pattern across the olivine crystals. These layers frequently demonstrate well defined crystallographic shapes, parallel to outermost rims of olivine grains.

brownish, and a large amount of various inclusions is responsible for weak transparency

The BSE images of individual olivine-II grains demonstrate compositional variability in terms of Fe-Mg relationships (higher and lower Fo correspond to *darker* and *lighter* areas, respectively; Fig. 7). Nearly all groundmass olivine crystals, even the smallest, exhibit intragrain compositional variability (Fig. 7). The commonly used term "zoning" is not appropriate in the case of olivine-II, as evident from the description below. Five main types of olivine "structure" account for most typical Fo variations within single grains (Fig. 7): 1. A single core, euhedral-subhedral in shape, that can be more forsteritic (1a) or less

2. A single resorbed core of variable shape, size and composition. The composition of resorbed cores can be more forsteritic (2a) or less forsteritic (2b) than the rim;

5. No distinct core – the grains are either compositionally uniform or have a mosaic-like

All olivine-II show abrupt change to extremely Mg-rich (Fo96) compositions at the very edge

The grains with a single core (types 1-3) are the most abundant (~80%); however, a single core of euhedral or subhedral shape (type 1) is very rare (5%). Some cores have almost perfect olivine crystal shapes, and as a rule the crystallographic outlines of inner cores are parallel to the whole grain outlines (Fig. 7 a, d-g). The majority of olivine grains have corroded core edges (Fig. 7 b-d, f, h), and the degree of irregularity varies even within a single core. In other words, some outlines of the core can be straight and parallel to the crystal's outer rims, whereas other boundaries of the same core appear highly diffuse. These

Type 2 grains have a single core of variable size (relatively to grain size) and degree of resorption. The majority of the type 2 crystals tend to have oval to very irregular outlines of cores (Fig. 7 b, c, f). Some cores exhibit linear features (e.g. cracks) along which the olivine

Types 1 and 2 are additionally subdivided into subtypes with normal (Focore>Forim) and

Type 3 grains with a single core are characterised by presence of a compositionally distinct layer, separating cores and rims (Fig. 7 a, e, f). These layers are variable in shape, continuity and width. Even within a single grain the "separating" layer shows significant variability in shape, width and composition. The composition of such layers in the grains with reverse

The crystals belonging to type 4 with two or three cores are relatively rare (14%), but can be very important for genetic interpretations. Typically type 4 is an intergrowth of two distinct grains, where the cores with different or similar Fo have the shape and orientation similar to those of the grain's edges (Fig. 7g). In grains with two or more cores of different compositions, the cores are usually separated from each other (Fig. 7h), although a few examples are noted where the cores coalesce. In some crystals, the core has layers of different compositions, manifesting a gradual or abrupt zoning pattern across the olivine crystals. These layers frequently demonstrate well defined crystallographic shapes, parallel

3. A single core separated from rims by a thin layer of distinct composition;

are transitional between types 1 and 2, and are more abundant than type 1.

"zoning" is always more Fo-rich than the composition of both cores and rims.

and "cloudy" appearance of their host crystals (Fig. 3c, d).

4. Two or more cores of different shape and composition;

of the grains (~5-10 µm thick) in contact with matrix carbonate.

forsteritic (1b) than the rim;

structure (Fig. 7i).

composition changes.

reverse (Focore<Forim) "zoning".

to outermost rims of olivine grains.

Fig. 7. Back-scattered electron images of olivine-II crystals demonstrating different types of zoning and core and rim relationships. Scale bars represent 100 µm

#### **3.3 Olivine-II: Compositional variation**

The inner parts ("cores") of olivine-II are strongly variable in Fo content (85.5 - 93.5 mol%), although the compositions 90.5-93 mol% Fo are most common (69%, Fig. 6b). The cores display relatively wide range of NiO (0.13-0.44 wt%, Fig. 6b), CaO (0-0.08 wt%), MnO (0-0.15 wt%), and Cr2O3 (0-0.09 wt%) contents. NiO contents are the highest and almost constant at Fo >89.5, and then gradually decrease in less magnesian olivine (Fig. 6b).

The outer parts ("rims") of olivine-II, although representing significant volumes of this population, have very constant Fo content 89.0 ± 0.2 mol% (Fig. 6b). In contrast, the trace

New Identity of the Kimberlite Melt: Constraints from

**ca ca**

carbonate

**ca**

**o**

**<sup>c</sup> <sup>c</sup> <sup>c</sup> <sup>p</sup> <sup>p</sup>**

**4.1 Melt inclusions in groundmass olivine-II** 

**o**

Fig. 8. Photomicrographs of (a) groundmass olivine and (b–g) olivine-hosted melt

inclusions. Scale bars represent 50 µm. B: Multiphase melt inclusion hosted in core of olivine (boxed in a). c: Typical melt inclusion at room temperature. d: Same inclusion at 580 oC shows immiscibility between carbonate (matrix) and chloride (globules) melt. e: Same inclusion at 680 oC shows complete miscibility and homogenisation transmitted light). Note sculptured surface of melt inclusion at temperature of homogenisation. f, g: Multiphase melt inclusion in transmitted and reflected light, respectively. Principal daughter phases: c sodium-potassium chloride; o—olivine; p—phlogopite; ca—sodium-potassium-calcium

Melt inclusions are trapped either individually within olivine cores and rims, or occur along healed fractures (Fig. 3, 8; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a). Many inclusions are interconnected by thin channels, and thus modifications of original melt compositions by "necking down" cannot be ruled out. Abundant secondary melt inclusions in fractures connected to the groundmass, and decrepitated inclusions, are assumed to have experienced exchange and loss of material, respectively, after entrapment.

**o**

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 191

**580 oC**

**680 20 oC oC**

**f g**

**a b**

**c d e**

element abundances in the rims are highly variable (in wt%: NiO 0.15-0.35, CaO 0.03-0.15, MnO 0.11-0.2, Cr2O3 0.01-0.11 and Al2O3 0-0.04). In general, the rims are richer in MnO, but poorer in NiO than the cores with the same Fo content (Fig. 6b). The outermost forsteritic (Fo96) rims are very enriched in CaO (up to 1 wt%).

#### **4. Mineral and melt inclusions in olivine**

Inclusions of different composition are present in almost all grains of the Udachnaya-East olivine. They can be very abundant in some grains, but rare in others. Three main types of magmatic inclusions are recognized in the studied samples: crystals, fluid and melt. Inclusion sizes are variable (<1 to ~400 µm) and the distribution of inclusions within a single olivine crystal is very heterogeneous, with some parts totally devoid of inclusions, and some parts so packed with inclusions as to make olivine almost opaque (Fig. 3, 8). The highest density of inclusions is observed along internal fractures and growth planes (Fig. 3). Crystal inclusions in olivine of both populations are always primary. Inclusions of melt and fluid in olivine-I and cores of olivine-II are always restricted to fractures healed with olivine of different composition, and thus are secondary in origin with respect to their host olivine. Similar inclusions in the rims of olivine-II show features reminiscent of both primary and secondary origin (Fig. 8). Melt inclusions in olivine of both populations are predominantly alkali carbonate-chloride in composition (Fig. 8). Silicate melt inclusions have not been found in our studies.

The rims of olivine-II grains contain abundant inclusions of different minerals that are never present in the cores (Kamenetsky et al., 2008; Kamenetsky et al., 2009a). Among them, Crspinel, phlogopite, perovskite and rutile are relatively abundant, whereas magnetite and picroilmenite are less common. Inclusions of low-Ca pyroxene (Mg# 88-92) occur in both cores and rims (Fo86-91) in clusters of several (10-30) round and euhedral grains (Kamenetsky et al., 2008; Kamenetsky et al., 2009a). A common association of low-Ca pyroxene in the rims includes numerous melt and fluid inclusions, and CO2-rich bubbles adhered to surfaces of pyroxene crystals. The compositions of low-Ca pyroxene inclusions are characterised by high SiO2 (53.3-58 wt%), Na2O (0.1-0.9 wt%), elevated TiO2 (0-0.5 wt%), and low Al2O3 (0.7-1.4 wt%), CaO (0.7-1.7 wt%) and Cr2O3 (0.1-0.6 wt%), compared to mantle orthopyroxene.

Rare inclusions of high-Ca pyroxene in the Udachnaya-East olivine are restricted to olivine-I and cores of olivine-II (Fig. 9; Kamenetsky et al., 2008; Kamenetsky et al., 2009a). They occur as single crystals or clusters of several crystals. They vary in size (25-400 µm), colour (emerald-green to greyish-green) and shape (round to euhedral-subhedral). Most of them are intimately associated with the carbonate-chloride material, which forms coating on surfaces and inclusions inside clinopyroxene grains (Fig. 9). The clinopyroxene inclusions (Mg# 87.5-94.5 mol%) are in Mg-Fe equilibrium with the host olivine Fo86.3-93, and characterised by low Al2O3 (0.65-2.9 wt%), and high CaO (19.5-23.8 wt%), Na2O (0.75-2.3 wt%) and Cr2O3 (0.9-2.6 wt%) contents. Individual crystals show fine-scale compositional zoning, with a general pattern of MgO and CaO increase, and Na2O, Cr2O3 and in some cases Al2O3, decrease towards the rims. Major and trace element compositions of high-Ca pyroxene inclusions overlap with compositions of clinopyroxene from lherzolite nodules in the Udachnaya-East kimberlite (Kamenetsky et al., 2009a).

element abundances in the rims are highly variable (in wt%: NiO 0.15-0.35, CaO 0.03-0.15, MnO 0.11-0.2, Cr2O3 0.01-0.11 and Al2O3 0-0.04). In general, the rims are richer in MnO, but poorer in NiO than the cores with the same Fo content (Fig. 6b). The outermost forsteritic

Inclusions of different composition are present in almost all grains of the Udachnaya-East olivine. They can be very abundant in some grains, but rare in others. Three main types of magmatic inclusions are recognized in the studied samples: crystals, fluid and melt. Inclusion sizes are variable (<1 to ~400 µm) and the distribution of inclusions within a single olivine crystal is very heterogeneous, with some parts totally devoid of inclusions, and some parts so packed with inclusions as to make olivine almost opaque (Fig. 3, 8). The highest density of inclusions is observed along internal fractures and growth planes (Fig. 3). Crystal inclusions in olivine of both populations are always primary. Inclusions of melt and fluid in olivine-I and cores of olivine-II are always restricted to fractures healed with olivine of different composition, and thus are secondary in origin with respect to their host olivine. Similar inclusions in the rims of olivine-II show features reminiscent of both primary and secondary origin (Fig. 8). Melt inclusions in olivine of both populations are predominantly alkali carbonate-chloride in composition (Fig. 8). Silicate melt inclusions have not been

The rims of olivine-II grains contain abundant inclusions of different minerals that are never present in the cores (Kamenetsky et al., 2008; Kamenetsky et al., 2009a). Among them, Crspinel, phlogopite, perovskite and rutile are relatively abundant, whereas magnetite and picroilmenite are less common. Inclusions of low-Ca pyroxene (Mg# 88-92) occur in both cores and rims (Fo86-91) in clusters of several (10-30) round and euhedral grains (Kamenetsky et al., 2008; Kamenetsky et al., 2009a). A common association of low-Ca pyroxene in the rims includes numerous melt and fluid inclusions, and CO2-rich bubbles adhered to surfaces of pyroxene crystals. The compositions of low-Ca pyroxene inclusions are characterised by high SiO2 (53.3-58 wt%), Na2O (0.1-0.9 wt%), elevated TiO2 (0-0.5 wt%), and low Al2O3 (0.7-1.4 wt%), CaO (0.7-1.7 wt%) and Cr2O3 (0.1-0.6 wt%), compared to

Rare inclusions of high-Ca pyroxene in the Udachnaya-East olivine are restricted to olivine-I and cores of olivine-II (Fig. 9; Kamenetsky et al., 2008; Kamenetsky et al., 2009a). They occur as single crystals or clusters of several crystals. They vary in size (25-400 µm), colour (emerald-green to greyish-green) and shape (round to euhedral-subhedral). Most of them are intimately associated with the carbonate-chloride material, which forms coating on surfaces and inclusions inside clinopyroxene grains (Fig. 9). The clinopyroxene inclusions (Mg# 87.5-94.5 mol%) are in Mg-Fe equilibrium with the host olivine Fo86.3-93, and characterised by low Al2O3 (0.65-2.9 wt%), and high CaO (19.5-23.8 wt%), Na2O (0.75-2.3 wt%) and Cr2O3 (0.9-2.6 wt%) contents. Individual crystals show fine-scale compositional zoning, with a general pattern of MgO and CaO increase, and Na2O, Cr2O3 and in some cases Al2O3, decrease towards the rims. Major and trace element compositions of high-Ca pyroxene inclusions overlap with compositions of clinopyroxene from lherzolite nodules in

the Udachnaya-East kimberlite (Kamenetsky et al., 2009a).

(Fo96) rims are very enriched in CaO (up to 1 wt%).

**4. Mineral and melt inclusions in olivine** 

found in our studies.

mantle orthopyroxene.

Fig. 8. Photomicrographs of (a) groundmass olivine and (b–g) olivine-hosted melt inclusions. Scale bars represent 50 µm. B: Multiphase melt inclusion hosted in core of olivine (boxed in a). c: Typical melt inclusion at room temperature. d: Same inclusion at 580 oC shows immiscibility between carbonate (matrix) and chloride (globules) melt. e: Same inclusion at 680 oC shows complete miscibility and homogenisation transmitted light). Note sculptured surface of melt inclusion at temperature of homogenisation. f, g: Multiphase melt inclusion in transmitted and reflected light, respectively. Principal daughter phases: c sodium-potassium chloride; o—olivine; p—phlogopite; ca—sodium-potassium-calcium carbonate

#### **4.1 Melt inclusions in groundmass olivine-II**

Melt inclusions are trapped either individually within olivine cores and rims, or occur along healed fractures (Fig. 3, 8; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a). Many inclusions are interconnected by thin channels, and thus modifications of original melt compositions by "necking down" cannot be ruled out. Abundant secondary melt inclusions in fractures connected to the groundmass, and decrepitated inclusions, are assumed to have experienced exchange and loss of material, respectively, after entrapment.

New Identity of the Kimberlite Melt: Constraints from

**5. Chloride-carbonate nodules in kimberlite** 

detected.

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 193

During heating stage experiments with round, relatively small (40-60 µm) melt inclusions, melting begins at ~160oC, as indicated by jolting movements of either solid phases or vapour bubbles. At 420-580oC bubble movements increase, indicating the appearance of the liquid phase (melt). Daughter phases experience some changes in their relative position, size and shape at 540-600oC. At >600oC we record a number of liquid globules that move freely and change shape continuously (Fig. 8d). The outline of a single globule is always smoothly curved: it can instantaneously change from spherical to cylindrical, embayed or lopsided, similar to an amoeba. With further heating, the number and size of the globules, as well as the number and size of vapour bubbles, gradually decreases. Homogenisation of the inclusions (except some opaque crystals) occurs when the globules and vapour bubbles

During slow cooling (5-20oC/min), vapour bubbles nucleate at 690-650oC and then progressively increases in size. Cooling to 610-580°C, the inclusions acquire a 'foggy" appearance for a split second. This process can be best described as the formation of emulsion, i.e, microglobules of liquid in another liquid (melt immiscibility). Microglobules coalesce immediately into elongate or sausage-like pinkish globules. The neighbouring globules ("boudins") are subparallel, and are grouped into regularly aligned formations with a common angle of ~75-80o. A resemblance to a skeletal or spinifex texture is evident for several seconds, after which the original "pinch-and-swell structure" pulls apart giving rise to individual blebs of melt. The latter coalesce and become spherical with time or further cooling. They continue floating, but slow down with decreasing temperature and further coalescence. The exact moment of crystallisation or complete solidification is not

The major component of the kimberlite groundmass, carbonate-chloride in composition, sometimes form large segragations ("nodules", Fig. 10; Kamenetsky et al., 2007a; Kamenetsky et al., 2007b). Such samples were collected from fresh kimberlite at the stockpiles of the Udachnaya-East pipe. The assumed depth of their origin in the mine pit is ~500 m. The nodules vary in size from a few cm to 0.5 x 1.5 m, but are commonly 5 to 30 cm across. The shapes are usually round and ellipsoidal, but angular nodules were also encountered. The nodules have very distinct contacts with the host kimberlite, but without any thermometamorphic effects. The contacts are composed of thin (< 1mm) breccia-like aggregate of olivine, calcite, sodalite, phlogopite-tetraferriphlogopite, humite-clinohumite, Fe-Mg carbonates, perovskite, apatite, magnetite, djerfisherite (K6(Cu,Fe,Ni)25S26Cl) and alkali sulphates in a matrix of chlorides. Olivine grains present at the contact with nodules belong to two types: zoned euhedral crystals similar to the Udachnaya-East groundmass olivine-II, and grains with highly irregular shapes and "mosaic" distributions of Fe-Mg. Based on mineralogy the nodules can be separated into two major groups – chloride (Fig. 10a, b) and chloride-carbonate (Fig. 10 c-e). Chloride minerals are mainly represented by halite with included round grains of sylvite. The grain size, halite colour and transparency are highly variable, ranging from translucent to milky white and from white to all shades of blue. White and blue halite is often randomly interspersed, although in some coarse-grained nodules the interior parts are blue and dark-blue coloured, whereas rims are almost colourless (Fig. 10b). Chloride nodules always contain variable amount of fine-grained

disappear almost simultaneously (within 20-30oC) at 660-760oC (Fig. 8e).

Fig. 9. A plane transmitted light photomicrograph (a) and back-scattered electron image (b) and X-ray element maps (c) of olivine-hosted clinopyroxene inclusions showing carbonate– chloride coatings and melt inclusions associated with clinopyroxene, and fine-scale compositional heterogeneity in terms of Fe, Ca and Na. Clinopyroxene on (c) is a larger inclusion on Fig. 9b. A contour of this inclusion is shown on the Cl Kα map by a dashed line.

"Necking down" can explain variable proportions of fluid and mineral phases in the studied melt inclusions. Fluid components are represented by low-density CO2 bubbles, whereas solid phases are mainly Na-K-Ca carbonates, halite, sylvite, olivine, phlogopitetetraferriphlopite, calcite, Fe-Ti-Cr oxides, aphthitalite and djerfisherite (Fig. 8f, g; Golovin et al., 2003; Kamenetsky et al., 2004; Sharygin et al., 2003). The inclusions occasionally contain monticellite, humite-clinohumite, northupite, and Ca-Mg-Fe-carbonates.

**Na**

**Cl K**

**Fe**

50 m <sup>200</sup><sup>m</sup>

**(b)**

**C**a

Fig. 9. A plane transmitted light photomicrograph (a) and back-scattered electron image (b) and X-ray element maps (c) of olivine-hosted clinopyroxene inclusions showing carbonate–

chloride coatings and melt inclusions associated with clinopyroxene, and fine-scale compositional heterogeneity in terms of Fe, Ca and Na. Clinopyroxene on (c) is a larger inclusion on Fig. 9b. A contour of this inclusion is shown on the Cl Kα map by a dashed line. "Necking down" can explain variable proportions of fluid and mineral phases in the studied melt inclusions. Fluid components are represented by low-density CO2 bubbles, whereas solid phases are mainly Na-K-Ca carbonates, halite, sylvite, olivine, phlogopitetetraferriphlopite, calcite, Fe-Ti-Cr oxides, aphthitalite and djerfisherite (Fig. 8f, g; Golovin et al., 2003; Kamenetsky et al., 2004; Sharygin et al., 2003). The inclusions occasionally contain

monticellite, humite-clinohumite, northupite, and Ca-Mg-Fe-carbonates.

50 m

**(c)**

**(a)**

During heating stage experiments with round, relatively small (40-60 µm) melt inclusions, melting begins at ~160oC, as indicated by jolting movements of either solid phases or vapour bubbles. At 420-580oC bubble movements increase, indicating the appearance of the liquid phase (melt). Daughter phases experience some changes in their relative position, size and shape at 540-600oC. At >600oC we record a number of liquid globules that move freely and change shape continuously (Fig. 8d). The outline of a single globule is always smoothly curved: it can instantaneously change from spherical to cylindrical, embayed or lopsided, similar to an amoeba. With further heating, the number and size of the globules, as well as the number and size of vapour bubbles, gradually decreases. Homogenisation of the inclusions (except some opaque crystals) occurs when the globules and vapour bubbles disappear almost simultaneously (within 20-30oC) at 660-760oC (Fig. 8e).

During slow cooling (5-20oC/min), vapour bubbles nucleate at 690-650oC and then progressively increases in size. Cooling to 610-580°C, the inclusions acquire a 'foggy" appearance for a split second. This process can be best described as the formation of emulsion, i.e, microglobules of liquid in another liquid (melt immiscibility). Microglobules coalesce immediately into elongate or sausage-like pinkish globules. The neighbouring globules ("boudins") are subparallel, and are grouped into regularly aligned formations with a common angle of ~75-80o. A resemblance to a skeletal or spinifex texture is evident for several seconds, after which the original "pinch-and-swell structure" pulls apart giving rise to individual blebs of melt. The latter coalesce and become spherical with time or further cooling. They continue floating, but slow down with decreasing temperature and further coalescence. The exact moment of crystallisation or complete solidification is not detected.

### **5. Chloride-carbonate nodules in kimberlite**

The major component of the kimberlite groundmass, carbonate-chloride in composition, sometimes form large segragations ("nodules", Fig. 10; Kamenetsky et al., 2007a; Kamenetsky et al., 2007b). Such samples were collected from fresh kimberlite at the stockpiles of the Udachnaya-East pipe. The assumed depth of their origin in the mine pit is ~500 m. The nodules vary in size from a few cm to 0.5 x 1.5 m, but are commonly 5 to 30 cm across. The shapes are usually round and ellipsoidal, but angular nodules were also encountered. The nodules have very distinct contacts with the host kimberlite, but without any thermometamorphic effects. The contacts are composed of thin (< 1mm) breccia-like aggregate of olivine, calcite, sodalite, phlogopite-tetraferriphlogopite, humite-clinohumite, Fe-Mg carbonates, perovskite, apatite, magnetite, djerfisherite (K6(Cu,Fe,Ni)25S26Cl) and alkali sulphates in a matrix of chlorides. Olivine grains present at the contact with nodules belong to two types: zoned euhedral crystals similar to the Udachnaya-East groundmass olivine-II, and grains with highly irregular shapes and "mosaic" distributions of Fe-Mg. Based on mineralogy the nodules can be separated into two major groups – chloride (Fig. 10a, b) and chloride-carbonate (Fig. 10 c-e). Chloride minerals are mainly represented by halite with included round grains of sylvite. The grain size, halite colour and transparency are highly variable, ranging from translucent to milky white and from white to all shades of blue. White and blue halite is often randomly interspersed, although in some coarse-grained nodules the interior parts are blue and dark-blue coloured, whereas rims are almost colourless (Fig. 10b). Chloride nodules always contain variable amount of fine-grained

New Identity of the Kimberlite Melt: Constraints from

**5.1 Mineralogy of chloride-carbonate nodules** 

and at the contacts with the rims.

spaces in carbonates (Fig. 11).

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 195

The chloride component of the nodules is dominated by halite, whereas individual grains of sylvite are rare. Typically, sylvite is included in halite, making up to 30 vol% of the chloride assemblage, and in places halite is sprinkled with minute sylvite crystals. Sometimes sylvite inclusions in halite show crystallographic outlines, however, round, lens-shaped and ameboid-like blebs of sylvite with different sizes and orientations are a prominent feature of the chloride masses (Fig. 11). Sylvite domains are often extremely irregular in shape, with curved re-entrances and attenuated swellings. Some domains are thin and elongated, and they can be either subparallel or perpendicular to the contacts with the carbonate sheets

The carbonate sheets are very heterogeneous in texture and composition (Figs. 11). In some occurrences a patchy distribution of textures and compositions is observed, but commonly a symmetrical zoning across carbonate sheets exists (Fig. 11b). The Na-Ca carbonate (shortitelike) at the rims, near contacts with chlorides forms intergrowths of acicular crystals. The interstitial space between these crystals (at polished surfaces) is either porous or filled with chlorides and Na-K sulphates. The transition from rims to cores is very distinct (Fig. 11b), as the cores do not show crystalline structure and are principally different in composition. On average the carbonate core is characterised by Na-Ca composition with significant K2O and SO3. Highly variable, but with good correlation, amounts of SO3 (up to 13 wt%) and K2O (up to 14 wt%) in the individual analyses of core carbonates suggest that Na-Ca carbonates are intermixed with tiny K-(Na) sulphate phases, the presence of which can be identified at high magnification. The Ca/Na in the core carbonate is higher than in the rim carbonate. Another Na-Ca carbonate with the highest Ca/Na is developed along the cleavage planes in the core

An alkali sulphate, aphthitalite (Na0.25K0.75)2SO4, is a minor but widespread component of the carbonate-chloride nodules. It is always associated with halite as irregular blebs, fringing the outmost rims of carbonate sheets (Fig. 11d), and filling fractures and interstitial

Anhydrous and hydrated Na-Ca carbonates with variable Ca/Na ratios are typical in all nodules, but in one sample (UV-2-03, Fig. 10e) an end-member shortite composition Na2Ca2(CO3)3 was found in close association with Cl-bearing Na-Mg carbonate (northupite – Na3Mg(CO3)2Cl). Unlike heterogeneous and thus barely transparent carbonates in other nodules, well-formed crystals of shortite and northupite are clear and can be used for the inclusion studies. The mineral assemblage in this nodule is very complex, and includes euhedral crystals of apatite and phlogopite, as well as tetraferriphlogopite, djerfisherite, K-Na and Na-Ca sulphates, Ba-, Ca- and Sr-Ca-Ba- sulphates and carbonates, calcite, perovskite, and bradleyite Na3Mg(PO4)(CO3). The above minerals are present in aggregates

Maas et al. (2005) concluded that Sr-Nd-Pb isotopic ratios for the silicate, carbonate and halide components in the groundmass of the Udachnaya-East kimberlite support a mantle origin for the carbonate/chloride components. This conclusion relies in part on accurate age corrections to measured 87Sr/86Sr. However, the extreme instability of magmatic halides and alkali carbonates in air, even on the timescale of hours and days (Zaitsev & Keller, 2006), means that Rb-Sr isotope systematics of these kimberlites may have been modified since kimberlite emplacement in the late Devonian. An attempt to use Cl isotopes as a direct

within the interstitial chloride cement and as inclusions in shortite.

(Fig. 11 a-c). Chloride minerals also seal fractures in carbonates (Fig. 11).

silicate-carbonate material (from 1 to 20 vol%) that is either present interstitially among halite crystals or forms irregular compact masses veined by chlorides. Contacts between silicate-carbonate material and chlorides are decorated by euhedral grains of olivine, monticellite, djerfisherite, perovskite, pyrrhotite, shortite and magnetite.

Fig. 10. Occurrence of chloride nodules in kimberlite (a, b) and textural characteristics and mineral relationships in the chloride–carbonate nodules (c-e). c, d—sample UV-5a-03 show texture resembling liquid immiscibility; white zoned sheets are composed of carbonates (Na–Ca±K±S), greyish masses cementing sheets are chlorides (halite–sylvite). e—sample UV-2-03, composed of shortite, northupite and chlorides. Scale: 1 graticule=1 mm

Chloride-carbonate nodules contain roughly similar amounts of chloride and carbonate minerals that are regularly interspersed (Fig. 10 c-e). Carbonates are present as 1-5 mm thick sheets with a bumpy or boudin-like surface. The groups of aligned, subparallel sheets make up rhombohedron formations (2-2.5 cm) that resemble hollow (skeletal) carbonate crystals (~78o angle) in shape. Cross-sections of inflated parts of the sheets show symmetrical zoning that reflects the change from translucent to milky-white carbonate (Fig. 10 c, d). The intrasheet space and cracks in carbonate sheets are filled with sugary aggregates of chloride minerals. A texturally and mineralogically different variety of the chloride-carbonate nodules is represented by a single sample UV-2-03 (Fig. 10e). In this ~15 cm nodule, carbonates are present as very thin (< 0.2 mm) aligned white calcite-shortite sheets, as well as individual well-formed yellowish crystals of shortite and northupite (up to 1 cm). In the carbonate intergrowths northupite is interstitial and less abundant (25-30%), and can be distinguished from shortite by crystallographic properties and higher transparency.

#### **5.1 Mineralogy of chloride-carbonate nodules**

194 Advances in Data, Methods, Models and Their Applications in Geoscience

silicate-carbonate material (from 1 to 20 vol%) that is either present interstitially among halite crystals or forms irregular compact masses veined by chlorides. Contacts between silicate-carbonate material and chlorides are decorated by euhedral grains of olivine,

**a b**

**c d e**

Fig. 10. Occurrence of chloride nodules in kimberlite (a, b) and textural characteristics and mineral relationships in the chloride–carbonate nodules (c-e). c, d—sample UV-5a-03 show texture resembling liquid immiscibility; white zoned sheets are composed of carbonates (Na–Ca±K±S), greyish masses cementing sheets are chlorides (halite–sylvite). e—sample UV-2-03, composed of shortite, northupite and chlorides. Scale: 1 graticule=1 mm

Chloride-carbonate nodules contain roughly similar amounts of chloride and carbonate minerals that are regularly interspersed (Fig. 10 c-e). Carbonates are present as 1-5 mm thick sheets with a bumpy or boudin-like surface. The groups of aligned, subparallel sheets make up rhombohedron formations (2-2.5 cm) that resemble hollow (skeletal) carbonate crystals (~78o angle) in shape. Cross-sections of inflated parts of the sheets show symmetrical zoning that reflects the change from translucent to milky-white carbonate (Fig. 10 c, d). The intrasheet space and cracks in carbonate sheets are filled with sugary aggregates of chloride minerals. A texturally and mineralogically different variety of the chloride-carbonate nodules is represented by a single sample UV-2-03 (Fig. 10e). In this ~15 cm nodule, carbonates are present as very thin (< 0.2 mm) aligned white calcite-shortite sheets, as well as individual well-formed yellowish crystals of shortite and northupite (up to 1 cm). In the carbonate intergrowths northupite is interstitial and less abundant (25-30%), and can be

distinguished from shortite by crystallographic properties and higher transparency.

monticellite, djerfisherite, perovskite, pyrrhotite, shortite and magnetite.

The chloride component of the nodules is dominated by halite, whereas individual grains of sylvite are rare. Typically, sylvite is included in halite, making up to 30 vol% of the chloride assemblage, and in places halite is sprinkled with minute sylvite crystals. Sometimes sylvite inclusions in halite show crystallographic outlines, however, round, lens-shaped and ameboid-like blebs of sylvite with different sizes and orientations are a prominent feature of the chloride masses (Fig. 11). Sylvite domains are often extremely irregular in shape, with curved re-entrances and attenuated swellings. Some domains are thin and elongated, and they can be either subparallel or perpendicular to the contacts with the carbonate sheets (Fig. 11 a-c). Chloride minerals also seal fractures in carbonates (Fig. 11).

The carbonate sheets are very heterogeneous in texture and composition (Figs. 11). In some occurrences a patchy distribution of textures and compositions is observed, but commonly a symmetrical zoning across carbonate sheets exists (Fig. 11b). The Na-Ca carbonate (shortitelike) at the rims, near contacts with chlorides forms intergrowths of acicular crystals. The interstitial space between these crystals (at polished surfaces) is either porous or filled with chlorides and Na-K sulphates. The transition from rims to cores is very distinct (Fig. 11b), as the cores do not show crystalline structure and are principally different in composition. On average the carbonate core is characterised by Na-Ca composition with significant K2O and SO3. Highly variable, but with good correlation, amounts of SO3 (up to 13 wt%) and K2O (up to 14 wt%) in the individual analyses of core carbonates suggest that Na-Ca carbonates are intermixed with tiny K-(Na) sulphate phases, the presence of which can be identified at high magnification. The Ca/Na in the core carbonate is higher than in the rim carbonate. Another Na-Ca carbonate with the highest Ca/Na is developed along the cleavage planes in the core and at the contacts with the rims.

An alkali sulphate, aphthitalite (Na0.25K0.75)2SO4, is a minor but widespread component of the carbonate-chloride nodules. It is always associated with halite as irregular blebs, fringing the outmost rims of carbonate sheets (Fig. 11d), and filling fractures and interstitial spaces in carbonates (Fig. 11).

Anhydrous and hydrated Na-Ca carbonates with variable Ca/Na ratios are typical in all nodules, but in one sample (UV-2-03, Fig. 10e) an end-member shortite composition Na2Ca2(CO3)3 was found in close association with Cl-bearing Na-Mg carbonate (northupite – Na3Mg(CO3)2Cl). Unlike heterogeneous and thus barely transparent carbonates in other nodules, well-formed crystals of shortite and northupite are clear and can be used for the inclusion studies. The mineral assemblage in this nodule is very complex, and includes euhedral crystals of apatite and phlogopite, as well as tetraferriphlogopite, djerfisherite, K-Na and Na-Ca sulphates, Ba-, Ca- and Sr-Ca-Ba- sulphates and carbonates, calcite, perovskite, and bradleyite Na3Mg(PO4)(CO3). The above minerals are present in aggregates within the interstitial chloride cement and as inclusions in shortite.

Maas et al. (2005) concluded that Sr-Nd-Pb isotopic ratios for the silicate, carbonate and halide components in the groundmass of the Udachnaya-East kimberlite support a mantle origin for the carbonate/chloride components. This conclusion relies in part on accurate age corrections to measured 87Sr/86Sr. However, the extreme instability of magmatic halides and alkali carbonates in air, even on the timescale of hours and days (Zaitsev & Keller, 2006), means that Rb-Sr isotope systematics of these kimberlites may have been modified since kimberlite emplacement in the late Devonian. An attempt to use Cl isotopes as a direct

New Identity of the Kimberlite Melt: Constraints from

**ol**

**mtc**

**ac**

**h**

**ol ol**

**s**

**ol**

**P**

**mtc**

**phl**

**P**

**c phl**

**P**

**ac**

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 197

**a b**

**P**

**phl**

**mtc d**

**phl**

**P**

**phl**

**P**

**ac**

**P**

**P**

**ol**

**P**

**phl**

**ol**

**P**

**phl**

**ol**

**phl**

**phl**

**P**

Fig. 12. Backscattered electron images of polished surfaces of the Udachnaya-East kimberlites (a — host kimberlite; b–d — perovskite- and phlogopite-rich clast), showing typical groundmass assemblage of co-crystallised chlorides, halite (h) and sylvite (s), alkali

carbonates (ac), perovskite (P), phlogopite (phl), monticellite (mtc) and olivine (ol).

Perovskite is particularly abundant (10%) in sample UV31k-05 (Fig. 12 b-d), an ultramafic (31 wt% MgO), spherical clast ("nucleated autholith" after Mitchell, 1986) found at ~500 m depth in the pipe (Kamenetsky et al., 2009c). Accumulation of perovskite in kimberlite magmas is not unusual and has been reported in other kimberlites (Dawson & Hawthorne, 1973; Mitchell, 1986). The autolith and its host kimberlite are broadly similar in composition, and have the same groundmass assemblage, including interstitial carbonates, chlorides and perovskite (Fig. 2, 12a). Importantly, perovskite is interstitial to phlogopite crystals (Fig. 2b), and thus appears to be later than phlogopite in crystallisation sequence. On the other hand, textural relationships between perovskite and alkali carbonates and chlorides (Fig. 12a, c, d) suggest their co-precipitation from the melt. The melt that crystallised olivine and

**P**

**P**

tracer of chlorine also proved inconclusive because of the similar 37Cl/35Cl ratios in mantle and crustal rocks (Sharp et al., 2007).

Fig. 11. The nodule texture is determined by a carbonate–chloride grid. Chloride minerals are represented by massive halite (light-grey, hosting amoeboid blebs of sylvite (white). Halite away from large sylvite formations is sprinkled with minute sylvite grains. Often sylvite forms streaks that show distinctive alignment. The overall texture of chloride layers and shape and distribution of sylvite, are reminiscent of liquid immiscibility. Carbonate sheets are symmetrically zoned (a, b). Irregular aphthitalite (grey) is present in halite, always near contacts with carbonate and in veinlets in carbonate (d).

### **6. Radiogenic isotope composition**

An alternative approach to tracing relative contribution of mantle and crustal sources to the primary kimberlite melt is based on a study of perovskite, a common late-stage groundmass mineral in kimberlites (Chakhmouradian & Mitchell, 2000). Perovskite (CaTiO3, >1000 ppm Sr, Rb/Sr≈0) should record the 87Sr/86Sr of the kimberlite melt at the time of perovskite formation (Heaman, 1989; Paton et al., 2007).

tracer of chlorine also proved inconclusive because of the similar 37Cl/35Cl ratios in mantle

and crustal rocks (Sharp et al., 2007).

a b

c d

**6. Radiogenic isotope composition** 

formation (Heaman, 1989; Paton et al., 2007).

always near contacts with carbonate and in veinlets in carbonate (d).

Fig. 11. The nodule texture is determined by a carbonate–chloride grid. Chloride minerals are represented by massive halite (light-grey, hosting amoeboid blebs of sylvite (white). Halite away from large sylvite formations is sprinkled with minute sylvite grains. Often sylvite forms streaks that show distinctive alignment. The overall texture of chloride layers and shape and distribution of sylvite, are reminiscent of liquid immiscibility. Carbonate sheets are symmetrically zoned (a, b). Irregular aphthitalite (grey) is present in halite,

An alternative approach to tracing relative contribution of mantle and crustal sources to the primary kimberlite melt is based on a study of perovskite, a common late-stage groundmass mineral in kimberlites (Chakhmouradian & Mitchell, 2000). Perovskite (CaTiO3, >1000 ppm Sr, Rb/Sr≈0) should record the 87Sr/86Sr of the kimberlite melt at the time of perovskite

Fig. 12. Backscattered electron images of polished surfaces of the Udachnaya-East kimberlites (a — host kimberlite; b–d — perovskite- and phlogopite-rich clast), showing typical groundmass assemblage of co-crystallised chlorides, halite (h) and sylvite (s), alkali carbonates (ac), perovskite (P), phlogopite (phl), monticellite (mtc) and olivine (ol).

Perovskite is particularly abundant (10%) in sample UV31k-05 (Fig. 12 b-d), an ultramafic (31 wt% MgO), spherical clast ("nucleated autholith" after Mitchell, 1986) found at ~500 m depth in the pipe (Kamenetsky et al., 2009c). Accumulation of perovskite in kimberlite magmas is not unusual and has been reported in other kimberlites (Dawson & Hawthorne, 1973; Mitchell, 1986). The autolith and its host kimberlite are broadly similar in composition, and have the same groundmass assemblage, including interstitial carbonates, chlorides and perovskite (Fig. 2, 12a). Importantly, perovskite is interstitial to phlogopite crystals (Fig. 2b), and thus appears to be later than phlogopite in crystallisation sequence. On the other hand, textural relationships between perovskite and alkali carbonates and chlorides (Fig. 12a, c, d) suggest their co-precipitation from the melt. The melt that crystallised olivine and

New Identity of the Kimberlite Melt: Constraints from

**7.2 Alkali carbonate-chloride parental melt** 

in preventing ingress of external fluids.

carbonates and perovskite (Kamenetsky et al., 2009c).

nodules.

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 199

dissolution of alkali chlorides in crustal environments (Zaitsev & Keller, 2006) can be responsible for depriving kimberlites (carbonatites) of their original sodium and potassium.

The source and origin of alkali carbonates and chlorides in the groundmass of the Udachnaya-East kimberlites is still controversial, given the fact that other group-I kimberlites are devoid of these minerals, but have serpentine. Three possible scenarios of the alkali carbonate-chloride enrichment of the Udachnaya-East rocks can be considered: postmagmatic alteration, contamination of the magma in the crust en route to the surface and derivation from melting of the respectable mantle source. A possibility of postemplacement ingress of chloride- and carbonate-bearing fluids can be confidently rejected on the basis of petrographic evidence. Any alteration features, typical of kimberlite rocks, are absent in this case; macrocrysts and phenocrysts of olivine bear no serpentine, and the olivine- and phlogopite hosted melt inclusions, trapped at magmatic temperatures (> 660oC) are compositionally similar to the groundmass (Golovin et al., 2007; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Kamenetsky et al., 2009c). Moreover, water-soluble carbonate and chloride minerals in the groundmass were an important factor

A choice between crustal and mantle origin of the Udachnaya-East unique compositional features is utterly important in deciding whether the Udachnaya-East kimberlite is a "black sheep" in the kimberlite clan or a bearer of the true identity of the primary kimberlite melt, and by inference, the composition of the mantle source and mantle melting process. A potential Na- and Cl-rich contaminant in the form of carbonate–evaporate sedimentary sequence is present in the south and southwest of the Siberian platform, however, it is not confidently recorded in the north, beneath the Daldyn kimberlite field (Brasier & Sukhov, 1998). Moreover, such contaminant is not pronounced in the composition of kimberlites from upper levels of the Udachnaya-East pipe (< 450 m), Udachnaya-West and other pipes from the same field and other kimberlite fields in Siberia. In addition to indirect evidence against likelihood of contamination of the kimberlite magma by evaporites reported in (Kamenetsky et al., 2007a), the deep mantle origin of the carbonate-chloride enrichment of the Udachnaya-East melt is well supported by the isotope composition of Sr in groundmass

The non-silicate residual kimberlite magma has low temperatures (<650-750oC), as shown by the study of the Udachnaya-East melt inclusions (Kamenetsky et al., 2004), experimental data on the fluorine-bearing Na2CO3-CaCO3 system (Jago & Gittins, 1991) and direct temperature measurements in the halogen-rich (up to 15 wt% F+Cl, Jago & Gittins, 1991) natrocarbonatite lava lakes and flows of the Oldoinyo Lengai volcano (Dawson et al., 1990; Keller & Krafft, 1990; Krafft & Keller, 1989). However, even at these temperatures it is highly fluid. Thus, we envisage that droplets of residual melt separate from a solid aluminosilicate framework of the magma, percolate into weaker, less solidified zones, and finally coalesce, forming melt pockets. The latter are now seen in the kimberlite as chloride-carbonate

We emphasise that in the Udachnaya-East kimberlite the combination of such features such as extraordinary freshness, high abundances of Na, K and Cl, depletion in H2O, and preservation of water-soluble minerals and chloride-carbonate melt pockets cannot be coincidental. From the analogy with dry carbonatite magmas of Oldoinyo Lengai (Keller &

phlogopite, the earliest minerals in this assemblage, is recorded in melt inclusions. Phlogopite-hosted melt inclusions in this sample (Kamenetsky et al., 2009c) are identical to olivine-hosted melt inclusions, described in the host kimberlite, in having essentially carbonate-chloride compositions and low homogenisation temperatures (650-700oC).

Three Sr isotope analyses of UV31k-05 perovskite by solution-mode average 0.70305±7 (2σ, age-corrected), similar to laser ablation MC-ICPMS results for 20 individual perovskite grains (average 0.70312±5, 2σ, age-corrected). These 87Sr/86Sri ratios are lower than those for the host kimberlite (0.7043-0.7049, Kostrovitsky et al., 2007; Maas et al., 2005; Pearson et al., 1995), although results for acid-leached kimberlite (0.7034-0.7037, Maas et al., 2005) provide a closer match. Such offsets between perovskite and host kimberlite were also noticed elsewhere (Paton et al., 2007), and probably reflect minor disturbance of bulk rock Rb-Sr systems. The perovskite-derived Sr isotope ratios are therefore considered a more robust estimate of kimberlite melt 87Sr/86Sri. A ratio of ~0.7031 is the most unradiogenic among bulk rock compositions for group-I archetypal (Nowell et al., 2004; Smith, 1983; Smith et al., 1985) and Siberian kimberlites (Kostrovitsky et al., 2007), and similar to ratios for modern oceanic basalts, including MORB. The Sr isotope data, together with εNd-εHf near +5, are consistent with a parental magma derived from a depleted mantle-like source and suggest an absence of crustal (higher 87Sr/86Sr, lower εNd) components in the Udachanya-East kimberlite melt, even at the time when perovskite and associated late-stage minerals, including chlorides, crystallised within autolith UV31k-05. This in turn supports a mantle origin of the chlorides in UV31k-05 and similar halides in the host kimberlite.

#### **7. Discussion**

#### **7.1 Major mineral and chemical components of kimberlites**

In general, the broad compositional range of kimberlites is defined by two end-members, magnesian silicate (olivine and serpentine) and carbonatitic (calcite). Thus, the kimberlites worldwide form a trend between these two end-members. It is likely that several processes can account for this compositional array. For example, crystallisation of olivine and segregation of carbonatitic melt (Ca increase) is counter-balanced by olivine accumulation and removal of carbonatitic melt (Ca decrease). Whatever the reason for the build-up in Ca, a general consensus exists that the magmatic carbonatitic component is an integral part of all kimberlite rocks, and their parental magmas. What still remains to be understood is why an expected increase in concentrations of alkali elements (Na and K) during the evolution of the kimberlite magmas is not reflected in the compositions of common kimberlites (e.g., Na2O is invariably <0.3 wt%). Moreover, low abundances of these elements relative to the elements of similar incompatibility are not easily reconciled with expected geochemical characteristics of low-degree mantle melts, even if residual phlogopite is present in the source peridotite (le Roex et al., 2003).

The idea of an alkali element loss and a H2O gain in kimberlites during post-magmatic processes can be promoted based on the fact that all kimberlites studied to date are inherently altered rocks. The alteration of the carbonate fraction towards essentially alkalifree calcitic compositions has been advocated since the discovery of modern alkali natrocarbonatite lavas from the Oldoinyo Lengai volcano and their altered counterparts (Clarke & Roberts, 1986; Dawson, 1962a; Dawson, 1989; Dawson et al., 1987; Deans & Roberts, 1984; Gittins & McKie, 1980; Hay, 1983). Rapid degradation of alkali carbonates and dissolution of alkali chlorides in crustal environments (Zaitsev & Keller, 2006) can be responsible for depriving kimberlites (carbonatites) of their original sodium and potassium.

#### **7.2 Alkali carbonate-chloride parental melt**

198 Advances in Data, Methods, Models and Their Applications in Geoscience

phlogopite, the earliest minerals in this assemblage, is recorded in melt inclusions. Phlogopite-hosted melt inclusions in this sample (Kamenetsky et al., 2009c) are identical to olivine-hosted melt inclusions, described in the host kimberlite, in having essentially

Three Sr isotope analyses of UV31k-05 perovskite by solution-mode average 0.70305±7 (2σ, age-corrected), similar to laser ablation MC-ICPMS results for 20 individual perovskite grains (average 0.70312±5, 2σ, age-corrected). These 87Sr/86Sri ratios are lower than those for the host kimberlite (0.7043-0.7049, Kostrovitsky et al., 2007; Maas et al., 2005; Pearson et al., 1995), although results for acid-leached kimberlite (0.7034-0.7037, Maas et al., 2005) provide a closer match. Such offsets between perovskite and host kimberlite were also noticed elsewhere (Paton et al., 2007), and probably reflect minor disturbance of bulk rock Rb-Sr systems. The perovskite-derived Sr isotope ratios are therefore considered a more robust estimate of kimberlite melt 87Sr/86Sri. A ratio of ~0.7031 is the most unradiogenic among bulk rock compositions for group-I archetypal (Nowell et al., 2004; Smith, 1983; Smith et al., 1985) and Siberian kimberlites (Kostrovitsky et al., 2007), and similar to ratios for modern oceanic basalts, including MORB. The Sr isotope data, together with εNd-εHf near +5, are consistent with a parental magma derived from a depleted mantle-like source and suggest an absence of crustal (higher 87Sr/86Sr, lower εNd) components in the Udachanya-East kimberlite melt, even at the time when perovskite and associated late-stage minerals, including chlorides, crystallised within autolith UV31k-05. This in turn supports a mantle

carbonate-chloride compositions and low homogenisation temperatures (650-700oC).

origin of the chlorides in UV31k-05 and similar halides in the host kimberlite.

In general, the broad compositional range of kimberlites is defined by two end-members, magnesian silicate (olivine and serpentine) and carbonatitic (calcite). Thus, the kimberlites worldwide form a trend between these two end-members. It is likely that several processes can account for this compositional array. For example, crystallisation of olivine and segregation of carbonatitic melt (Ca increase) is counter-balanced by olivine accumulation and removal of carbonatitic melt (Ca decrease). Whatever the reason for the build-up in Ca, a general consensus exists that the magmatic carbonatitic component is an integral part of all kimberlite rocks, and their parental magmas. What still remains to be understood is why an expected increase in concentrations of alkali elements (Na and K) during the evolution of the kimberlite magmas is not reflected in the compositions of common kimberlites (e.g., Na2O is invariably <0.3 wt%). Moreover, low abundances of these elements relative to the elements of similar incompatibility are not easily reconciled with expected geochemical characteristics of low-degree mantle melts, even if residual phlogopite is present in the

The idea of an alkali element loss and a H2O gain in kimberlites during post-magmatic processes can be promoted based on the fact that all kimberlites studied to date are inherently altered rocks. The alteration of the carbonate fraction towards essentially alkalifree calcitic compositions has been advocated since the discovery of modern alkali natrocarbonatite lavas from the Oldoinyo Lengai volcano and their altered counterparts (Clarke & Roberts, 1986; Dawson, 1962a; Dawson, 1989; Dawson et al., 1987; Deans & Roberts, 1984; Gittins & McKie, 1980; Hay, 1983). Rapid degradation of alkali carbonates and

**7.1 Major mineral and chemical components of kimberlites** 

**7. Discussion** 

source peridotite (le Roex et al., 2003).

The source and origin of alkali carbonates and chlorides in the groundmass of the Udachnaya-East kimberlites is still controversial, given the fact that other group-I kimberlites are devoid of these minerals, but have serpentine. Three possible scenarios of the alkali carbonate-chloride enrichment of the Udachnaya-East rocks can be considered: postmagmatic alteration, contamination of the magma in the crust en route to the surface and derivation from melting of the respectable mantle source. A possibility of postemplacement ingress of chloride- and carbonate-bearing fluids can be confidently rejected on the basis of petrographic evidence. Any alteration features, typical of kimberlite rocks, are absent in this case; macrocrysts and phenocrysts of olivine bear no serpentine, and the olivine- and phlogopite hosted melt inclusions, trapped at magmatic temperatures (> 660oC) are compositionally similar to the groundmass (Golovin et al., 2007; Golovin et al., 2003; Kamenetsky et al., 2004; Kamenetsky et al., 2007a; Kamenetsky et al., 2009c). Moreover, water-soluble carbonate and chloride minerals in the groundmass were an important factor in preventing ingress of external fluids.

A choice between crustal and mantle origin of the Udachnaya-East unique compositional features is utterly important in deciding whether the Udachnaya-East kimberlite is a "black sheep" in the kimberlite clan or a bearer of the true identity of the primary kimberlite melt, and by inference, the composition of the mantle source and mantle melting process. A potential Na- and Cl-rich contaminant in the form of carbonate–evaporate sedimentary sequence is present in the south and southwest of the Siberian platform, however, it is not confidently recorded in the north, beneath the Daldyn kimberlite field (Brasier & Sukhov, 1998). Moreover, such contaminant is not pronounced in the composition of kimberlites from upper levels of the Udachnaya-East pipe (< 450 m), Udachnaya-West and other pipes from the same field and other kimberlite fields in Siberia. In addition to indirect evidence against likelihood of contamination of the kimberlite magma by evaporites reported in (Kamenetsky et al., 2007a), the deep mantle origin of the carbonate-chloride enrichment of the Udachnaya-East melt is well supported by the isotope composition of Sr in groundmass carbonates and perovskite (Kamenetsky et al., 2009c).

The non-silicate residual kimberlite magma has low temperatures (<650-750oC), as shown by the study of the Udachnaya-East melt inclusions (Kamenetsky et al., 2004), experimental data on the fluorine-bearing Na2CO3-CaCO3 system (Jago & Gittins, 1991) and direct temperature measurements in the halogen-rich (up to 15 wt% F+Cl, Jago & Gittins, 1991) natrocarbonatite lava lakes and flows of the Oldoinyo Lengai volcano (Dawson et al., 1990; Keller & Krafft, 1990; Krafft & Keller, 1989). However, even at these temperatures it is highly fluid. Thus, we envisage that droplets of residual melt separate from a solid aluminosilicate framework of the magma, percolate into weaker, less solidified zones, and finally coalesce, forming melt pockets. The latter are now seen in the kimberlite as chloride-carbonate nodules.

We emphasise that in the Udachnaya-East kimberlite the combination of such features such as extraordinary freshness, high abundances of Na, K and Cl, depletion in H2O, and preservation of water-soluble minerals and chloride-carbonate melt pockets cannot be coincidental. From the analogy with dry carbonatite magmas of Oldoinyo Lengai (Keller &

New Identity of the Kimberlite Melt: Constraints from

unmixing of liquids rather than solids is more likely.

within the carbonate at subsolidus temperatures.

**7.4 Rheological properties of kimberlite magmas** 

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 201

thus the chloride liquid was supercooled. On the other hand, it was close to the point of solid solution unmixing in the system 75% NaCl – 25% KCl (543oC at 1 atm), and in this case

Crystallisation from a homogeneous chloride-carbonate liquid (i.e., prior to immiscibility) is possible, and very unusual Na-Mg carbonates containing a NaCl molecule (northupite NaCl\*Na2Mg(CO3)2, Fig. 10e), is an example. Disruption of the melt structure caused by chloride-carbonate immiscibility and followed by reduction in solubility of the phosphate and Fe-Mg aluminosilicate components, prompted rapid crystallisation of zoned and often skeletal micro-crystals of apatite and phlogopite - tetraferriphlogopite. Fibrous aggregates of phlogopite in carbonates and sylvite are common and suggestive of incomplete extraction of the phlogopite component from carbonate and chloride melts by post-immiscibility crystallisation. After chloride-carbonate liquid unmixing the sulphate component of the original melt was largely accommodated within the carbonate melt. It was partially released as an aphthitalite melt at the chloride-carbonate interfaces (Fig. 11d), leaving porous K- and S-free carbonate behind (Fig. 11b), and it was also partially exsolved and re-distributed

Kimberlites, especially those with preserved diamonds (Haggerty, 1999) are undoubtedly fast ascending magmas (>4 m/s; see review in Sparks et al., 2006). Support to this contention also comes from experimentally studied rates of dissolution of garnet in H2O-bearing kimberlite melt (Canil & Fedortchouk, 1999) and Ar diffusive loss profiles of phlogopite in mantle xenoliths (Kelley & Wartho, 2000). Other indirect evidence includes inferred low viscosity of the kimberlite magma and its low density, contributing to high buoyancy (Spence & Turcotte, 1990). The unique physical properties of the kimberlite magma are governed by high abundances of chemical components that reduce melt polymerization (e.g. volatiles). The kimberlite magmas are assigned significant H2O contents in controlling transport and eruption, and only a few studies cast doubts on magmatic origin of H2O in

kimberlites (e.g., Marshintsev, 1986; Sheppard & Dawson, 1975; Sparks et al., 2006).

**7.5 Implications from kimberlites and carbonatites worldwide** 

Rapid transport and emplacement of the Udachnaya-East kimberlite is supported by the fact that this pipe is one of the most diamond-enriched in the world. However, our study denies the control from H2O on rheological properties of the Udachnaya-East kimberlite magma as the measured H2O abundances are particular low (<0.5 wt%). Instead, we are in position to draw analogy with the Oldoinyo Lengai natrocarbonatite magma, given the observed similarities in temperature (Kamenetsky et al., 2004) and composition. At low eruption temperature (< 600oC) the natrocarbonatite magma has exceptionally low density (2170 kg/m3 ; Dawson et al. (1996), viscosity (0.1-5 Pa s ; Dawson et al., 1996; Keller & Krafft, 1990; Norton & Pinkerton, 1997) and fast flow velocities (1-5 m/s ; Keller & Krafft, 1990). The effect of halogens on reducing apparent viscosity of the carbonatite magma (three orders of magnitude for a three-fold increase in halogen content; Norton & Pinkerton, 1997) makes us confident that enrichment of the Udachnaya-East kimberlite in chlorine (at least 3 wt%) is a key chemical factor responsible for unique rheological properties of kimberlite magmas.

The enrichment of the Udachnaya-East kimberlite in alkali carbonates and chlorides, if a primary mantle-derived signature, could have been present in other group-I kimberlites

Krafft, 1990; Keller & Spettel, 1995) and experimental evidence that alkali carbonatite magmas "will persist only if the magma is dry" (Cooper et al., 1975) we conclude that the parental magma of the studied kimberlite was essentially anhydrous and carbonate-rich. This is indirectly supported by the spectroscopic study of micro-inclusions in Udachnaya cubic diamonds that showed that their parental media was a H2O-poor carbonatitic melt (Zedgenizov et al., 2004).

Chlorine and H2O show opposing solubilities in fluid-saturated silicate melts, as they apparently compete for similar structural positions in the melt. Although Cl does not form complexes with Si in a melt, it may complex with network modifier cations, especially the alkalies, Ca and Mg (Carroll & Webster, 1994). General "dryness" of carbonatites and enrichment of natrocarbonatites in halogens (Gittins, 1989; Jago & Gittins, 1991; Keller & Krafft, 1990) suggest that Cl and H2O decouple which can be an intrinsic feature of carbonate-rich kimberlite magmas. If this is the case, the conventional role of H2O in governing low temperatures and low viscosities of kimberlite magmas can be readdressed to Cl. Furthermore, the data on carbonate-chloride compositions of melt inclusions in diamonds (Bulanova et al., 1998; Izraeli et al., 2001; Izraeli et al., 2004; Klein-BenDavid et al., 2004), nucleation and growth of diamonds in alkaline carbonate melts (Pal'yanov et al., 2002) and catalytic effect of Cl on the growth of diamonds in the system C–K2CO3–KCl (Tomlinson et al., 2004) concur with the proposed mantle origin of chloride and alkali carbonate components in the Udachnaya-East kimberlite.

#### **7.3 Liquid immiscibility and crystallisation of residual kimberlite magma**

Liquid immiscibility is observed in the olivine-hosted melt inclusions at ~600oC on cooling (Fig. 8d). The immiscible liquids are recognized as the carbonate and chloride on the basis that these minerals are dominantly present in the unheated melt inclusions (Golovin et al., 2003; Kamenetsky et al., 2004). Remarkable textures, observed in melt inclusions at the exact moment of melt unmixing (Fig. 8d), is governed by the carbonate crystallographic properties. The presence of similar textures in the chloride-carbonate nodules (Fig. 10 c-e) is the first "snapshot" record of the unambiguous chloride-carbonate melt immiscibility in rocks. The previous natural evidence was based on melt and fluid inclusions in the skarn minerals of Mt Vesuvius (Fulignati et al., 2001) and kimberlitic diamonds (Bulanova et al., 1998; Izraeli et al., 2001; Izraeli et al., 2004; Klein-BenDavid et al., 2004). However, the extensive review of experimental studies (Veksler, 2004) points to the lack of data for chloride–carbonate systems.

Given the analogy with the texture of melt inclusions at the onset of immiscibility, the boudin-like shape of the carbonate sheets and their subparallel alignment (Fig. 10c, e), argues for preservation of primary (instantaneous) immiscibility texture. This means that post-immiscibility (< 600oC) cooling and crystallisation were fast enough to prevent aggregation of one of the immiscible liquids into ovoid or spherical globules that are more typical of steady-state immiscibility. Occurrence of the chloride-rich veinlets in the carbonate sheets (Fig. 11) testifies to later solidification of the chloride liquid relative to carbonate crystallisation. The round and ameboid-like bleb textures of sylvite in halite (Fig. 11) are also reminiscent of liquid immiscibility. In theory this contradicts the fact of complete miscibility in the system NaCl-KCl above the eutectic point of ~660oC. However, the separation of the Na-K chloride melt from the carbonatitic melt, in the case of Udachnaya-East residual melt pockets, occurred at temperatures below the eutectic, and

Krafft, 1990; Keller & Spettel, 1995) and experimental evidence that alkali carbonatite magmas "will persist only if the magma is dry" (Cooper et al., 1975) we conclude that the parental magma of the studied kimberlite was essentially anhydrous and carbonate-rich. This is indirectly supported by the spectroscopic study of micro-inclusions in Udachnaya cubic diamonds that showed that their parental media was a H2O-poor carbonatitic melt

Chlorine and H2O show opposing solubilities in fluid-saturated silicate melts, as they apparently compete for similar structural positions in the melt. Although Cl does not form complexes with Si in a melt, it may complex with network modifier cations, especially the alkalies, Ca and Mg (Carroll & Webster, 1994). General "dryness" of carbonatites and enrichment of natrocarbonatites in halogens (Gittins, 1989; Jago & Gittins, 1991; Keller & Krafft, 1990) suggest that Cl and H2O decouple which can be an intrinsic feature of carbonate-rich kimberlite magmas. If this is the case, the conventional role of H2O in governing low temperatures and low viscosities of kimberlite magmas can be readdressed to Cl. Furthermore, the data on carbonate-chloride compositions of melt inclusions in diamonds (Bulanova et al., 1998; Izraeli et al., 2001; Izraeli et al., 2004; Klein-BenDavid et al., 2004), nucleation and growth of diamonds in alkaline carbonate melts (Pal'yanov et al., 2002) and catalytic effect of Cl on the growth of diamonds in the system C–K2CO3–KCl (Tomlinson et al., 2004) concur with the proposed mantle origin of chloride and alkali

(Zedgenizov et al., 2004).

chloride–carbonate systems.

carbonate components in the Udachnaya-East kimberlite.

**7.3 Liquid immiscibility and crystallisation of residual kimberlite magma** 

Liquid immiscibility is observed in the olivine-hosted melt inclusions at ~600oC on cooling (Fig. 8d). The immiscible liquids are recognized as the carbonate and chloride on the basis that these minerals are dominantly present in the unheated melt inclusions (Golovin et al., 2003; Kamenetsky et al., 2004). Remarkable textures, observed in melt inclusions at the exact moment of melt unmixing (Fig. 8d), is governed by the carbonate crystallographic properties. The presence of similar textures in the chloride-carbonate nodules (Fig. 10 c-e) is the first "snapshot" record of the unambiguous chloride-carbonate melt immiscibility in rocks. The previous natural evidence was based on melt and fluid inclusions in the skarn minerals of Mt Vesuvius (Fulignati et al., 2001) and kimberlitic diamonds (Bulanova et al., 1998; Izraeli et al., 2001; Izraeli et al., 2004; Klein-BenDavid et al., 2004). However, the extensive review of experimental studies (Veksler, 2004) points to the lack of data for

Given the analogy with the texture of melt inclusions at the onset of immiscibility, the boudin-like shape of the carbonate sheets and their subparallel alignment (Fig. 10c, e), argues for preservation of primary (instantaneous) immiscibility texture. This means that post-immiscibility (< 600oC) cooling and crystallisation were fast enough to prevent aggregation of one of the immiscible liquids into ovoid or spherical globules that are more typical of steady-state immiscibility. Occurrence of the chloride-rich veinlets in the carbonate sheets (Fig. 11) testifies to later solidification of the chloride liquid relative to carbonate crystallisation. The round and ameboid-like bleb textures of sylvite in halite (Fig. 11) are also reminiscent of liquid immiscibility. In theory this contradicts the fact of complete miscibility in the system NaCl-KCl above the eutectic point of ~660oC. However, the separation of the Na-K chloride melt from the carbonatitic melt, in the case of Udachnaya-East residual melt pockets, occurred at temperatures below the eutectic, and thus the chloride liquid was supercooled. On the other hand, it was close to the point of solid solution unmixing in the system 75% NaCl – 25% KCl (543oC at 1 atm), and in this case unmixing of liquids rather than solids is more likely.

Crystallisation from a homogeneous chloride-carbonate liquid (i.e., prior to immiscibility) is possible, and very unusual Na-Mg carbonates containing a NaCl molecule (northupite NaCl\*Na2Mg(CO3)2, Fig. 10e), is an example. Disruption of the melt structure caused by chloride-carbonate immiscibility and followed by reduction in solubility of the phosphate and Fe-Mg aluminosilicate components, prompted rapid crystallisation of zoned and often skeletal micro-crystals of apatite and phlogopite - tetraferriphlogopite. Fibrous aggregates of phlogopite in carbonates and sylvite are common and suggestive of incomplete extraction of the phlogopite component from carbonate and chloride melts by post-immiscibility crystallisation. After chloride-carbonate liquid unmixing the sulphate component of the original melt was largely accommodated within the carbonate melt. It was partially released as an aphthitalite melt at the chloride-carbonate interfaces (Fig. 11d), leaving porous K- and S-free carbonate behind (Fig. 11b), and it was also partially exsolved and re-distributed within the carbonate at subsolidus temperatures.

#### **7.4 Rheological properties of kimberlite magmas**

Kimberlites, especially those with preserved diamonds (Haggerty, 1999) are undoubtedly fast ascending magmas (>4 m/s; see review in Sparks et al., 2006). Support to this contention also comes from experimentally studied rates of dissolution of garnet in H2O-bearing kimberlite melt (Canil & Fedortchouk, 1999) and Ar diffusive loss profiles of phlogopite in mantle xenoliths (Kelley & Wartho, 2000). Other indirect evidence includes inferred low viscosity of the kimberlite magma and its low density, contributing to high buoyancy (Spence & Turcotte, 1990). The unique physical properties of the kimberlite magma are governed by high abundances of chemical components that reduce melt polymerization (e.g. volatiles). The kimberlite magmas are assigned significant H2O contents in controlling transport and eruption, and only a few studies cast doubts on magmatic origin of H2O in kimberlites (e.g., Marshintsev, 1986; Sheppard & Dawson, 1975; Sparks et al., 2006).

Rapid transport and emplacement of the Udachnaya-East kimberlite is supported by the fact that this pipe is one of the most diamond-enriched in the world. However, our study denies the control from H2O on rheological properties of the Udachnaya-East kimberlite magma as the measured H2O abundances are particular low (<0.5 wt%). Instead, we are in position to draw analogy with the Oldoinyo Lengai natrocarbonatite magma, given the observed similarities in temperature (Kamenetsky et al., 2004) and composition. At low eruption temperature (< 600oC) the natrocarbonatite magma has exceptionally low density (2170 kg/m3 ; Dawson et al. (1996), viscosity (0.1-5 Pa s ; Dawson et al., 1996; Keller & Krafft, 1990; Norton & Pinkerton, 1997) and fast flow velocities (1-5 m/s ; Keller & Krafft, 1990). The effect of halogens on reducing apparent viscosity of the carbonatite magma (three orders of magnitude for a three-fold increase in halogen content; Norton & Pinkerton, 1997) makes us confident that enrichment of the Udachnaya-East kimberlite in chlorine (at least 3 wt%) is a key chemical factor responsible for unique rheological properties of kimberlite magmas.

#### **7.5 Implications from kimberlites and carbonatites worldwide**

The enrichment of the Udachnaya-East kimberlite in alkali carbonates and chlorides, if a primary mantle-derived signature, could have been present in other group-I kimberlites

New Identity of the Kimberlite Melt: Constraints from

1986; Moore, 1988; Skinner, 1989).

argue against their phenocrystic origin.

transported upwards in a crystal mush.

**7.7 Evolutionary storyline of the kimberlite parental melt** 

started ascent.

1989).

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 203

rounded grains (olivine-I of disputed origin), whereas another type of olivine is typically smaller but better shaped crystals (olivine-II or groundmass phenocrysts). It has been advocated in the literature that olivine may provide valuable clues to processes of kimberlite formation, transport and emplacement (e.g. Boyd & Clement, 1977; Mitchell, 1973; Mitchell,

Mitchell & Tappe (2010), Mitchell (1973; 1986), and Moore (1988) considered olivine from both populations to be phenocrysts (cognate phenocrysts of olivine-I from high-pressure crystallisation of the kimberlite melt, and groundmass olivine-II), although up to 40 % of olivine was assigned to xenocrystic origin from various mantle and lithospheric sources. A similar conclusion can be endorsed by the extreme diversity of peridotite xenoliths within the Udachnaya-East kimberlite (Shimizu et al., 1997; Sobolev, 1977; Sobolev et al., 2009). The absence of primary melt inclusions and presence of Cr-diopside inclusions in olivine-I also

Xenocrystic origin of some or all grains of olivine-I does not preclude this olivine being overgrown by the "phenocrystic" olivine. Both types of olivine are transported together, and thus all changes related to chemical and mechanical resorption should be equally imposed on them, making a morphological distinction subjective. Both olivine populations in the studied Udachnaya-East samples demonstrate striking compositional similarity in their Fo values (Fig. 6) and oxygen isotope values (Kamenetsky et al., 2008). Trace elements abundances are also indistinguishable for the olivine-I and core sections of the groundmass olivine (Fig. 6). Moreover, in many cases the olivine-II cores have original crystal faces ground away (Fig. 7), and thus their shapes are similar to those of round olivine-I. It is most likely that crystals that now show as relics in the olivine-II cores were formed at depth and

Morphological and chemical resemblance between olivine-I and cores of olivine-II can be related to similar chemical and physical conditions exerted during olivine growth (or recrystallisation) and transport to the surface. If both olivine populations are related, their common origin might be tracked down to the earliest and deepest stages of the kimberlite evolutionary story, i.e. when and where primary (protokimberlite) magma derived and

The Udachnaya-East groundmass olivine has a clear compositional structure, where the cores with variable Fo values can be distinguished from the rims with limited range in Fo values (Fig. 6b). It should be emphasised again that the olivine-II rims are essentially uniform with respect to major elements, but minor elements fluctuate strongly, especially Ni abundances which reach maximum near the core-rim boundary, then decrease rapidly towards the outer rims (Fig. 6b). Broadly similar compositional features, namely two groups of olivine with normal and reversed core to rim zonation and similar ranges in Fo and trace element contents, have been previously described in the groundmass olivine in other kimberlites, diamondiferous and barren (Fedortchouk & Canil, 2004; Moore, 1988; Skinner,

Although the origin of olivine cores (cognate vs exotic) is still debatable, the overall compositional analogy between groundmass olivine from different pipes and different kimberlite provinces argue for that 1) origin of cores and rims of groundmass olivine are intimately linked to kimberlite genesis and evolution; 2) in each case physical and chemical

prior to obliteration by common pervasive alteration. Study of melt inclusions trapped in magmatic phenocrysts during crystallisation allows seeing compositions beyond effects of postmagmatic modifications. The study of other least altered kimberlites emplaced into magmatic or metamorphic rocks in the terranes containing little or no sedimentary cover, namely the Gahcho Kué, Jericho, Aaron and Leslie pipes in the Slave Craton (Canada) and the Majuagaa dyke in southern West Greenland, helped to further enhanced the significance of the carbonate-chloride melt composition (Kamenetsky et al., 2009b).

The study of olivine and olivine-hosted melt inclusions in partially altered kimberlites from Canada and Greenland (Kamenetsky et al., 2009b), aimed at comparison with the fresh Udachnaya-East kimberlite and followed by implications of sodium- and chlorine-rich compositions of the parental kimberlite melt, has a precedent in the history of petrological and mineralogical studies of carbonatites. Unlike all ancient intrusive and extrusive carbonatite rocks composed of calcite and/or dolomite, the presently erupting carbonatitic magmas of the Oldoinyo Lengai volcano in Tanzania provides evidence for alkali- and halogen-rich anhydrous melts forming carbonatites. Following the discovery of these natrocarbonatite lavas (Dawson, 1962b) and building on the ideas of von Eckermann (1948), the primary/parental nature of such compositions was defended in a number of empirical (e.g., Clarke & Roberts, 1986; Dawson et al., 1987; Deans & Roberts, 1984; Gittins & McKie, 1980; Hay, 1983; Keller & Zaitsev, 2006; Le Bas, 1987; Schultz et al., 2004; Turner, 1988) and experimental (Safonov et al., 2007; Wallace & Green, 1988) studies. A strong support for the role of alkalies and halogens in magmas parental to mafic silicate intrusions and related carbonatites is further provided by melt/fluid inclusion research (e.g., Andreeva et al., 2006; Aspden, 1980; Aspden, 1981; Kogarko et al., 1991; Le Bas, 1981; Le Bas & Aspden, 1981; Panina, 2005; Panina & Motorina, 2008; Veksler et al., 1998). Syn- and postmagmatic release of alkalies from carbonatite magmas and rocks is recorded respectively in alkaline (mainly soda-dominant) metasomatic "fenitisation halos" around intrusive carbonatite bodies (e.g., (Bailey, 1993; Buhn & Rankin, 1999; Le Bas, 1987; McKie, 1966; Morogan & Lindblom, 1995) and references therein) and rapid decomposition of alkali- and chlorine-bearing minerals in the natrocarbonatites (Dawson, 1962b; Genge et al., 2001; Keller & Zaitsev, 2006; Mitchell, 2006). Same processes can be applicable to kimberlitic magmas in general, during and after their emplacement, as recorded in fenitisation of country rocks (Masun et al., 2004; Smith et al., 2004 and references therein) and gradation from Na-rich "deep" to Na-poor "shallow" kimberlite in the Udachnaya-East pipe.

The groundmass of most kimberlites, including altered kimberlites from the Udachnaya pipe, contain no alkali carbonates and chlorides and have very little Na2O (<0.2 wt%). We believe that alteration disturbs original melt compositions, with the alkaline elements and chlorine being mostly affected. However, the compositions of melt inclusions and Cl-rich serpentine are indicative of the chemical signature of a melt in which olivine crystallised and accumulated. It appears that enrichment in alkalies and chlorine, as seen in unaltered Udachnaya-East kimberlites, has been significant in other kimberlites prior to their alteration, and thus can be assigned deep mantle origin.

#### **7.6 Two populations of olivine in kimberlites: Fellow-travellers or close relatives?**

Our work on the uniquely unaltered Udachnaya-East kimberlite concurs with what has been shown in other mineralogical studies of other kimberlites, namely, the presence of morphologically distinct populations of olivine. One population is represented by large

prior to obliteration by common pervasive alteration. Study of melt inclusions trapped in magmatic phenocrysts during crystallisation allows seeing compositions beyond effects of postmagmatic modifications. The study of other least altered kimberlites emplaced into magmatic or metamorphic rocks in the terranes containing little or no sedimentary cover, namely the Gahcho Kué, Jericho, Aaron and Leslie pipes in the Slave Craton (Canada) and the Majuagaa dyke in southern West Greenland, helped to further enhanced the significance

The study of olivine and olivine-hosted melt inclusions in partially altered kimberlites from Canada and Greenland (Kamenetsky et al., 2009b), aimed at comparison with the fresh Udachnaya-East kimberlite and followed by implications of sodium- and chlorine-rich compositions of the parental kimberlite melt, has a precedent in the history of petrological and mineralogical studies of carbonatites. Unlike all ancient intrusive and extrusive carbonatite rocks composed of calcite and/or dolomite, the presently erupting carbonatitic magmas of the Oldoinyo Lengai volcano in Tanzania provides evidence for alkali- and halogen-rich anhydrous melts forming carbonatites. Following the discovery of these natrocarbonatite lavas (Dawson, 1962b) and building on the ideas of von Eckermann (1948), the primary/parental nature of such compositions was defended in a number of empirical (e.g., Clarke & Roberts, 1986; Dawson et al., 1987; Deans & Roberts, 1984; Gittins & McKie, 1980; Hay, 1983; Keller & Zaitsev, 2006; Le Bas, 1987; Schultz et al., 2004; Turner, 1988) and experimental (Safonov et al., 2007; Wallace & Green, 1988) studies. A strong support for the role of alkalies and halogens in magmas parental to mafic silicate intrusions and related carbonatites is further provided by melt/fluid inclusion research (e.g., Andreeva et al., 2006; Aspden, 1980; Aspden, 1981; Kogarko et al., 1991; Le Bas, 1981; Le Bas & Aspden, 1981; Panina, 2005; Panina & Motorina, 2008; Veksler et al., 1998). Syn- and postmagmatic release of alkalies from carbonatite magmas and rocks is recorded respectively in alkaline (mainly soda-dominant) metasomatic "fenitisation halos" around intrusive carbonatite bodies (e.g., (Bailey, 1993; Buhn & Rankin, 1999; Le Bas, 1987; McKie, 1966; Morogan & Lindblom, 1995) and references therein) and rapid decomposition of alkali- and chlorine-bearing minerals in the natrocarbonatites (Dawson, 1962b; Genge et al., 2001; Keller & Zaitsev, 2006; Mitchell, 2006). Same processes can be applicable to kimberlitic magmas in general, during and after their emplacement, as recorded in fenitisation of country rocks (Masun et al., 2004; Smith et al., 2004 and references therein) and gradation from Na-rich "deep" to Na-poor "shallow"

The groundmass of most kimberlites, including altered kimberlites from the Udachnaya pipe, contain no alkali carbonates and chlorides and have very little Na2O (<0.2 wt%). We believe that alteration disturbs original melt compositions, with the alkaline elements and chlorine being mostly affected. However, the compositions of melt inclusions and Cl-rich serpentine are indicative of the chemical signature of a melt in which olivine crystallised and accumulated. It appears that enrichment in alkalies and chlorine, as seen in unaltered Udachnaya-East kimberlites, has been significant in other kimberlites prior to their

**7.6 Two populations of olivine in kimberlites: Fellow-travellers or close relatives?**  Our work on the uniquely unaltered Udachnaya-East kimberlite concurs with what has been shown in other mineralogical studies of other kimberlites, namely, the presence of morphologically distinct populations of olivine. One population is represented by large

of the carbonate-chloride melt composition (Kamenetsky et al., 2009b).

kimberlite in the Udachnaya-East pipe.

alteration, and thus can be assigned deep mantle origin.

rounded grains (olivine-I of disputed origin), whereas another type of olivine is typically smaller but better shaped crystals (olivine-II or groundmass phenocrysts). It has been advocated in the literature that olivine may provide valuable clues to processes of kimberlite formation, transport and emplacement (e.g. Boyd & Clement, 1977; Mitchell, 1973; Mitchell, 1986; Moore, 1988; Skinner, 1989).

Mitchell & Tappe (2010), Mitchell (1973; 1986), and Moore (1988) considered olivine from both populations to be phenocrysts (cognate phenocrysts of olivine-I from high-pressure crystallisation of the kimberlite melt, and groundmass olivine-II), although up to 40 % of olivine was assigned to xenocrystic origin from various mantle and lithospheric sources. A similar conclusion can be endorsed by the extreme diversity of peridotite xenoliths within the Udachnaya-East kimberlite (Shimizu et al., 1997; Sobolev, 1977; Sobolev et al., 2009). The absence of primary melt inclusions and presence of Cr-diopside inclusions in olivine-I also argue against their phenocrystic origin.

Xenocrystic origin of some or all grains of olivine-I does not preclude this olivine being overgrown by the "phenocrystic" olivine. Both types of olivine are transported together, and thus all changes related to chemical and mechanical resorption should be equally imposed on them, making a morphological distinction subjective. Both olivine populations in the studied Udachnaya-East samples demonstrate striking compositional similarity in their Fo values (Fig. 6) and oxygen isotope values (Kamenetsky et al., 2008). Trace elements abundances are also indistinguishable for the olivine-I and core sections of the groundmass olivine (Fig. 6). Moreover, in many cases the olivine-II cores have original crystal faces ground away (Fig. 7), and thus their shapes are similar to those of round olivine-I. It is most likely that crystals that now show as relics in the olivine-II cores were formed at depth and transported upwards in a crystal mush.

Morphological and chemical resemblance between olivine-I and cores of olivine-II can be related to similar chemical and physical conditions exerted during olivine growth (or recrystallisation) and transport to the surface. If both olivine populations are related, their common origin might be tracked down to the earliest and deepest stages of the kimberlite evolutionary story, i.e. when and where primary (protokimberlite) magma derived and started ascent.

#### **7.7 Evolutionary storyline of the kimberlite parental melt**

The Udachnaya-East groundmass olivine has a clear compositional structure, where the cores with variable Fo values can be distinguished from the rims with limited range in Fo values (Fig. 6b). It should be emphasised again that the olivine-II rims are essentially uniform with respect to major elements, but minor elements fluctuate strongly, especially Ni abundances which reach maximum near the core-rim boundary, then decrease rapidly towards the outer rims (Fig. 6b). Broadly similar compositional features, namely two groups of olivine with normal and reversed core to rim zonation and similar ranges in Fo and trace element contents, have been previously described in the groundmass olivine in other kimberlites, diamondiferous and barren (Fedortchouk & Canil, 2004; Moore, 1988; Skinner, 1989).

Although the origin of olivine cores (cognate vs exotic) is still debatable, the overall compositional analogy between groundmass olivine from different pipes and different kimberlite provinces argue for that 1) origin of cores and rims of groundmass olivine are intimately linked to kimberlite genesis and evolution; 2) in each case physical and chemical

New Identity of the Kimberlite Melt: Constraints from

the saturation in olivine acquired?

(Kamenetsky et al., 2007a).

**8. Concluding remarks** 

Unaltered Diamondiferous Udachnaya-East Pipe Kimberlite, Russia 205

olivine from this melt implies saturation in the olivine component, which makes this melt different from the alkali carbonate melt experimentally produced at mantle P-T conditions and low melting extents (Sweeney et al., 1995; Wallace & Green, 1988). How and where is

Study of the olivine populations and complex zoning of the groundmass olivine in the Udachnaya-East and other kimberlites (Kamenetsky et al., 2008; Kamenetsky et al., 2009b) provides evidence that olivine crystals were first entrapped by the melt at depth, then partly abraded, dissolved and recrystallised on ascent, and finally regenerated during emplacement. We suggest that the history of kimberlitic olivine is owed to the extraordinary melt composition, as well as conditions during melt generation and emplacement. In our scenario, a key role is played by the chloride-carbonate (presumably protokimberlite) melt, which forces strong mechanical abrasion and dissolution of the silicate minerals from country rocks in the mantle and lithosphere. Such a melt is capable of accumulating Si and Mg, but only to a certain limit, above which an immiscible Cl-bearing carbonate-silicate liquid appears (Safonov et al., 2007). The amount of forsterite that can be dissolved in the sodium carbonate liquid at 10 kbar and 1300oC is found to be 16 wt% (Hammouda & Laporte, 2000). Dissolution of olivine and other silicate phases at high pressure does not proceed beyond the saturation, and is closely followed by precipitation of olivine (Hammouda & Laporte, 2000). Therefore, ascending kimberlite magma, although being more Si-rich than its parental melt and loaded with xenocrysts and xenoliths, remains buoyant enough to continue rapid ascent. At emplacement, the magma releases the dissolved silicate component in the form of groundmass olivine rims and minor silicate minerals, thus driving the residual melt towards original chloride-carbonate compositions

Dry, chlorine-bearing alkali minerals in the Udachnaya-East kimberlite are products of crystallisation of the mantle-derived, uncontaminated melt. We suggest that a composition rich in alkalies, CO2 and Cl may be a viable alternative to the currently favoured ultramafic kimberlite magma. A "salty" kimberlite composition can explain trace element signatures consistent with low degrees of partial melting, low temperatures of crystallisation and exceptional rheological properties responsible for fast ascent and the magma's ability to carry abundant high-density mantle nodules and crystals. Evidence for these components, notably Cl and alkalies, is only preserved in an ultrafresh kimberlite such as Udachnaya-East. Nevertheless, Cl-bearing minerals of the type reported here have also been found in the groundmass and melt inclusions in kimberlites from Canada and Greenland (Kamenetsky et al., 2009b). The possible existence of chloride–carbonate liquids within the diamond stability field can be inferred from experiments in the model silicate system with addition of Na-Ca carbonate and K-chloride (Safonov et al., 2010; Safonov et al., 2007; Safonov et al., 2009). These experiments also show that Cl-bearing carbonate-silicate and Sibearing chloride-carbonate melts evolve towards Cl-rich carbonatitic liquids with decreasing temperature, providing a possible explanation for chlorine- and alkali-enriched microinclusions in some diamonds from Udachnaya-East (Zedgenizov & Ragozin, 2007) and other kimberlites in South Africa and Canada (Izraeli et al., 2001; Klein-BenDavid et al., 2007; Tomlinson et al., 2006). Brine inclusions in diamonds from various kimberlites, and the inferred role of chlorides in diamond nucleation and growth (Palyanov et al., 2007;

conditions of olivine formation are closely similar; 3) olivine cores and rims originate in different conditions; and 4) variable Fo compositions of cores reflect varying sources or changing conditions, whereas similar Fo values of rims reflect major buffering event.

Composition and zoning of the Udachnaya-East olivine-II are not unique; similar principle compositional characteristics of groundmass olivine phenocrysts (variable and constant Fo of cores and rims, respectively, and variable trace elements at a given Fo of the olivine rims; Fig. 6b) are described in a number of kimberlite suites (e.g., Boyd & Clement, 1977; Emeleus & Andrews, 1975; Fedortchouk & Canil, 2004; Hunter & Taylor, 1984; Kirkley et al., 1989; Mitchell, 1978; Mitchell, 1986; Moore, 1988; Nielsen & Jensen, 2005; Skinner, 1989). Compared to the ambiguous origin of the olivine cores, the rims of olivine-II most certainly crystallised from a melt transporting these crystals to the surface. This is best supported by the cases where several cores of different size, shape and composition are enclosed within a single olivine-II grain (Fig. 7 g, h). As indicated by mineral inclusions, the olivine-II rims formed together with phlogopite, perovskite, minerals of spinel group, rutile and orthopyroxene, i.e. common groundmass minerals (except orthopyroxene) from a melt that is present as melt inclusions in the olivine rims and healed fractures in the olivine-II cores and olivine-I (Fig. 3, 8).

Numerous studies indicate that most common xenoliths in kimberlites are garnet lherzolites, but surprisingly low abundance of orthopyroxene among xenocrysts and macrocrysts has been intriguing (Mitchell, 1973; Mitchell, 2008; Patterson et al., 2009; Skinner, 1989). Low silica activity in the kimberlite magma was offered as an explanation for instability of orthopyroxene, especially at sub-surface pressures (Mitchell, 1973). On the other hand, crystallising groundmass olivine rims and the presence of orthopyroxene inclusions in this olivine (Kamenetsky et al., 2008; Kamenetsky et al., 2009a) seem to be inconsistent with each other. One explanation is that orthopyroxene inclusions (often in groups and always associated with CO2 bubbles) can result from the local reaction of olivine with CO2 fluid (2SiO4-4 + 2CO2 Si2O6-4 + 2CO3-2).

A limited range of Fo content in the olivine-II rims, but variable trace element abundances (Fig. 6b) suggest crystallisation over a small temperature range or/and buffering of the magma at a constant Fe/Mg with fractionating Ni, Mn and Ca. In many instances, where the cores are seemingly affected by diffusion (Fig. 7 b, c, f, h) and have a surrounding layer of distinct composition (Fig. 7 a, e, h), the uniform Fo in the rims can reflect attempts by the crystals to equilibrate with a final hybrid magma (Mitchell, 1986). We also propose that the buffering of Fe/Mg can occur if the Mg–Fe distribution coefficient (Kd) between olivine and a carbonate-rich kimberlite melt is significantly higher than for common basaltic systems (i.e. 0.3±0.03). This reflects significantly smaller Mg-Fe fractionation between silicates and carbonate melt, possibly as a result of complexing between carbonate and Mg2+ ions (Green & Wallace, 1988; Moore, 1988). The implied higher Kd for carbonatitic liquids, and especially Ca-rich carbonate, has been supported by experimental evidence (Dalton & Wood, 1993; Girnis et al., 2005). Probably an increase in Kd is even more pronounced for alkali-rich carbonatitic liquids.

The melt crystallising the rims of the Udachnaya-East groundmass olivine is represented by the carbonate-chloride matrix of the rocks (Kamenetsky et al., 2004; Kamenetsky et al., 2007a), and by the melt inclusions in olivine (Fig. 3, 8). The composition of this melt is unusually enriched in alkali carbonates and chlorides, but low in aluminosilicate components (Kamenetsky et al., 2004; Kamenetsky et al., 2007a). The crystallisation of olivine from this melt implies saturation in the olivine component, which makes this melt different from the alkali carbonate melt experimentally produced at mantle P-T conditions and low melting extents (Sweeney et al., 1995; Wallace & Green, 1988). How and where is the saturation in olivine acquired?

Study of the olivine populations and complex zoning of the groundmass olivine in the Udachnaya-East and other kimberlites (Kamenetsky et al., 2008; Kamenetsky et al., 2009b) provides evidence that olivine crystals were first entrapped by the melt at depth, then partly abraded, dissolved and recrystallised on ascent, and finally regenerated during emplacement. We suggest that the history of kimberlitic olivine is owed to the extraordinary melt composition, as well as conditions during melt generation and emplacement. In our scenario, a key role is played by the chloride-carbonate (presumably protokimberlite) melt, which forces strong mechanical abrasion and dissolution of the silicate minerals from country rocks in the mantle and lithosphere. Such a melt is capable of accumulating Si and Mg, but only to a certain limit, above which an immiscible Cl-bearing carbonate-silicate liquid appears (Safonov et al., 2007). The amount of forsterite that can be dissolved in the sodium carbonate liquid at 10 kbar and 1300oC is found to be 16 wt% (Hammouda & Laporte, 2000). Dissolution of olivine and other silicate phases at high pressure does not proceed beyond the saturation, and is closely followed by precipitation of olivine (Hammouda & Laporte, 2000). Therefore, ascending kimberlite magma, although being more Si-rich than its parental melt and loaded with xenocrysts and xenoliths, remains buoyant enough to continue rapid ascent. At emplacement, the magma releases the dissolved silicate component in the form of groundmass olivine rims and minor silicate minerals, thus driving the residual melt towards original chloride-carbonate compositions (Kamenetsky et al., 2007a).

### **8. Concluding remarks**

204 Advances in Data, Methods, Models and Their Applications in Geoscience

conditions of olivine formation are closely similar; 3) olivine cores and rims originate in different conditions; and 4) variable Fo compositions of cores reflect varying sources or

Composition and zoning of the Udachnaya-East olivine-II are not unique; similar principle compositional characteristics of groundmass olivine phenocrysts (variable and constant Fo of cores and rims, respectively, and variable trace elements at a given Fo of the olivine rims; Fig. 6b) are described in a number of kimberlite suites (e.g., Boyd & Clement, 1977; Emeleus & Andrews, 1975; Fedortchouk & Canil, 2004; Hunter & Taylor, 1984; Kirkley et al., 1989; Mitchell, 1978; Mitchell, 1986; Moore, 1988; Nielsen & Jensen, 2005; Skinner, 1989). Compared to the ambiguous origin of the olivine cores, the rims of olivine-II most certainly crystallised from a melt transporting these crystals to the surface. This is best supported by the cases where several cores of different size, shape and composition are enclosed within a single olivine-II grain (Fig. 7 g, h). As indicated by mineral inclusions, the olivine-II rims formed together with phlogopite, perovskite, minerals of spinel group, rutile and orthopyroxene, i.e. common groundmass minerals (except orthopyroxene) from a melt that is present as melt inclusions in the olivine rims and healed fractures in the olivine-II cores

Numerous studies indicate that most common xenoliths in kimberlites are garnet lherzolites, but surprisingly low abundance of orthopyroxene among xenocrysts and macrocrysts has been intriguing (Mitchell, 1973; Mitchell, 2008; Patterson et al., 2009; Skinner, 1989). Low silica activity in the kimberlite magma was offered as an explanation for instability of orthopyroxene, especially at sub-surface pressures (Mitchell, 1973). On the other hand, crystallising groundmass olivine rims and the presence of orthopyroxene inclusions in this olivine (Kamenetsky et al., 2008; Kamenetsky et al., 2009a) seem to be inconsistent with each other. One explanation is that orthopyroxene inclusions (often in groups and always associated with CO2 bubbles) can result from the local reaction of olivine with CO2 fluid

A limited range of Fo content in the olivine-II rims, but variable trace element abundances (Fig. 6b) suggest crystallisation over a small temperature range or/and buffering of the magma at a constant Fe/Mg with fractionating Ni, Mn and Ca. In many instances, where the cores are seemingly affected by diffusion (Fig. 7 b, c, f, h) and have a surrounding layer of distinct composition (Fig. 7 a, e, h), the uniform Fo in the rims can reflect attempts by the crystals to equilibrate with a final hybrid magma (Mitchell, 1986). We also propose that the buffering of Fe/Mg can occur if the Mg–Fe distribution coefficient (Kd) between olivine and a carbonate-rich kimberlite melt is significantly higher than for common basaltic systems (i.e. 0.3±0.03). This reflects significantly smaller Mg-Fe fractionation between silicates and carbonate melt, possibly as a result of complexing between carbonate and Mg2+ ions (Green & Wallace, 1988; Moore, 1988). The implied higher Kd for carbonatitic liquids, and especially Ca-rich carbonate, has been supported by experimental evidence (Dalton & Wood, 1993; Girnis et al., 2005). Probably an increase in Kd is even more pronounced for

The melt crystallising the rims of the Udachnaya-East groundmass olivine is represented by the carbonate-chloride matrix of the rocks (Kamenetsky et al., 2004; Kamenetsky et al., 2007a), and by the melt inclusions in olivine (Fig. 3, 8). The composition of this melt is unusually enriched in alkali carbonates and chlorides, but low in aluminosilicate components (Kamenetsky et al., 2004; Kamenetsky et al., 2007a). The crystallisation of

changing conditions, whereas similar Fo values of rims reflect major buffering event.

and olivine-I (Fig. 3, 8).

(2SiO4-4 + 2CO2 Si2O6-4 + 2CO3-2).

alkali-rich carbonatitic liquids.

Dry, chlorine-bearing alkali minerals in the Udachnaya-East kimberlite are products of crystallisation of the mantle-derived, uncontaminated melt. We suggest that a composition rich in alkalies, CO2 and Cl may be a viable alternative to the currently favoured ultramafic kimberlite magma. A "salty" kimberlite composition can explain trace element signatures consistent with low degrees of partial melting, low temperatures of crystallisation and exceptional rheological properties responsible for fast ascent and the magma's ability to carry abundant high-density mantle nodules and crystals. Evidence for these components, notably Cl and alkalies, is only preserved in an ultrafresh kimberlite such as Udachnaya-East. Nevertheless, Cl-bearing minerals of the type reported here have also been found in the groundmass and melt inclusions in kimberlites from Canada and Greenland (Kamenetsky et al., 2009b). The possible existence of chloride–carbonate liquids within the diamond stability field can be inferred from experiments in the model silicate system with addition of Na-Ca carbonate and K-chloride (Safonov et al., 2010; Safonov et al., 2007; Safonov et al., 2009). These experiments also show that Cl-bearing carbonate-silicate and Sibearing chloride-carbonate melts evolve towards Cl-rich carbonatitic liquids with decreasing temperature, providing a possible explanation for chlorine- and alkali-enriched microinclusions in some diamonds from Udachnaya-East (Zedgenizov & Ragozin, 2007) and other kimberlites in South Africa and Canada (Izraeli et al., 2001; Klein-BenDavid et al., 2007; Tomlinson et al., 2006). Brine inclusions in diamonds from various kimberlites, and the inferred role of chlorides in diamond nucleation and growth (Palyanov et al., 2007;

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#### **9. Acknowledgments**

We are indebted to Victor Sharygin, Alexander Golovin and Nikolai Pokhilenko who collected and supplied kimberlite samples for these studies and co-authored previous publications. Alexander Sobolev initiated and supervised PhD studies of Maya Kamenetsky and contributed a wealth of provocative ideas for discussion. We thank D. Kuzmin, P. Robinson, S. Gilbert, K. McGoldrick, K. Gőmann, and L. Danyushevsky for providing help with different analyses. The results and ideas were discussed with many researchers at different conferences. In particular, we are grateful to D.H. Green, B. Dawson, G. Brey, C. Ballhaus, G. Yaxley, R. Mitchell, O. Navon, N. Sobolev, O. Safonov, A. Chakhmouradian, S. Kostrovitsky, S. Tappe, S. Matveev, M. Kopylova, L. Heaman, Ya. Fedortchouk and I. Veksler for advice, moral support and friendly criticism. This study was initially (2003-2005) supported by the Alexander von Humboldt Foundation (Germany) in the form of the Wolfgang Paul Award to A. Sobolev and the Friedrich Wilhelm Bessel Award to V. Kamenetsky. Financial support for these studies in 2005-2009 was provided by an Australian Research Council Professorial Fellowship and Discovery Grant to V. Kamenetsky "Unmixing in Magmas: Melt and Fluid Inclusion Constraints on Identity, Timing, and Evolution of Immiscible Fluids, Salt and Sulphide Melts ".

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**11** 

*USA* 

**Next Generation Geological Modeling for** 

**Hydrocarbon Reservoir Characterization** 

Hydrocarbon reservoir characterization is a process for quantitatively assigning reservoir properties, recognizing geological and geophysical information and quantifying uncertainties in spatial variability (Fowler *et al.*, 1999). It represents an indispensable tool for optimizing costly reservoir management decisions for hydrocarbon field development. In fact reservoir characterization is the first step in the reservoir development program taking into account structural and depositional architecture, pore systems, mineralogy of the reservoir, post deposition diagenesis and the distribution and nature of reservoir fluids. The technologies and tools for reservoir characterization continue to develop and expand, particularly with the aggressive proliferation of three-dimensional (3D) and lately 3D timelapse (4D) data. However, one of the most critical areas of inquiry remains development of workflows that best capture and represent geological uncertainty and apply that in the integrated environment to optimize reservoir development and production planning (Goins,

Although the challenges to find, develop and produce ever new hydrocarbon resources are numerous, the ability of petroleum industry to increase the recovery from existing resources has become a global endeavor. It has been generally accepted that the conventional oil production practices produce, on average, approximately one third of the original oil in place (Kramers, 1994) where estimated remaining unrecovered mobile oil varies with different depositional environments. For example, depositional systems with more complicated stratigraphy and facies architecture, such as fluvial systems or deep-sea fans, may demonstrate even larger amounts of unrecovered mobile oil, ranging from 40-80% (Tyler and Finley, 1991; Larue and Yue, 2003). This common industrial knowledge represents a great incentive to increase the overall production, geared by large capital investments in Smart Reservoir Management workflows and Enhanced Oil Recovery (EOR) operations (Alvarado and Manrique, 2010). Still, the use of oversimplified and uncertain geological models based on a sparse data from limited number of widely-spaced wells can render hydrocarbon recovery forecasting as a daunting task. Moreover, inaccurate description of reservoir heterogeneities is probably one of the outstanding reasons for erroneous description of reservoir connectivity leading to the failure in predicting field performance (Damsleth *et al.*, 1992). Overestimating performance could lead to investment disasters, whereas its underestimation could lead to under-designed production facilities

**1. Introduction** 

2000; Kramers, 1994).

that restrict hydrocarbon recovery.

M. Maučec, J.M. Yarus and R.L. Chambers

*Halliburton Energy Services, Landmark Graphics Corporation,* 


## **Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization**

M. Maučec, J.M. Yarus and R.L. Chambers *Halliburton Energy Services, Landmark Graphics Corporation, USA* 

#### **1. Introduction**

214 Advances in Data, Methods, Models and Their Applications in Geoscience

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using C-K2CO3-KCl as an analogue for Cl-bearing carbonate fluid. *Lithos*, 77(1-4),

from Gardiner and Kovdor ultramafic alkaline complexes: Implications for

Hydrocarbon reservoir characterization is a process for quantitatively assigning reservoir properties, recognizing geological and geophysical information and quantifying uncertainties in spatial variability (Fowler *et al.*, 1999). It represents an indispensable tool for optimizing costly reservoir management decisions for hydrocarbon field development. In fact reservoir characterization is the first step in the reservoir development program taking into account structural and depositional architecture, pore systems, mineralogy of the reservoir, post deposition diagenesis and the distribution and nature of reservoir fluids. The technologies and tools for reservoir characterization continue to develop and expand, particularly with the aggressive proliferation of three-dimensional (3D) and lately 3D timelapse (4D) data. However, one of the most critical areas of inquiry remains development of workflows that best capture and represent geological uncertainty and apply that in the integrated environment to optimize reservoir development and production planning (Goins, 2000; Kramers, 1994).

Although the challenges to find, develop and produce ever new hydrocarbon resources are numerous, the ability of petroleum industry to increase the recovery from existing resources has become a global endeavor. It has been generally accepted that the conventional oil production practices produce, on average, approximately one third of the original oil in place (Kramers, 1994) where estimated remaining unrecovered mobile oil varies with different depositional environments. For example, depositional systems with more complicated stratigraphy and facies architecture, such as fluvial systems or deep-sea fans, may demonstrate even larger amounts of unrecovered mobile oil, ranging from 40-80% (Tyler and Finley, 1991; Larue and Yue, 2003). This common industrial knowledge represents a great incentive to increase the overall production, geared by large capital investments in Smart Reservoir Management workflows and Enhanced Oil Recovery (EOR) operations (Alvarado and Manrique, 2010). Still, the use of oversimplified and uncertain geological models based on a sparse data from limited number of widely-spaced wells can render hydrocarbon recovery forecasting as a daunting task. Moreover, inaccurate description of reservoir heterogeneities is probably one of the outstanding reasons for erroneous description of reservoir connectivity leading to the failure in predicting field performance (Damsleth *et al.*, 1992). Overestimating performance could lead to investment disasters, whereas its underestimation could lead to under-designed production facilities that restrict hydrocarbon recovery.

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 217

workflows for quantitative uncertainty assessment and risk management (Maučec and Cullick, 2011) combining two critical steps of reservoir characterization: a) the reconciliation of geomodels with well-production and seismic data, referred to as history-matching (HM) (Oliver and Chen, 2011) and b) dynamic ranking and selection of representative model

To capture diversity of geologically-complex reservoirs, the next-generation of geological modeling tools are relying increasingly on geostatistical methodologies (Isaaks and Srivastava, 1989; Yarus and Chambers, 1994; Chambers *et al.*, 2000a; Chambers *et al.*, 2000b; Deutsch, 2002; Yarus and Chambers, 2010). The in-depth explanation of geostatistical terminology is available in Olea, 1991. Tailored to identify data limitations and provide better representation of reservoir heterogeneity, geostatistical tools are particularly effective when dealing with data sets with vastly different degrees of spatial density and diverse vertical and horizontal resolution. Classical statistics methods are based on an underlying assumption of data independence in randomly sampled measurements. These assumptions are not true for geosciences data sets, where the data gathered are regionalized (map-able) and demonstrate strong dependence on the distance and orientation. Geostatistical tools provide the unique ability to integrate different types of data, with pronounced variation in scales and direction of continuity. One of the fundamental tools in geostatistics is the *variogram*, a measure of statistical dissimilarity between the pairs of data measurements. It represents a model of spatial correlation and continuity that quantifies the directions and scales of continuity. Variogram analysis can be applied to any regionalized variable *X* and is used to compute the average square differences between data measurements based on

2

(1)

*(h)* is given in Fig. 2. The left-hand panel corresponds

( )

*n*

*(h)* corresponds to the semivariogram (note that denominator *2n* represents the

*X X*

*i ih*

1

symmetry relation between data points *Xi* and *Xi+h*) and index *i* runs over the number of data pairs, *n*. We will in this document refer to semivariogram simply as a variogram.

to three distinctive cases of geological continuity: the red curve describes the omnidirectional or isotopic variogram that assumes a single, average characteristic direction of continuity, while blue and green curves, correspond to the minimum and maximum direction of continuity, respectively; an anisotropic variogram. The curve of omnidirectional variogram will converge to the black line that represents the true variance of the data and is usually referred to as *sill*. One additional parameter of the variogram, which is not depicted in Fig. 2 is the *nugget* effect and corresponds to a discontinuity along the Y-axis resulting in a vertical shift of the variogram curve at the origin. The distance at which the variogram curve levels out at the sill corresponds to the data *correlation range*. The righthand panel of Fig. 2 is an example of the variogram polar plot, with the major ellipse axis, corresponding to maximum and the (perpendicular) minor ellipse axis, to the minimum

( ) <sup>2</sup>

*i*

 

*h*

*n*

realizations for reservoir production forecast.

**2.1 Highlights of geostatistical analysis and modeling** 

different separation intervals *h*, known as the *lag* interval.

Visualization of a generic variogram

direction of continuity.

**2. Methods and techniques** 

where 

To mitigate and manage such scenarios, the modern workflows optimize field recovery performance by combining major disciplines of reservoir geosciences, *e.g.* geology, geophysics and petrophysics with numerical simulations into integrated flow models for a variety of field development operations. To maximize reservoir profitability, quantification of the effect of stratigraphic and structural uncertainties on its dynamic performance becomes of principal importance (Charles *et al.*, 2001; Seiler *et al.*, 2009). However, it continues to be an issue in geological modeling that the underlying structural frameworks do not correctly portray the true reservoir structure configuration or size, and this uncertainty impacts an accurate evaluation of hydrocarbon gross volumes. It is therefore essential to validate accordingly the role of individual components of high-resolution geological model (HRGM; see Fig. 1) and rank their impact on the uncertainty of HRGM at various levels (Fig. 1).

Fig. 1. Generation of High-resolution Geological Model, schematic depiction. The central panel outlines the role of individual phases in overall workflow sequence, with the impact on overall modeling uncertainty ranked to the right.

This paper focuses on recent advances in the technology for building high-resolution, geocellular models and its role in state-of-the-art and future EOR workflows. We first introduce some very basic tools and concepts of geostatistical spatial analysis and modeling, relevant for further understanding of the subject. Furthermore, we highlight what are perceived as some of the outstanding capabilities that differentiate the DecisionSpace Desktop Earth Modeling, as the next-generation geological modeling tool, from standard industrial approaches and workflows. Current geomodeling practice uses grids to represent 3D reservoir volumes. Estimating gridding parameters is a difficult task and commonly results in artifacts due to topological constraints and misrepresentation of important aspects of the structural framework which may introduce substantial difficulties for dynamic reservoir simulator later in the workflow. We describe a fundamentally novel method that has a potential to resolve most of the common geocellular modeling issues by implementing the concept of interpolation or simulation of reservoir properties using Local Continuity Directions (Yarus *et al.*, 2009; Maučec *et al.*, 2010). Finally, we address some latest developments in the integration of next-generation geological modeling into advanced workflows for quantitative uncertainty assessment and risk management (Maučec and Cullick, 2011) combining two critical steps of reservoir characterization: a) the reconciliation of geomodels with well-production and seismic data, referred to as history-matching (HM) (Oliver and Chen, 2011) and b) dynamic ranking and selection of representative model realizations for reservoir production forecast.

#### **2. Methods and techniques**

216 Advances in Data, Methods, Models and Their Applications in Geoscience

To mitigate and manage such scenarios, the modern workflows optimize field recovery performance by combining major disciplines of reservoir geosciences, *e.g.* geology, geophysics and petrophysics with numerical simulations into integrated flow models for a variety of field development operations. To maximize reservoir profitability, quantification of the effect of stratigraphic and structural uncertainties on its dynamic performance becomes of principal importance (Charles *et al.*, 2001; Seiler *et al.*, 2009). However, it continues to be an issue in geological modeling that the underlying structural frameworks do not correctly portray the true reservoir structure configuration or size, and this uncertainty impacts an accurate evaluation of hydrocarbon gross volumes. It is therefore essential to validate accordingly the role of individual components of high-resolution geological model (HRGM; see Fig. 1) and rank their impact on the uncertainty of HRGM at

Fig. 1. Generation of High-resolution Geological Model, schematic depiction. The central panel outlines the role of individual phases in overall workflow sequence, with the impact

This paper focuses on recent advances in the technology for building high-resolution, geocellular models and its role in state-of-the-art and future EOR workflows. We first introduce some very basic tools and concepts of geostatistical spatial analysis and modeling, relevant for further understanding of the subject. Furthermore, we highlight what are perceived as some of the outstanding capabilities that differentiate the DecisionSpace Desktop Earth Modeling, as the next-generation geological modeling tool, from standard industrial approaches and workflows. Current geomodeling practice uses grids to represent 3D reservoir volumes. Estimating gridding parameters is a difficult task and commonly results in artifacts due to topological constraints and misrepresentation of important aspects of the structural framework which may introduce substantial difficulties for dynamic reservoir simulator later in the workflow. We describe a fundamentally novel method that has a potential to resolve most of the common geocellular modeling issues by implementing the concept of interpolation or simulation of reservoir properties using Local Continuity Directions (Yarus *et al.*, 2009; Maučec *et al.*, 2010). Finally, we address some latest developments in the integration of next-generation geological modeling into advanced

Model **Higher**

**Facies model** controls depositional continuity

**Petrophysical model** defines property distribution

**Stratigraphic model** layering controls lateral connectivity variogram range controls vertical connectivity

**Structural model** defines gross volumes

**Lower**

**Uncertainty impact**

on overall modeling uncertainty ranked to the right.

Petrophysical Model

Facies Model

Stratigraphic Model

various levels (Fig. 1).

(HRGM)

High Resolution Geological Model

Structural

#### **2.1 Highlights of geostatistical analysis and modeling**

To capture diversity of geologically-complex reservoirs, the next-generation of geological modeling tools are relying increasingly on geostatistical methodologies (Isaaks and Srivastava, 1989; Yarus and Chambers, 1994; Chambers *et al.*, 2000a; Chambers *et al.*, 2000b; Deutsch, 2002; Yarus and Chambers, 2010). The in-depth explanation of geostatistical terminology is available in Olea, 1991. Tailored to identify data limitations and provide better representation of reservoir heterogeneity, geostatistical tools are particularly effective when dealing with data sets with vastly different degrees of spatial density and diverse vertical and horizontal resolution. Classical statistics methods are based on an underlying assumption of data independence in randomly sampled measurements. These assumptions are not true for geosciences data sets, where the data gathered are regionalized (map-able) and demonstrate strong dependence on the distance and orientation. Geostatistical tools provide the unique ability to integrate different types of data, with pronounced variation in scales and direction of continuity. One of the fundamental tools in geostatistics is the *variogram*, a measure of statistical dissimilarity between the pairs of data measurements. It represents a model of spatial correlation and continuity that quantifies the directions and scales of continuity. Variogram analysis can be applied to any regionalized variable *X* and is used to compute the average square differences between data measurements based on different separation intervals *h*, known as the *lag* interval.

$$\sum\_{i=1}^{n} (X\_i - X\_{i+h})^2$$

$$\gamma(h) = \frac{\sum\_{i=1}^{n} (X\_i - X\_{i+h})^2}{2n} \tag{1}$$

where *(h)* corresponds to the semivariogram (note that denominator *2n* represents the symmetry relation between data points *Xi* and *Xi+h*) and index *i* runs over the number of data pairs, *n*. We will in this document refer to semivariogram simply as a variogram. Visualization of a generic variogram *(h)* is given in Fig. 2. The left-hand panel corresponds to three distinctive cases of geological continuity: the red curve describes the omnidirectional or isotopic variogram that assumes a single, average characteristic direction of continuity, while blue and green curves, correspond to the minimum and maximum direction of continuity, respectively; an anisotropic variogram. The curve of omnidirectional variogram will converge to the black line that represents the true variance of the data and is usually referred to as *sill*. One additional parameter of the variogram, which is not depicted in Fig. 2 is the *nugget* effect and corresponds to a discontinuity along the Y-axis resulting in a vertical shift of the variogram curve at the origin. The distance at which the variogram curve levels out at the sill corresponds to the data *correlation range*. The righthand panel of Fig. 2 is an example of the variogram polar plot, with the major ellipse axis, corresponding to maximum and the (perpendicular) minor ellipse axis, to the minimum direction of continuity.

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 219

and orientation. The constraint for an unbiased estimator is satisfied by maintaining

High-resolution geomodeling of lithofacies and reservoir properties begins by creating a properly sealed structural framework and then integrating available data from cores, welllogs and seismic surveys. Ideally the lithology model is based on the interpretation of deposition facies from core description. However, for siliciclastic environments, the lithologies are typically electro-facies based on wireline logs calibrated to a few core descriptions. Finally, we often used petro-facies for carbonate reservoir as the primary depositional facies are destroyed by post depositional diagenetic processes. Once the

lithology is created, facies are populated with characteristic petrophysical properties.

Micro-logs can identify very thin impermeable shale layers, as thin as 1-2 ft. In order to maintain vertical communication and small scale heterogeneity in the model, particularly in assessing the sweep efficiency of EOR applications (Maučec and Chambers, 2009), *e.g.* CO2 flooding (Culham *et al.*, 2010), it is critical for well blocking to preserve small-scale facies heterogeneities in each interval, assign them correctly to common lithotypes and prevent inadvertently eliminating the essential geological information. The integrity of the blocking and preservation of small scale features is directly proportional to the vertical cells size. If small scale, thin bedding, is critical to sweep efficiencies, then a small vertical cell is required in the model, often resulting in a large multi-million cell geological model, which may be

Modeling complex geologic environments (*e.g.* fluvial, deltaic) require the ability to control vertical relationships and lateral relationships between the facies. In stratigraphic modeling, which is done on an interval-by-interval basis, the task is to identify the depositional environment and primary depositional facies. Each depositional environment is controlled by physical processes of sedimentation and erosion, which requires the creation of internal bedding geometry, *e.g.* layers representative of the depositional system. These layers act as lines of internal correlation that affect the gathering of statistical information in variogram computation and the distribution of properties in subsequent modeling steps. Once the layering styles are specified for each interval, the well data are re-sampled (coarsened or blocked) at the scale of the layers and a single property value assigned to each layer along the wellbore. For continuous properties, DecisionSpace Desktop Earth Modeling uses standard averaging methods to assign a value to the gravity center of each grid cell (layer) along the wellbore, biased to the lithology code. For discrete properties, coded by integers

Conventional modeling approaches use the average or global facies proportions per interval of interest, which implicitly assumes that the facies proportions are unrealistically the same everywhere throughout the interval and therefore applying a constant lithotype proportion curve (LPC) to the entire interval is inaccurate. Traditional techniques to introduce a geological trend in the data usually require laborious creation of pseudo-wells or application of a generic trend map. The use of a generalized trend map implies that the geological continuity throughout the interval would be fairly similar. In other words, the interpretation of underlying statistics (*e.g.* histograms, variograms) and characteristics such as anisotropy and correlation length, would in mathematical terms, assume the condition of stationarity (Caers, 2005). However, most reservoirs are non-stationary and the introduction

**2.2 Definition of lithofacies and mapping of lithotype proportions** 

used without upscaling in the dynamic simulator.

(*e.g.* facies) the most commonly occurring facies code is chosen.

<sup>1</sup> *<sup>i</sup>* .

Fig. 2. Visualization of a generic variogram *(h)*. The left-hand panel corresponds to three distinctive cases of geological continuity: single, average characteristic direction of continuity (red curve), minimum and maximum direction of continuity (blue and green curves, respectively). The black line represents the true variance of the data and is referred to as *sill*. The right-hand panel depicts the variogram polar plot, with the major ellipse axis, corresponding to maximum and the (perpendicular) minor ellipse axis, to the minimum direction of continuity.

Fig. 3. Principles of kriging, the geostatistical interpolation method. The value of the unsampled location *Z0*, is estimated based on linear combination of measurements at locations *Z1* to *Z3*, where weights *<sup>i</sup>* at locations *Zi* are calculated from the variogram model.

Among the numerous interpolation methods, the geostatistical kriging algorithm is commonly used in the geosciences. Kriging is an unbiased, linear, least-square regression technique that automatically "de-clusters" data to produce best local or block estimates with minimized error variance. Figure 3 depicts the principles of linear, weighted estimation of the value at location *Z0*, based on measured values at locations *Z1* to *Z3*:

$$Z\_0 = \sum\_{i=1}^{n} \lambda\_i Z\_i \tag{2}$$

where the weights *<sup>i</sup>* at locations *Zi* are calculated from the variogram model. Unlike the more conventional linear weighting estimators, the kriging weights, *i,* account for distance

distinctive cases of geological continuity: single, average characteristic direction of continuity (red curve), minimum and maximum direction of continuity (blue and green curves, respectively). The black line represents the true variance of the data and is referred to as *sill*. The right-hand panel depicts the variogram polar plot, with the major ellipse axis, corresponding to maximum and the (perpendicular) minor ellipse axis, to the minimum

Fig. 3. Principles of kriging, the geostatistical interpolation method. The value of the unsampled location *Z0*, is estimated based on linear combination of measurements at

**Z** 1

<sup>3</sup>

<sup>1</sup>

0

Among the numerous interpolation methods, the geostatistical kriging algorithm is commonly used in the geosciences. Kriging is an unbiased, linear, least-square regression technique that automatically "de-clusters" data to produce best local or block estimates with minimized error variance. Figure 3 depicts the principles of linear, weighted estimation of

1

*i Z Z*

*i i*

*<sup>i</sup>* at locations *Zi* are calculated from the variogram model. Unlike the

*n*

the value at location *Z0*, based on measured values at locations *Z1* to *Z3*:

more conventional linear weighting estimators, the kriging weights,

*(h)*. The left-hand panel corresponds to three

*<sup>i</sup>* at locations *Zi* are calculated from the variogram model.

**<sup>Z</sup>**<sup>2</sup> <sup>2</sup>

(2)

*i,* account for distance

Fig. 2. Visualization of a generic variogram

0 500 1000 1500 2000 Distance (m) 0 0 500 500 1000 1000 1500 1500 2000 2000 Distance (m)

**Z**3

Distance (h)

direction of continuity.

Semi-variogram

0

5

10

15

 (

)

locations *Z1* to *Z3*, where weights

where the weights

and orientation. The constraint for an unbiased estimator is satisfied by maintaining <sup>1</sup> *<sup>i</sup>* .

#### **2.2 Definition of lithofacies and mapping of lithotype proportions**

High-resolution geomodeling of lithofacies and reservoir properties begins by creating a properly sealed structural framework and then integrating available data from cores, welllogs and seismic surveys. Ideally the lithology model is based on the interpretation of deposition facies from core description. However, for siliciclastic environments, the lithologies are typically electro-facies based on wireline logs calibrated to a few core descriptions. Finally, we often used petro-facies for carbonate reservoir as the primary depositional facies are destroyed by post depositional diagenetic processes. Once the lithology is created, facies are populated with characteristic petrophysical properties.

Micro-logs can identify very thin impermeable shale layers, as thin as 1-2 ft. In order to maintain vertical communication and small scale heterogeneity in the model, particularly in assessing the sweep efficiency of EOR applications (Maučec and Chambers, 2009), *e.g.* CO2 flooding (Culham *et al.*, 2010), it is critical for well blocking to preserve small-scale facies heterogeneities in each interval, assign them correctly to common lithotypes and prevent inadvertently eliminating the essential geological information. The integrity of the blocking and preservation of small scale features is directly proportional to the vertical cells size. If small scale, thin bedding, is critical to sweep efficiencies, then a small vertical cell is required in the model, often resulting in a large multi-million cell geological model, which may be used without upscaling in the dynamic simulator.

Modeling complex geologic environments (*e.g.* fluvial, deltaic) require the ability to control vertical relationships and lateral relationships between the facies. In stratigraphic modeling, which is done on an interval-by-interval basis, the task is to identify the depositional environment and primary depositional facies. Each depositional environment is controlled by physical processes of sedimentation and erosion, which requires the creation of internal bedding geometry, *e.g.* layers representative of the depositional system. These layers act as lines of internal correlation that affect the gathering of statistical information in variogram computation and the distribution of properties in subsequent modeling steps. Once the layering styles are specified for each interval, the well data are re-sampled (coarsened or blocked) at the scale of the layers and a single property value assigned to each layer along the wellbore. For continuous properties, DecisionSpace Desktop Earth Modeling uses standard averaging methods to assign a value to the gravity center of each grid cell (layer) along the wellbore, biased to the lithology code. For discrete properties, coded by integers (*e.g.* facies) the most commonly occurring facies code is chosen.

Conventional modeling approaches use the average or global facies proportions per interval of interest, which implicitly assumes that the facies proportions are unrealistically the same everywhere throughout the interval and therefore applying a constant lithotype proportion curve (LPC) to the entire interval is inaccurate. Traditional techniques to introduce a geological trend in the data usually require laborious creation of pseudo-wells or application of a generic trend map. The use of a generalized trend map implies that the geological continuity throughout the interval would be fairly similar. In other words, the interpretation of underlying statistics (*e.g.* histograms, variograms) and characteristics such as anisotropy and correlation length, would in mathematical terms, assume the condition of stationarity (Caers, 2005). However, most reservoirs are non-stationary and the introduction

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 221

presence of high density, closely spaced wells, highly computationally intensive and reliant on the (3D) training image models (Caers, 2005). Multi-Point GeoStatistics (MPS) (Strebelle and Journel, 2001) is rapidly growing in popularity offering the modeler the ability to create geological models with complex geometries, while conditioning to large amounts of well and seismic data. However, as pointed out by Daly and Mariethoz (2011), it is still a relatively new topic, which has had a long academic history and is now just finding its way into commercial software. They also pointed several deficiencies in current implementations

The DecisionSpace Desktop Earth Modeling approaches facies modeling very differently from most current software offerings. The facies simulation workflow utilizes a powerful combination of describing the geological trends with LPMs created from multiple VPCs, as described previously, integrated with Plurigaussian simulation (PGS), a robust and welltested algorithm with a long industrial history. The PGS is an expansion of TGS method and uses two Gaussian variograms simultaneously. There are a numerous advantages of PGS

 as trends for each facies within each layer and every reservoir interval in the model are calculated, based on the LPMs that account for spatial non-stationarity, the PGS methodology, captures most inter- and intra-facies relationships including post

 as a pixel-based method, PGS works easily with closely spaced or sparse well control. PGS has been available in two commercial software offerings (HERESIM™ and

 While it is possible to overcome some of the challenges presented by traditional algorithms through the intervention by experts, the implementation of a LPM with PGS

The next-generation earth model approach to facies modeling introduces a set of facies templates based on the understanding of realistic depositional environments (Walker and James, 1992). The DecisionSpace Desktop Earth Modeling implements a library of more than forty standard depositional systems, presented with maps and cross-sectional views

The PGS facies modeling requires a set of rules to establish lithotype relationships, where a lithotype is a group of facies sharing common depositional and petrophysical properties. Knowledge of the proportions is not sufficient for accurate modeling of the lithotypes and the depositional system templates help modelers to visualize relationships between the facies and to provide an associated lithotype "rule box" (see: upper left schematics, Fig. 5 expanded view) that specifies their mathematical relationship. Rules are based on simple or complex lithotype transitions; a) simple transitions corresponds to a strict transition from one lithotype to another and are modeled with one variogram, b) complex transitions require the definition of two lithotype sets, each controlled by its own variogram that can have different anisotropy directions. A lithotype set is a set of lithotypes that share a common spatial model, such as a channel and its associated levy. An example of modeling complex transition of lithotypes, represented by two lithosets and associated variogram models is given in Fig. 6. In this figure the vertical and horizontal sets are schematic representations depicting which variogram controls a lithotype set, when in reality the two variogram models interact to create the final facies model. Because PGS uses lithology proportions, rather than indicators as in SIS, a wider variety variogram model types are

ISATIS™) since the early 1990s, however its use is not necessarily intuitive.

related to 1) performance, 2) training image generation, and 3) non-stationarity.

depositional overprinting, such as diagenesis.

workflow can be presented simply and intuitively.

over other methods:

(see Fig. 5).

of simple trend (vertical or horizontal) could "de-trend" the data, resulting in inadequate solutions and further complicate the computation and interpretation of variograms. The next-generation earth modeling reintroduces a graphical method that generates individual LPCs for each well in the field with the ability to create pseudo-wells to invoke a geological trend that honors the conceptual depositional model.

Fig. 4. Lithotype proportion mapping: a) example of a map view that uses existing proportion curves, with the ability to create pseudo-wells and impose a trend to honor the conceptual model, b) example of vertical proportion curves organized into vertical proportion matrix (VPM), describing how the facies behave vertically and laterally over the area of the reservoir.

When displayed in the map view (Fig. 4a), the LPCs allow for a quick QC of the vertical variation of the facies distribution and proportions, even before creating the facies model. Editing and copy/move functionality allows the modeler to impose an interpretation to better control trends. The lithotype proportion map (LPM), created from the VPCs, literally consists of hundreds of high resolution trend maps accounting for vertical and lateral nonstationarity (Fig. 4b).

#### **2.3 Geologically-driven facies modeling**

Facies simulation algorithms, commonly used in earth modeling suffer from a variety of challenges when trying to generate models based on often sparse real data, particularly when attempting to honor depositional facies boundary conditions and proportions, capture depositional overprinting or accounting for geological non-stationarity. For example, the Sequential Indicator Simulation (SIS) (Caers, 2005), lacks the ability to control facies boundary conditions, the Truncated Gaussian Simulation (TGS) (Caers, 2005), provides for only simple facies transitional boundaries and while Object (also termed Boolean) Simulation (OS) can manage most non-overprinted complex facies sets, it is unstable in the

of simple trend (vertical or horizontal) could "de-trend" the data, resulting in inadequate solutions and further complicate the computation and interpretation of variograms. The next-generation earth modeling reintroduces a graphical method that generates individual LPCs for each well in the field with the ability to create pseudo-wells to invoke a geological

trend that honors the conceptual depositional model.

a) b)

area of the reservoir.

stationarity (Fig. 4b).

**2.3 Geologically-driven facies modeling** 

Fig. 4. Lithotype proportion mapping: a) example of a map view that uses existing

conceptual model, b) example of vertical proportion curves organized into vertical

proportion curves, with the ability to create pseudo-wells and impose a trend to honor the

proportion matrix (VPM), describing how the facies behave vertically and laterally over the

When displayed in the map view (Fig. 4a), the LPCs allow for a quick QC of the vertical variation of the facies distribution and proportions, even before creating the facies model. Editing and copy/move functionality allows the modeler to impose an interpretation to better control trends. The lithotype proportion map (LPM), created from the VPCs, literally consists of hundreds of high resolution trend maps accounting for vertical and lateral non-

Facies simulation algorithms, commonly used in earth modeling suffer from a variety of challenges when trying to generate models based on often sparse real data, particularly when attempting to honor depositional facies boundary conditions and proportions, capture depositional overprinting or accounting for geological non-stationarity. For example, the Sequential Indicator Simulation (SIS) (Caers, 2005), lacks the ability to control facies boundary conditions, the Truncated Gaussian Simulation (TGS) (Caers, 2005), provides for only simple facies transitional boundaries and while Object (also termed Boolean) Simulation (OS) can manage most non-overprinted complex facies sets, it is unstable in the presence of high density, closely spaced wells, highly computationally intensive and reliant on the (3D) training image models (Caers, 2005). Multi-Point GeoStatistics (MPS) (Strebelle and Journel, 2001) is rapidly growing in popularity offering the modeler the ability to create geological models with complex geometries, while conditioning to large amounts of well and seismic data. However, as pointed out by Daly and Mariethoz (2011), it is still a relatively new topic, which has had a long academic history and is now just finding its way into commercial software. They also pointed several deficiencies in current implementations related to 1) performance, 2) training image generation, and 3) non-stationarity.

The DecisionSpace Desktop Earth Modeling approaches facies modeling very differently from most current software offerings. The facies simulation workflow utilizes a powerful combination of describing the geological trends with LPMs created from multiple VPCs, as described previously, integrated with Plurigaussian simulation (PGS), a robust and welltested algorithm with a long industrial history. The PGS is an expansion of TGS method and uses two Gaussian variograms simultaneously. There are a numerous advantages of PGS over other methods:


The next-generation earth model approach to facies modeling introduces a set of facies templates based on the understanding of realistic depositional environments (Walker and James, 1992). The DecisionSpace Desktop Earth Modeling implements a library of more than forty standard depositional systems, presented with maps and cross-sectional views (see Fig. 5).

The PGS facies modeling requires a set of rules to establish lithotype relationships, where a lithotype is a group of facies sharing common depositional and petrophysical properties. Knowledge of the proportions is not sufficient for accurate modeling of the lithotypes and the depositional system templates help modelers to visualize relationships between the facies and to provide an associated lithotype "rule box" (see: upper left schematics, Fig. 5 expanded view) that specifies their mathematical relationship. Rules are based on simple or complex lithotype transitions; a) simple transitions corresponds to a strict transition from one lithotype to another and are modeled with one variogram, b) complex transitions require the definition of two lithotype sets, each controlled by its own variogram that can have different anisotropy directions. A lithotype set is a set of lithotypes that share a common spatial model, such as a channel and its associated levy. An example of modeling complex transition of lithotypes, represented by two lithosets and associated variogram models is given in Fig. 6. In this figure the vertical and horizontal sets are schematic representations depicting which variogram controls a lithotype set, when in reality the two variogram models interact to create the final facies model. Because PGS uses lithology proportions, rather than indicators as in SIS, a wider variety variogram model types are

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 223

Separate lithology rules are used for each depositional sequence with up to two variograms to controlling different directions and scales. Petrophysical Property Modeling populates facies models with petrophysical properties (porosity, permeability, water saturation, *etc.*) by interval and constrained by facies. The DecisionSpace Desktop Earth Modeling uses the Turning Bands algorithm as the simulation method with Collocated CoSimulation as one of the options. Kriging and Collocated CoKriging are additional geostatistical algorithms available. Collocated CoKriging is a variation of the classical kriging interpolation, where the variogram is computed from a secondary variable that serves as an additional spatial constraint. Fig. 7, gives an example of facies model realization and facies-constrained model

Fig. 7. An example of facies model realization (sand fraction in white, shale fraction in blue) and facies-constrained model of porosity distribution of Brugge synthetic model (Peters e*t* 

Traditional reservoir modeling techniques use simplified *two-point statistics* to describe the pattern of spatial variation in geological properties. Such techniques implement a *variogram* model that quantifies the average of expected variability as a function of *distance* and *direction*. In reservoirs, where the geological characteristics are very continuous and easily correlated from well to well, the range (or scale) of correlation will be large while in reservoirs, where the geological characteristics change quickly over short distances, the correlation scales will be shorter. The later phenomenon is very common in sedimentary environments, where the primary mechanism of transport during deposition is water, resulting in highly *channelized* structures (*e.g.* deltaic channels, fluvial deposits, turbidities). These environments usually demonstrate a large degree of local anisotropy and of correlation variation between directions along the channel axis and perpendicular to the

Because the principles of conventional (*i.e.* two-point) geostatistical practice still require the nomination of a *single* (average) direction of maximum continuity its use for modeling complex sedimentary environments becomes highly challenging if not impossible. Recently, technology for 3D volumetric modeling of geological properties, using a Maximum Continuity Field (MCF) (Yarus *et al.*, 2009) has been proposed. The new method represents geological properties within a volume of the subsurface by distributing a plurality of data points in the absence of the grid with the notion of geological continuity and directionality represented by MCF, hence entitled as the Point-Vector (PV) method. It introduces several

*al.*, 2009), generated by DecisionSpace Desktop Earth Modeling.

**2.4 Novel concepts in local continuity modeling** 

game-changing components to the area of geomodeling:

of porosity distribution.

channel axis.

available to the modeler. It also provides the ability to model two lithosets, each can exhibit different anisotropic conditions that can be used with calculated LPM to produce realistic models of geological facies distributions.

Fig. 5. The DecisionSpace Desktop Earth Modeling implements a library of more than forty depositional systems, presented with maps and cross-sectional views.

Fig. 6. An example of modeling complex transition of lithotypes, represented by two lithotype sets and associated variogram models

available to the modeler. It also provides the ability to model two lithosets, each can exhibit different anisotropic conditions that can be used with calculated LPM to produce realistic

Fig. 5. The DecisionSpace Desktop Earth Modeling implements a library of more than forty

Fig. 6. An example of modeling complex transition of lithotypes, represented by two

lithotype sets and associated variogram models

depositional systems, presented with maps and cross-sectional views.

models of geological facies distributions.

Separate lithology rules are used for each depositional sequence with up to two variograms to controlling different directions and scales. Petrophysical Property Modeling populates facies models with petrophysical properties (porosity, permeability, water saturation, *etc.*) by interval and constrained by facies. The DecisionSpace Desktop Earth Modeling uses the Turning Bands algorithm as the simulation method with Collocated CoSimulation as one of the options. Kriging and Collocated CoKriging are additional geostatistical algorithms available. Collocated CoKriging is a variation of the classical kriging interpolation, where the variogram is computed from a secondary variable that serves as an additional spatial constraint. Fig. 7, gives an example of facies model realization and facies-constrained model of porosity distribution.

Fig. 7. An example of facies model realization (sand fraction in white, shale fraction in blue) and facies-constrained model of porosity distribution of Brugge synthetic model (Peters e*t al.*, 2009), generated by DecisionSpace Desktop Earth Modeling.

#### **2.4 Novel concepts in local continuity modeling**

Traditional reservoir modeling techniques use simplified *two-point statistics* to describe the pattern of spatial variation in geological properties. Such techniques implement a *variogram* model that quantifies the average of expected variability as a function of *distance* and *direction*. In reservoirs, where the geological characteristics are very continuous and easily correlated from well to well, the range (or scale) of correlation will be large while in reservoirs, where the geological characteristics change quickly over short distances, the correlation scales will be shorter. The later phenomenon is very common in sedimentary environments, where the primary mechanism of transport during deposition is water, resulting in highly *channelized* structures (*e.g.* deltaic channels, fluvial deposits, turbidities). These environments usually demonstrate a large degree of local anisotropy and of correlation variation between directions along the channel axis and perpendicular to the channel axis.

Because the principles of conventional (*i.e.* two-point) geostatistical practice still require the nomination of a *single* (average) direction of maximum continuity its use for modeling complex sedimentary environments becomes highly challenging if not impossible. Recently, technology for 3D volumetric modeling of geological properties, using a Maximum Continuity Field (MCF) (Yarus *et al.*, 2009) has been proposed. The new method represents geological properties within a volume of the subsurface by distributing a plurality of data points in the absence of the grid with the notion of geological continuity and directionality represented by MCF, hence entitled as the Point-Vector (PV) method. It introduces several game-changing components to the area of geomodeling:

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 225

property remains "substantially the same", *e.g.* within 10%. This allows flexibility in specifying local directions of maximum continuity and interpolation of properties in 3D geological models, aligned with underlying geological structure. The PV property

1. Define structural model and 3D grids where MCF is stored and the property values are

2. Define the MCF, using some predefined azimuth map (see Fig. 9b) and the local dip (an

4. Add known data points (*i.e.* spatially located known reservoir property) to the model, create the covariance neighborhood and the variogram. The covariance calculations take local continuity into account by aligning the axes of the variogram with the local

5. Run ordinary kriging estimator (see Eq. 2), using the created covariance neighborhood. For each point to estimate, the kriging finds the nearest set of known data along

The center of the search ellipse (or ellipsoid in 3D) is associated with the location of MCV denoted by V1 and V2. The data points, detected inside the search ellipse ("blue" triangles) are considered in the interpolation along the MCV while the data outside the ellipse ("red" squares) are not included. The relative dimensions of the search ellipsoid, *i.e.* the ratios between major (M), intermediate (I) and minor (m) axis length correspond to "local" anisotropy factor. In a faulted reservoir the property associated with MCV V2 is interpolated across the fault line, following the fault throw vector FT. To validate the PV method, the sealed structural framework, containing top and bottom horizons with a single internal fault, was built from a fluvial reservoir of the Brugge synthetic model (Peters e*t al.*, 2009).

The 2D implementation of property interpolation is schematically depicted in Fig. 8.

Additional details on the validation of PV method are available in Maučec *et al.* 2010.

In Fig. 9a an example of a facies realization for the Brugge fluvial reservoir zone is given. The blue area represents the sand body (pay zone) distributed on shale (non-pay zone in red). Using the facies distribution as a basis or constraint for the generation of a vector field emulates a certain "pre-knowledge" on the geological structure but is in no way a required step. Fig. 9b represents MCF defined on virtually regular mesh of points. No particular continuity information was assumed for the shale zone, only for the discrete sand bodies. The azimuth alone is used from the MCF; the dip angle is calculated as the normal direction relative to the local curvature of the horizon. Fig. 9c visualizes fault displacement vector

An example permeability distribution, generated with the MCF-based method of reservoir property interpolation is shown in Fig. 9d, depicting the flattened 2D map view of the major-minor plane and the fault location. The PV method allows the user to define variable sizes of search ellipsoids throughout the model volume of interest (VOI). By this notion, a single-size search sphere was defined for the shale facies, where no particular continuity information was assumed (see Fig. 9b). A variable sized search ellipsoid and different anisotropy factors (*i.e.* ratios between the length (in ft) of the major direction and minor direction of the search ellipsoid in M-m plane) were considered for the sand zone to validate the impact on the interpolation. Qualitatively, the anisotropy ratio of 10:1 (major/minor = 10000/1000) can be interpreted for example as the case with less uncertain (and more trusted) MCF data, used to obtain permeability distribution as depicted in Fig. 9d. The

interpolation workflow follows the methodology of Maučec *et al.* 2010:

angle from the horizontal/azimuth plane) of the horizons. 3. Pre-process of all the fault displacements in the 3D grid (see Fig. 9c).

shortest geometrical (or Euclidean) distances.

interpolated.

continuity direction.

field with a constant throw of ~50 m.


The key to implementation of these ideas emerges from interpretation of concepts of MCF and their implementation into kriging equations (Eq. 2) for geostatistical estimation. Almost all available geostatistical software restricts the user to certain types of variogram model functions (*e.g.* spherical, exponential, Gaussian etc.) to ensure that a unique set of kriging weights can always be found and to "force" a *single* direction of maximum continuity. However, it is very rare in geology to have a single direction of maximum continuity representative everywhere. Instead, the PV method defines the attributes of Maximum Continuity Vector (MCV) as location, magnitude, direction and length, representing the correlation length (see insert of Fig. 8), along which the magnitude of the geological

Fig. 8. Interpolation of properties in PV method (2D visualization): the structural framework is represented by top and bottom horizons (in blue) and fault line (in red). The maximum continuity vectors and fault throws are depicted with V and FT, respectively. The data points included in the search neighborhood (ellipse depicted in orange) are represented with triangles in blue, while red squares represent data points excluded from the search.

 Direct control over local continuity directions is controlled using a predefined azimuth map and the local dip (an angle from the horizontal/azimuth plane) of the horizons. The Fault Displacement Field (FDF), annotated in Fig. 8 with symbol FT (fault throw) can be, for example, calculated from the underlying seismic amplitude data (Liang *et al.*,

Interactive operation with "geologically intuitive" datasets, such as layering intervals,

 Retention of the maximum fidelity of geological model by postponing the creation of grid/mesh until the final stage of (static) model building, immediately before integrating into dynamic model. The reservoir property modeling does not need a standard grid but only the "correct" distance between the points to estimate/simulate

The key to implementation of these ideas emerges from interpretation of concepts of MCF and their implementation into kriging equations (Eq. 2) for geostatistical estimation. Almost all available geostatistical software restricts the user to certain types of variogram model functions (*e.g.* spherical, exponential, Gaussian etc.) to ensure that a unique set of kriging weights can always be found and to "force" a *single* direction of maximum continuity. However, it is very rare in geology to have a single direction of maximum continuity representative everywhere. Instead, the PV method defines the attributes of Maximum Continuity Vector (MCV) as location, magnitude, direction and length, representing the correlation length (see insert of Fig. 8), along which the magnitude of the geological

Fig. 8. Interpolation of properties in PV method (2D visualization): the structural framework is represented by top and bottom horizons (in blue) and fault line (in red). The maximum continuity vectors and fault throws are depicted with V and FT, respectively. The data points included in the search neighborhood (ellipse depicted in orange) are represented with triangles in blue, while red squares represent data points excluded from the search.

V2

FT

Location

Magnitude and direction

Length

projection maps and hand drawings via the notion of MCF and the

2010).

the property and data around it.

V1

property remains "substantially the same", *e.g.* within 10%. This allows flexibility in specifying local directions of maximum continuity and interpolation of properties in 3D geological models, aligned with underlying geological structure. The PV property interpolation workflow follows the methodology of Maučec *et al.* 2010:


The 2D implementation of property interpolation is schematically depicted in Fig. 8.

The center of the search ellipse (or ellipsoid in 3D) is associated with the location of MCV denoted by V1 and V2. The data points, detected inside the search ellipse ("blue" triangles) are considered in the interpolation along the MCV while the data outside the ellipse ("red" squares) are not included. The relative dimensions of the search ellipsoid, *i.e.* the ratios between major (M), intermediate (I) and minor (m) axis length correspond to "local" anisotropy factor. In a faulted reservoir the property associated with MCV V2 is interpolated across the fault line, following the fault throw vector FT. To validate the PV method, the sealed structural framework, containing top and bottom horizons with a single internal fault, was built from a fluvial reservoir of the Brugge synthetic model (Peters e*t al.*, 2009). Additional details on the validation of PV method are available in Maučec *et al.* 2010.

In Fig. 9a an example of a facies realization for the Brugge fluvial reservoir zone is given. The blue area represents the sand body (pay zone) distributed on shale (non-pay zone in red). Using the facies distribution as a basis or constraint for the generation of a vector field emulates a certain "pre-knowledge" on the geological structure but is in no way a required step. Fig. 9b represents MCF defined on virtually regular mesh of points. No particular continuity information was assumed for the shale zone, only for the discrete sand bodies. The azimuth alone is used from the MCF; the dip angle is calculated as the normal direction relative to the local curvature of the horizon. Fig. 9c visualizes fault displacement vector field with a constant throw of ~50 m.

An example permeability distribution, generated with the MCF-based method of reservoir property interpolation is shown in Fig. 9d, depicting the flattened 2D map view of the major-minor plane and the fault location. The PV method allows the user to define variable sizes of search ellipsoids throughout the model volume of interest (VOI). By this notion, a single-size search sphere was defined for the shale facies, where no particular continuity information was assumed (see Fig. 9b). A variable sized search ellipsoid and different anisotropy factors (*i.e.* ratios between the length (in ft) of the major direction and minor direction of the search ellipsoid in M-m plane) were considered for the sand zone to validate the impact on the interpolation. Qualitatively, the anisotropy ratio of 10:1 (major/minor = 10000/1000) can be interpreted for example as the case with less uncertain (and more trusted) MCF data, used to obtain permeability distribution as depicted in Fig. 9d. The

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 227

permeability, represents a crucial part of any modeling activity. To quantify and reduce the uncertainty in the description of hydrocarbon reservoirs, the parameters of geological model are usually adjusted and reconciled with pressure and multi-phase production data by history-matching (HM). With an advent of computing capabilities in recent decades, the classical (*i.e*. manual) HM has evolved to so-called computer-Assisted (or Automated) HM (AHM) technology. When we hereafter in this document refer to the history-matching

As an inverse problem, HM is highly non-linear and ill-posed by its nature, which means that, depending on the *prior* information, one can obtain a set of non-unique solutions that honor both the prior constraints and conditioned data with associated uncertainty. To assess the uncertainty in estimated reservoir parameters, one must sample from the *posterior* distribution, and the Bayesian methods (Lee, 1997) provide a very efficient framework to perform this operation. Using Bayes' formula, the posterior distribution (*i.e.,* the probability of occurrence of model simulated parameter, **m**, given the measured data values, **d**) is represented as being proportional to the product of prior and likelihood probability

*dm m*

*d p p*


where, | *pm d* ( |) **m d** , | (| ) *pd m* **d m** and *pm*( ) **m** represent the posterior, likelihood, and prior distribution, respectively. The normalization factor ( ) *<sup>d</sup> p* **d** represents the probability

When the distribution of prior model parameters, **m** ( *<sup>M</sup>* **m** , where *M* represents the number of parameters), follows a multi-Gaussian probability density function (pdf), the

exp

with **CM** as the prior covariance matrix ( *MxM* **CM** ). The distribution of likelihood data is

<sup>|</sup> /2 1/2

with **C***D* as the data covariance matrix ( *NxN* **C***<sup>D</sup>* ). The relationship between the data and the model parameters is expressed as a non-linear function that maps the model parameters into the data space, **d g(m)** , where **d** is the data vector with *N* observations representing the output of the model, **m** is a vector of model parameters, and **g** is the forward model operator that maps the model parameters into the data domain. For history-matching problems, **g** represents the reservoir simulator. Using Bayes' theorem (Eq. 3), both prior and

 1 2 <sup>2</sup> 1

**<sup>1</sup> mm C mm**

**m** (4)

**d m d gm d gm** (5)


<sup>2</sup> <sup>2</sup> *<sup>m</sup> M / / <sup>p</sup>*

**M**

defined as the conditional pdf | (| ) *pd m* **d m** of data, **d**, given model parameters, **m**:

*d m N D D*

**C**

1 1 <sup>|</sup> exp 2 2

**C**

*m d*

*p*

associated with the data and usually treated as a constant.

*pm*( ) **m** , centered around the prior mean **<sup>0</sup> m** , is given by:

*π*

likelihood pdfs are combined to define the posterior pdf as:

*p*

*<sup>p</sup>* **d|m m m|d <sup>d</sup>** (3)

**<sup>T</sup> 01 0 M**

*T*

**<sup>1</sup> C**

*p O m d*<sup>|</sup> exp **m|d m** (6)

process, the AHM workflow is assumed.

distributions of the reservoir model:

corner insert of Fig. 9d represents the M-I plane cross-section, indicating the fault location. The permeability model effectively represents a VOI with no imposed stratigraphic grid and as such retains the maximum available resolution and information density, limited only by the resolution of underlying data and MCF.

Fig. 9. Validation of property (permeability) interpolation with the PV method: a) facies realization used to generate spatially constrained MCF (sand in "blue", shale in "red"), b) generated MCF, depicted with MCV's (dimensions of panels a) and b) given in meters), c) 3D visualization of fault displacement vector field and d) interpolated permeability maps generated with the search anisotropy ratio of 10:1. Dimensions given in meters, color-bar in mD. Larger image: top view of M-m plane, smaller image: side view of M-I plane. Permeability maps are smoothed with recursive Gaussian filter (two samples half-width).

#### **2.5 Conditioning reservoir models to production data**

Accurate modeling of the hydrocarbon reservoir production behavior is of fundamental importance in reservoir engineering workflows for optimization of reservoir performance, operational activities, and development plans. A realistic description of geological formations and their fluid-flow-related properties, such as lithofacies distribution and

corner insert of Fig. 9d represents the M-I plane cross-section, indicating the fault location. The permeability model effectively represents a VOI with no imposed stratigraphic grid and as such retains the maximum available resolution and information density, limited only by

Fig. 9. Validation of property (permeability) interpolation with the PV method: a) facies realization used to generate spatially constrained MCF (sand in "blue", shale in "red"), b) generated MCF, depicted with MCV's (dimensions of panels a) and b) given in meters), c) 3D visualization of fault displacement vector field and d) interpolated permeability maps generated with the search anisotropy ratio of 10:1. Dimensions given in meters, color-bar in

Permeability maps are smoothed with recursive Gaussian filter (two samples half-width).

Accurate modeling of the hydrocarbon reservoir production behavior is of fundamental importance in reservoir engineering workflows for optimization of reservoir performance, operational activities, and development plans. A realistic description of geological formations and their fluid-flow-related properties, such as lithofacies distribution and

mD. Larger image: top view of M-m plane, smaller image: side view of M-I plane.

**2.5 Conditioning reservoir models to production data** 

the resolution of underlying data and MCF.

permeability, represents a crucial part of any modeling activity. To quantify and reduce the uncertainty in the description of hydrocarbon reservoirs, the parameters of geological model are usually adjusted and reconciled with pressure and multi-phase production data by history-matching (HM). With an advent of computing capabilities in recent decades, the classical (*i.e*. manual) HM has evolved to so-called computer-Assisted (or Automated) HM (AHM) technology. When we hereafter in this document refer to the history-matching process, the AHM workflow is assumed.

As an inverse problem, HM is highly non-linear and ill-posed by its nature, which means that, depending on the *prior* information, one can obtain a set of non-unique solutions that honor both the prior constraints and conditioned data with associated uncertainty. To assess the uncertainty in estimated reservoir parameters, one must sample from the *posterior* distribution, and the Bayesian methods (Lee, 1997) provide a very efficient framework to perform this operation. Using Bayes' formula, the posterior distribution (*i.e.,* the probability of occurrence of model simulated parameter, **m**, given the measured data values, **d**) is represented as being proportional to the product of prior and likelihood probability distributions of the reservoir model:

$$p\_{m|d}\left(\mathbf{m}\mid\mathbf{d}\right) = \frac{p\_{d|m}\left(\mathbf{d}\mid\mathbf{m}\right)p\_m\left(\mathbf{m}\right)}{p\_d\left(\mathbf{d}\right)}\tag{3}$$

where, | *pm d* ( |) **m d** , | (| ) *pd m* **d m** and *pm*( ) **m** represent the posterior, likelihood, and prior distribution, respectively. The normalization factor ( ) *<sup>d</sup> p* **d** represents the probability associated with the data and usually treated as a constant.

When the distribution of prior model parameters, **m** ( *<sup>M</sup>* **m** , where *M* represents the number of parameters), follows a multi-Gaussian probability density function (pdf), the *pm*( ) **m** , centered around the prior mean **<sup>0</sup> m** , is given by:

$$p\_m(\mathbf{m}) = \frac{\mathbf{1}}{\left(2\pi\right)^{M/2} \left|\mathbf{C\_M}\right|^{1/2}} \exp\left[-\frac{1}{2}\left(\mathbf{m} - \mathbf{m}^0\right)^T \mathbf{C\_M}^{-1} \left(\mathbf{m} - \mathbf{m}^0\right)\right] \tag{4}$$

with **CM** as the prior covariance matrix ( *MxM* **CM** ). The distribution of likelihood data is defined as the conditional pdf | (| ) *pd m* **d m** of data, **d**, given model parameters, **m**:

$$p\_{d|m}\left(\mathbf{d}\mid\mathbf{m}\right) = \frac{1}{\left(2\pi\right)^{N/2}\left|\mathbf{C}\_{D}\right|^{1/2}}\exp\left[-\frac{1}{2}\left(\mathbf{d}-\mathbf{g}\left(\mathbf{m}\right)\right)^{T}\mathbf{C}\_{D}^{-1}\left(\mathbf{d}-\mathbf{g}\left(\mathbf{m}\right)\right)\right] \tag{5}$$

with **C***D* as the data covariance matrix ( *NxN* **C***<sup>D</sup>* ). The relationship between the data and the model parameters is expressed as a non-linear function that maps the model parameters into the data space, **d g(m)** , where **d** is the data vector with *N* observations representing the output of the model, **m** is a vector of model parameters, and **g** is the forward model operator that maps the model parameters into the data domain. For history-matching problems, **g** represents the reservoir simulator. Using Bayes' theorem (Eq. 3), both prior and likelihood pdfs are combined to define the posterior pdf as:

$$p\_{m|d}\left(\mathbf{m}\mid\mathbf{d}\right) \propto \exp\left[-O\left(\mathbf{m}\right)\right] \tag{6}$$

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 229

*J y t t y t f t*

Fig. 10. Illustration of Generalized Travel-Time (GTT) inversion by systematically shifting the calculated fractional flow curve *fw* to the observed history (modified from Datta-Gupta and King, 2007). Red and magenta symbols correspond to the initially-calculated and shifted

This is illustrated in Fig. 10, where the calculated fractional flow response1 is systematically shifted in small-time increments towards the observed response, every data point in the

computed for each time increment. The misfit function *J* directly corresponds to the term **d g(m)** , given in Eqs. 5 and 7 that defines the misfit between the observed data and simulated response. The objective of HM inversion workflow is to minimize the misfit in production response by reconciling the geological model with observed (measured)

The two-step MCMC algorithm (Efendiev *et al.* 2005) uses an approximate likelihood calculation to improve on the (low) acceptance rate of the one-step algorithm (Ma *et al*, 2008). This approach does not compromise the rigor in traditional MCMC sampling, as it adequately samples from the posterior distribution and obeys the *detailed balance* (Maučec *et al.,* 2007), thus, a sufficient condition for a unique stationary distribution. The main steps of the streamline-based, two-step MCMC algorithm are depicted in a flowchart in Fig. 11. A pre-screening based on approximate likelihood calculations eliminates most of the rejected samples, and the exact MCMC is performed only on the accepted proposals, with higher acceptance rate. The approximate likelihood calculations are fast and typically involve a linearized approximation around an already accepted state rather than an

1 In water-injection EOR operations, the fractional flow curve frequently corresponds to water-cut curve

that represents the water breakthrough at the well as a function of well production time.

 

curve, respectively, while the black line represents the observed curve.

fractional-flow curve has the same shift time, 1 2

dynamic production data.

*j i j ji j*

*obs cal*

1

to observed and calculated production data, respectively, at well *j*.

where *Ndj* stands for the number of observed data (**d**) at well *j* and *obs*

*i*

*Ndj*

2

( )

*<sup>j</sup> y* and *cal*

*tt t* ... and the data misfit is

*<sup>j</sup> y* correspond

(8)

where, the objective function *O***m** combines prior and likelihood terms:

$$O\left(\mathbf{m}\right) = \frac{1}{2} \left(\mathbf{d} - \mathbf{g}\left(\mathbf{m}\right)\right)^{\mathrm{T}} \mathbf{C}\_{D}^{-1} \left(\mathbf{d} - \mathbf{g}\left(\mathbf{m}\right)\right) + \frac{1}{2} \left(\mathbf{m} - \mathbf{m}^{0}\right)^{\mathrm{T}} \mathbf{C}\_{\mathrm{M}}^{-1} \left(\mathbf{m} - \mathbf{m}^{0}\right) \tag{7}$$

The *Maximum A Posteriori* (MAP) | *pm d* ( |) **m d** pdf corresponds to the minimum of *O* **m** , with the set of parameters, **m** that minimizes *O***m** as the most probable estimate. The HM minimization algorithm renders multiple plausible model realizations and the consequence of non-linearity is that it requires an *iterative* solution. When considering realistic field conditions, the number of parameters of the prior model expands dramatically (*i.e.,* order of 106) and computation of the prior term of the objective function becomes highly demanding and time consuming. A variety of model parameterization and reduction techniques have been implemented in HM workflows, ranging from methods based on linear expansion of weighted eigenvectors of the specific block covariance matrix **CM** (Rodriguez *et al.,* 2007; Jafarpour and McLaughlin, 2009; Le Ravalec Dupin, 2005) to methods, where expensive covariance matrix computations are avoided by generating model updates in wave-number domain (Maučec *et al.,* 2007; Jafarpour and McLaughlin, 2009; Maučec, 2010) that do not require specifying the model covariance matrix, **CM** , and performing expensive inversions.

#### **2.5.1 Sampling from the posterior distribution**

Two methods have been proposed to sample parameters of posterior distribution, for example, sequential Markov chain Monte Carlo (MCMC) algorithms (Neal, 1993) and approximate sampling methods, such as Randomized Maximum Likelihood (RML) (Kitanidis, 1995), both with some inherent deficiencies. Traditional Markov chain Monte Carlo (MCMC) methods attempt to simulate direct draws from some complex statistical distribution of interest. MCMC techniques use the previous sample values to randomly generate the next sample value in a form of a chain, where the transition probabilities between sample values are only a function of the most recent sample value. The MCMC methods arguably provide, statistically, the most rigorous and accurate basis for sampling posterior distribution and uncertainty quantification but they come at high computational costs. On the other hand, the approximate, but faster, RML methods are, in practice, applicable mostly to linear problems.

In an attempt to improve computational efficiency and mixing for the MCMC algorithm, Oliver *et al*., 1996, proposed a two-step approach in which (1) model and data variables were jointly sampled from the prior distribution and (2) the sampled model variables were calibrated to the sampled data variables, with Metropolis-Hastings sampler (Hastings, 1970) used as the acceptance test. The method works well for linear problems, though it does not hold for non-linear problems, such as HM studied here. To improve on that, Efendiev *et al.*, 2005, proposed a *rigorous* two-step MCMC approach to increase the acceptance rate and reduce the computational effort by using the sensitivities calculated from tracing streamlines (Datta-Gupta and King, 2007). When the sensitivities are known, the solution of the HM inverse problem is greatly simplified. One of the most important advantages of the streamline approach is the ability to analytically compute the sensitivity of the streamline Generalized-Travel-Time (GTT) with respect to reservoir parameters, *e.g.* porosity or permeability. The GTT is defined as an optimal time-shift *t* at each well, so as to minimize the production data misfit function *J*:

1 1 0 0

**<sup>T</sup> <sup>T</sup> 1 1 m d <sup>g</sup> m d C C <sup>g</sup> m mm mm <sup>M</sup>** (7)

The *Maximum A Posteriori* (MAP) | *pm d* ( |) **m d** pdf corresponds to the minimum of *O* **m** , with the set of parameters, **m** that minimizes *O***m** as the most probable estimate. The HM minimization algorithm renders multiple plausible model realizations and the consequence of non-linearity is that it requires an *iterative* solution. When considering realistic field conditions, the number of parameters of the prior model expands dramatically (*i.e.,* order of 106) and computation of the prior term of the objective function becomes highly demanding and time consuming. A variety of model parameterization and reduction techniques have been implemented in HM workflows, ranging from methods based on linear expansion of weighted eigenvectors of the specific block covariance matrix **CM** (Rodriguez *et al.,* 2007; Jafarpour and McLaughlin, 2009; Le Ravalec Dupin, 2005) to methods, where expensive covariance matrix computations are avoided by generating model updates in wave-number domain (Maučec *et al.,* 2007; Jafarpour and McLaughlin, 2009; Maučec, 2010) that do not require specifying the model covariance matrix, **CM** , and performing expensive inversions.

Two methods have been proposed to sample parameters of posterior distribution, for example, sequential Markov chain Monte Carlo (MCMC) algorithms (Neal, 1993) and approximate sampling methods, such as Randomized Maximum Likelihood (RML) (Kitanidis, 1995), both with some inherent deficiencies. Traditional Markov chain Monte Carlo (MCMC) methods attempt to simulate direct draws from some complex statistical distribution of interest. MCMC techniques use the previous sample values to randomly generate the next sample value in a form of a chain, where the transition probabilities between sample values are only a function of the most recent sample value. The MCMC methods arguably provide, statistically, the most rigorous and accurate basis for sampling posterior distribution and uncertainty quantification but they come at high computational costs. On the other hand, the approximate, but faster, RML methods are, in practice,

In an attempt to improve computational efficiency and mixing for the MCMC algorithm, Oliver *et al*., 1996, proposed a two-step approach in which (1) model and data variables were jointly sampled from the prior distribution and (2) the sampled model variables were calibrated to the sampled data variables, with Metropolis-Hastings sampler (Hastings, 1970) used as the acceptance test. The method works well for linear problems, though it does not hold for non-linear problems, such as HM studied here. To improve on that, Efendiev *et al.*, 2005, proposed a *rigorous* two-step MCMC approach to increase the acceptance rate and reduce the computational effort by using the sensitivities calculated from tracing streamlines (Datta-Gupta and King, 2007). When the sensitivities are known, the solution of the HM inverse problem is greatly simplified. One of the most important advantages of the streamline approach is the ability to analytically compute the sensitivity of the streamline Generalized-Travel-Time (GTT) with respect to reservoir parameters, *e.g.* porosity or

at each well, so as to minimize

where, the objective function *O***m** combines prior and likelihood terms:

*O <sup>D</sup>*

**2.5.1 Sampling from the posterior distribution** 

applicable mostly to linear problems.

the production data misfit function *J*:

permeability. The GTT is defined as an optimal time-shift *t*

2 2

$$J = \sum\_{i=1}^{Ndj} \left[ y\_j^{obs} \left( t\_i + \Delta t\_j \right) - y\_j^{cal} \left( t\_i \right) \right]^2 = f \left( \Delta t\_j \right) \tag{8}$$

where *Ndj* stands for the number of observed data (**d**) at well *j* and *obs <sup>j</sup> y* and *cal <sup>j</sup> y* correspond to observed and calculated production data, respectively, at well *j*.

Fig. 10. Illustration of Generalized Travel-Time (GTT) inversion by systematically shifting the calculated fractional flow curve *fw* to the observed history (modified from Datta-Gupta and King, 2007). Red and magenta symbols correspond to the initially-calculated and shifted curve, respectively, while the black line represents the observed curve.

This is illustrated in Fig. 10, where the calculated fractional flow response1 is systematically shifted in small-time increments towards the observed response, every data point in the fractional-flow curve has the same shift time, 1 2 *tt t* ... and the data misfit is computed for each time increment. The misfit function *J* directly corresponds to the term **d g(m)** , given in Eqs. 5 and 7 that defines the misfit between the observed data and simulated response. The objective of HM inversion workflow is to minimize the misfit in production response by reconciling the geological model with observed (measured) dynamic production data.

The two-step MCMC algorithm (Efendiev *et al.* 2005) uses an approximate likelihood calculation to improve on the (low) acceptance rate of the one-step algorithm (Ma *et al*, 2008). This approach does not compromise the rigor in traditional MCMC sampling, as it adequately samples from the posterior distribution and obeys the *detailed balance* (Maučec *et al.,* 2007), thus, a sufficient condition for a unique stationary distribution. The main steps of the streamline-based, two-step MCMC algorithm are depicted in a flowchart in Fig. 11.

A pre-screening based on approximate likelihood calculations eliminates most of the rejected samples, and the exact MCMC is performed only on the accepted proposals, with higher acceptance rate. The approximate likelihood calculations are fast and typically involve a linearized approximation around an already accepted state rather than an

<sup>1</sup> In water-injection EOR operations, the fractional flow curve frequently corresponds to water-cut curve that represents the water breakthrough at the well as a function of well production time.

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 231

In general, the real-field HM workflows can be highly computationally demanding, mostly on the account of time-consuming forward reservoir simulations. Furthermore, when the full-fledged uncertainty analysis of the high-resolution geological model is addressed through the generation of multiple (*i.e.,* sometimes in the order of 100s) static model realizations, the multi-iteration AHM workflows may become prohibitively expensive. The QuantUM AHM module addresses the issue of computational efficiency in two ways: a) takes full advantage of parallel execution of VIP® and/or Nexus® reservoir simulator, wherever multi-CPU cores are available and b) uses the option of computational load distribution via standard submission protocol wherever the multi-node computational

The proposals generated by the Metropolis-Hastings sampler of the two-step MCMC-based inversion workflow are very likely positively correlated; therefore, the convergence diagnostics ought to be governed by the estimators averaged over the ensemble of realizations. QuantUM AHM workflow implements the *maximum entropy* test (Full *et al.,* 1983), where the (negative) entropy, *S*, of the sampled stationary (posterior) distribution is defined as the expected value of the logarithms of posterior terms of the objective function, <sup>|</sup> *pm d* ( |) **m d** . Further mathematical derivations of the entropy, *S* and its variance, implemented as convergence measures in AHM workflow are given in Maučec *et al.* 2007 and Maučec *et al.* 2011a. Selected results of QuantUM AHM workflow validation are given in Fig. 12, with additional information available in (Maučec *et al.* 2011a; Maučec *et al.* 2011b): The behavior of (negative) entropy, *S* (Fig. 12a) and the objective function, defined as the logarithm of transition probability of two-step Metropolis-Hastings sampler (Fig. 12b) demonstrate the convergence rate of the MCMC sequence with the burn-in period of approximately 750 samples (*i.e.*, the total number of processed samples is 1500, a

 Comparison of dynamic well production responses, here defined as the water-cut curves, calculated with prior (Fig. 12c) and posterior (Fig. 12d) model realizations demonstrate the efficiency of water-cut misfit reduction, between the simulated and observed data. To demonstrate the case, the production response of one of the wells with the most pronounced production dynamics over the 10-year period, is depicted.

 The HM workflow demonstrates a significant reduction in the discrepancy of mean dynamic response (Fig. 12e), calculated over ensemble of 50 history-matched models with respect to observed watercut well water-cut curve as well as impressive reduction of the ensemble-averaged variance (Fig. 12f) of history-matched responses with respect

 Figs. 12g and 12h, depict log-permeability maps for one realization of top layer of Brugge fluvial reservoir, corresponding to prior (*i.e.*, initial, not history-matched) and posterior (*i.e.*, history-matched) models, respectively. The areas where the historymatching algorithm attempts to reconcile the static model with dynamic data, by connecting spatially-separated high-permeability areas to facilitate the fluid flow, as

By its nature, the probabilistic history-matching workflows use multiple equally probable but non-unique realizations of geological models that honor prior spatial constraints and

product of 50 model realizations and 30 MCMC iterations).

to observed production curves.

Such non-monotonic behavior is usually most challenging to match.

governed by the calculated streamline-sensitivities, are emphasized.

**2.6 Quantification of reservoir production forecast uncertainty** 

resources are available.

expensive computation, such as a flow simulation, using the streamline sensitivities, calculated per geomodel grid block and per production well.

Fig. 11. Flowchart of the streamline-based, two-step MCMC algorithm as implemented in AHM workflow (Maučec *et al.* 2007; Maučec *et al.* 2011a; Maučec *et al.* 2011b).

The streamline-based, two-step MCMC history-matching workflow represents an integral component of the new prototype technology for Quantitative Uncertainty Management (QuantUM) (Maučec and Cullick, 2011) that seamlessly integrates the next-generation Earth Modeling API, VIP® and/or Nexus® reservoir simulators and the code DESTINY (MCERI Research Group, 2008), used as a generator of streamline-based sensitivities. The workflow was validated by reconciling the dynamic well production data with a completely synthetic model of the Brugge field (Maučec *et al.* 2011a). The stratigraphy of Brugge field combines four different depositional environments and one internal fault with a modest throw. The dimensions of the field are roughly 10x3 km. In the original (referred to as the "truth-case") high-resolution model of 20 million grid cells essential reservoir properties, including sedimentary facies, porosity and permeability, Net-To-Gross (NTG), and water saturation were created for the purpose of generating well log curves in the 30 wells (Peters *et al.* 2009). Multiple realizations of high-resolution (211x76x56, *i.e.,* approximately 900k grid cells) of facies-constrained permeability model (referred to as "initial") were generated using the information on the structural model, well properties and depositional environments based on the "truth-case" model.

expensive computation, such as a flow simulation, using the streamline sensitivities,

**Generate model realizations**

**Calculate exact likelihood**

**Generate new proposal**

**Calculate approximate likelihood with sensitivities**

> **Proposal accepted?**

**Forward simulation (response & sensitivities)**

yes

no

no

**Calculate exact likelihood**

**Proposal accepted?**

Fig. 11. Flowchart of the streamline-based, two-step MCMC algorithm as implemented in

**Collect proposal**

yes

yes

**Promote proposal**

**Convergence achieved?**

The streamline-based, two-step MCMC history-matching workflow represents an integral component of the new prototype technology for Quantitative Uncertainty Management (QuantUM) (Maučec and Cullick, 2011) that seamlessly integrates the next-generation Earth Modeling API, VIP® and/or Nexus® reservoir simulators and the code DESTINY (MCERI Research Group, 2008), used as a generator of streamline-based sensitivities. The workflow was validated by reconciling the dynamic well production data with a completely synthetic model of the Brugge field (Maučec *et al.* 2011a). The stratigraphy of Brugge field combines four different depositional environments and one internal fault with a modest throw. The dimensions of the field are roughly 10x3 km. In the original (referred to as the "truth-case") high-resolution model of 20 million grid cells essential reservoir properties, including sedimentary facies, porosity and permeability, Net-To-Gross (NTG), and water saturation were created for the purpose of generating well log curves in the 30 wells (Peters *et al.* 2009). Multiple realizations of high-resolution (211x76x56, *i.e.,* approximately 900k grid cells) of facies-constrained permeability model (referred to as "initial") were generated using the information on the structural model, well properties and depositional environments based

AHM workflow (Maučec *et al.* 2007; Maučec *et al.* 2011a; Maučec *et al.* 2011b).

no

on the "truth-case" model.

calculated per geomodel grid block and per production well.

In general, the real-field HM workflows can be highly computationally demanding, mostly on the account of time-consuming forward reservoir simulations. Furthermore, when the full-fledged uncertainty analysis of the high-resolution geological model is addressed through the generation of multiple (*i.e.,* sometimes in the order of 100s) static model realizations, the multi-iteration AHM workflows may become prohibitively expensive. The QuantUM AHM module addresses the issue of computational efficiency in two ways: a) takes full advantage of parallel execution of VIP® and/or Nexus® reservoir simulator, wherever multi-CPU cores are available and b) uses the option of computational load distribution via standard submission protocol wherever the multi-node computational resources are available.

The proposals generated by the Metropolis-Hastings sampler of the two-step MCMC-based inversion workflow are very likely positively correlated; therefore, the convergence diagnostics ought to be governed by the estimators averaged over the ensemble of realizations. QuantUM AHM workflow implements the *maximum entropy* test (Full *et al.,* 1983), where the (negative) entropy, *S*, of the sampled stationary (posterior) distribution is defined as the expected value of the logarithms of posterior terms of the objective function, <sup>|</sup> *pm d* ( |) **m d** . Further mathematical derivations of the entropy, *S* and its variance, implemented as convergence measures in AHM workflow are given in Maučec *et al.* 2007 and Maučec *et al.* 2011a. Selected results of QuantUM AHM workflow validation are given in Fig. 12, with additional information available in (Maučec *et al.* 2011a; Maučec *et al.* 2011b):


#### **2.6 Quantification of reservoir production forecast uncertainty**

By its nature, the probabilistic history-matching workflows use multiple equally probable but non-unique realizations of geological models that honor prior spatial constraints and

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 233

simulation as a tool for pre-screening geological models (Gilman *et. al.,* 2002) or Experimental Design (ED) techniques that optimally identify values of uncertainty and their variation range (Prada *et. al.,* 2005). Unfortunately, in realistic reservoir forecasting projects, not all of the flow simulations may be necessary but the clear distinction between important and un-important parameters is unknown *a priori*. A workflow aiming to identify and isolate model realizations, relevant to reservoir forecast analysis, out of a full spectrum of statistically probable models has recently been proposed by Scheidt and Caers, 2009

 Computation of a single parameter, namely, pattern-dissimilarity distance, used to distinguish two individual model realizations in terms of dynamic performance. The objective is to identify a set of representative reservoir models through patterndissimilarity distance analysis focusing on the dynamic properties of the realizations. Computation of pattern-dissimilarity distances are computed via rapid streamline simulations carried out for each ensemble member. Analysis of pattern-distances gives rise to a set of representative models, which are then simulated using a full-physics

Derivation of the forecast uncertainty from the outcome of these intelligently selected

To describe the degree of (dis)similarity between reservoir model realizations in an ensemble it is not required to identify individual reservoir characteristics and corresponding dynamic responses for each ensemble member as knowledge about a representative "difference" (hereafter referred to as "distance") between any two realizations is sufficient. An example of pattern-dissimilarity distance *θ*, defined as an Euclidean measure, that describes the degree of (dis)similarity between any two of reservoir realizations **m** indexed with *k* and *l* within an ensemble of size *I*, in terms of geologic characteristics and pertinent

1

Multi-dimensional scaling (MDS) is used to translate the pattern-dissimilarity matrix models into a *p*-dimensional Euclidean space (Borg and Groenen, 2005) where each element of the matrix is represented with a unique point. Hereafter, Euclidean space will be simply referred to as the *E* space, with individual points arranged in such a way that their distances correspond in a least-squares sense to the dissimilarities of individual realizations. Euclidean distances tend to exhibit strong correlation with pattern-dissimilarity distances.

*I kl ki li i*

 *r r* 

where, by definition, the pattern-dissimilarity distance honors self-similarity ( 0 *kk*

2

). Pattern-dissimilarity distances are evaluated using rapid streamline

(9)

*kl* , where *IxI* **Θ** .

) and

( )

Further details are available in (Scheidt and Caers, 2009; Maučec *et al.,* 2011b).

combining the following steps (Fig. 13):

finite-difference simulator.

few full-physics simulations.

symmetry ( *kl lk* 

**2.6.1 The concept of dynamic data (dis)similarity** 

dynamic response, *kl r* , *i.e.* recovery factor, oil production rate, *etc.*

simulation, and assembled into a pattern-dissimilarity matrix, **Θ**

**2.6.2 Multi dimensional scaling and cluster analysis** 

Fig. 12. Validation of QuantUM AHM workflow with dynamic inversion of Brugge synthetic model (Peters *et al.* 2009): a) and b) algorithm convergence diagnostics, (negative) entropy and objective function, respectively, c) and d) well water-cut response curves, obtained with an ensemble of prior and posterior models, respectively, e) and f) ensembleaveraged statistical estimators, mean and variance, respectively and g) and h) prior and posterior log-permeability distribution maps of model top layer, respectively

are conditioned to the data as well as approximate the forecast uncertainty. But the crux of the matter here is two-fold: a) throughout the inversion, some model realizations may have created non-geologically realistic features and b) many of the underlying geological parameters may have an insignificant effect on recovery performance.

In addition to the traditional, single-parameter sensitivity studies to identify the important and geologically relevant parameters, a more sophisticated version uses streamline

Fig. 12. Validation of QuantUM AHM workflow with dynamic inversion of Brugge

posterior log-permeability distribution maps of model top layer, respectively

parameters may have an insignificant effect on recovery performance.

synthetic model (Peters *et al.* 2009): a) and b) algorithm convergence diagnostics, (negative) entropy and objective function, respectively, c) and d) well water-cut response curves, obtained with an ensemble of prior and posterior models, respectively, e) and f) ensembleaveraged statistical estimators, mean and variance, respectively and g) and h) prior and

are conditioned to the data as well as approximate the forecast uncertainty. But the crux of the matter here is two-fold: a) throughout the inversion, some model realizations may have created non-geologically realistic features and b) many of the underlying geological

In addition to the traditional, single-parameter sensitivity studies to identify the important and geologically relevant parameters, a more sophisticated version uses streamline simulation as a tool for pre-screening geological models (Gilman *et. al.,* 2002) or Experimental Design (ED) techniques that optimally identify values of uncertainty and their variation range (Prada *et. al.,* 2005). Unfortunately, in realistic reservoir forecasting projects, not all of the flow simulations may be necessary but the clear distinction between important and un-important parameters is unknown *a priori*. A workflow aiming to identify and isolate model realizations, relevant to reservoir forecast analysis, out of a full spectrum of statistically probable models has recently been proposed by Scheidt and Caers, 2009 combining the following steps (Fig. 13):


Further details are available in (Scheidt and Caers, 2009; Maučec *et al.,* 2011b).

#### **2.6.1 The concept of dynamic data (dis)similarity**

To describe the degree of (dis)similarity between reservoir model realizations in an ensemble it is not required to identify individual reservoir characteristics and corresponding dynamic responses for each ensemble member as knowledge about a representative "difference" (hereafter referred to as "distance") between any two realizations is sufficient. An example of pattern-dissimilarity distance *θ*, defined as an Euclidean measure, that describes the degree of (dis)similarity between any two of reservoir realizations **m** indexed with *k* and *l* within an ensemble of size *I*, in terms of geologic characteristics and pertinent dynamic response, *kl r* , *i.e.* recovery factor, oil production rate, *etc.*

$$\theta\_{kl} = \sqrt{\sum\_{i=1}^{l} \left(\tilde{r}\_{ki} - \tilde{r}\_{li}\right)^2} \tag{9}$$

where, by definition, the pattern-dissimilarity distance honors self-similarity ( 0 *kk* ) and symmetry ( *kl lk* ). Pattern-dissimilarity distances are evaluated using rapid streamline simulation, and assembled into a pattern-dissimilarity matrix, **Θ** *kl* , where *IxI* **Θ** .

#### **2.6.2 Multi dimensional scaling and cluster analysis**

Multi-dimensional scaling (MDS) is used to translate the pattern-dissimilarity matrix models into a *p*-dimensional Euclidean space (Borg and Groenen, 2005) where each element of the matrix is represented with a unique point. Hereafter, Euclidean space will be simply referred to as the *E* space, with individual points arranged in such a way that their distances correspond in a least-squares sense to the dissimilarities of individual realizations. Euclidean distances tend to exhibit strong correlation with pattern-dissimilarity distances.

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 235

cluster-centroids are selected as the "representative samples" of the entire uncertainty space and simulated with the full-physics simulator as the reference case. Simulation outcome is post-processed to compute the distribution of ultimate recovery factor (URF) after a lengthy period of production, usually selected as the target forecast uncertainty for quantification. The cumulative density functions (CDFs) are finally constructed for the selected model realizations with weights assigned to URFs based on the number of models in each particular cluster and finally quantitatively compared to the reference CDF derived from

Reservoir characterization encompasses techniques and methods that improve understanding of geological petrophysical controls on a reservoir fluid flow. Presence of a large number of geological uncertainties and limited well data often render recovery forecasting a difficult task in typical appraisal and early development settings. Moreover, in geologically-complex, heavily faulted reservoirs, quantification of the effect of stratigraphic and structural uncertainties on the dynamic performance, fluid mobility and *in situ* hydrocarbons is of principal importance. Although the generation of a sound structural framework is one of the major contributors to uncertainty in hydrocarbons volumes, and therefore risk, in reservoir characterization it often represents a compromise between the actual structure and what the modern modeling technology allows (Hoffman *et al.*, 2007). In this paper we focus on some of the outstanding features that have the potential to significantly differentiate the DecisionSpace Desktop Earth Modeling, as the nextgeneration geological modeling technology, from standard industrial approaches and workflows mainly in the areas of geologically-driven facies modeling, reservoir property modeling in grid-less modality and the state-of-the-art workflows for dynamic quantitative uncertainty and risk management throughout the asset lifecycle. The facies simulation workflow utilizes a powerful combination of describing the spatial geological trends with lithotype proportion curves and matrices, integrated with Plurigaussian simulation (PGS), a robust and widely-tested algorithm with long industrial history. While the implementation of PGS is not unique to DecisionSpace Desktop Earth Modeling its geologically highly intuitive approach to modeling, based on understanding of realistic depositional environments puts the geologist back into the driver's seat. However, even the most recent advances in geomodeling practice that represents 3D reservoir volumes with highresolution geocellular grids may only mitigate but not eliminate the fact that estimating gridding parameters commonly results in artifacts due to topological constraints and misrepresentation of important aspects of the structural framework, which may introduce substantial difficulties for dynamic reservoir simulator later in the workflow. Hence we look into the future of building geological models and present and validate the evolving technology, with the truly game-changing industrial potential to utilize Maximum Continuity Fields for 3D reservoir property interpolation, performed in the absence of a geocellular grid. The selection of optimal geocellular parameters with attributes like cell size, number of cells and layering, is postponed throughout the process and rendered at

. The geological realizations, corresponding to identified

Eq. 9 as <sup>2</sup> ( ) *kl k l t T*

 *RF RF* 

full-physics simulations.

**3. Discussion and conclusions** 

Fig. 13. Workflow diagram using Multi Dimensional Scaling (MDS), k-PCA and k-means clustering (modified from Scheidt and Caers, 2009 for three model realizations).

The workflow of Scheidt and Caers, 2009 incorporates a classical variant of metric MDS where intervals and ratios between points are preserved in a manner of highest fidelity and where it is assumed that the pattern-dissimilarity distances directly correspond to distances in the *E* space. MDS finds the appropriate coordinates consistent with Euclidean distance measure and the resulting map is governed exclusively by the pattern-dissimilarity distances. Subject to the condition, that the distances are strongly correlated with the dynamic response *r* , points within close proximity of each other exhibit similar recovery characteristics, and hence, they are expected to contain similar geologic features. A clustering algorithm is used to compartmentalize the Euclidean space into few distinct clusters and to identify the realizations within the closest proximity of the cluster centroids. The characteristic nonlinear structure of points in the *E* calls for kernel techniques such as kernel Principal Component Analysis (k-PCA) (Schölkopf *et al.,* 1996), where prior to clustering nonlinear domains are mapped into a linear domain. When the MDS data are mapped into a linear, high-dimensional feature domain *F*, using appropriate kernel method *e.g.* k-PCA, cluster analysis, such as *k-*means clustering (Tabachnick and Fidell, 2006) may be applied to further compartmentalize the feature space F in order to identify cluster centroids, where centroid of a cluster corresponds to a point whose parameter values are the mean of the parameter values of all the points in the clusters. The pattern-dissimilarity distances θ, closest to the cluster centroids in the Euclidean space are defined with respect to recovery factor (RF) responses of two individual realizations *k* and *l* at times *t T*, following

$$\text{Eq. 9 as } \quad \theta\_{kl} = \sqrt{\sum\_{l \in T} (\text{RF}\_k - \text{RF}\_l)^2}. \text{ The geological realizations, corresponding to identified } k \text{ are } \quad \theta\_{kl} = \sqrt{\sum\_{l \in T} (\text{RF}\_l - \text{RF}\_l)^2}. \text{ The same result follows from the following:}$$

cluster-centroids are selected as the "representative samples" of the entire uncertainty space and simulated with the full-physics simulator as the reference case. Simulation outcome is post-processed to compute the distribution of ultimate recovery factor (URF) after a lengthy period of production, usually selected as the target forecast uncertainty for quantification. The cumulative density functions (CDFs) are finally constructed for the selected model realizations with weights assigned to URFs based on the number of models in each particular cluster and finally quantitatively compared to the reference CDF derived from full-physics simulations.

#### **3. Discussion and conclusions**

234 Advances in Data, Methods, Models and Their Applications in Geoscience

MDS

Dissimilarity-distance matrix

Dissimilarity matrix

**1**

Fast streamline simulations on reconciled models

12

**3 2**

**Cumulative density**

RFP10 RFP50 RFP90

23

13

Fig. 13. Workflow diagram using Multi Dimensional Scaling (MDS), k-PCA and k-means

The workflow of Scheidt and Caers, 2009 incorporates a classical variant of metric MDS where intervals and ratios between points are preserved in a manner of highest fidelity and where it is assumed that the pattern-dissimilarity distances directly correspond to distances in the *E* space. MDS finds the appropriate coordinates consistent with Euclidean distance measure and the resulting map is governed exclusively by the pattern-dissimilarity distances. Subject to the condition, that the distances are strongly correlated with the dynamic response *r* , points within close proximity of each other exhibit similar recovery characteristics, and hence, they are expected to contain similar geologic features. A clustering algorithm is used to compartmentalize the Euclidean space into few distinct clusters and to identify the realizations within the closest proximity of the cluster centroids. The characteristic nonlinear structure of points in the *E* calls for kernel techniques such as kernel Principal Component Analysis (k-PCA) (Schölkopf *et al.,* 1996), where prior to clustering nonlinear domains are mapped into a linear domain. When the MDS data are mapped into a linear, high-dimensional feature domain *F*, using appropriate kernel method *e.g.* k-PCA, cluster analysis, such as *k-*means clustering (Tabachnick and Fidell, 2006) may be applied to further compartmentalize the feature space F in order to identify cluster centroids, where centroid of a cluster corresponds to a point whose parameter values are the mean of the parameter values of all the points in the clusters. The pattern-dissimilarity distances θ, closest to the cluster centroids in the Euclidean space are defined with respect to

= simulated model (closest to the cluster centroids)

clustering (modified from Scheidt and Caers, 2009 for three model realizations).

Full-physics simulation

recovery factor (RF) responses of two individual realizations *k* and *l* at times *t* 

 *T*, following

*E*

Kernel PCA

Non-linear Euclidean domain

> Linear Feature domain

*E F*

Clustering and pre-image construction

Reservoir characterization encompasses techniques and methods that improve understanding of geological petrophysical controls on a reservoir fluid flow. Presence of a large number of geological uncertainties and limited well data often render recovery forecasting a difficult task in typical appraisal and early development settings. Moreover, in geologically-complex, heavily faulted reservoirs, quantification of the effect of stratigraphic and structural uncertainties on the dynamic performance, fluid mobility and *in situ* hydrocarbons is of principal importance. Although the generation of a sound structural framework is one of the major contributors to uncertainty in hydrocarbons volumes, and therefore risk, in reservoir characterization it often represents a compromise between the actual structure and what the modern modeling technology allows (Hoffman *et al.*, 2007).

In this paper we focus on some of the outstanding features that have the potential to significantly differentiate the DecisionSpace Desktop Earth Modeling, as the nextgeneration geological modeling technology, from standard industrial approaches and workflows mainly in the areas of geologically-driven facies modeling, reservoir property modeling in grid-less modality and the state-of-the-art workflows for dynamic quantitative uncertainty and risk management throughout the asset lifecycle. The facies simulation workflow utilizes a powerful combination of describing the spatial geological trends with lithotype proportion curves and matrices, integrated with Plurigaussian simulation (PGS), a robust and widely-tested algorithm with long industrial history. While the implementation of PGS is not unique to DecisionSpace Desktop Earth Modeling its geologically highly intuitive approach to modeling, based on understanding of realistic depositional environments puts the geologist back into the driver's seat. However, even the most recent advances in geomodeling practice that represents 3D reservoir volumes with highresolution geocellular grids may only mitigate but not eliminate the fact that estimating gridding parameters commonly results in artifacts due to topological constraints and misrepresentation of important aspects of the structural framework, which may introduce substantial difficulties for dynamic reservoir simulator later in the workflow. Hence we look into the future of building geological models and present and validate the evolving technology, with the truly game-changing industrial potential to utilize Maximum Continuity Fields for 3D reservoir property interpolation, performed in the absence of a geocellular grid. The selection of optimal geocellular parameters with attributes like cell size, number of cells and layering, is postponed throughout the process and rendered at

Next Generation Geological Modeling for Hydrocarbon Reservoir Characterization 237

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user's discretion only before incorporation into the reservoir simulator. Models, generated in such fashion, retain the maximum available resolution and information density, limited only by the resolution of underlying data and structural continuity.

Regardless of the modeling approach, geoscientists and engineers often select diverse geomodel realizations such that the reservoir simulation outcome will cover a sufficiently large range of uncertainty to approximate the reservoir recovery forecast statistics throughout the asset lifecycle. One of the differentiating attributes of next-generation reservoir characterization is to integrate the reconciliation of geomodels with wellproduction and seismic data, with dynamic ranking and selection of representative model realizations for reservoir production forecasting. We outline and validate the evolving technology for Quantitative Uncertainty Management that seamlessly interfaces the DecisionSpace Desktop, VIP® and/or Nexus® reservoir simulators. The highest available adherence to geological detail with respect to structural features that control depositional continuity (*e.g.* facies) is maintained through implementation of advanced model parameterization, based on Discrete Cosine Transform (Rao and Yip, 1990), an industrial standard in image compression. The AHM algorithm utilizes a highly efficient derivative of sequential (Markov chain) Monte Carlo sampling, where the acceptance rate is increased and computational effort reduced, by the utilization of streamline-based sensitivities.

By its nature, the probabilistic HM workflows render multiple equally probable but nonunique realizations of geological models that honor both, prior constraints and production data, with associated uncertainty. Throughout the inversion, however, some model realizations may have created non-geologically realistic features and these models are inadequate for forecasting of recovery performance. We outline the workflow for dynamic quantification production uncertainty that utilizes rapid streamline simulations to calculate data-pattern dissimilarities, Multi Dimensional Scaling to correlate dynamic model responses with pattern dissimilarities and kernel-based clustering methods to intelligently identification and ranking of geo-models, representative in forecasting decisions. When integrated into the DecisionSpace Desktop suite of reservoir characterization tools, such technology will assist in Smart Reservoir Management and decision making by combining multiple types and scales of data, honoring most first order effects, capturing a full range of outcomes and reducing analysis and decision time.

#### **4. Acknowledgement**

The authors would like to acknowledge Halliburton/Landmark for the permission to publish this text.

#### **5. References**


user's discretion only before incorporation into the reservoir simulator. Models, generated in such fashion, retain the maximum available resolution and information density, limited

Regardless of the modeling approach, geoscientists and engineers often select diverse geomodel realizations such that the reservoir simulation outcome will cover a sufficiently large range of uncertainty to approximate the reservoir recovery forecast statistics throughout the asset lifecycle. One of the differentiating attributes of next-generation reservoir characterization is to integrate the reconciliation of geomodels with wellproduction and seismic data, with dynamic ranking and selection of representative model realizations for reservoir production forecasting. We outline and validate the evolving technology for Quantitative Uncertainty Management that seamlessly interfaces the DecisionSpace Desktop, VIP® and/or Nexus® reservoir simulators. The highest available adherence to geological detail with respect to structural features that control depositional continuity (*e.g.* facies) is maintained through implementation of advanced model parameterization, based on Discrete Cosine Transform (Rao and Yip, 1990), an industrial standard in image compression. The AHM algorithm utilizes a highly efficient derivative of sequential (Markov chain) Monte Carlo sampling, where the acceptance rate is increased

and computational effort reduced, by the utilization of streamline-based sensitivities. By its nature, the probabilistic HM workflows render multiple equally probable but nonunique realizations of geological models that honor both, prior constraints and production data, with associated uncertainty. Throughout the inversion, however, some model realizations may have created non-geologically realistic features and these models are inadequate for forecasting of recovery performance. We outline the workflow for dynamic quantification production uncertainty that utilizes rapid streamline simulations to calculate data-pattern dissimilarities, Multi Dimensional Scaling to correlate dynamic model responses with pattern dissimilarities and kernel-based clustering methods to intelligently identification and ranking of geo-models, representative in forecasting decisions. When integrated into the DecisionSpace Desktop suite of reservoir characterization tools, such technology will assist in Smart Reservoir Management and decision making by combining multiple types and scales of data, honoring most first order effects, capturing a full range of

The authors would like to acknowledge Halliburton/Landmark for the permission to

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publish this text.

**5. References** 

only by the resolution of underlying data and structural continuity.


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**12** 

*Tanzania* 

**Developing Sediment Yield** 

**Catchments in Tanzania** 

Preksedis Marco Ndomba *University of Dar es Salaam,* 

**Prediction Equations for Small** 

Sediment yield refers to the amount of sediment exported by a basin over a period of time, which is also the amount which will enter a reservoir or pond located at the downstream limit of the basin (Morris and Fan, 1998). Estimate of long-term sediment yield have been used for many decades to size the sediment storage pool and estimate reservoir life. However, these estimates are often inaccurate especially for small catchments. Besides, it is known from literature that long term period sampling programmes are required to capture the high variability of sediment fluxes in these catchments (Horowitz, 2004; Thodsen *et al*., 2004). The correlation of sediment yields to erosion is complicated by problem of determining the sediment delivery ratio, which makes it difficult to estimate the sediment load entering a reservoir/pond on the basis of erosion rate within the catchment (Morris and Fan, 1998). Sediment yield from the dam catchment is one of the parameters controlling sedimentation of small dams. This has to be estimated if future sedimentation rates in a dam

Non Governmental Organizations (NGOs) and Government Agencies (GAs) have constructed thousands of small dams in semi-arid regions of East and Southern Africa including Tanzania to provide water for livestock and small-scale irrigation (Lawrence *et al*, 2004; Faraji, 1995). In Tanzania, in particular, at present it is not known whether the original storage capacities of these dams still exist as a result of many years of operations. Besides, irrigation/water supply schemes ponds/reservoirs are normally draining small catchments. Most of the small catchments are characterized as ungauged. The effective life of many of these dams is reduced by excessive siltation – some small dams silt up after only 2 years. This issue is poorly covered in the many small dam design manuals that are available, which mostly focus on civil engineering design and construction aspects. While a capability to estimate future siltation is needed to ensure that dams are sized correctly, and are not constructed in catchments with very high sediment yields, little guidance is available to small dam planners and designers (Lawrence *et al*, 2004). Therefore, prediction of sediment yields from catchments is very important where water resources sedimentation is a serious

problem like Tanzania and construction of dams is needed (Mulengera, 2008).

These studies were selected in order to cover a wide range of study methods.

This chapter discusses also the findings of a few previous representative and related research works in Tanzania and the region at large as this study is a follow up research.

**1. Introduction** 

are to be predicted.

Yarus, J.M., Srivastava, R.M., Gehin, M. & Chambers, R.L. (2009). Distribution of properties in a 3D volumetric model using a maximum continuity field, PCT Patent, WO 2009/151441 A1.

## **Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania**

Preksedis Marco Ndomba *University of Dar es Salaam, Tanzania* 

#### **1. Introduction**

240 Advances in Data, Methods, Models and Their Applications in Geoscience

Yarus, J.M., Srivastava, R.M., Gehin, M. & Chambers, R.L. (2009). Distribution of properties

2009/151441 A1.

in a 3D volumetric model using a maximum continuity field, PCT Patent, WO

Sediment yield refers to the amount of sediment exported by a basin over a period of time, which is also the amount which will enter a reservoir or pond located at the downstream limit of the basin (Morris and Fan, 1998). Estimate of long-term sediment yield have been used for many decades to size the sediment storage pool and estimate reservoir life. However, these estimates are often inaccurate especially for small catchments. Besides, it is known from literature that long term period sampling programmes are required to capture the high variability of sediment fluxes in these catchments (Horowitz, 2004; Thodsen *et al*., 2004). The correlation of sediment yields to erosion is complicated by problem of determining the sediment delivery ratio, which makes it difficult to estimate the sediment load entering a reservoir/pond on the basis of erosion rate within the catchment (Morris and Fan, 1998). Sediment yield from the dam catchment is one of the parameters controlling sedimentation of small dams. This has to be estimated if future sedimentation rates in a dam are to be predicted.

Non Governmental Organizations (NGOs) and Government Agencies (GAs) have constructed thousands of small dams in semi-arid regions of East and Southern Africa including Tanzania to provide water for livestock and small-scale irrigation (Lawrence *et al*, 2004; Faraji, 1995). In Tanzania, in particular, at present it is not known whether the original storage capacities of these dams still exist as a result of many years of operations. Besides, irrigation/water supply schemes ponds/reservoirs are normally draining small catchments. Most of the small catchments are characterized as ungauged. The effective life of many of these dams is reduced by excessive siltation – some small dams silt up after only 2 years. This issue is poorly covered in the many small dam design manuals that are available, which mostly focus on civil engineering design and construction aspects. While a capability to estimate future siltation is needed to ensure that dams are sized correctly, and are not constructed in catchments with very high sediment yields, little guidance is available to small dam planners and designers (Lawrence *et al*, 2004). Therefore, prediction of sediment yields from catchments is very important where water resources sedimentation is a serious problem like Tanzania and construction of dams is needed (Mulengera, 2008).

This chapter discusses also the findings of a few previous representative and related research works in Tanzania and the region at large as this study is a follow up research. These studies were selected in order to cover a wide range of study methods.

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 243

Mtalo and Ndomba (2002) have reported alarming high rate of soil erosion of up to 2,400 t/km2/yr or 24 t/ha-yr in the upstream of Pangani river basin covering parts of Arusha, Kilimanjaro and Tanga regions (Fig. 2.1). Mtalo and Ndomba used USLE equation to map and estimate on site potential soil loss. In the basin high erosion rates can be measured in different perspectives such as increased agricultural and other human activities. For instance, in Arumeru district, which is one of the districts in the Arusha region, soil erosion is one of the major obstacles to increasing or sustaining the agriculture production. The whole district is affected by soil erosion, but the reasons differ from place to place. The amount of livestock in the district is considered to be far above the carrying capacity of the present land area devoted to grazing. Agricultural activities are a contributing factor to increased soil erosion rates in the Pangani basin upstream of Nyumba Ya Mungu reservoir

Of recent, there have been attempts to apply complex distributed, physics-based sediment yield models such as Soil and Water Assessment Tool (SWAT) for poor data large catchments, Kagera, Simiyu and upstream part of Pangani River catchment, in Kagera, Mwanza and Arusha/Kilimanjaro regions, respectively, in Tanzania. SWAT model uses the Modified Universal Soil Loss Equation (MUSLE) to estimate sediment yield (Arnold *et al*., 1995). The model operates at daily time step with output frequency of up to month/annual. However, in order to adopt the model for general applications in watershed management studies, researchers recommended for SWAT model improvements (Ndomba *et al*., 2005;

One would note that most of the previous sediment yield estimates studies in Tanzania and the region at large were catchment specific. The results could not be transferred easily to other hydrologic similar catchments (Rapp *et al*., 1972; Mulengera and Payton, 1999; Mulengera, 2008; Ndomba, 2007, 2010). In order to estimate catchment yield researchers were forced to use uncertain factor such as sediment delivery ratio (Ndomba *et al*., 2009). In some studies attempts were made to develop only a simple procedure which would distinguish between dams that will silt up rapidly from dams that will have a sedimentation lifetime well in excess of twenty years (Lawrence *et al*, 2004). The estimation tools used were either complex for operational and wider application or data intensive (Ndomba *et al*. 2008). In some cases due to limitation in data the developed Sediment yield predictive tools could not be validated (Rapp *et al*., 1972; Lawrence *et al*, 2004). As acknowledged by Faraji (1995) and others, at present, there is very scanty knowledge about reservoir sedimentation in Tanzania. Previous studies were done on few reservoirs/dams. The studies gave some guidelines on the rate of sedimentation of the respective areas (Rapp *et al*., 1972). However, this knowledge should be backed with further extensive surveys and resurveys to get improved relationships. Critical tools in this context include sediment yield and/or reservoir life estimation. The country has limited resources in terms of funding and human capital for developing the planning tools (Mulengera, 2008). The latter problem might be

Based on the discussions above and literature, generally, sediment yield models may vary greatly in complexity from simple regression relationships linking annual sediment yields to climatic physiographic variable such as regional regression relationships to complex distributed simulation model (Garde and Ranga Raju, 2000). Modelling as one of the approaches for estimating catchment sediment yields, if properly applied, can provide information on both the type of erosion and its spatial distribution across the catchment. Sediment mobilized by sheet and rill erosion may be deposited by a variety of mechanisms

(Mtalo and Ndomba, 2002).

Ndomba *et al.*, 2008).

common to most of the developing countries.

Christiansson (1981) made detailed recording of the soil erosion complex within five selected catchments in Dodoma, the semi-arid savannah areas of central Tanzania, 4 of which with reservoirs (Fig. 2.1). The principal methods employed include field surveying and air photo interpretation. The main approach was physical geographical aiming at studying the existing features of soil erosion and sedimentation and analysis of the underlying causes of the processes. Christiansson (1981) estimated sediment yields of 260 – 900 t/km2/yr or 2.6 – 9 t/ha/yr as averages for the longest periods of available records. Although, Christiansson asserted that the estimated sediment yields from his study were of the same order of magnitude as those recorded in similar environments in other parts of East Africa, the scope of the study was limited in-terms of spatial and climate representation.

Mulengera and Payton (1999) in their review of the soil loss estimation equations noted that most of the countries in the tropics have no appropriate and accurate soil erosion prediction equations, although the Soil Loss Estimation Model for Southern Africa (SLEMSA) and the Universal Soil Loss Equation (USLE) are used in different tropical countries. The SLEMSA( developed in Zimbabwe) still needs some modifications and has, so far, not been widely used or tested outside Zimbabwe and in some instances have shown to give unrealistic soil loss values (Mulengera and Payton,1999). The USLE (developed in the USA) and widely used throughout the world has in most cases been found to be inapplicable in the tropics. This is due to the fact that the equation's soil erodibility nomograph commonly gives unrealistic values for tropical soils. Although derivation of the erodibility equations for the tropical soils have shown that soil erodibility is strongly related to texture-related soil characteristics as has been shown for soils in temperate regions, there are differences in the magnitudes of the characteristics for soils with relatively similar erodibility values in both regions (Mulengera and Payton, 1999). This is due to differences in clay, silt, and sand fractions of the soils and possibly rainfall characteristics found in the two regions. While soils in the temperate region have all the three fractions well distributed, soils in the tropics are mainly composed of clay and (or) sand fractions with a relatively small fraction of silt content (Mulengera and Payton, 1999). So Mulengera and Payton concluded that it is impossible to develop one universal soil erodibility equation. Therefore, the prediction of soil erosion in the tropics using the USLE or its revised version (RUSLE), had been hampered by the common inapplicability of the soil erodibilty nomograph for tropical soils. Furthermore, the table values developed in the U.S.A. for estimating the crop and soil management factor of the equation are not applicable for farming practices and conditions found in the tropics (Mulengera and Payton, 1999). However, some recent studies have shown that it can give good results, especially, when its recent version, the Modified Universal Soil Loss Equation (MUSLE) is used (Ndomba, 2007).

Mulengera and Payton (1999) presented an equation for estimating the USLE -Soil erodibility factor, which resulted from a wider research programme initiated to identify a suitable soil loss prediction equation for use under Tanzanian conditions. The derived equation based on soil texture-related parameters which is technically accurate (i.e. explaining about 84 % of the erodibility variations) for estimating the erodibility factor of the ( R )USLE in the tropics for soils whose physical and chemical characteristics are similar to the soils used in the derivation. The equation is useful for soil conservation planning in these areas currently suffering from severe soil erosion (Mulengera and Payton, 1999). The equation was successfully used by Mtalo and Ndomba (2002) in Pangani basin, in the Northeastern part of Tanzania.

Christiansson (1981) made detailed recording of the soil erosion complex within five selected catchments in Dodoma, the semi-arid savannah areas of central Tanzania, 4 of which with reservoirs (Fig. 2.1). The principal methods employed include field surveying and air photo interpretation. The main approach was physical geographical aiming at studying the existing features of soil erosion and sedimentation and analysis of the underlying causes of the processes. Christiansson (1981) estimated sediment yields of 260 – 900 t/km2/yr or 2.6 – 9 t/ha/yr as averages for the longest periods of available records. Although, Christiansson asserted that the estimated sediment yields from his study were of the same order of magnitude as those recorded in similar environments in other parts of East Africa, the scope of the study was limited in-terms of spatial and climate

Mulengera and Payton (1999) in their review of the soil loss estimation equations noted that most of the countries in the tropics have no appropriate and accurate soil erosion prediction equations, although the Soil Loss Estimation Model for Southern Africa (SLEMSA) and the Universal Soil Loss Equation (USLE) are used in different tropical countries. The SLEMSA( developed in Zimbabwe) still needs some modifications and has, so far, not been widely used or tested outside Zimbabwe and in some instances have shown to give unrealistic soil loss values (Mulengera and Payton,1999). The USLE (developed in the USA) and widely used throughout the world has in most cases been found to be inapplicable in the tropics. This is due to the fact that the equation's soil erodibility nomograph commonly gives unrealistic values for tropical soils. Although derivation of the erodibility equations for the tropical soils have shown that soil erodibility is strongly related to texture-related soil characteristics as has been shown for soils in temperate regions, there are differences in the magnitudes of the characteristics for soils with relatively similar erodibility values in both regions (Mulengera and Payton, 1999). This is due to differences in clay, silt, and sand fractions of the soils and possibly rainfall characteristics found in the two regions. While soils in the temperate region have all the three fractions well distributed, soils in the tropics are mainly composed of clay and (or) sand fractions with a relatively small fraction of silt content (Mulengera and Payton, 1999). So Mulengera and Payton concluded that it is impossible to develop one universal soil erodibility equation. Therefore, the prediction of soil erosion in the tropics using the USLE or its revised version (RUSLE), had been hampered by the common inapplicability of the soil erodibilty nomograph for tropical soils. Furthermore, the table values developed in the U.S.A. for estimating the crop and soil management factor of the equation are not applicable for farming practices and conditions found in the tropics (Mulengera and Payton, 1999). However, some recent studies have shown that it can give good results, especially, when its recent version, the Modified

Mulengera and Payton (1999) presented an equation for estimating the USLE -Soil erodibility factor, which resulted from a wider research programme initiated to identify a suitable soil loss prediction equation for use under Tanzanian conditions. The derived equation based on soil texture-related parameters which is technically accurate (i.e. explaining about 84 % of the erodibility variations) for estimating the erodibility factor of the ( R )USLE in the tropics for soils whose physical and chemical characteristics are similar to the soils used in the derivation. The equation is useful for soil conservation planning in these areas currently suffering from severe soil erosion (Mulengera and Payton, 1999). The equation was successfully used by Mtalo and Ndomba (2002) in Pangani basin, in the North-

Universal Soil Loss Equation (MUSLE) is used (Ndomba, 2007).

eastern part of Tanzania.

representation.

Mtalo and Ndomba (2002) have reported alarming high rate of soil erosion of up to 2,400 t/km2/yr or 24 t/ha-yr in the upstream of Pangani river basin covering parts of Arusha, Kilimanjaro and Tanga regions (Fig. 2.1). Mtalo and Ndomba used USLE equation to map and estimate on site potential soil loss. In the basin high erosion rates can be measured in different perspectives such as increased agricultural and other human activities. For instance, in Arumeru district, which is one of the districts in the Arusha region, soil erosion is one of the major obstacles to increasing or sustaining the agriculture production. The whole district is affected by soil erosion, but the reasons differ from place to place. The amount of livestock in the district is considered to be far above the carrying capacity of the present land area devoted to grazing. Agricultural activities are a contributing factor to increased soil erosion rates in the Pangani basin upstream of Nyumba Ya Mungu reservoir (Mtalo and Ndomba, 2002).

Of recent, there have been attempts to apply complex distributed, physics-based sediment yield models such as Soil and Water Assessment Tool (SWAT) for poor data large catchments, Kagera, Simiyu and upstream part of Pangani River catchment, in Kagera, Mwanza and Arusha/Kilimanjaro regions, respectively, in Tanzania. SWAT model uses the Modified Universal Soil Loss Equation (MUSLE) to estimate sediment yield (Arnold *et al*., 1995). The model operates at daily time step with output frequency of up to month/annual. However, in order to adopt the model for general applications in watershed management studies, researchers recommended for SWAT model improvements (Ndomba *et al*., 2005; Ndomba *et al.*, 2008).

One would note that most of the previous sediment yield estimates studies in Tanzania and the region at large were catchment specific. The results could not be transferred easily to other hydrologic similar catchments (Rapp *et al*., 1972; Mulengera and Payton, 1999; Mulengera, 2008; Ndomba, 2007, 2010). In order to estimate catchment yield researchers were forced to use uncertain factor such as sediment delivery ratio (Ndomba *et al*., 2009). In some studies attempts were made to develop only a simple procedure which would distinguish between dams that will silt up rapidly from dams that will have a sedimentation lifetime well in excess of twenty years (Lawrence *et al*, 2004). The estimation tools used were either complex for operational and wider application or data intensive (Ndomba *et al*. 2008). In some cases due to limitation in data the developed Sediment yield predictive tools could not be validated (Rapp *et al*., 1972; Lawrence *et al*, 2004). As acknowledged by Faraji (1995) and others, at present, there is very scanty knowledge about reservoir sedimentation in Tanzania. Previous studies were done on few reservoirs/dams. The studies gave some guidelines on the rate of sedimentation of the respective areas (Rapp *et al*., 1972). However, this knowledge should be backed with further extensive surveys and resurveys to get improved relationships. Critical tools in this context include sediment yield and/or reservoir life estimation. The country has limited resources in terms of funding and human capital for developing the planning tools (Mulengera, 2008). The latter problem might be common to most of the developing countries.

Based on the discussions above and literature, generally, sediment yield models may vary greatly in complexity from simple regression relationships linking annual sediment yields to climatic physiographic variable such as regional regression relationships to complex distributed simulation model (Garde and Ranga Raju, 2000). Modelling as one of the approaches for estimating catchment sediment yields, if properly applied, can provide information on both the type of erosion and its spatial distribution across the catchment. Sediment mobilized by sheet and rill erosion may be deposited by a variety of mechanisms

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 245

The study area, Tanzania, is situated in East Africa just south of the equator (Fig. 2.1). Tanzania lies between the area of the great Lakes—Victoria, Tanganyika, and Nyasa—and the Indian Ocean. It contains a total area of 945,087 km2, including 59,050 km2 of inland water (Fig. 2.1). It is bounded on the North by Uganda and Kenya, on the East by the Indian Ocean, on the South by Mozambique and Malawi, on the South West by Zambia, and on the West by Democratic Republic of Congo, Burundi, and Rwanda, with a total boundary length

Tanzania has a tropical climate with 3 major climatic zones (Fig. 2.2) viz. dry, moderate and wet. Moderate Climatic zone occupies a large area of Tanzania (URT, 1999). It receives rainfall for 1 to 3 months in a year. The administrative regions which fall under this climatic zone are Tabora, Mwanza, Mara, Iringa, Morogoro, Arusha, Tanga, Moshi, Lindi and Bukoba. In the highlands, temperatures range between 10 and 20 °C (50 and 68 °F) during cold and hot seasons, respectively. The rest of the country has temperatures rarely falling lower than 20 °C (68 °F). The hottest period extends between November and February (25 – 31 °C) while the coldest period occurs between May and August (15 – 20 °C ). Tanzania has two major rainfall regions. One is unimodal (December - April) and the other is bimodal (October - December and March - May). The former is experienced in southern, south-west, central and western parts of the country, and the latter is found to the north and northern coast. In the bimodal regime the March - May rains are referred to as the long rains or "Masika", whereas the

October - December rains are generally known as short rains or "Vuli".

**2. Materials and methods** 

**2.1 Description of the study area** 

of 4,826 km, of which 1,424 km is coastline.

Fig. 2.1. Location map of Tanzania

 prior to reaching stream channels. Six major factors which influence the long-term sediment yields/delivery from a catchment based on Renfro (1975) as reported in Morris and Fan (1998) and critically reviewed by Ndomba (2007) are: i) Erosion process - the sediment delivered to the catchment outlet will generally be higher for sediment derived from channel-type erosion which immediately places sediment into the main channels of the transport system, as compared to sheet erosion; ii) Proximity to catchment outlet - sediment delivery will be influenced by the geographic distribution of sediment sources within the catchment and their relationship to depositional areas. Sediment is more likely to be exported from a source area near the catchment outlet as compared to a distant sediment source, since sediment from the distant sources will typically encounter more opportunities for re-deposition before reaching the catchment outlet; iii) Drainage efficiency- hydraulically efficient channels networks with a high drainage density will be more efficient in exporting sediment as compared to catchments having low channel density; iv) Soil and land cover characteristics - finer particles tend to be transported with greater facility than coarse particles. Because of the formation of particle aggregates by clays, silts tend to be more erosive and produce higher delivery ratios than clay soils; v) Depositional features - the presence of depositional areas, including vegetation, ponds, wetlands, reservoirs and floodplains, will decrease the sediment yields at the catchment outlet. Most eroded sediments from large catchments may be re-deposited at the base of slopes, as outwash fans below gullies, in channels or on floodplains; vi) catchment size and slope - a large, gently sloping catchment will characteristically have a lower delivery ratio than a smaller and steeper catchment.

This chapter is therefore reporting the developed sediment yield-fill equations as categorized as regional regression relationships for various climatic regions in Tanzania as simple and efficient planning tools of water supply schemes small reservoirs/pond with limited data. In this study additional new data on dams is used. It should be noted that requirements for data and computational modelling skills rule out the use of more sophisticated methods to predict sediment yields, and as a result a simple regional sediment yield predictor was chosen for this application. The equations are developed from readily available data on catchment area and reservoir sediment fill from Ministries and Government Agencies. The size of the area is very important factor in respect to the total yield of sediment from a catchment. However, it should be noted that its relative importance to the influence of the sediment delivery ratio and sediment production rate is subject to questioning. It is suggested in the literature that sediment production rates declined with increasing catchment area (Morris and Fan, 1998). This theory is supported by the fact that the probability of entrapment and lodgment of a particle being transported downstream increases as the drainage area increases. Besides, for the same length of a river network, the smaller the catchment area the higher the drainage density as well the sediment yields. The proximity to the catchment outlet may also be indirectly related to catchment size. The preceding discussions suggest that catchment area size may sometimes be directly or indirectly linked to various factors controlling sediment delivery to the outlet of the catchment. However, catchment area size could not be directly related to erosion process, soil type and land cover. Such limitations would render the general relationships between catchment area size as independent variable and the sediment yield-fill be used only for preliminary planning purposes or as a rough check. It is anticipated that small dam designers/planners would be able to use these tools /methods; they typically need to carry out assessments rapidly using limited local data, and may not have software skills or access to computers.

#### **2. Materials and methods**

244 Advances in Data, Methods, Models and Their Applications in Geoscience

 prior to reaching stream channels. Six major factors which influence the long-term sediment yields/delivery from a catchment based on Renfro (1975) as reported in Morris and Fan (1998) and critically reviewed by Ndomba (2007) are: i) Erosion process - the sediment delivered to the catchment outlet will generally be higher for sediment derived from channel-type erosion which immediately places sediment into the main channels of the transport system, as compared to sheet erosion; ii) Proximity to catchment outlet - sediment delivery will be influenced by the geographic distribution of sediment sources within the catchment and their relationship to depositional areas. Sediment is more likely to be exported from a source area near the catchment outlet as compared to a distant sediment source, since sediment from the distant sources will typically encounter more opportunities for re-deposition before reaching the catchment outlet; iii) Drainage efficiency- hydraulically efficient channels networks with a high drainage density will be more efficient in exporting sediment as compared to catchments having low channel density; iv) Soil and land cover characteristics - finer particles tend to be transported with greater facility than coarse particles. Because of the formation of particle aggregates by clays, silts tend to be more erosive and produce higher delivery ratios than clay soils; v) Depositional features - the presence of depositional areas, including vegetation, ponds, wetlands, reservoirs and floodplains, will decrease the sediment yields at the catchment outlet. Most eroded sediments from large catchments may be re-deposited at the base of slopes, as outwash fans below gullies, in channels or on floodplains; vi) catchment size and slope - a large, gently sloping catchment will characteristically have a lower delivery ratio than a smaller and

This chapter is therefore reporting the developed sediment yield-fill equations as categorized as regional regression relationships for various climatic regions in Tanzania as simple and efficient planning tools of water supply schemes small reservoirs/pond with limited data. In this study additional new data on dams is used. It should be noted that requirements for data and computational modelling skills rule out the use of more sophisticated methods to predict sediment yields, and as a result a simple regional sediment yield predictor was chosen for this application. The equations are developed from readily available data on catchment area and reservoir sediment fill from Ministries and Government Agencies. The size of the area is very important factor in respect to the total yield of sediment from a catchment. However, it should be noted that its relative importance to the influence of the sediment delivery ratio and sediment production rate is subject to questioning. It is suggested in the literature that sediment production rates declined with increasing catchment area (Morris and Fan, 1998). This theory is supported by the fact that the probability of entrapment and lodgment of a particle being transported downstream increases as the drainage area increases. Besides, for the same length of a river network, the smaller the catchment area the higher the drainage density as well the sediment yields. The proximity to the catchment outlet may also be indirectly related to catchment size. The preceding discussions suggest that catchment area size may sometimes be directly or indirectly linked to various factors controlling sediment delivery to the outlet of the catchment. However, catchment area size could not be directly related to erosion process, soil type and land cover. Such limitations would render the general relationships between catchment area size as independent variable and the sediment yield-fill be used only for preliminary planning purposes or as a rough check. It is anticipated that small dam designers/planners would be able to use these tools /methods; they typically need to carry out assessments rapidly using limited local data, and may not have software skills or access

steeper catchment.

to computers.

#### **2.1 Description of the study area**

The study area, Tanzania, is situated in East Africa just south of the equator (Fig. 2.1). Tanzania lies between the area of the great Lakes—Victoria, Tanganyika, and Nyasa—and the Indian Ocean. It contains a total area of 945,087 km2, including 59,050 km2 of inland water (Fig. 2.1). It is bounded on the North by Uganda and Kenya, on the East by the Indian Ocean, on the South by Mozambique and Malawi, on the South West by Zambia, and on the West by Democratic Republic of Congo, Burundi, and Rwanda, with a total boundary length of 4,826 km, of which 1,424 km is coastline.

Tanzania has a tropical climate with 3 major climatic zones (Fig. 2.2) viz. dry, moderate and wet. Moderate Climatic zone occupies a large area of Tanzania (URT, 1999). It receives rainfall for 1 to 3 months in a year. The administrative regions which fall under this climatic zone are Tabora, Mwanza, Mara, Iringa, Morogoro, Arusha, Tanga, Moshi, Lindi and Bukoba. In the highlands, temperatures range between 10 and 20 °C (50 and 68 °F) during cold and hot seasons, respectively. The rest of the country has temperatures rarely falling lower than 20 °C (68 °F). The hottest period extends between November and February (25 – 31 °C) while the coldest period occurs between May and August (15 – 20 °C ). Tanzania has two major rainfall regions. One is unimodal (December - April) and the other is bimodal (October - December and March - May). The former is experienced in southern, south-west, central and western parts of the country, and the latter is found to the north and northern coast. In the bimodal regime the March - May rains are referred to as the long rains or "Masika", whereas the October - December rains are generally known as short rains or "Vuli".

Fig. 2.1. Location map of Tanzania

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 247

The following are the descriptions of the respective regions from which the dam data for this study were collected. These are Dodoma, Shinyanga, Singida, Tabora, and Arusha

**Dodoma region** 

**Capacity at FSL** 

**(Million m3)** 

1 Mambali 2.7 *NA* 1958 21500 1978 1075 2 Mabisilo 25 *NA* 1956 31500 1978 1431.8 3 Kakola 3.7 *NA* 0.202 1954 19700 1978 820.8 4 Manolea 3 *NA* 0.033 1956 15400 1978 700 5 Kasisi 3.2 *NA* 0.02 1968 7300 1978 730 6 Mbola 6.4 *NA* 0.016 1972 7500 1978 1250 7 Igingwa 10 *NA* 0.20 1958 2800 1978 1400 8 Matumbuhi 16.8 59.74 0.31 1960 1978 1322.4 9 Buigiri 10.3 35.26 0.48 1969 1978 1410 10 Imagi 2.2 *NA* 0.1695 1934 1971 950 11 Matumbulu 15 *NA* 0.333 1949 1962-74 1374.5 12 Msalatu 8.5 *NA* 0.42 1944 1974 1225.8 13 Kisongo 9.3 *NA* 0.1265 1969-71 1228 **Shinyanga region**  14 Bubiki 11 2.75 0.35 1584 15 Ibadakuli 10 4.9 0.37 1472 16 Malya 15 5.8 1.49 2011 17 Nguliati 12 3.35 0.49 1593 18 Sakwe 9 3.65 0.28 1357.4

Table 2.2.1. Sedimentation data of small dams in Dry climatic zone for regions of Dodoma

Dodoma region is characterized by long dry seasons (April to December) and short rainy seasons (December to March). Mean annual rainfall in the area range from 500 to 600 mm/annum and potential evaporation ranges between 2000 to 2500 mm per annum (Christiansson, 1981). The topography of the central semi arid Tanzania is characterized by plains and scattered inselberg or ridge. The soils appear in catena sequence where the upper

**Year of Construction** 

**Sed Fill** 

**(m3)** 

**Year(Data Collected)** 

**Sed Fill rate** 

**(m3 Per Year)** 

(Tables 2.2.1 & 2.2.2).

**Names Of dams** 

**Catchment Area** 

Note: "NA" and "blank" imply No Any data.

and Shinyanga

**(km2)** 

**Full Supply Level,** 

**FSL,(m)** 

**Serial No.** 

Fig. 2.2. Map showing Climatic zones of Tanzania (as adopted from URT, 1999)

According to PLDPT (1984) Tanzanian soils are very varied, a simplified classification follows: a) Volcanic soils: are of high agricultural potential and livestock production tends to be restricted to zero-grazing systems. They predominate in Arusha, Kilimanjaro and South west Highlands, Kitulo plateau. At high and medium altitudes they are notable for the production of forage for dairy production; b) Light sandy soils: predominate in the coastal areas. Grazing is available during the rains but the soils dry out rapidly thereafter and the forage has little worth; c) Soils of granite/gneiss origin: are poor and occur mainly in midwest especially in Mwanza and Tabora; d) Red soils: occupy most of central plateau. They produce good grazing in the limited rainy seasons and the quality of herbage persists into the dry seasons; e) Ironstone soils: found in the far west, mainly in Kagera, Kigoma and Sumbawanga. They are poor and acidic but can be productive with inputs, *i.e.*, mulching and manuring; and f) The mbuga black vertisols are widespread and an important source of dry season grazing.

Fig. 2.2. Map showing Climatic zones of Tanzania (as adopted from URT, 1999)

dry season grazing.

According to PLDPT (1984) Tanzanian soils are very varied, a simplified classification follows: a) Volcanic soils: are of high agricultural potential and livestock production tends to be restricted to zero-grazing systems. They predominate in Arusha, Kilimanjaro and South west Highlands, Kitulo plateau. At high and medium altitudes they are notable for the production of forage for dairy production; b) Light sandy soils: predominate in the coastal areas. Grazing is available during the rains but the soils dry out rapidly thereafter and the forage has little worth; c) Soils of granite/gneiss origin: are poor and occur mainly in midwest especially in Mwanza and Tabora; d) Red soils: occupy most of central plateau. They produce good grazing in the limited rainy seasons and the quality of herbage persists into the dry seasons; e) Ironstone soils: found in the far west, mainly in Kagera, Kigoma and Sumbawanga. They are poor and acidic but can be productive with inputs, *i.e.*, mulching and manuring; and f) The mbuga black vertisols are widespread and an important source of The following are the descriptions of the respective regions from which the dam data for this study were collected. These are Dodoma, Shinyanga, Singida, Tabora, and Arusha (Tables 2.2.1 & 2.2.2).


Note: "NA" and "blank" imply No Any data.

Table 2.2.1. Sedimentation data of small dams in Dry climatic zone for regions of Dodoma and Shinyanga

Dodoma region is characterized by long dry seasons (April to December) and short rainy seasons (December to March). Mean annual rainfall in the area range from 500 to 600 mm/annum and potential evaporation ranges between 2000 to 2500 mm per annum (Christiansson, 1981). The topography of the central semi arid Tanzania is characterized by plains and scattered inselberg or ridge. The soils appear in catena sequence where the upper

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 249

**Serial No. Names of Dams Cat Area (km2) Full Supply Level (m) Capacity At FSL (Million m3) Year of Construction Year (Data Collected) Sed Fill (m3) Sed Fill rate (m3 Per Year)** 

27 Leken 183 6.972 223104 28 Kimokouwa 110 0.950 40850 29 Lossimingori 94 1.640 57400 30 Moriatata 120 1.342 34892 31 Losirwa 65 0.670 20783.95 32 Ngamuriak 76 1.104 18768 33 Bashay 78 1.420 8520 34 Meserani 56 0.568 17608 35 Lepurko 87 0.856 24837.05

Table 2.2.2. Sedimentation data of small dams in Moderate climatic zone for regions of

Shinyanga region is characterized by a tropical type of climate with clearly distinguished rainy and long dry seasons. According to meteorological statistics the average temperature for the region is about 28oC. The region experiences rainfall of 600 mm as minimum and 900 mm as maximum per year. The rainy season usually starts between mid-October and December and ends in the second week of May. Normally it has two peak seasons. The first peak occurs between mid- October and December, while the second one, the longer season, falls between February and mid-May. As such, the whole rainy season covers a total of almost 6 months, with a dry spell which usually occurs in January. The dry season begins in mid-May and ends in mid-October. This is a period of about 5 months. The dry season is the worst period for the Shinyanga region. The topography of Shinyanga region is characterized by flat, gently undulating plains covered with low sparse vegetation. The North-Western and North- Eastern parts of the region are covered by natural forests which are mainly "miombo" woodland. The Eastern part of the region is dominated by heavy black clay soils with areas of red loam and sandy soil. It is observed that most of the Shinyanga region is dry flat lowland. Thus its agro-economic zones are not well pronounced as it is with some regions in the country. The soils are hard to cultivate, pastures become very poor, and availability of water for domestic use and livestock become acute. The amount and distribution pattern of rainfall in the region is generally unequal and unpredictable. This implies that rainfall as a source of water for domestic and production purposes in the region is less reliable for sustainable water supply. Despite of the recent mushrooming of mine industry, agriculture has continued to dominate the livelihood and economic performance of Shinyanga region. The sector contributes about 75 percent to the regional economy and employs about 90 percent of the working population in the region. Agriculture is dominated by peasantry farming. Main cash crops are cotton and tobacco while the main food crops are maize, sorghum, paddy, sweet potatoes, millet and cassava. The region has the largest planted area of maize and second largest for paddy and sorghum than other regions in

Tabora and Arusha

slopes of inselberg have thin stony soils. The valley bottoms and flood plains have black and grey deposits. Natural vegetation of dense thicket or "miombo" woodland has generally been replaced by semi natural vegetation of grasses and herbs. The inhabitant of the study area are cultivating pastoralist. They mainly practice shifting cultivation where no manure is applied. They maintain large heards of cattle, sheep, and goats. The staple crops grown are sorghum and bulrush millet, maize also grown on significant areas.


slopes of inselberg have thin stony soils. The valley bottoms and flood plains have black and grey deposits. Natural vegetation of dense thicket or "miombo" woodland has generally been replaced by semi natural vegetation of grasses and herbs. The inhabitant of the study area are cultivating pastoralist. They mainly practice shifting cultivation where no manure is applied. They maintain large heards of cattle, sheep, and goats. The staple crops grown are

**Tabora region** 

**Capacity At FSL** 

1 Malolo 15 35.7 0.936 1962 1975 19300 1485 2 Itambo 25 29.3 0.234 1947 1978 96200 3103 3 Magulya 15.8 35 *NA* 1957 1978 35200 1676 4 Ulaya 8.3 30.8 0.298 1947 1978 31600 1019 5 Igurubi 1.2 26.7 0.113 1959 1978 20900 1100 6 Charo 6.7 28.5 0.015 1969 1978 11700 1300 7 Kakolo 3.7 33.8 0.202 1954 1978 19700 820 8 Manolea 3 30.6 0.033 1956 1978 15400 700 9 Kasisi 3.2 13.2 0.02 1968 1978 7300 730 10 Mbola 6.4 31.8 0.016 1972 1978 7500 1250 11 Usoke Mission 1.9 28.2 0.02 1971 1978 3150 450 12 Kalangali 2.8 1200.7 0.84 1958 1978 88400 4420 13 Uchama 11 36.9 1.322 1955 1978 27700 1204.3 14 Mambali 2.7 24.9 *NA* 1956 1978 21500 977.3 15 Mabisilo 25 35.0 *NA* 1956 1978 31500 1431.8 16 Nkinazawa 180 29.6 0.75 1956 1978 110000 5000 17 Iduduma 267 32.9 0.86 1959 1978 140000 7368 18 Mwamashimba 16.5 25.0 *NA* 1973 1978 21500 4300 19 Bulenya Hills 194 36 1.62 1961 1978 96400 5670.5 20 Sorefu 7.5 28.1 0.045 1970 1978 9400 1175 21 Urambo 38 18.2 *NA* 1956 1978 75717 3441.7 22 Tura 105 30.8 0.27 1948 1978 108003 3600 23 Utatya 4 *NA* 35.4 1959 1978 11050 581.6 24 Igingwa 10 26.2 0.2 1958 1978 28000 1400 **Arusha region**  25 Moita Bwawani 97 1.556 31120 26 Moita Kiloriti 115 1.257 37710

**(Million m3)** 

**Year of** 

**Construction** 

**Year** 

**(Data Collected)** 

**Sed Fill (m3)** 

**Sed Fill rate** 

**(m3 Per Year)** 

sorghum and bulrush millet, maize also grown on significant areas.

**Full Supply Level** 

**(m)** 

**Serial No.** 

**Names of Dams** 

**Cat Area** 

**(km2)** 


Table 2.2.2. Sedimentation data of small dams in Moderate climatic zone for regions of Tabora and Arusha

Shinyanga region is characterized by a tropical type of climate with clearly distinguished rainy and long dry seasons. According to meteorological statistics the average temperature for the region is about 28oC. The region experiences rainfall of 600 mm as minimum and 900 mm as maximum per year. The rainy season usually starts between mid-October and December and ends in the second week of May. Normally it has two peak seasons. The first peak occurs between mid- October and December, while the second one, the longer season, falls between February and mid-May. As such, the whole rainy season covers a total of almost 6 months, with a dry spell which usually occurs in January. The dry season begins in mid-May and ends in mid-October. This is a period of about 5 months. The dry season is the worst period for the Shinyanga region. The topography of Shinyanga region is characterized by flat, gently undulating plains covered with low sparse vegetation. The North-Western and North- Eastern parts of the region are covered by natural forests which are mainly "miombo" woodland. The Eastern part of the region is dominated by heavy black clay soils with areas of red loam and sandy soil. It is observed that most of the Shinyanga region is dry flat lowland. Thus its agro-economic zones are not well pronounced as it is with some regions in the country. The soils are hard to cultivate, pastures become very poor, and availability of water for domestic use and livestock become acute. The amount and distribution pattern of rainfall in the region is generally unequal and unpredictable. This implies that rainfall as a source of water for domestic and production purposes in the region is less reliable for sustainable water supply. Despite of the recent mushrooming of mine industry, agriculture has continued to dominate the livelihood and economic performance of Shinyanga region. The sector contributes about 75 percent to the regional economy and employs about 90 percent of the working population in the region. Agriculture is dominated by peasantry farming. Main cash crops are cotton and tobacco while the main food crops are maize, sorghum, paddy, sweet potatoes, millet and cassava. The region has the largest planted area of maize and second largest for paddy and sorghum than other regions in

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 251

made it difficult to establish a linear relationship between sediment load and river discharge. Surveys of reservoirs/dams whose relevant technical maps were available were done. Profiles available from old/design maps were compared with the new sounding.

Although the data collected are scarce (*i.e.*, only 53 dams) but one could see that based on climatic zonation about seventy percent (70%) of Tanzania land is represented. Besides, the data coverage represents a wide range of dam and catchment physical characteristics viz. catchment area 1 - 267 km2; dam capacity at FSL, 0.02 - 35 Million m3 (Table 2.3). The mean values are 41.7 km2 and 1.5 Million m3 for catchment area and dam capacity, respectively. Notwithstanding the high spatial variability of data as captured by high Coefficient of variation (Cv), the data represent the population as demonstrated by low Standard Error of

1. Lowest 1.20 0.02 2. Maximum 267.00 35.40 3. Mean 41.66 1.52 4. Standard Deviation (STD) 59.62 6.41 5. Coefficient of Variation, Cv (%) 143.12 422.76 6. Standard Error of the Mean, SEM 8.19 1.17 Table 2.3. Summary statistics of catchment size and dam capacity of data used in this study

Sediment yield-fill equations were developed by regression analysis approach. It should be noted that if data on sediment yield-fill and catchment characteristics are available from many sites, it may be possible to develop a regression relationship which describes the sediment yield within the region as a function of independent variables such as catchment area, slope, land use, and rainfall erosivity (Morris and Fan, 1998). The only independent variable used for this study is the catchment area as it was readily available. This study assumed the following: i) the sample is representative of the population for the inference prediction; ii) the error is a random variable with a mean of zero conditional on the explanatory variables; iii) the independent variables based on low standard error of the mean (SEM) as presented in Table 2.3 were measured with no error; iv) the predictors are linearly independent, *i.e*. it is not possible to express any predictor as a linear combination of the others; v) the errors are uncorrelated, that is, the variance-covariance matrix of the errors is diagonal and each non-zero element is the variance of the error; and vi) the variance of the error is constant across observations (homoscedasticity). These are sufficient conditions for the least-squares estimator to possess desirable properties, in particular, these assumptions imply that the parameter estimates will be unbiased, consistent, and efficient in the class of linear unbiased estimators. Besides, sediment yield is assumed as equal to sediment fill due to the uncertainty involved in estimating trap efficiency of small dams in the study area. It should be noted that previous researchers such as Mulengera (2008) adopted a similar

(km2)

Dam capacity at Full Supply Level (Million m3)

Serial No. Statistics Catchment area

**2.4 Development of sediment yield-fill equations** 

**2.3 Data analysis** 

the Mean (SEM).

Tanzania. Besides farming, livestock keeping is also a major activity in the region. Cattle, goats and sheep are the major domesticated animals. Modern diary farming and poultry keeping are confined to urban centers

Tabora region is among the areas of Tanzania which are in moderate climatic zones. Tabora region is located in the mid-western part of Mainland Tanzania. Tabora is characterized as tropical type of climate with clearly distinguished rainy and dry seasons. According to meteorological statistics the average temperature for the region is about 270C. Tabora receives Mean Annual Rainfall of 892 mm/annum or 74 mm/month. In Tabora, about 76% of the population are farmers, and thus agriculture is the largest single sector in the economy directory producing about 80 percent of Tabora region's wealth of goods and services. Main cash crops grown are tobacco, cotton and paddy. Tobacco and cotton are mainly grown for export markets. Principal food crops are maize, sorghum, cassava, sweet potatoes and legumes.

Arusha region lies in moderate climatic zone. With the exception of a few spots the region is in the high altitudes ranging from 800 to 4,500 meters above sea level. Because of the high altitude the region experiences moderate temperatures with rainfall varying with the altitude. The average annual temperature is 210C in the highlands and 240C in the low lands. Arusha region has two types of rainfall patterns: unimodal and bimodal. The southern district of Karatu normally enjoys unimodal rainfall which usually starts in November and ends in April. The rainfall in this district is usually reliable, ranging from 800 to 1,000 mm/annum. The major crop produced is cereals. Soils have been classified by colour into grey, brown and red brown. The extensive soils which originate from recent volcanic ash are found to the north-western parts of the region, west of the rift valley and in the Ngorongoro massif. Brown soils cover large areas in the central part and western side of the region. The southern- eastern areas are characterised by grey brown and red-brown soils. Soil erosion is particularly severe in the heavily settled central part of the region. Generally soil erosion is widespread throughout the region and is deemed to be an environmental disaster in the making.

#### **2.2 Data type and sources**

This study collected readily available secondary data from reports of Ministry of Water and Irrigation (Husebye and Torblaa, 1995) as adopted in Tables 2.2.1 & 2.2.2. However, data from Arusha in Table 2.2.2 were sourced from a recent study by Malisa (2007). They include name of the dam, full supply level of the dam, capacity of the dam at full supply level, year of construction, accumulated sediment volume in the dam (Sed Fill ), dam survey Year (Year Data Collected), volumetric rate of sediment accumulation in the dam (Sed Fill per Year), catchment area, and Sediment yield. It should be noted also that important data such as geographical locations of these dams are missing. The dams were built for various purposes, including and not limited to irrigation, domestic water supply, livestock watering, flood control and fishing.

It should be noted that most of these sedimentation data presented in Tables 2.2.1 and 2.2.2 were collected using mainly two approaches, namely, direct measurement of transported materials (*i.e.*, suspended sediment concentration) and measurement of the rate of siltation of reservoirs/dams. The author would like to note that the first procedure has some setbacks, especially, when practiced in tropics. For instance, a majority of sediment would be transported in one or two days. Typically for Tanzania, most of sediment samples had been taken at medium or low stage. The high stages were hardly sampled. This might have made it difficult to establish a linear relationship between sediment load and river discharge. Surveys of reservoirs/dams whose relevant technical maps were available were done. Profiles available from old/design maps were compared with the new sounding.

#### **2.3 Data analysis**

250 Advances in Data, Methods, Models and Their Applications in Geoscience

Tanzania. Besides farming, livestock keeping is also a major activity in the region. Cattle, goats and sheep are the major domesticated animals. Modern diary farming and poultry

Tabora region is among the areas of Tanzania which are in moderate climatic zones. Tabora region is located in the mid-western part of Mainland Tanzania. Tabora is characterized as tropical type of climate with clearly distinguished rainy and dry seasons. According to meteorological statistics the average temperature for the region is about 270C. Tabora receives Mean Annual Rainfall of 892 mm/annum or 74 mm/month. In Tabora, about 76% of the population are farmers, and thus agriculture is the largest single sector in the economy directory producing about 80 percent of Tabora region's wealth of goods and services. Main cash crops grown are tobacco, cotton and paddy. Tobacco and cotton are mainly grown for export markets. Principal food crops are maize, sorghum, cassava, sweet

Arusha region lies in moderate climatic zone. With the exception of a few spots the region is in the high altitudes ranging from 800 to 4,500 meters above sea level. Because of the high altitude the region experiences moderate temperatures with rainfall varying with the altitude. The average annual temperature is 210C in the highlands and 240C in the low lands. Arusha region has two types of rainfall patterns: unimodal and bimodal. The southern district of Karatu normally enjoys unimodal rainfall which usually starts in November and ends in April. The rainfall in this district is usually reliable, ranging from 800 to 1,000 mm/annum. The major crop produced is cereals. Soils have been classified by colour into grey, brown and red brown. The extensive soils which originate from recent volcanic ash are found to the north-western parts of the region, west of the rift valley and in the Ngorongoro massif. Brown soils cover large areas in the central part and western side of the region. The southern- eastern areas are characterised by grey brown and red-brown soils. Soil erosion is particularly severe in the heavily settled central part of the region. Generally soil erosion is widespread throughout the region and is deemed to be an environmental disaster in the

This study collected readily available secondary data from reports of Ministry of Water and Irrigation (Husebye and Torblaa, 1995) as adopted in Tables 2.2.1 & 2.2.2. However, data from Arusha in Table 2.2.2 were sourced from a recent study by Malisa (2007). They include name of the dam, full supply level of the dam, capacity of the dam at full supply level, year of construction, accumulated sediment volume in the dam (Sed Fill ), dam survey Year (Year Data Collected), volumetric rate of sediment accumulation in the dam (Sed Fill per Year), catchment area, and Sediment yield. It should be noted also that important data such as geographical locations of these dams are missing. The dams were built for various purposes, including and not limited to irrigation, domestic water supply, livestock watering, flood

It should be noted that most of these sedimentation data presented in Tables 2.2.1 and 2.2.2 were collected using mainly two approaches, namely, direct measurement of transported materials (*i.e.*, suspended sediment concentration) and measurement of the rate of siltation of reservoirs/dams. The author would like to note that the first procedure has some setbacks, especially, when practiced in tropics. For instance, a majority of sediment would be transported in one or two days. Typically for Tanzania, most of sediment samples had been taken at medium or low stage. The high stages were hardly sampled. This might have

keeping are confined to urban centers

potatoes and legumes.

making.

**2.2 Data type and sources** 

control and fishing.

Although the data collected are scarce (*i.e.*, only 53 dams) but one could see that based on climatic zonation about seventy percent (70%) of Tanzania land is represented. Besides, the data coverage represents a wide range of dam and catchment physical characteristics viz. catchment area 1 - 267 km2; dam capacity at FSL, 0.02 - 35 Million m3 (Table 2.3). The mean values are 41.7 km2 and 1.5 Million m3 for catchment area and dam capacity, respectively. Notwithstanding the high spatial variability of data as captured by high Coefficient of variation (Cv), the data represent the population as demonstrated by low Standard Error of the Mean (SEM).


Table 2.3. Summary statistics of catchment size and dam capacity of data used in this study

#### **2.4 Development of sediment yield-fill equations**

Sediment yield-fill equations were developed by regression analysis approach. It should be noted that if data on sediment yield-fill and catchment characteristics are available from many sites, it may be possible to develop a regression relationship which describes the sediment yield within the region as a function of independent variables such as catchment area, slope, land use, and rainfall erosivity (Morris and Fan, 1998). The only independent variable used for this study is the catchment area as it was readily available. This study assumed the following: i) the sample is representative of the population for the inference prediction; ii) the error is a random variable with a mean of zero conditional on the explanatory variables; iii) the independent variables based on low standard error of the mean (SEM) as presented in Table 2.3 were measured with no error; iv) the predictors are linearly independent, *i.e*. it is not possible to express any predictor as a linear combination of the others; v) the errors are uncorrelated, that is, the variance-covariance matrix of the errors is diagonal and each non-zero element is the variance of the error; and vi) the variance of the error is constant across observations (homoscedasticity). These are sufficient conditions for the least-squares estimator to possess desirable properties, in particular, these assumptions imply that the parameter estimates will be unbiased, consistent, and efficient in the class of linear unbiased estimators. Besides, sediment yield is assumed as equal to sediment fill due to the uncertainty involved in estimating trap efficiency of small dams in the study area. It should be noted that previous researchers such as Mulengera (2008) adopted a similar

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 253

correlation increases substantially with log-transformation of selected data set, *i.e*., from R2

**R² = 0.037**

**R² = 0.665**

Fig. 3.1. (a) Scatter diagram of Sediment Yield-Fill in m3/year against catchment area in km2

0 5 10 15 20 25 30

**Catchment area (km2)**

0

500

1000

1500

**Sediment Fill (m3/year)** 

2000

2500

Fig. 3.1. (b) Scatter diagram of log-tranformed values of sediment yield-fill and catchment

2.8 3 3.2 3.4

**Log (Catchment area)**

Sample regression analysis result for dry climatic zone is presented in Tables 3.2.1 & 3.2.2

equal to 0.037 to 0.665.

for dry climatic zone.

area for dry climatic zone

below:

**3.2 Developed sediment yield prediction equations** 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

**Log (Sediment Fill)**

approach. However, the author is aware that the actual data rarely satisfies the assumptions. That is, the method is used even though at some points the assumptions are not necessarily true.

Firstly, the analysis was conducted to choose type of regression equation forms. Two candidate's forms of equations were investigated, which are straight line and power function (Equations 2.4.1 & 2.4.2). This was achieved by comparing the strength of correlation between sediment fill and catchment area, and corresponding log-transformed values (2.4.3). A power relationship is confirmed when the correlation of log-transformed is high, otherwise, a linear model is chosen.

$$\mathbf{y}\_{i} = \boldsymbol{\beta}\_{o} + \boldsymbol{\beta}\_{i}\mathbf{x}\_{i} + \boldsymbol{\varepsilon}\_{i}, \mathbf{i} = \mathbf{1}, \dots, \mathbf{n}. \tag{2.4.1}$$

Where *n* is a number of observations, *xi*, is independent variable (catchment area), *yi,* dependent variable (Sediment yield-fill), and two parameters, *β0* and *β1*, and *<sup>i</sup>* is an error term and the subscript *i* indexes a particular observation.

$$\mathbf{y}\_{i} = \mathbf{a} \times \boldsymbol{\uprho} \tag{2.4.2}$$

where *α* and *β* are coefficient and exponent of the equation, respectively, *yi* and *xi* are as defined above.

$$\text{Log } \mathbf{y}\_i = \text{Log } \mathbf{a} + \boldsymbol{\beta} \, \text{Log } \mathbf{X}\_i \tag{2.4.3}$$

Secondly, the parameter values were estimated under Excel 2007's Regression Analysis Tool using 70% of the data set, where applicable. The splitting of data was possible for cases where the sample size was adequate for 2 independent variables (*i.e*., α, β) as presented above. As recommended by Statsoft (2011) at least 10 to 20 times as many observations (cases, respondents) as variables, should be used for stable estimates of the regression line and replicability of the results. The tool outputs, among others; the *t* statistic (a measure of how extreme a statistical estimate is); a *p*-value (a measure of how much evidence we have against the null hypothesis, *Ho*, no change or no effect; confidence interval (an interval in which a measurement or trial falls corresponding to a given probability, the best confidence interval used is 95%); degrees of freedom (the minimal number of values which should be specified to determine all the data points), *df*; the standardized residual value (observed minus predicted divided by the square root of the residual mean square), Coefficient of determination, *R2* (this is the square of the product-moment correlation between two variables -It expresses the amount of common variation between the two variables); Multiple R (is the positive square root of R-square - this statistic is useful in multivariate regression when you want to describe the relationship between the variables); The standard error ( is the standard deviation of a mean). The developed equations were validated using independent data set (30%), where appropriate.

#### **3. Results and discussions**

#### **3.1 Selected regression model**

As a result of conducting correlation analysis as described under section 2.4 above and qualitative analysis of scatter plots (Figs. 3.1a,b) below, the power function was chosen as the best regression model for this study. It can be seen from the plots that the strength of

approach. However, the author is aware that the actual data rarely satisfies the assumptions. That is, the method is used even though at some points the assumptions are not necessarily

Firstly, the analysis was conducted to choose type of regression equation forms. Two candidate's forms of equations were investigated, which are straight line and power function (Equations 2.4.1 & 2.4.2). This was achieved by comparing the strength of correlation between sediment fill and catchment area, and corresponding log-transformed values (2.4.3). A power relationship is confirmed when the correlation of log-transformed is

Where *n* is a number of observations, *xi*, is independent variable (catchment area), *yi,*

 yi = α xi <sup>β</sup> (2.4.2) where *α* and *β* are coefficient and exponent of the equation, respectively, *yi* and *xi* are as

Secondly, the parameter values were estimated under Excel 2007's Regression Analysis Tool using 70% of the data set, where applicable. The splitting of data was possible for cases where the sample size was adequate for 2 independent variables (*i.e*., α, β) as presented above. As recommended by Statsoft (2011) at least 10 to 20 times as many observations (cases, respondents) as variables, should be used for stable estimates of the regression line and replicability of the results. The tool outputs, among others; the *t* statistic (a measure of how extreme a statistical estimate is); a *p*-value (a measure of how much evidence we have against the null hypothesis, *Ho*, no change or no effect; confidence interval (an interval in which a measurement or trial falls corresponding to a given probability, the best confidence interval used is 95%); degrees of freedom (the minimal number of values which should be specified to determine all the data points), *df*; the standardized residual value (observed minus predicted divided by the square root of the residual mean square), Coefficient of determination, *R2* (this is the square of the product-moment correlation between two variables -It expresses the amount of common variation between the two variables); Multiple R (is the positive square root of R-square - this statistic is useful in multivariate regression when you want to describe the relationship between the variables); The standard error ( is the standard deviation of a mean). The developed equations were validated using

As a result of conducting correlation analysis as described under section 2.4 above and qualitative analysis of scatter plots (Figs. 3.1a,b) below, the power function was chosen as the best regression model for this study. It can be seen from the plots that the strength of

<sup>1</sup> , i = 1, …, n. (2.4.1)

Log yi = Log α + β Log Xi (2.4.3)

*<sup>i</sup>* is an error

*<sup>i</sup> <sup>o</sup> <sup>i</sup> <sup>i</sup> y x* 

dependent variable (Sediment yield-fill), and two parameters, *β0* and *β1*, and

term and the subscript *i* indexes a particular observation.

independent data set (30%), where appropriate.

**3. Results and discussions 3.1 Selected regression model** 

true.

defined above.

high, otherwise, a linear model is chosen.

correlation increases substantially with log-transformation of selected data set, *i.e*., from R2 equal to 0.037 to 0.665.

Fig. 3.1. (a) Scatter diagram of Sediment Yield-Fill in m3/year against catchment area in km2 for dry climatic zone.

Fig. 3.1. (b) Scatter diagram of log-tranformed values of sediment yield-fill and catchment area for dry climatic zone

#### **3.2 Developed sediment yield prediction equations**

Sample regression analysis result for dry climatic zone is presented in Tables 3.2.1 & 3.2.2 below:

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 255

Fig. 3.2. Relationship between sediment fill-yield and catchment area for both dry and

were developed in the form of a power function as proposed in section 3.1 above (Table 3.2.2) and as illustrated in Equation 3.2. Besides, the estimated parameter uncertainty bounds are presented in the table. Specific equations for administrative regions are also

Observed data Predicted fill-yield Upper 95% Predicted fill-yield Lower 95% Predicted fill-yield Average fit

0 50 100 150 200 250 300

**Catchment area (km2)**

One would note from Table 3.2.2 below that the performances, as measured by coefficient of determination, R2, of the developed prediction equations are higher in moderate climate zone than in dry climatic zones. The strength of correlations between sediment yields and catchment area sizes could be categorized as high, moderate and low for Arusha and Tabora, Dodoma, and Dodoma and Shinyanga and Singida regions, respectively. These results suggest that large variance in sediment yields remains unexplained by the developed regressions in dry climatic zone. This may be attributed to high uncertainty in representations of long term sediment yields in catchment with high temporal variability of rainfall intensity, runoff and sediment (Mulengera, 2008). However, independent analysis indicates that sediment fill-yield data used for the dry climatic zones are good in space representation with coefficient of variation, CV, between 23 and 26 in percent. The corresponding values for the moderate and all climatic zones (*i.e.*, dry and moderate) range from 64 to 128 in percent. The high sediment yields for Arusha region were expected as the soils in the region are mostly recent volcanic ash and/or highly erodible. The overall

moderate climatic zones of Tanzania

**Sediment fill-yield (m3/yr.)**

included.


ANOVA



Table 3.2.1. Regression statistics in log scale for both dry and moderate zones data points

From Table 3.2.1 results we have, Log α = 2.7452 ± Standard Error, and thus α would range from 439.20 to 632.27. And if you take the average you will get α = 556.16. Also the value of β obtained as β = 0.4313± Standard Error. β would therefore range from 0.3824 to 0.4802 with the average value 0.4313. The resulting equation will look like (Equation 3.2)

$$\text{SF} = \text{556.2 A}^{0.4313} \tag{3.2}$$

Where; SF= Sediment fill (m3/yr); A = Catchment area (km2); α = constant; and β = scaling exponent.

The corresponding graph of sediment fill-yield versus catchment area in dry and moderate climatic zone (all regions analysed) is presented in Fig. 3.2.

One would note from Fig. 3.2 below that the developed equations satisfactorily predict the sediment fill in small catchment at 95 % confidence interval. It is worth noting that a few of the observed sediment fill-yield data points, for instance, for a catchment sizes of 2.8 and 16.5 km2 from Tabora region (Table 2.2.2) plotted outside the prediction range (*i.e.*, outlier). The author is attributing it to uncertainty in field measurements. As reported in literature, all techniques for estimating reservoir volume incorporate errors (Morris and Fan, 1998). An estimated error of about ±30% in determining reservoir capacity volumes have been reported in Morris and Fan (1998) by various workers. These discussions may suggest that the error observed above could be explained by uncertainty in determining actual sediment fill (reservoir sedimentation rate), (Ndomba, 2007). Such errors are also acknowledged by Mulengera (2008). A set of sediment fill-yield prediction equations for various climatic zones

 *df SS MS F Significance F*  Regression 1 2.013449766 2.01345 73.423838 1.67761E-10

 *Coefficients Standard Error t Stat P-value Lower 95% Upper 95%*  Intercept 2.7452 0.05577 49.21851 1.01E-36 2.632384636 2.858019 X variable 0.4313 0.04885 8.568771 1.678E-10 0.319783073 0.5174043 Table 3.2.1. Regression statistics in log scale for both dry and moderate zones data points

From Table 3.2.1 results we have, Log α = 2.7452 ± Standard Error, and thus α would range from 439.20 to 632.27. And if you take the average you will get α = 556.16. Also the value of β obtained as β = 0.4313± Standard Error. β would therefore range from 0.3824 to 0.4802

 SF = 556.2 A0.4313 (3.2) Where; SF= Sediment fill (m3/yr); A = Catchment area (km2); α = constant; and β = scaling

The corresponding graph of sediment fill-yield versus catchment area in dry and moderate

One would note from Fig. 3.2 below that the developed equations satisfactorily predict the sediment fill in small catchment at 95 % confidence interval. It is worth noting that a few of the observed sediment fill-yield data points, for instance, for a catchment sizes of 2.8 and 16.5 km2 from Tabora region (Table 2.2.2) plotted outside the prediction range (*i.e.*, outlier). The author is attributing it to uncertainty in field measurements. As reported in literature, all techniques for estimating reservoir volume incorporate errors (Morris and Fan, 1998). An estimated error of about ±30% in determining reservoir capacity volumes have been reported in Morris and Fan (1998) by various workers. These discussions may suggest that the error observed above could be explained by uncertainty in determining actual sediment fill (reservoir sedimentation rate), (Ndomba, 2007). Such errors are also acknowledged by Mulengera (2008). A set of sediment fill-yield prediction equations for various climatic zones

with the average value 0.4313. The resulting equation will look like (Equation 3.2)

Residual 39 1.0694693 0.027422

Total 40 3.082919067

climatic zone (all regions analysed) is presented in Fig. 3.2.

*Regression Statistics*  Multiple R 0.8081451 R Square 0.6530985

Square 0.6442036

Error 0.1655968 Observations 41

Adjusted R

Standard

ANOVA

exponent.

Fig. 3.2. Relationship between sediment fill-yield and catchment area for both dry and moderate climatic zones of Tanzania

were developed in the form of a power function as proposed in section 3.1 above (Table 3.2.2) and as illustrated in Equation 3.2. Besides, the estimated parameter uncertainty bounds are presented in the table. Specific equations for administrative regions are also included.

One would note from Table 3.2.2 below that the performances, as measured by coefficient of determination, R2, of the developed prediction equations are higher in moderate climate zone than in dry climatic zones. The strength of correlations between sediment yields and catchment area sizes could be categorized as high, moderate and low for Arusha and Tabora, Dodoma, and Dodoma and Shinyanga and Singida regions, respectively. These results suggest that large variance in sediment yields remains unexplained by the developed regressions in dry climatic zone. This may be attributed to high uncertainty in representations of long term sediment yields in catchment with high temporal variability of rainfall intensity, runoff and sediment (Mulengera, 2008). However, independent analysis indicates that sediment fill-yield data used for the dry climatic zones are good in space representation with coefficient of variation, CV, between 23 and 26 in percent. The corresponding values for the moderate and all climatic zones (*i.e.*, dry and moderate) range from 64 to 128 in percent. The high sediment yields for Arusha region were expected as the soils in the region are mostly recent volcanic ash and/or highly erodible. The overall

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 257

relationship developed from data collected from both dry and moderate climatic regions combined has an improved performance according to R2 of 0.732 as compared to 0.451 for dry climatic zone alone. This could be partly due the fact that the number of data points used to fit the regression is adequate for robust relationship as recommended by Statsoft (2011). However, the author would like to recommend the use of a specific equation for particular purpose/climate, especially Arusha region, as they have been developed. Validation result for the developed prediction equation was much better than during model training phase with R2 of 0.873. This was attempted only to regions/climatic zone/region where splitting of data into 70% and 30% for calibration and validation was possible, that is Tabora. The number of observations used for this purpose was 7 (serial numbers 18 through

Although the performances of the developed Regional Regression Relationships are satisfactory, the author caution the reader, as supported by Morris and Fan (1998) that these equations express only the general relationships between independent variables and the sediment yield-fill and should therefore be used only for preliminary planning purposes or as a rough check. Because these equations reflect regional average conditions, the actual yields will tend to be higher (or much higher) than predicted in erosive areas and lower than predicted in areas of undisturbed catchments. Local site-specific conditions can influence sediment yield much more than drainage area or runoff, for

This study uses readily available data on catchment area and reservoir sediment fill and/or sediment yield to calibrate the prediction equations' parameters by regression analysis approach. The influence of rainfall and/or runoff as important input variables were indirectly captured by developing and grouping the equations with respect to their climatic zones. The equations were validated and parameter uncertainty bounds estimated. The data set was split into 70% and 30% proportions for calibration and validation purpose, respectively. The measured and predicted reservoir sediment fillyield rates have satisfactory to good correlations with Coefficient of determination , *R2*, between 0.46 and 0.77 with a degree of freedom of, *n*, 11 to 41 at probability level of significance, *p*, of 5%. R2 of 0.87 at *n* equals 7 was achieved in one of the validation experiments in moderate climatic zone. Although the performances of the developed Regional Regression Relationship are satisfactory, the author would like to caution the reader that these equations express only the general relationships between independent variables and the sediment yield-fill and should therefore be used only for preliminary

It should be noted that in this work the study area was ill-defined as the wet climatic zone of Tanzania was not adequately represented. Notwithstanding a satisfactory performance achieved, this chapter recommends both extending the data set to cover the wetter regions and incorporating other parameters affecting sediment yield for processes studies and better

24 in Table 2.2.2).

instance.

**4.1 Conclusions** 

**4. Conclusions and recommendations** 

planning purposes or as a rough check.

**4.2 Recommendations** 


Note:

\* Only 70% of data points for Tabora region were used to fit the regression relationship. Thirty percent (30%), i.e. 7 data points were used for validation purposes.

\*\* The data for Arusha region was not included in fitting the regression for all regions (i.e. dry and moderate climatic zone) as it presents itself with unique soil/erodibility characteristics as discussed under section 2.1 of this chapter..

Table 3.2.2. A summary of developed sediment fill-yield prediction equations for small catchments in Tanzania

relationship developed from data collected from both dry and moderate climatic regions combined has an improved performance according to R2 of 0.732 as compared to 0.451 for dry climatic zone alone. This could be partly due the fact that the number of data points used to fit the regression is adequate for robust relationship as recommended by Statsoft (2011). However, the author would like to recommend the use of a specific equation for particular purpose/climate, especially Arusha region, as they have been developed. Validation result for the developed prediction equation was much better than during model training phase with R2 of 0.873. This was attempted only to regions/climatic zone/region where splitting of data into 70% and 30% for calibration and validation was possible, that is Tabora. The number of observations used for this purpose was 7 (serial numbers 18 through 24 in Table 2.2.2).

Although the performances of the developed Regional Regression Relationships are satisfactory, the author caution the reader, as supported by Morris and Fan (1998) that these equations express only the general relationships between independent variables and the sediment yield-fill and should therefore be used only for preliminary planning purposes or as a rough check. Because these equations reflect regional average conditions, the actual yields will tend to be higher (or much higher) than predicted in erosive areas and lower than predicted in areas of undisturbed catchments. Local site-specific conditions can influence sediment yield much more than drainage area or runoff, for instance.

#### **4. Conclusions and recommendations**

#### **4.1 Conclusions**

256 Advances in Data, Methods, Models and Their Applications in Geoscience

**Range of** 

**β =Coefficient ±** 

**Standard Error** 

**Average values of** 

**Sediment Fill/Yield** 

0.4914 0.4313 SF = 580A0.4313 0.4586

0.3288 0.1962 SF = 619.6A0.1962 0.5708

0.4745 0.3867 SF = 637.2A0.3867 0.7591

0.5613 0.511 SF = 3264.4A0.511 0.7689

0.4802 0.4313 SF = 556.2A0.4313 0.7318

**prediction Equation** 

**(SF or SY=**

**R2**

**α**

**Aβ)** 

**β**

**Climatic zone Region (s) No. of data points, n Range of** 

Dodoma, Shinyanga, & Singida

Dry climatic zones

Moderate climatic zone

Dry and Moderate

Note:

zone

All regions

under section 2.1 of this chapter..

catchments in Tanzania

**α=Coefficient ±** 

<sup>18</sup>508.42 –

Tabora 17\* 505 -

Arusha 11 333.43 –

analyzed\*\* <sup>41</sup>439.2 –

(30%), i.e. 7 data points were used for validation purposes.

Dodoma 13 471 - 815 619.6 0.0636 –

**Standard Error** 

**Average values of** 

663.8 580 0.3712 –

802.8 637.2 0.2989-

31974.22 3264.37 0.4609 –

632.27 556.16 0.3824 –

\* Only 70% of data points for Tabora region were used to fit the regression relationship. Thirty percent

\*\* The data for Arusha region was not included in fitting the regression for all regions (i.e. dry and moderate climatic zone) as it presents itself with unique soil/erodibility characteristics as discussed

Table 3.2.2. A summary of developed sediment fill-yield prediction equations for small

**α**

This study uses readily available data on catchment area and reservoir sediment fill and/or sediment yield to calibrate the prediction equations' parameters by regression analysis approach. The influence of rainfall and/or runoff as important input variables were indirectly captured by developing and grouping the equations with respect to their climatic zones. The equations were validated and parameter uncertainty bounds estimated. The data set was split into 70% and 30% proportions for calibration and validation purpose, respectively. The measured and predicted reservoir sediment fillyield rates have satisfactory to good correlations with Coefficient of determination , *R2*, between 0.46 and 0.77 with a degree of freedom of, *n*, 11 to 41 at probability level of significance, *p*, of 5%. R2 of 0.87 at *n* equals 7 was achieved in one of the validation experiments in moderate climatic zone. Although the performances of the developed Regional Regression Relationship are satisfactory, the author would like to caution the reader that these equations express only the general relationships between independent variables and the sediment yield-fill and should therefore be used only for preliminary planning purposes or as a rough check.

#### **4.2 Recommendations**

It should be noted that in this work the study area was ill-defined as the wet climatic zone of Tanzania was not adequately represented. Notwithstanding a satisfactory performance achieved, this chapter recommends both extending the data set to cover the wetter regions and incorporating other parameters affecting sediment yield for processes studies and better

Developing Sediment Yield Prediction Equations for Small Catchments in Tanzania 259

Mtalo, F.W. & Ndomba, P.M., (2002). Estimation of Soil erosion in the Pangani basin

Mulengera, M.K., and Payton, R.W., (1999). Estimating the USLE-Soil erodibility factor in developing tropical countries. *Trop. Agric. (Trinidad) Vol. 76 No. 1, pp17-22*. Mulengera, M.K. (2008). Sediment Yield Prediction in Tanzania: Case Study of Dodoma

Ndomba, P.M., Mtalo, F.W., and Killingtveit, A., (2005). The Suitability of SWAT Model in

Ndomba, P.M., Mtalo, F.W., and Killingtveit, A., (2008). A Guided SWAT Model

Ndomba, P.M., Mtalo, F.W., and Killingtveit, A., (2009). Estimating Gully Erosion

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*(No.1)* March 2008, pp63-71.

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prediction in the follow up research. This can be achieved if more data such as sediment Particle Size Distribution (PSD), bulky density, dam trap efficiency, catchment environmental variables (*i.e*., land cover/use, slope, slope length, runoff, rainfall, etc), and operational data and geographic locations of the small dams could be supplemented.

#### **5. Acknowledgment**

I acknowledge the cordial cooperation rendered to me by staff of the then Ministry of Water and Irrigation for availing previous reports on the subject matter. I'm also indebted to Mr. Kipagile, D., an undergraduate student of University of Dar es Salaam, for collecting and providing some data. FRIEND/Nile project funded by UNESCO Cairo Office is also acknowledged for co-sponsoring the write-up of this chapter.

#### **6. References**


prediction in the follow up research. This can be achieved if more data such as sediment Particle Size Distribution (PSD), bulky density, dam trap efficiency, catchment environmental variables (*i.e*., land cover/use, slope, slope length, runoff, rainfall, etc), and operational data and geographic locations of the small dams could be

I acknowledge the cordial cooperation rendered to me by staff of the then Ministry of Water and Irrigation for availing previous reports on the subject matter. I'm also indebted to Mr. Kipagile, D., an undergraduate student of University of Dar es Salaam, for collecting and providing some data. FRIEND/Nile project funded by UNESCO Cairo Office is also

Arnold, J.G., Williams, J.R., and Maidment, D.R., (1995). Continuous-time water and

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Lawrence, P., Cascio, A., Goldsmith, O., & Abott, C.L. (2004). *Sedimentation in small dams –* 

Malisa, J., (2007). *Dam Safety Analysis Using Physical And Numerical Models For Small Dams In* 

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**6. References** 

*pp171-183*.

New Delhi, India.

Publication no. 288.

Chapter 7, 7.1–7.44.

**5. Acknowledgment** 


**Suitability of SWAT Model for** 

*2UNESCO-IHE, Institute for Water Education, Delft,* 

Preksedis Marco Ndomba1 and Ann van Griensven2

Sediment yield refers to the amount of sediment exported by a basin over a period of time, which is also the amount that will enter a reservoir located at the downstream limit of the basin (Morris and Fan, 1998). The subject of sediment yield modelling has attracted the attention of many scientists but lack of data, resources and widely accepted methods to predict/estimate sediment yields are some of the barriers against this direction of research (Summer *et al*., 1992; Wasson 2002; Lawrence *et al.*, 2004; Ndomba, 2007; Ndomba *et al*., 2005,

The sediment yield model evaluated in this paper is the Soil and Water Assessment Tool (SWAT). It is hypothesized in the presented study cases that distributed and process based mathematical models such as SWAT could be a potential tool in predicting and estimating sediment yield especially at a catchment scale. Application of the distributed and processbased models could minimize the uncertainty resulting from assuming lumped, stationary and linear systems. Besides, the SWAT model has particular advantages for the study of basin change impacts and applications to basins with limited records (Bathurst, 2002; Ndomba, 2007). In principle, their parameters have a physical meaning and can be measured in the field, and therefore model validation can be concluded on the basis of a short field survey and a

SWAT was originally developed by the United States Department of Agriculture (USDA) to predict the impact of land management practices on water, sediment and agricultural chemical yields in large ungauged basins (Arnold *et al*., 1995). The SWAT model has a long modelling history since it incorporates features of several Agriculture Research Service (ARS) models (Neitsch *et al*., 2005). The SWAT model is a catchment-scale continuous time model that operates on a daily time step with up to monthly/annual output frequency. The major components of the model include weather, hydrology, erosion, soil temperature, plant growth, nutrients, pesticides, land management, channel and reservoir routing. It divides a catchment into subcatchments. Each subcatchment is connected through a stream channel and further divided into a Hydrologic Response Unit (HRU). The HRU is a unique combination of a soil and vegetation types within the subcatchment. Sediment yield is estimated for each HRU with the Modified Universal Soil Loss Equation (MUSLE)

short time series of meteorological and hydrological data (Bathurst, 2002).

**1. Introduction** 

2008b, 2009; Shimelis *et al*., 2010).

(Williams, 1975) (Equation 1).

**Sediment Yields Modelling** 

*1University of Dar es Salaam, Dar es Salaam,* 

**in the Eastern Africa** 

*1Tanzania 2Netherlands* 

URT, United Republic of Tanzania, (1999). Highway Design Manual Ministry of Works Tanzania. **13** 

## **Suitability of SWAT Model for Sediment Yields Modelling in the Eastern Africa**

Preksedis Marco Ndomba1 and Ann van Griensven2 *1University of Dar es Salaam, Dar es Salaam, 2UNESCO-IHE, Institute for Water Education, Delft, 1Tanzania 2Netherlands* 

#### **1. Introduction**

260 Advances in Data, Methods, Models and Their Applications in Geoscience

URT, United Republic of Tanzania, (1999). Highway Design Manual Ministry of Works

Sediment yield refers to the amount of sediment exported by a basin over a period of time, which is also the amount that will enter a reservoir located at the downstream limit of the basin (Morris and Fan, 1998). The subject of sediment yield modelling has attracted the attention of many scientists but lack of data, resources and widely accepted methods to predict/estimate sediment yields are some of the barriers against this direction of research (Summer *et al*., 1992; Wasson 2002; Lawrence *et al.*, 2004; Ndomba, 2007; Ndomba *et al*., 2005, 2008b, 2009; Shimelis *et al*., 2010).

The sediment yield model evaluated in this paper is the Soil and Water Assessment Tool (SWAT). It is hypothesized in the presented study cases that distributed and process based mathematical models such as SWAT could be a potential tool in predicting and estimating sediment yield especially at a catchment scale. Application of the distributed and processbased models could minimize the uncertainty resulting from assuming lumped, stationary and linear systems. Besides, the SWAT model has particular advantages for the study of basin change impacts and applications to basins with limited records (Bathurst, 2002; Ndomba, 2007). In principle, their parameters have a physical meaning and can be measured in the field, and therefore model validation can be concluded on the basis of a short field survey and a short time series of meteorological and hydrological data (Bathurst, 2002).

SWAT was originally developed by the United States Department of Agriculture (USDA) to predict the impact of land management practices on water, sediment and agricultural chemical yields in large ungauged basins (Arnold *et al*., 1995). The SWAT model has a long modelling history since it incorporates features of several Agriculture Research Service (ARS) models (Neitsch *et al*., 2005). The SWAT model is a catchment-scale continuous time model that operates on a daily time step with up to monthly/annual output frequency. The major components of the model include weather, hydrology, erosion, soil temperature, plant growth, nutrients, pesticides, land management, channel and reservoir routing. It divides a catchment into subcatchments. Each subcatchment is connected through a stream channel and further divided into a Hydrologic Response Unit (HRU). The HRU is a unique combination of a soil and vegetation types within the subcatchment. Sediment yield is estimated for each HRU with the Modified Universal Soil Loss Equation (MUSLE) (Williams, 1975) (Equation 1).

Suitability of SWAT Model for Sediment Yields Modelling in the Eastern Africa 263

River begins in the Central Ethiopian Highlands at an altitude of 3000 m to the west of Addis Ababa. After flowing through Koka Reservoir, it flows northeastwards along the rift valley until eventually discharging into Lake Abbe. The Koka Reservoir is situated about 90 km southeast of Addis Ababa at a longitude of 39 10' E and latitude of 8 25' N. The erosion rates in the KRC and in the Awash Basin as a whole are high with values generally

The climate of the Awash Basin is characterized by the Inter-Tropical Convergence Zone (ITCZ). The Mean annual rainfall (MAR) and temperature vary spatially across the catchment between 170 and 1978 mm/annum and 12.8 and 31.5oC, respectively. The area is dominated by a bimodal rainfall pattern. According to the National Meteorological Services Agency, the study area is characterized by a quasi-double maxima rainfall pattern with a small peak in April and maximum peak in August. The rainfall in the highlands shows a strong correlation with altitude (Lemma, 1996). The mean annual wind speed in the KRC is

Two major relief features are found in the Awash Basin: the highlands of the Ethiopian Plateau and the lowlands of the Rift Valley. The bedrock and soil in the area determine the amount and composition of transported sediments in the river. The geology of the basin is dominated by sedimentary rocks such as limestone and sandstone. The alluvium deposits consist of clay,

Case study 2, the Nyumba Ya Mungu (NYM) Reservoir subcatchment, has runoff that is highly regulated by the man-made Nyumba Ya Mungu (NYM) Reservoir of some 140 km2. The NYM Reservoir subcatchment is located in the upstream part of Pangani River catchment (PRC) (Figure 1 & Table 1). The PRC is located between coordinates 36o20' E, 02o55' S and 39o02' E, 05o40' S in the northeastern part of Tanzania and covers an area of about 42,200 km2, with approximately 5% in Kenya (Figure 1). The Pangani River has two main tributaries, the Kikuletwa (1DD1) and the Ruvu (1DC1) (Figure 1), which join at the

The catchment of NYM occupies a total land and water area of about 12,000 km2 (Ndomba, 2007). It is located between coordinates 36o20'00'' E, 3o00'00'' S and 38o00'00'' E, 4o3'50'' S. This area has a Mean Annual Rainfall (MAR) of about 1000 mm/annum. The rainfall pattern is bimodal with two distinct rainy seasons, long rains from March to June and short rains from November to December. Rohr and Killingtveit (2003) indicated that the maximum precipitation on the southern hillside of Mt. Kilimanjaro takes place at about 2,200 m.a.s.l., which is 400 – 500 m higher than previously assumed. The mean annual wind speed is 1.87 m/s. The altitude in the study area ranges from 700 and 5,825 m.a.s.l. with the peak of Mt. Kilimanjaro as the highest ground. Based on the Soil Atlas of Tanzania, the main soil type in the study area is clay with good drainage (Hathout, 1983). The landcover of the catchment is dominated by actively-induced vegetation, forest, bushland and thickets with some alpine desert. The majority of the population in the basin directly or indirectly depends on irrigated agriculture. Agriculture is concentrated in the highlands with area coverage less than 20% (Ndomba, 2007). Lowlands are better suited for pastoralism. The main runoffsediment generating subcatchments in the study area upstream of NYM reservoir are Weruweru, Kikafu, Sanya, Upper Kikuletwa and Mt. Meru. The basin is also important for hydropower generation, which is connected to the national grid. Hydropower plants, which are downstream of NYM Reservoir are NYM (8 MW), Hale (21 MW), and New Pangani falls

exceeding 6,000 t/km2/yr and occasionally as high as 20,000 t/km2/yr.

sand and tuff. The long rains occur between June and September.

Nyumba Ya Mungu (NYM) reservoir.

1.9 m/s.

(66 MW).

$$\text{Sed} = 11.8 \left( Q\_{surf} q\_{peak} A \text{rea}\_{hru} \right)^{0.56} K\_{\text{USLE}} C\_{\text{USLE}} P\_{\text{USLE}} L S\_{\text{USLE}} \text{CFRG} \tag{1}$$

Where *Sed* is defined as Sediment yield rate (tones/day), *Qsurf* is the surface runoff volume (mm/day), *qpeak* is the peak runoff rate (m3/s), *Areahru* is the area of the HRU (ha), *KUSLE* is the USLE soil erodibility factor (0.013 metric ton m2 hr/(m3-metric ton cm)), CUSLE is the USLE crop management factor or cover management factor, PUSLE is the USLE support practice factor, LSUSLE is the USLE topographic factor, and CFRG is the coarse fragment factor.

The runoff component of the SWAT model supplies estimates of runoff volume and peak runoff rate using the curve number method (SCS, 1972) and modified rational method, respectively, which, along with the subbasin area, are used to calculate the runoff erosive energy variable. The crop management factor or cover management factor is recalculated every day that runoff occurs. It is a function of above-ground biomass, residue on the soil surface and the minimum cover factor for the plant. The KUSLE factor is estimated using an equation proposed by Mulengera and Payton (1999) for tropics. Other factors of the erosion equation are estimated as described by Neitsch *et al*. (2005). The current version of the SWAT model uses the simplified stream power equation of Bagnold's (1977) to route sediment in the channel. The maximum amount of sediment that can be transported from a reach segment is a function of the peak channel velocity. Sediment transport in the channel network is a function of two processes, degradation and aggradation (*i.e.* deposition), operating simultaneously in the reach (Neitsch *et al*., 2005).

The SWAT model includes an automated calibration procedure. The calibration procedure is based on the Shuffled Complex Evolution-University of Arizona algorithm (SCE-UA) as proposed by Duan *et al.* (1992). The autocalibration option in SWAT provides a powerful, labour saving tool that can be used to substantially reduce the frustration and uncertainty that often characterizes manual calibration (Van Liew *et al*, 2005). In one of the study cases other calibration tools such as the 'Sequential Uncertainty Fitting Algorithm' (SUFI-2) program (Abbaspour *et al*., 2004, 2007) were used.

Although general SWAT applications have shown that the model performs satisfactorily (Ndomba and Birhanu, 2008), its suitability for specific applications such as sediment yield modelling has yet to be ascertained. In this paper, various sediment yield modelling issues involved with using SWAT such as data requirements and analysis, calibration, sensitivity and uncertainty are critically evaluated in three well-studied cases, the Nyumba Ya Mungu (NYM) Reservoir subcatchment located in the upstream part of the Pangani River catchment (PRC), (a trans-boundary catchment shared between Kenya and Tanzania); the Simiyu River catchment (SRC), (a Lake Victoria Basin subcatchment in Tanzania); and the Koka Reservoir catchment (KRC) in Ethiopia. Growing population, growing demand of cultivated land, mostly inaccurate traditional land usage and dangerously increasing deforestation have increased soil erosion. Erosion has a major impact on nature and diminished the agriculture potential of the selected study cases. Excessive exploitation increases the susceptibility of the soil to fluvial and upland erosion, which is responsible for the increased sediment transport and deposition into the reservoirs.

#### **2. Materials and methods**

#### **2.1 Description of the study cases**

Case study 1, the Koka Reservoir catchment (KRC) lies within the western part of the Awash Basin and has an area of approximately 11,000 km2 (Figure 1(a-d) & Table 1). The Awash

11.8 *Sed Q q Area K C P LS CFRG surf peak hru USLE USLE USLE USLE* (1)

0.56

Where *Sed* is defined as Sediment yield rate (tones/day), *Qsurf* is the surface runoff volume (mm/day), *qpeak* is the peak runoff rate (m3/s), *Areahru* is the area of the HRU (ha), *KUSLE* is the USLE soil erodibility factor (0.013 metric ton m2 hr/(m3-metric ton cm)), CUSLE is the USLE crop management factor or cover management factor, PUSLE is the USLE support practice factor, LSUSLE is the USLE topographic factor, and CFRG is the coarse fragment factor. The runoff component of the SWAT model supplies estimates of runoff volume and peak runoff rate using the curve number method (SCS, 1972) and modified rational method, respectively, which, along with the subbasin area, are used to calculate the runoff erosive energy variable. The crop management factor or cover management factor is recalculated every day that runoff occurs. It is a function of above-ground biomass, residue on the soil surface and the minimum cover factor for the plant. The KUSLE factor is estimated using an equation proposed by Mulengera and Payton (1999) for tropics. Other factors of the erosion equation are estimated as described by Neitsch *et al*. (2005). The current version of the SWAT model uses the simplified stream power equation of Bagnold's (1977) to route sediment in the channel. The maximum amount of sediment that can be transported from a reach segment is a function of the peak channel velocity. Sediment transport in the channel network is a function of two processes, degradation and aggradation (*i.e.* deposition),

The SWAT model includes an automated calibration procedure. The calibration procedure is based on the Shuffled Complex Evolution-University of Arizona algorithm (SCE-UA) as proposed by Duan *et al.* (1992). The autocalibration option in SWAT provides a powerful, labour saving tool that can be used to substantially reduce the frustration and uncertainty that often characterizes manual calibration (Van Liew *et al*, 2005). In one of the study cases other calibration tools such as the 'Sequential Uncertainty Fitting Algorithm' (SUFI-2)

Although general SWAT applications have shown that the model performs satisfactorily (Ndomba and Birhanu, 2008), its suitability for specific applications such as sediment yield modelling has yet to be ascertained. In this paper, various sediment yield modelling issues involved with using SWAT such as data requirements and analysis, calibration, sensitivity and uncertainty are critically evaluated in three well-studied cases, the Nyumba Ya Mungu (NYM) Reservoir subcatchment located in the upstream part of the Pangani River catchment (PRC), (a trans-boundary catchment shared between Kenya and Tanzania); the Simiyu River catchment (SRC), (a Lake Victoria Basin subcatchment in Tanzania); and the Koka Reservoir catchment (KRC) in Ethiopia. Growing population, growing demand of cultivated land, mostly inaccurate traditional land usage and dangerously increasing deforestation have increased soil erosion. Erosion has a major impact on nature and diminished the agriculture potential of the selected study cases. Excessive exploitation increases the susceptibility of the soil to fluvial and upland erosion, which is responsible for the increased sediment transport

Case study 1, the Koka Reservoir catchment (KRC) lies within the western part of the Awash Basin and has an area of approximately 11,000 km2 (Figure 1(a-d) & Table 1). The Awash

operating simultaneously in the reach (Neitsch *et al*., 2005).

program (Abbaspour *et al*., 2004, 2007) were used.

and deposition into the reservoirs.

**2.1 Description of the study cases** 

**2. Materials and methods** 

River begins in the Central Ethiopian Highlands at an altitude of 3000 m to the west of Addis Ababa. After flowing through Koka Reservoir, it flows northeastwards along the rift valley until eventually discharging into Lake Abbe. The Koka Reservoir is situated about 90 km southeast of Addis Ababa at a longitude of 39 10' E and latitude of 8 25' N. The erosion rates in the KRC and in the Awash Basin as a whole are high with values generally exceeding 6,000 t/km2/yr and occasionally as high as 20,000 t/km2/yr.

The climate of the Awash Basin is characterized by the Inter-Tropical Convergence Zone (ITCZ). The Mean annual rainfall (MAR) and temperature vary spatially across the catchment between 170 and 1978 mm/annum and 12.8 and 31.5oC, respectively. The area is dominated by a bimodal rainfall pattern. According to the National Meteorological Services Agency, the study area is characterized by a quasi-double maxima rainfall pattern with a small peak in April and maximum peak in August. The rainfall in the highlands shows a strong correlation with altitude (Lemma, 1996). The mean annual wind speed in the KRC is 1.9 m/s.

Two major relief features are found in the Awash Basin: the highlands of the Ethiopian Plateau and the lowlands of the Rift Valley. The bedrock and soil in the area determine the amount and composition of transported sediments in the river. The geology of the basin is dominated by sedimentary rocks such as limestone and sandstone. The alluvium deposits consist of clay, sand and tuff. The long rains occur between June and September.

Case study 2, the Nyumba Ya Mungu (NYM) Reservoir subcatchment, has runoff that is highly regulated by the man-made Nyumba Ya Mungu (NYM) Reservoir of some 140 km2. The NYM Reservoir subcatchment is located in the upstream part of Pangani River catchment (PRC) (Figure 1 & Table 1). The PRC is located between coordinates 36o20' E, 02o55' S and 39o02' E, 05o40' S in the northeastern part of Tanzania and covers an area of about 42,200 km2, with approximately 5% in Kenya (Figure 1). The Pangani River has two main tributaries, the Kikuletwa (1DD1) and the Ruvu (1DC1) (Figure 1), which join at the Nyumba Ya Mungu (NYM) reservoir.

The catchment of NYM occupies a total land and water area of about 12,000 km2 (Ndomba, 2007). It is located between coordinates 36o20'00'' E, 3o00'00'' S and 38o00'00'' E, 4o3'50'' S. This area has a Mean Annual Rainfall (MAR) of about 1000 mm/annum. The rainfall pattern is bimodal with two distinct rainy seasons, long rains from March to June and short rains from November to December. Rohr and Killingtveit (2003) indicated that the maximum precipitation on the southern hillside of Mt. Kilimanjaro takes place at about 2,200 m.a.s.l., which is 400 – 500 m higher than previously assumed. The mean annual wind speed is 1.87 m/s. The altitude in the study area ranges from 700 and 5,825 m.a.s.l. with the peak of Mt. Kilimanjaro as the highest ground. Based on the Soil Atlas of Tanzania, the main soil type in the study area is clay with good drainage (Hathout, 1983). The landcover of the catchment is dominated by actively-induced vegetation, forest, bushland and thickets with some alpine desert. The majority of the population in the basin directly or indirectly depends on irrigated agriculture. Agriculture is concentrated in the highlands with area coverage less than 20% (Ndomba, 2007). Lowlands are better suited for pastoralism. The main runoffsediment generating subcatchments in the study area upstream of NYM reservoir are Weruweru, Kikafu, Sanya, Upper Kikuletwa and Mt. Meru. The basin is also important for hydropower generation, which is connected to the national grid. Hydropower plants, which are downstream of NYM Reservoir are NYM (8 MW), Hale (21 MW), and New Pangani falls (66 MW).

Suitability of SWAT Model for Sediment Yields Modelling in the Eastern Africa 265

(Ndomba *et al*., 2005) and normally stays dry in the months of August, September and October. During the long rainy season, discharge from the river reaches as high as 331m3/s.

Case study 1

Case study 2

Case study 3

Fig. 1a. A map showing the three case studies in Eastern Africa


Table 1. Major characteristics of the three study cases in Eastern Africa

Case study 3, the Simiyu River catchment (SRC), is located in the northern part of Tanzania southeast of Lake Victoria (Figure 1 & Table 1). It covers an area of 10,659 km2 and is located between the coordinates 33o15'00" E, 02o30'00" S and 35o00'00" E, 03o30'00" S. The SRC is occupied by about one million inhabitants. The catchment is mainly covered by agricultural land for farming, grassland for grazing, and bushland. The Simiyu River flows from the Serengeti National Park Plains to Lake Victoria in the downstream region. The two major tributaries of the Simiyu River are Simiyu-Duma and Simiyu-Ndagalu and they merge shortly before the Simiyu River enters Lake Victoria. The river is characterized as ephemeral

Actively induced vegetation, forest, bushland and thickets with some alpine desert and agricultural

land for farming

land for

land for farming, grassland for grazing, and bushland.

Case study 3, the Simiyu River catchment (SRC), is located in the northern part of Tanzania southeast of Lake Victoria (Figure 1 & Table 1). It covers an area of 10,659 km2 and is located between the coordinates 33o15'00" E, 02o30'00" S and 35o00'00" E, 03o30'00" S. The SRC is occupied by about one million inhabitants. The catchment is mainly covered by agricultural land for farming, grassland for grazing, and bushland. The Simiyu River flows from the Serengeti National Park Plains to Lake Victoria in the downstream region. The two major tributaries of the Simiyu River are Simiyu-Duma and Simiyu-Ndagalu and they merge shortly before the Simiyu River enters Lake Victoria. The river is characterized as ephemeral

farming, Acacia and eucalyptus trees are prevailing ones

Topography Land use/cover Geology and

Soil type

Neogene

including calcareous tuffaceosus; Clay with moderate to good drainage

Sedimentary rocks such as limestone and sandstone; clay, sand and tuff

Dominated by Precambrian rocks and some quaternary sediments; There are also some extensive areas overlain by recent alluvial deposits; sandy loam covers a large part of the catchment

Volcanic and pre-Cambrian metamorphic rocks extensively covered by superficial Neogene deposits Climate

Semi arid humid

Tropical

Warm tropical savannah climate/ Diverse

Case study Catchment area (km2)

12,000 Plains -

mountainous

11,000 Rugged Agricultural

10,659 Relatively flat Agricultural

Table 1. Major characteristics of the three study cases in Eastern Africa

Nyumba Ya Mungu (NYM) Reservoir catchment in the upstream part of the Pangani River catchment

Koka Reservoir catchment (KRC)

Simiyu River catchment (SRC)

(Ndomba *et al*., 2005) and normally stays dry in the months of August, September and October. During the long rainy season, discharge from the river reaches as high as 331m3/s.

Fig. 1a. A map showing the three case studies in Eastern Africa

Suitability of SWAT Model for Sediment Yields Modelling in the Eastern Africa 267

Fig. 1c. A location map of Case study 2, Nyumba Ya Mungu Reservoir, in the upstream part

of the Pangani River catchment as adopted from (Ndomba, 2007)

Fig. 1b. A location map of Case study 1, Koka Reservoir catchment (KRC), as adopted from Endale(2008)

The catchment has a warm tropical savannah climate with an average temperature of about 23oC. The total average annual precipitation varies between 700 and 800 mm/annum. The mean annual wind speed is 1.60 m/s. The SRC is considered to be one of the main contributors to the deterioration of water quality (*i.e*., sediments and nutrients) in the Lake Victoria. This is because of its relatively large size, its large inflow contribution and its many agricultural activities using agrochemicals which generate high yields of sediments.

#

\$T

#

Fig. 1b. A location map of Case study 1, Koka Reservoir catchment (KRC), as adopted from

The catchment has a warm tropical savannah climate with an average temperature of about 23oC. The total average annual precipitation varies between 700 and 800 mm/annum. The mean annual wind speed is 1.60 m/s. The SRC is considered to be one of the main contributors to the deterioration of water quality (*i.e*., sediments and nutrients) in the Lake Victoria. This is because of its relatively large size, its large inflow contribution and its many

agricultural activities using agrochemicals which generate high yields of sediments.

\$T Koka Reservoir

**S**

**N**

Rainfall stations

Flows stations

Koka Reservoir

Rivers

**W E**

Mojo Flow Gauge St. Mojo Flow Gauge St.
