**Meet the author**

Dr. Anthony Okiwelu holds a PhD degree in Geophysics from the University of Calabar, Nigeria, and MSc degree in Geophysics and BSc degree in Geology from the Universities of Ibadan and Calabar, respectively. His main research interest is in magnetics, gravimetry, and tectonics. He has also published some papers in geodesy, geopotential field models, and seismic and electrical

methods. He is a professor of Geophysics in Geophysics Unit, Physics Department, University of Calabar, Nigeria, where he teaches magnetic prospecting, gravimetry, geomathematics, and Earth Physics. He is an active member of International body, Society of Exploration Geophysicists (SEG), Nigerian Institute of Physics (NIP), and Nigerian Mining and Geoscience Society (NMGS).

Contents

**Preface VII**

**Section 1 Seismic and Potential Field Methods 1**

**Seismicity: A Review 19**

Zbigniew Krajewski

**Near-Surface Inhomogeneities 3**

**Based on Magnetic Amplitude 41**

**Seismic and Potential Field Data 65**

**Section 2 Geo-Hazard: Seismicity and Geoelectric 83**

**Hilbert-Huang Transform 101**

Eneanwan Ekpo, David Eaton and Ronald Weir

Guevara and María Ladrón de Guevara-Torres

Chapter 6 **Characterization of Seismic Responses in Mexico City Using**

Silvia Raquel García Benítez and Leonardo Alcántara Nolasco

Shuang Liu and Xiangyun Hu

Chapter 1 **Three–Dimensional Seismic Diffraction Imaging for Detecting**

Shemer Keydar, Vladimir Shtivelman and Avner Arzi

Leszek R. Jaroszewicz, Anna Kurzych, Krzysztof P. Teisseyre and

**Presence of Significant Remanence and Self-Demagnetization**

Chapter 2 **Measurement of Rotational Events in Regions Prone to**

Chapter 3 **Inversion and Interpretation of Magnetic Anomaly in the**

Chapter 4 **Basement Tectonics and Fault Reactivation in Alberta Based on**

Chapter 5 **Characterization of Hydrocarbon-Contaminated Sites Based on Geoelectrical Methods of Geophysical Exploration 85** Omar Delgado-Rodríguez, Vladimir Shevnin, Héctor Peinado-

## Contents

#### **Preface XI**


**Hilbert-Huang Transform 101** Silvia Raquel García Benítez and Leonardo Alcántara Nolasco

#### **X** Contents

#### **Section 3 Earth Planetary System 117**

#### Chapter 7 **Dynamics of the Early Stage of Formation of the Earth's-Moon System 119** Yurie Khachay, Olga Hachay and Alexander Antipin

#### **Section 4 Electrical Resistivity Surveying 133**

#### Chapter 8 **Geoelectrical Sounding and Imaging over the Central Zone of Panama 135** Alexis Mojica

Preface

This book is focused on different aspects of geophysical research, particularly on modern ap‐ proach in subsurface imaging, tectonics, geohazard, seismicity, and Earth planetary system. Syntheses of results from regional and local studies combined with new techniques of geo‐ physical data acquisition and interpretation from diverse geological provinces are presented. The first group of chapters is dedicated to seismic and potential field methods. S. Keyder used seismic diffracted (scattered) waves to locate near-surface sources in Israel. Diffracted waves are usually considered as noise in seismic exploration. This imaging technique could be a 3D volume in which prominent diffraction anomalies appear at spatial locations close to the imaged source. The fundamental concept of this study is based on spatial summation of diffracted wave field along diffracted time surfaces, which is defined by source-receiver geometry in 2D or 3D space. This method which reveals localized inhomogeneities has ap‐ plication in engineering, environment, and archeogeophysics. The authors tested this techni‐ que with both synthetic and field data. The synthetic examples demonstrated the application of the method to locate both small quasi-isometric source such as small karstic cavity and a linear elongated source such as tunnel/tube. Field examples in this study are from the Dead Sea, Chalky Hills (23km east of Mediterranean Sea), modern operating aque‐ duct and limestone quarry. The field datasets revealed the depths to the local sources.

R. Leszek and others in their chapter presented the fundamental requirements in the area of rotational seismology. They defined rotation in this context as displacement of rocks, soils, and various objects during earthquake in the focal area and its vicinity. Reversible rotational oscillations in the seismic wave field are called seismic rotations. In seismological perspec‐ tive, it is an area of a rotational seismology, which deals with all aspects of a rotational ground motion induced by earthquakes, explosions, and ambient vibrations. This field of study is very interesting for researchers from a wide range of geophysical disciplines, in‐ cluding broadband seismology, strong-motion seismology, earthquake physics, seismic haz‐ ards, seismotectonics, and geodesy and for physicists using Earth-based observatories for detecting gravitational waves generated by astronomical sources. In addition, it is interest‐ ing for researchers of earthquake engineering, where seismic signals of different engineering structures are investigated, to search for their optimal seismic design. This chapter gave viv‐ id illustrations of modern seismometers for the study of rotational seismics and compared the results obtained from optical and mechanical rotational seismometers. It was concluded

that technologies based on optical interferometer are the most promising ones.

One of the chapters by Liu and Hu specifically explained how remanent magnetization and self-demagnetization complicate the inversion and interpretation of magnetic anomaly. They used both synthetic data and field data from iron deposit in South Australia to demon‐

## Preface

**Section 3 Earth Planetary System 117**

**VI** Contents

**of Panama 135** Alexis Mojica

Chapter 7 **Dynamics of the Early Stage of Formation of the**

Yurie Khachay, Olga Hachay and Alexander Antipin

Chapter 8 **Geoelectrical Sounding and Imaging over the Central Zone**

**Earth's-Moon System 119**

**Section 4 Electrical Resistivity Surveying 133**

This book is focused on different aspects of geophysical research, particularly on modern ap‐ proach in subsurface imaging, tectonics, geohazard, seismicity, and Earth planetary system. Syntheses of results from regional and local studies combined with new techniques of geo‐ physical data acquisition and interpretation from diverse geological provinces are presented.

The first group of chapters is dedicated to seismic and potential field methods. S. Keyder used seismic diffracted (scattered) waves to locate near-surface sources in Israel. Diffracted waves are usually considered as noise in seismic exploration. This imaging technique could be a 3D volume in which prominent diffraction anomalies appear at spatial locations close to the imaged source. The fundamental concept of this study is based on spatial summation of diffracted wave field along diffracted time surfaces, which is defined by source-receiver geometry in 2D or 3D space. This method which reveals localized inhomogeneities has ap‐ plication in engineering, environment, and archeogeophysics. The authors tested this techni‐ que with both synthetic and field data. The synthetic examples demonstrated the application of the method to locate both small quasi-isometric source such as small karstic cavity and a linear elongated source such as tunnel/tube. Field examples in this study are from the Dead Sea, Chalky Hills (23km east of Mediterranean Sea), modern operating aque‐ duct and limestone quarry. The field datasets revealed the depths to the local sources.

R. Leszek and others in their chapter presented the fundamental requirements in the area of rotational seismology. They defined rotation in this context as displacement of rocks, soils, and various objects during earthquake in the focal area and its vicinity. Reversible rotational oscillations in the seismic wave field are called seismic rotations. In seismological perspec‐ tive, it is an area of a rotational seismology, which deals with all aspects of a rotational ground motion induced by earthquakes, explosions, and ambient vibrations. This field of study is very interesting for researchers from a wide range of geophysical disciplines, in‐ cluding broadband seismology, strong-motion seismology, earthquake physics, seismic haz‐ ards, seismotectonics, and geodesy and for physicists using Earth-based observatories for detecting gravitational waves generated by astronomical sources. In addition, it is interest‐ ing for researchers of earthquake engineering, where seismic signals of different engineering structures are investigated, to search for their optimal seismic design. This chapter gave viv‐ id illustrations of modern seismometers for the study of rotational seismics and compared the results obtained from optical and mechanical rotational seismometers. It was concluded that technologies based on optical interferometer are the most promising ones.

One of the chapters by Liu and Hu specifically explained how remanent magnetization and self-demagnetization complicate the inversion and interpretation of magnetic anomaly. They used both synthetic data and field data from iron deposit in South Australia to demon‐

strate that intensity and direction of internal magnetization can be distorted by remanence. In this study, the primary advantage magnitude of magnetic anomaly inversion is that the magnetization is not assumed to be parallel to the magnetic field. 2D magnetic anomaly was computed in the frequency domain and related to magnetization direction and shape of magnetic sources.

vulnerability of the aquifers in the study areas. One of the highlights of this study is that the

Preface IX

The next chapter on geohazard based on seismic response in Mexico was written by S. Gar‐ cia and L. Alcantara. In this study, they used Hilbert-Huang transform (HHT) as an alterna‐ tive technique, which has advantage over other methods for extracting data that will be useful for the assessment of potential earthquake and, if integrated with the empirical mode decomposition (EMD) and the Hilbert transform (HT), enables engineers to analyze data from nonlinear and nonstationary processes. The HHT proposed by Huang and others con‐ sists of two parts: (i) Empirical Mode Decomposition (EMD), and (ii) Hilbert spectral analy‐ sis. Signals to be analyzed are decomposed into a finite number of intrinsic mode functions or IMFs in what is called the EMD process. The Hilbert transform allows the computation of

The two authors demonstrated that the use of Fourier spectral analysis for studying nonsta‐ tionary-nonlinear data is not a robust tool for these kinds of analyses since it cannot show the detailed information about the peculiarities of the energy-frequency distribution. By using Hilbert spectra, events in the database will have direct important characteristics such as the arrival time, and the duration of intense phase of the earthquakes can be detected. In addition to the well-defined zone of maximum accelerations, the huge variations of the response fre‐ quencies between the beginning (the maximum amplitude cycles) and the end of the event can be clearly detected and quantified. The Hilbert spectral transformation permits the recog‐

OGEOMET reduced the number of drillings and soil samples for chemical analyses.

instantaneous frequencies and amplitudes and describes the signal more locally.

nition of oscillation modes that would have been masked by Fourier spectral analysis.

ues of which are known with a high degree of uncertainty.

Y. Khachay and his colleagues presented the results of a numerical simulation of the thermal evolution of a 3D spherical segment of a protoplanet of an increasing radius, taking into account the accidental falling of bodies and particles. Some new questions were raised such as what is beyond the boundaries of our universe? Is the universe only one? Are there any measurable physical fields and processes that will allow one to detect real objects external to our universe? They employed algorithm for the numerical solution of the problem consider‐ ing the dissipation of tidal energy in the Earth-Moon system at the stage of planetary accu‐ mulation. The study noted that at all stages of the Earth's formation, convective heat and mass transfer are the most important factors in the dynamics of the planet. Their result shows that the temperature of the growing surface sharply decreases as the transparency of the atmosphere increases, due to the increase of the gravitational radius of the protoplanet and the possibility of retaining the silicate content of the cloud. The following conclusions could be derived from this study: (1) As the mass increases, the distance between their cen‐ ters of mass and the speed of the orbital rotation of the Moon around the Earth change. From the law of conservation of angular momentum, it follows that the tidal interaction as the mass of the central body increases provides the transfer of the orbital angular momen‐ tum of the satellite to the central massive body. (2) Due to the continued transfer of the satel‐ lite's orbital moment to the central body, its own angular velocity continued to grow. This should lead to an increase in the orbital angular velocity of the satellite and an increase in the radius of its orbit, which is observed up to the present time. (3) The results obtained depend on the parameters, primarily the viscosity versus temperature and pressure, the val‐

A. Mojica, in the chapter on electrical resistivity surveying, gave a short description of elec‐ trical properties of rocks and basic principles of the geoelectrical resistivity. He used electri‐

Another chapter by Ekpo and others is very interesting and comprehensive in the sense that the chapter used integrated methods in geophysics. Using regional gravity and magnetic datasets combined with Lithoprobe crustal seismic profile and well data, they investigated basement tectonics and crustal structure in Alberta, western Canada. The Precambrian base‐ ment beneath Alberta was formed by amalgamation of disparate domains that were assem‐ bled by the plate-tectonic processes of subduction. Basement domains that are the focus of this study occurred between the Snowbird Tectonic Zone (STZ) and Great Slave Lake Shear Zone (GSLs Z) and have Paleoproterozoic crystallization ages (1.9–2.4 GA). This area is prone to induced seismicity, and brittle faults are poorly imaged by seismic data due to ob‐ scuring effects of multiple. Thus, the use of potential-field fabrics was able to establish the tectonic setting of basement domains with additional information provided by magnetic, Bouguer, and isostatic residual anomalies based on 2D modeling constrained by seismic profiles. The main objective of this study is to present new insights arising from geophysical imaging and mapping of representative basement fault structure and how they may lead to the understanding of induced seismicity. To achieve this objective, the authors used the in‐ terpretation approach, which involves mapping and identification of basement structures combined with 2D gravity and magnetic modeling for selected profiles. The analyses showed that regional gravity anomaly patterns clearly revealed large-scale crustal features. An example is a Bouguer gravity low that marks the isostatic root beneath the Rocky Moun‐ tains, an isostatic gravity high that reflects a flexurally supported topographic load in the Rock Mountain frost ranges of Alberta and NE-SW linear fabrics associated with the Snow‐ bird Tectonic Zone (STZ). The result of this study also demonstrated that magnetic anomaly map can provide a method for delimiting the extent of basement tectonic domain. While the magnetic anomalies predominantly reflect the magnetic susceptibility of the upper base‐ ment due to the wavelength differences, the gravity anomalies are primarily sensitive to deeper crustal level.

Two chapters are devoted to geohazard. The chapter based on the optimal geoelectric meth‐ odology (OGEOMET) written by O. Delgado-Rodríguez as the lead author integrated geo‐ electric methods to investigate hydrocarbon-contaminated sites in Mexico. The electromagnetic profiling provided a reliable and fast method that unraveled the configura‐ tion of oil-contaminated plume from apparent resistivity map and was used to guide the subsequent electrical resistivity tomography survey. Electrical resistivity tomography (ERT) and electromagnetic profiling (EMP) methods were used for the delimitation of the resistivi‐ ty anomalies caused by different types of hydrocarbon contaminants and rocks in rural, in‐ dustrial, and urban sites. Another method used in this study includes the use of petrophysical model. In the laboratory, the behavior of soil resistivity versus water salinity in clean soil samples is measured, and clay content, porosity, and cation exchange capacity (CEC) were determined. The knowledge of these petrophysical parameters was used to de‐ fine the geoelectric boundary between contaminated and clean zones. This chapter revealed the migration pathways of contaminants and located the sources of contaminants and the vulnerability of the aquifers in the study areas. One of the highlights of this study is that the OGEOMET reduced the number of drillings and soil samples for chemical analyses.

strate that intensity and direction of internal magnetization can be distorted by remanence. In this study, the primary advantage magnitude of magnetic anomaly inversion is that the magnetization is not assumed to be parallel to the magnetic field. 2D magnetic anomaly was computed in the frequency domain and related to magnetization direction and shape of

Another chapter by Ekpo and others is very interesting and comprehensive in the sense that the chapter used integrated methods in geophysics. Using regional gravity and magnetic datasets combined with Lithoprobe crustal seismic profile and well data, they investigated basement tectonics and crustal structure in Alberta, western Canada. The Precambrian base‐ ment beneath Alberta was formed by amalgamation of disparate domains that were assem‐ bled by the plate-tectonic processes of subduction. Basement domains that are the focus of this study occurred between the Snowbird Tectonic Zone (STZ) and Great Slave Lake Shear Zone (GSLs Z) and have Paleoproterozoic crystallization ages (1.9–2.4 GA). This area is prone to induced seismicity, and brittle faults are poorly imaged by seismic data due to ob‐ scuring effects of multiple. Thus, the use of potential-field fabrics was able to establish the tectonic setting of basement domains with additional information provided by magnetic, Bouguer, and isostatic residual anomalies based on 2D modeling constrained by seismic profiles. The main objective of this study is to present new insights arising from geophysical imaging and mapping of representative basement fault structure and how they may lead to the understanding of induced seismicity. To achieve this objective, the authors used the in‐ terpretation approach, which involves mapping and identification of basement structures combined with 2D gravity and magnetic modeling for selected profiles. The analyses showed that regional gravity anomaly patterns clearly revealed large-scale crustal features. An example is a Bouguer gravity low that marks the isostatic root beneath the Rocky Moun‐ tains, an isostatic gravity high that reflects a flexurally supported topographic load in the Rock Mountain frost ranges of Alberta and NE-SW linear fabrics associated with the Snow‐ bird Tectonic Zone (STZ). The result of this study also demonstrated that magnetic anomaly map can provide a method for delimiting the extent of basement tectonic domain. While the magnetic anomalies predominantly reflect the magnetic susceptibility of the upper base‐ ment due to the wavelength differences, the gravity anomalies are primarily sensitive to

Two chapters are devoted to geohazard. The chapter based on the optimal geoelectric meth‐ odology (OGEOMET) written by O. Delgado-Rodríguez as the lead author integrated geo‐ electric methods to investigate hydrocarbon-contaminated sites in Mexico. The electromagnetic profiling provided a reliable and fast method that unraveled the configura‐ tion of oil-contaminated plume from apparent resistivity map and was used to guide the subsequent electrical resistivity tomography survey. Electrical resistivity tomography (ERT) and electromagnetic profiling (EMP) methods were used for the delimitation of the resistivi‐ ty anomalies caused by different types of hydrocarbon contaminants and rocks in rural, in‐ dustrial, and urban sites. Another method used in this study includes the use of petrophysical model. In the laboratory, the behavior of soil resistivity versus water salinity in clean soil samples is measured, and clay content, porosity, and cation exchange capacity (CEC) were determined. The knowledge of these petrophysical parameters was used to de‐ fine the geoelectric boundary between contaminated and clean zones. This chapter revealed the migration pathways of contaminants and located the sources of contaminants and the

magnetic sources.

VIII Preface

deeper crustal level.

The next chapter on geohazard based on seismic response in Mexico was written by S. Gar‐ cia and L. Alcantara. In this study, they used Hilbert-Huang transform (HHT) as an alterna‐ tive technique, which has advantage over other methods for extracting data that will be useful for the assessment of potential earthquake and, if integrated with the empirical mode decomposition (EMD) and the Hilbert transform (HT), enables engineers to analyze data from nonlinear and nonstationary processes. The HHT proposed by Huang and others con‐ sists of two parts: (i) Empirical Mode Decomposition (EMD), and (ii) Hilbert spectral analy‐ sis. Signals to be analyzed are decomposed into a finite number of intrinsic mode functions or IMFs in what is called the EMD process. The Hilbert transform allows the computation of instantaneous frequencies and amplitudes and describes the signal more locally.

The two authors demonstrated that the use of Fourier spectral analysis for studying nonsta‐ tionary-nonlinear data is not a robust tool for these kinds of analyses since it cannot show the detailed information about the peculiarities of the energy-frequency distribution. By using Hilbert spectra, events in the database will have direct important characteristics such as the arrival time, and the duration of intense phase of the earthquakes can be detected. In addition to the well-defined zone of maximum accelerations, the huge variations of the response fre‐ quencies between the beginning (the maximum amplitude cycles) and the end of the event can be clearly detected and quantified. The Hilbert spectral transformation permits the recog‐ nition of oscillation modes that would have been masked by Fourier spectral analysis.

Y. Khachay and his colleagues presented the results of a numerical simulation of the thermal evolution of a 3D spherical segment of a protoplanet of an increasing radius, taking into account the accidental falling of bodies and particles. Some new questions were raised such as what is beyond the boundaries of our universe? Is the universe only one? Are there any measurable physical fields and processes that will allow one to detect real objects external to our universe? They employed algorithm for the numerical solution of the problem consider‐ ing the dissipation of tidal energy in the Earth-Moon system at the stage of planetary accu‐ mulation. The study noted that at all stages of the Earth's formation, convective heat and mass transfer are the most important factors in the dynamics of the planet. Their result shows that the temperature of the growing surface sharply decreases as the transparency of the atmosphere increases, due to the increase of the gravitational radius of the protoplanet and the possibility of retaining the silicate content of the cloud. The following conclusions could be derived from this study: (1) As the mass increases, the distance between their cen‐ ters of mass and the speed of the orbital rotation of the Moon around the Earth change. From the law of conservation of angular momentum, it follows that the tidal interaction as the mass of the central body increases provides the transfer of the orbital angular momen‐ tum of the satellite to the central massive body. (2) Due to the continued transfer of the satel‐ lite's orbital moment to the central body, its own angular velocity continued to grow. This should lead to an increase in the orbital angular velocity of the satellite and an increase in the radius of its orbit, which is observed up to the present time. (3) The results obtained depend on the parameters, primarily the viscosity versus temperature and pressure, the val‐ ues of which are known with a high degree of uncertainty.

A. Mojica, in the chapter on electrical resistivity surveying, gave a short description of elec‐ trical properties of rocks and basic principles of the geoelectrical resistivity. He used electri‐

cal resistivity method to define 1D and 2D electrical models from two datasets acquired in dry and rainy seasons in Panama (Central America). The results obtained enabled him to monitor the percentage changes of calculated resistivity values and define the stratigraphy of the area of study. He also obtained a relationship between electrical resistivity and volu‐ metric water content and correlated this with empirical equation of Archie. Petrophysical analyses show good fits between resistivity and volumetric water content and known pa‐ rameters for rocks and soils. Mojica used the Res2Dinv inversion software (Geotomo) to esti‐ mate the changes in subsurface resistivity values during the period of monitoring. In this software, the initial dataset for the inversion model is used as a reference model in the inver‐ sion of the later time-lapse datasets. The result of the electrical sounding tied to the well data at the site showed that the two first layers are linked to weathered and fractured sedimenta‐ ry rock, while the last layer is linked to hard sedimentary rock. The result of the electrical resistivity imaging and time lapse revealed high negative percentage change, which is linked to increase of water content in subsoil produced by rains that occurred on May 31, 2012, while positive percentage changes in model resistivity are related to inversion arti‐ facts. He concluded that these unrealistic changes can be linked to the removal electrode after the first test or inversion scheme used in the analyses.

> **Anthony Okiwelu** Department of Physics University of Calabar, Nigeria

**Section 1**

**Seismic and Potential Field Methods**

**Seismic and Potential Field Methods**

cal resistivity method to define 1D and 2D electrical models from two datasets acquired in dry and rainy seasons in Panama (Central America). The results obtained enabled him to monitor the percentage changes of calculated resistivity values and define the stratigraphy of the area of study. He also obtained a relationship between electrical resistivity and volu‐ metric water content and correlated this with empirical equation of Archie. Petrophysical analyses show good fits between resistivity and volumetric water content and known pa‐ rameters for rocks and soils. Mojica used the Res2Dinv inversion software (Geotomo) to esti‐ mate the changes in subsurface resistivity values during the period of monitoring. In this software, the initial dataset for the inversion model is used as a reference model in the inver‐ sion of the later time-lapse datasets. The result of the electrical sounding tied to the well data at the site showed that the two first layers are linked to weathered and fractured sedimenta‐ ry rock, while the last layer is linked to hard sedimentary rock. The result of the electrical resistivity imaging and time lapse revealed high negative percentage change, which is linked to increase of water content in subsoil produced by rains that occurred on May 31, 2012, while positive percentage changes in model resistivity are related to inversion arti‐ facts. He concluded that these unrealistic changes can be linked to the removal electrode

> **Anthony Okiwelu** Department of Physics

University of Calabar, Nigeria

after the first test or inversion scheme used in the analyses.

X Preface

**Chapter 1**

**Provisional chapter**

**Three–Dimensional Seismic Diffraction Imaging for**

One of the problems encountered in a variety of near-surface investigations is detecting and mapping localized inhomogeneities. Typical examples of such inhomogeneous sources are cavities, caves and tunnels. Different methods for detecting shallow subsurface sources utilizing seismic waves diffracted by these sources were proposed by many researchers in the last three decades. Most of these methods suggest that every subsurface point is a possible location of a point diffractor. Imaging of the diffractors is based on a spatial summation of the diffracted wavefield along diffraction time surfaces (defined by source-receiver geometry) in 2D or 3D space. The summation is performed with a fixed velocity value estimated from velocity analysis of the diffraction data. In this study, we present a path integral summation approach, where for every subsurface point the wavefield is stacked together along all possible diffraction time surfaces having a common apex at a given time. The result of the imaging is a 3D volume in which prominent diffraction anomalies appear at spatial locations close to the imaged sources. This path integral summation approach has been successfully tested on synthetic data and further applied at several sites with known subsurface sources.

**Keywords:** near surface, inhomogeneities, diffraction imaging, path integral

and tunnels and other natural and man-made local inhomogeneities.

The problem of detecting localized near-surface inhomogeneities is encountered in a variety of applications, such as engineering site investigation, environmental studies, archeology and security problems. Typical examples of such sources of inhomogeneities are cavities, caves

**Three**–**Dimensional Seismic Diffraction Imaging for** 

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.74059

**Detecting Near-Surface Inhomogeneities**

**Detecting Near-Surface Inhomogeneities**

Shemer Keydar, Vladimir Shtivelman and Avner Arzi

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Shemer Keydar, Vladimir Shtivelman and

http://dx.doi.org/10.5772/intechopen.74059

Avner Arzi

**Abstract**

summation, seismic

**1. Introduction**

#### **Three–Dimensional Seismic Diffraction Imaging for Detecting Near-Surface Inhomogeneities Three**–**Dimensional Seismic Diffraction Imaging for Detecting Near-Surface Inhomogeneities**

DOI: 10.5772/intechopen.74059

Shemer Keydar, Vladimir Shtivelman and Avner Arzi Shemer Keydar, Vladimir Shtivelman and Avner Arzi

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74059

#### **Abstract**

One of the problems encountered in a variety of near-surface investigations is detecting and mapping localized inhomogeneities. Typical examples of such inhomogeneous sources are cavities, caves and tunnels. Different methods for detecting shallow subsurface sources utilizing seismic waves diffracted by these sources were proposed by many researchers in the last three decades. Most of these methods suggest that every subsurface point is a possible location of a point diffractor. Imaging of the diffractors is based on a spatial summation of the diffracted wavefield along diffraction time surfaces (defined by source-receiver geometry) in 2D or 3D space. The summation is performed with a fixed velocity value estimated from velocity analysis of the diffraction data. In this study, we present a path integral summation approach, where for every subsurface point the wavefield is stacked together along all possible diffraction time surfaces having a common apex at a given time. The result of the imaging is a 3D volume in which prominent diffraction anomalies appear at spatial locations close to the imaged sources. This path integral summation approach has been successfully tested on synthetic data and further applied at several sites with known subsurface sources.

**Keywords:** near surface, inhomogeneities, diffraction imaging, path integral summation, seismic

#### **1. Introduction**

The problem of detecting localized near-surface inhomogeneities is encountered in a variety of applications, such as engineering site investigation, environmental studies, archeology and security problems. Typical examples of such sources of inhomogeneities are cavities, caves and tunnels and other natural and man-made local inhomogeneities.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In the past decades, many attempts have been made to solve the problem using various geophysical methods. The methods in use can be roughly subdivided into two groups. The first group includes low-resolution bulk techniques such as microgravity, geoelectric method and seismic surface wave method. A typical drawback of these methods is their low detectability, limiting them to relatively large sources, that is, such sources whose dimension-to-depth ratio exceeds 1/2 [1–4]. The second group includes the high-resolution ground – penetrating radar (GPR) method. The main drawback of this method is its high sensitivity to electrical conductivity of near-surface material which makes it limited to very shallow depths usually not exceeding a number of meters. Furthermore, our experience shows that the general problem of all the existing techniques is a high degree of ambiguity of data interpretation and, as a result, a high percentage of errors. One of the methods that may prove very effective for this purpose is active seismic, which is widely employed by seismic exploration industry in its extensive and detailed studies of the subsurface. Adaptation of these methods for the purpose of searching for local underground heterogeneities is not an easy task. The primary aim of seismic exploration is to study geological sources of large lateral extent, such as boundaries of geologic formations, oil and gas deposits, etc. To this end, seismic exploration ("reflection seismic") utilizes seismic waves emitted from man-made (active) seismic sources and reflected from the boundaries of interest back to the surface. The methodology, the data acquisition and processing techniques employed by the reflection seismic are largely based on the model of the subsurface consisting of a number of layers divided by smooth curvilinear boundaries with gradual changes of parameters within layers. Virtually, the same model of the subsurface is behind the refraction seismic method, another technology used primarily to study the shallow part of the subsurface (first tens of meters). Clearly, such methods are not directly applicable to a search for local subsurface inhomogeneities of small lateral extent (10–100 m). The amount of energy reflected by such small sources would be very small, and it would be indistinguishable from other geological features of the subsurface. In order to be effective, the search for local inhomogeneities has been employed to image the features of seismic wavefield, which is primarily associated with the presence of local heterogeneity in the subsurface. Such features are known as scattered (diffracted) waves. In a standard seismic prospecting, these waves are usually treated as noise. But for locating local sources these waves provide the most valuable source of information [5–12].

**2.2. Diffraction imaging**

located in different geological environments.

**2.3. Theoretical background**

relatively small objects.

Imaging of the local heterogeneities in 3D space can be performed by a spatial summation of

Three–Dimensional Seismic Diffraction Imaging for Detecting Near-Surface Inhomogeneities

http://dx.doi.org/10.5772/intechopen.74059

5

The summation can be implemented using one of the two approaches. In the first step (conventional approach), target waves are stacked along the time surfaces defined by some "optimal" velocity values. These values are usually estimated by a time-consuming procedure of velocity analysis involving visual examination and interpretation of intermediate seismic images. Recently, an alternative method, a more formal, path integral summation approach, has been proposed [7, 10–12]. Path integral summation is performed by stacking the target waves along all possible time surfaces having a common apex at the given point. This approach does not require any explicit information on velocities since the required multipath summation is performed for all possible velocity values within a wide specified range. Application of the path integral summation to synthetic and real data shows that it can provide reliable images of subsurface objects close to their true spatial locations [9]. However, the spatial resolution of the images obtained by the path integral summation is usually inferior to those obtained using the fixed velocity.

In the subsequent sections, we give a brief description of the main principles of the method and illustrate its application by two synthetic examples. Then, we present four case studies demonstrating how the method can be implemented for detecting various subsurface objects

The method suggests that every subsurface point is a possible location of a point diffractor. Imaging of the diffractors is based on a spatial summation of the diffracted wavefield along diffraction time surfaces (defined by source-receiver geometry) in 3D space. The result of the imaging is a 3D volume in which prominent diffraction anomalies appear at spatial locations close to the imaged objects. The proposed method proved to be a robust highresolution technique capable of providing reliable results under various geological conditions in a wide range of depths. The method seems to be especially suitable for detecting

The proposed method is based on a spatial summation of diffracted waves in 3D space. The principles of the method can be elucidated using a simple scheme represented in **Figure 1**.

diffractor (i.e., a void) at the point (XD, YD, ZD) within a homogeneous medium with a velocity V. When seismic waves generated by the source reach the diffractor, it starts to operate as a secondary source generating diffracted waves. At a certain time the diffracted wave arrives at a receiver located at the point (XR, YR, ZR). For the given source-receiver pair and a fixed diffractor position, the arrival time can be represented as a sum of two terms: source-to-diffractor time and diffractor-to-receiver time. In a homogeneous medium, this sum is totally defined by spatial coordinates of the source, receiver and diffractor and the velocity in the medium. Assuming that the source and receiver are located at the surface Z = 0 (i.e., Z<sup>S</sup> = ZR = 0), the

, YS , ZS

) and that there is a

Assume that a source of seismic energy is located at the point (X<sup>S</sup>

arrival time of the diffracted wave can be defined as follows [9]:

scattered/diffracted waves along the travel-time surfaces of those waves [9].

#### **2. Methods for locating subsurface heterogeneities**

#### **2.1. Wavefield**

Let us look at the resulting wavefield obtained from a typical underground heterogeneity in a typical layered geological environment. The wavefield could be divided into a number of different kinds of waves such as primary and multiple reflected waves, refracted waves and scattered/diffracted waves. The reflected waves originate from the layered boundaries, the refracted waves from boundaries of high contrast while the scattered/diffracted waves are generated by local heterogeneities. The reflected and refracted wavefields would only slightly be affected by the presence of the local heterogeneities. However, since the scattered/diffracted waves are generated by local heterogeneities, they may be used for the imaging of those heterogeneities.

#### **2.2. Diffraction imaging**

In the past decades, many attempts have been made to solve the problem using various geophysical methods. The methods in use can be roughly subdivided into two groups. The first group includes low-resolution bulk techniques such as microgravity, geoelectric method and seismic surface wave method. A typical drawback of these methods is their low detectability, limiting them to relatively large sources, that is, such sources whose dimension-to-depth ratio exceeds 1/2 [1–4]. The second group includes the high-resolution ground – penetrating radar (GPR) method. The main drawback of this method is its high sensitivity to electrical conductivity of near-surface material which makes it limited to very shallow depths usually not exceeding a number of meters. Furthermore, our experience shows that the general problem of all the existing techniques is a high degree of ambiguity of data interpretation and, as a result, a high percentage of errors. One of the methods that may prove very effective for this purpose is active seismic, which is widely employed by seismic exploration industry in its extensive and detailed studies of the subsurface. Adaptation of these methods for the purpose of searching for local underground heterogeneities is not an easy task. The primary aim of seismic exploration is to study geological sources of large lateral extent, such as boundaries of geologic formations, oil and gas deposits, etc. To this end, seismic exploration ("reflection seismic") utilizes seismic waves emitted from man-made (active) seismic sources and reflected from the boundaries of interest back to the surface. The methodology, the data acquisition and processing techniques employed by the reflection seismic are largely based on the model of the subsurface consisting of a number of layers divided by smooth curvilinear boundaries with gradual changes of parameters within layers. Virtually, the same model of the subsurface is behind the refraction seismic method, another technology used primarily to study the shallow part of the subsurface (first tens of meters). Clearly, such methods are not directly applicable to a search for local subsurface inhomogeneities of small lateral extent (10–100 m). The amount of energy reflected by such small sources would be very small, and it would be indistinguishable from other geological features of the subsurface. In order to be effective, the search for local inhomogeneities has been employed to image the features of seismic wavefield, which is primarily associated with the presence of local heterogeneity in the subsurface. Such features are known as scattered (diffracted) waves. In a standard seismic prospecting, these waves are usually treated as noise. But for locating local sources these waves provide the most valuable source of information [5–12].

**2. Methods for locating subsurface heterogeneities**

Let us look at the resulting wavefield obtained from a typical underground heterogeneity in a typical layered geological environment. The wavefield could be divided into a number of different kinds of waves such as primary and multiple reflected waves, refracted waves and scattered/diffracted waves. The reflected waves originate from the layered boundaries, the refracted waves from boundaries of high contrast while the scattered/diffracted waves are generated by local heterogeneities. The reflected and refracted wavefields would only slightly be affected by the presence of the local heterogeneities. However, since the scattered/diffracted waves are generated by local heterogeneities, they may be used for the imaging of those heterogeneities.

**2.1. Wavefield**

4 Geophysics

Imaging of the local heterogeneities in 3D space can be performed by a spatial summation of scattered/diffracted waves along the travel-time surfaces of those waves [9].

The summation can be implemented using one of the two approaches. In the first step (conventional approach), target waves are stacked along the time surfaces defined by some "optimal" velocity values. These values are usually estimated by a time-consuming procedure of velocity analysis involving visual examination and interpretation of intermediate seismic images. Recently, an alternative method, a more formal, path integral summation approach, has been proposed [7, 10–12]. Path integral summation is performed by stacking the target waves along all possible time surfaces having a common apex at the given point. This approach does not require any explicit information on velocities since the required multipath summation is performed for all possible velocity values within a wide specified range. Application of the path integral summation to synthetic and real data shows that it can provide reliable images of subsurface objects close to their true spatial locations [9]. However, the spatial resolution of the images obtained by the path integral summation is usually inferior to those obtained using the fixed velocity.

In the subsequent sections, we give a brief description of the main principles of the method and illustrate its application by two synthetic examples. Then, we present four case studies demonstrating how the method can be implemented for detecting various subsurface objects located in different geological environments.

#### **2.3. Theoretical background**

The method suggests that every subsurface point is a possible location of a point diffractor. Imaging of the diffractors is based on a spatial summation of the diffracted wavefield along diffraction time surfaces (defined by source-receiver geometry) in 3D space. The result of the imaging is a 3D volume in which prominent diffraction anomalies appear at spatial locations close to the imaged objects. The proposed method proved to be a robust highresolution technique capable of providing reliable results under various geological conditions in a wide range of depths. The method seems to be especially suitable for detecting relatively small objects.

The proposed method is based on a spatial summation of diffracted waves in 3D space. The principles of the method can be elucidated using a simple scheme represented in **Figure 1**. Assume that a source of seismic energy is located at the point (X<sup>S</sup> , YS , ZS ) and that there is a diffractor (i.e., a void) at the point (XD, YD, ZD) within a homogeneous medium with a velocity V. When seismic waves generated by the source reach the diffractor, it starts to operate as a secondary source generating diffracted waves. At a certain time the diffracted wave arrives at a receiver located at the point (XR, YR, ZR). For the given source-receiver pair and a fixed diffractor position, the arrival time can be represented as a sum of two terms: source-to-diffractor time and diffractor-to-receiver time. In a homogeneous medium, this sum is totally defined by spatial coordinates of the source, receiver and diffractor and the velocity in the medium. Assuming that the source and receiver are located at the surface Z = 0 (i.e., Z<sup>S</sup> = ZR = 0), the arrival time of the diffracted wave can be defined as follows [9]:

**Figure 1.** Schematic illustration of basic diffraction geometry.

$$T\_{SR} = \sqrt{\left\{\xi\_{SD}/V\right\}^2 + T\_D^2} + \sqrt{\left\{\xi\_{DR}/V\right\}^2 + T\_D^2} \tag{1}$$

**Figure 2a** is a schematic illustration of a 3D volume containing a diffraction anomaly obtained by the imaging. Note that the vertical axis is two-way time rather than depth, since the imaging is performed in the time domain. Subsequently, the results of the imaging will be presented in two forms. The first one is obtained by vertical slicing of the 3D volume parallel to the X axis, as illustrated by **Figure 2a**. In this manner, we obtain a set of vertical diffraction sections computed for a number of Y values and represented in the X-T plane (we call them D-sections). The second form is obtained as follows (**Figure 2b**): for every output trace *a*(*t*) resulting from the spatial summation of the corresponding input traces, we compute its energy by summing squared values of the trace amplitudes and put the resulting sum at the corresponding trace location (XD,YD) at the surface. In such a manner we obtain a map of trace energy (we will call it D-map) on which the diffraction anomaly is represented by its horizontal projection onto the X-Y plane, as

**Figure 2.** (a) Schematic illustration of a 3D volume and D-sections in X-T plane and (b) schematic illustration of D-map

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As mentioned above, the imaging can be performed using either a fixed velocity or path integral approach. The path integral imaging was described and applied in our previous work [9]. In this work we applied the fixed velocity imaging (which usually provides a better

The synthetic examples presented below illustrate application of the method for imaging two kinds of objects: a point diffractor (which can be considered as approximation of a small quasi-isometric source, such as a small karstic cavity) and a linear diffractor (roughly approxi-

illustrated by **Figure 2b**.

**3. Synthetic examples**

**3.1. Point and linear diffractors**

mating an elongated source, such as a tube or a tunnel).

resolution).

in X-Y plane.

where *<sup>ξ</sup> SD* <sup>=</sup> <sup>√</sup> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (*XD* − *XS*) <sup>2</sup> + (*YD* − *YS*) 2 is the horizontal source-to-diffractor distance; *<sup>ξ</sup> DR* <sup>=</sup> <sup>√</sup> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (*XR* − *XD*) <sup>2</sup> + (*YR* − *YD*) 2 is the horizontal diffractor-to-receiver distance; *TD* <sup>=</sup> *ZD*/*V* is vertical time above the diffractor; and V is the velocity in the medium. The velocity defines the shape of the diffraction time surface, whereas time T*D* defines its apex. For a spatial array of receivers, equation (1) defines a diffraction time surface with its apex at time 2TD. If the velocity in the medium is known, the diffractor can be imaged by summing seismic energy arriving at different receivers along the time surface defined by equation (1). The principles of the imaging can be formulated as follows:


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**Figure 2.** (a) Schematic illustration of a 3D volume and D-sections in X-T plane and (b) schematic illustration of D-map in X-Y plane.

**Figure 2a** is a schematic illustration of a 3D volume containing a diffraction anomaly obtained by the imaging. Note that the vertical axis is two-way time rather than depth, since the imaging is performed in the time domain. Subsequently, the results of the imaging will be presented in two forms. The first one is obtained by vertical slicing of the 3D volume parallel to the X axis, as illustrated by **Figure 2a**. In this manner, we obtain a set of vertical diffraction sections computed for a number of Y values and represented in the X-T plane (we call them D-sections). The second form is obtained as follows (**Figure 2b**): for every output trace *a*(*t*) resulting from the spatial summation of the corresponding input traces, we compute its energy by summing squared values of the trace amplitudes and put the resulting sum at the corresponding trace location (XD,YD) at the surface. In such a manner we obtain a map of trace energy (we will call it D-map) on which the diffraction anomaly is represented by its horizontal projection onto the X-Y plane, as illustrated by **Figure 2b**.

As mentioned above, the imaging can be performed using either a fixed velocity or path integral approach. The path integral imaging was described and applied in our previous work [9]. In this work we applied the fixed velocity imaging (which usually provides a better resolution).

#### **3. Synthetic examples**

*TSR* = √

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (*XD* − *XS*)

<sup>2</sup> + (*YD* − *YS*) 2

**Figure 1.** Schematic illustration of basic diffraction geometry.

where *<sup>ξ</sup>*

6 Geophysics

*SD* <sup>=</sup> <sup>√</sup>

and receiver points.

ers from all the sources.

ity analysis of the diffraction data.

appears as a distinct anomaly.

faces having a common apex at a given time [10].

\_\_\_\_\_\_\_\_\_\_\_\_ (*<sup>ξ</sup> SD*/*V*)<sup>2</sup> <sup>+</sup> *TD*

by equation (1). The principles of the imaging can be formulated as follows:

• Every point in the subsurface is considered as a possible diffractor.

• A targeted source (a void) acts as a secondary source of waves (diffracted waves).

<sup>2</sup> + √

is the horizontal source-to-diffractor distance; *<sup>ξ</sup>*

the horizontal diffractor-to-receiver distance; *TD* <sup>=</sup> *ZD*/*V* is vertical time above the diffractor; and V is the velocity in the medium. The velocity defines the shape of the diffraction time surface, whereas time T*D* defines its apex. For a spatial array of receivers, equation (1) defines a diffraction time surface with its apex at time 2TD. If the velocity in the medium is known, the diffractor can be imaged by summing seismic energy arriving at different receivers along the time surface defined

• Seismic data acquisition is performed by a 3D survey involving a large amount of source

• The imaging is based on a spatial summation of diffracted waves arriving at all the receiv-

• The summation is performed using Eq. (1) with a fixed velocity value estimated from veloc-

• Alternatively, it can be done using a path integral summation approach, where for every subsurface point, the wavefield is stacked together along all possible diffraction time sur-

• The result is a 3D image of the subsurface (a 3D volume) where the diffractor (the void)

\_\_\_\_\_\_\_\_\_\_\_\_ (*<sup>ξ</sup> DR*/*V*)<sup>2</sup> <sup>+</sup> *TD*

2, (1)

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (*XR* − *XD*)

<sup>2</sup> + (*YR* − *YD*) 2 is

*DR* <sup>=</sup> <sup>√</sup>

#### **3.1. Point and linear diffractors**

The synthetic examples presented below illustrate application of the method for imaging two kinds of objects: a point diffractor (which can be considered as approximation of a small quasi-isometric source, such as a small karstic cavity) and a linear diffractor (roughly approximating an elongated source, such as a tube or a tunnel).

#### *3.1.1. Point diffractor*

The model in the first example includes a point diffractor located at a point with the coordinates X = 40 m, Y = 10 m and Z = 10 m. The medium is assumed to be homogeneous with the velocity of 1000 m/s. The modeling was performed using a simulated acquisition system represented in **Figure 3***.* The system included 2 receiver lines with 48 receivers on each line and 5 source lines with 48 source points on each line. The source and receiver spacing along the lines (i.e., in the X direction) was 2.5 m. The distance between the source lines was 5 m and between the receiver lines 20 m, so that the area covered by the system was about 120 m × 20 m. Using this system, synthetic seismograms of diffracted waves were computed for each source position, given the total of 240

shot records with 48 traces in each record. Then, a spatially uncorrelated random noise with the average s/n ratio of 0.03 was added to the seismograms. **Figure 4** represents an example of one of the records. Due to the low s/n ratio, no traces of diffracted events were identified on the record. **Figure 5a** and **b** represents the results of the point diffractor imaging with the velocity of 1000 m/s. **Figure 5a** shows 5 D-sections computed along the lines defined by the Y values of 0. 5, 10, 15, and 20 m. The sections display a well-defined anomaly whose maximum is located

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**Figure 5.** (a) Point diffractor model: D-sections and (b) point diffractor model: D-map.

**Figure 3.** Source-receiver geometry used for a point diffractor modeling (plan view).

**Figure 4.** Point diffractor model: an example of a synthetic record.

shot records with 48 traces in each record. Then, a spatially uncorrelated random noise with the average s/n ratio of 0.03 was added to the seismograms. **Figure 4** represents an example of one of the records. Due to the low s/n ratio, no traces of diffracted events were identified on the record.

*3.1.1. Point diffractor*

8 Geophysics

**Figure 4.** Point diffractor model: an example of a synthetic record.

**Figure 3.** Source-receiver geometry used for a point diffractor modeling (plan view).

The model in the first example includes a point diffractor located at a point with the coordinates X = 40 m, Y = 10 m and Z = 10 m. The medium is assumed to be homogeneous with the velocity of 1000 m/s. The modeling was performed using a simulated acquisition system represented in **Figure 3***.* The system included 2 receiver lines with 48 receivers on each line and 5 source lines with 48 source points on each line. The source and receiver spacing along the lines (i.e., in the X direction) was 2.5 m. The distance between the source lines was 5 m and between the receiver lines 20 m, so that the area covered by the system was about 120 m × 20 m. Using this system, synthetic seismograms of diffracted waves were computed for each source position, given the total of 240

**Figure 5a** and **b** represents the results of the point diffractor imaging with the velocity of 1000 m/s. **Figure 5a** shows 5 D-sections computed along the lines defined by the Y values of 0. 5, 10, 15, and 20 m. The sections display a well-defined anomaly whose maximum is located

**Figure 5.** (a) Point diffractor model: D-sections and (b) point diffractor model: D-map.

at X = 40 m on the section with Y = 10 m. The amplitude of the anomaly is rapidly attenuated away from its maximum in both the X and Y directions. This can be seen even more clearly on the D-map (**Figure 5b**): the figure shows that the diffraction anomaly is very well localized on

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The model in the second synthetic example contains a linear diffractor (which can be considered as a set of densely spaced point diffractors). The diffractor crosses the X axis at the distance of 40 m from the origin at the angle of 30° (**Figure 6**). The model parameters and the

The D-sections obtained for this model with the velocity of 1000 m/s (**Figure 7a**) display a well-defined anomaly whose location on the sections varies along the Y axis in accordance with the inclination of the imaged linear diffractor. This is further illustrated by the D-map (**Figure 7b**). The map shows a prolongated quasi-linear anomaly whose location and inclina-

The first case is from a sinkhole site located in the Dead Sea area of Israel. A well drilled at the site revealed a water-filled cavity located in a salt layer within the depth of 22–28 m. The cavity was a target of the diffraction survey carried out at the site. The acquisition system used in the survey was similar to that described in the earlier synthetic examples. Imaging was performed with the velocity of 1200 m/s estimated from the velocity analysis of the data. The resulting D-sections (**Figure 8a**) show a prominent anomaly located in the area close to the well location. The depth of the anomaly was estimated to be about 25 m which is quite close to the depth of the cavity as revealed in the well. The D-map (**Figure 8b**) displays an isometric

The second case is from a limestone quarry where a number of karstic cavities were revealed by drilling shallow boreholes. The depth of the cavities varied between 8 and 23 m. At several sites in the quarry, diffraction surveys were carried out with the aim of detecting the cavities from the surface. We present an example from one of the surveys. The acquisition system used in this case was half as long as the system specified earlier (see **Figure 3**), that is, it included only 24 receivers and 24 source points per line, so that the area covered by the survey was about 60 m × 20 m. The well located near the point (X = 35 m, Y = 10 m) revealed a cavity at the depth of 8 m. Imaging was performed with the velocity of 1500 m/s. The D-sections (**Figure 9a**) show a well-defined anomaly with its maximum located very close to the well location. The amplitude of the anomaly decreases rapidly away from the maximum. The depth of the anomaly was estimated to be about 7 m. Thus, the estimated spatial location of the target

the X-Y plane around the imaged point diffractor.

acquisition system were the same as in the previous example.

tion on the X-Y plane correspond well with the imaged linear diffractor.

anomaly implying that the cavity might have a quasi-spherical shape.

*3.1.2. Linear diffractor*

**4. Case studies**

**4.1. Dead Sea-Israel**

**4.2. Limestone quarry**

**Figure 6.** Source-receiver geometry used for linear diffractor imaging (plan view).

**Figure 7.** (a) Linear diffractor model: D-sections and (b) linear diffractor model: D-map.

at X = 40 m on the section with Y = 10 m. The amplitude of the anomaly is rapidly attenuated away from its maximum in both the X and Y directions. This can be seen even more clearly on the D-map (**Figure 5b**): the figure shows that the diffraction anomaly is very well localized on the X-Y plane around the imaged point diffractor.

#### *3.1.2. Linear diffractor*

The model in the second synthetic example contains a linear diffractor (which can be considered as a set of densely spaced point diffractors). The diffractor crosses the X axis at the distance of 40 m from the origin at the angle of 30° (**Figure 6**). The model parameters and the acquisition system were the same as in the previous example.

The D-sections obtained for this model with the velocity of 1000 m/s (**Figure 7a**) display a well-defined anomaly whose location on the sections varies along the Y axis in accordance with the inclination of the imaged linear diffractor. This is further illustrated by the D-map (**Figure 7b**). The map shows a prolongated quasi-linear anomaly whose location and inclination on the X-Y plane correspond well with the imaged linear diffractor.

#### **4. Case studies**

**Figure 6.** Source-receiver geometry used for linear diffractor imaging (plan view).

10 Geophysics

**Figure 7.** (a) Linear diffractor model: D-sections and (b) linear diffractor model: D-map.

#### **4.1. Dead Sea-Israel**

The first case is from a sinkhole site located in the Dead Sea area of Israel. A well drilled at the site revealed a water-filled cavity located in a salt layer within the depth of 22–28 m. The cavity was a target of the diffraction survey carried out at the site. The acquisition system used in the survey was similar to that described in the earlier synthetic examples. Imaging was performed with the velocity of 1200 m/s estimated from the velocity analysis of the data. The resulting D-sections (**Figure 8a**) show a prominent anomaly located in the area close to the well location. The depth of the anomaly was estimated to be about 25 m which is quite close to the depth of the cavity as revealed in the well. The D-map (**Figure 8b**) displays an isometric anomaly implying that the cavity might have a quasi-spherical shape.

#### **4.2. Limestone quarry**

The second case is from a limestone quarry where a number of karstic cavities were revealed by drilling shallow boreholes. The depth of the cavities varied between 8 and 23 m. At several sites in the quarry, diffraction surveys were carried out with the aim of detecting the cavities from the surface. We present an example from one of the surveys. The acquisition system used in this case was half as long as the system specified earlier (see **Figure 3**), that is, it included only 24 receivers and 24 source points per line, so that the area covered by the survey was about 60 m × 20 m. The well located near the point (X = 35 m, Y = 10 m) revealed a cavity at the depth of 8 m. Imaging was performed with the velocity of 1500 m/s. The D-sections (**Figure 9a**) show a well-defined anomaly with its maximum located very close to the well location. The amplitude of the anomaly decreases rapidly away from the maximum. The depth of the anomaly was estimated to be about 7 m. Thus, the estimated spatial location of the target

**Figure 8.** (a) Case 1: D-sections and (b) case 1: D-map.

object is in good agreement with the location of the cavity revealed by drilling. This conclusion is further confirmed by the D-map (**Figure 9b**) that shows an isometric anomaly located in close vicinity around the well.

#### **4.3. Chalky hills**

The third case refers to an ancient subsurface aqueduct which has been recently discovered in Chalky hills, some 23 km east of the Mediterranean shore of Israel (**Figure 10a**). The aqueduct was part of a water supply system operating during the Roman and Byzantine periods. In the excavated part of the aqueduct, it is about 1.8 m high and 0.8 m wide and its depth from the surface is from 8 to 10 m. A diffraction survey was carried out at the site located above an extension of the aqueduct beyond its excavated part, at the distance

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**Figure 9.** (a) Case 2: D-sections and (b) case 2: D-map.

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**Figure 9.** (a) Case 2: D-sections and (b) case 2: D-map.

**Figure 8.** (a) Case 1: D-sections and (b) case 1: D-map.

in close vicinity around the well.

**4.3. Chalky hills**

12 Geophysics

object is in good agreement with the location of the cavity revealed by drilling. This conclusion is further confirmed by the D-map (**Figure 9b**) that shows an isometric anomaly located

The third case refers to an ancient subsurface aqueduct which has been recently discovered in Chalky hills, some 23 km east of the Mediterranean shore of Israel (**Figure 10a**). The aqueduct was part of a water supply system operating during the Roman and Byzantine periods. In the excavated part of the aqueduct, it is about 1.8 m high and 0.8 m wide and its depth from the surface is from 8 to 10 m. A diffraction survey was carried out at the site located above an extension of the aqueduct beyond its excavated part, at the distance

of about 200 m from the nearest excavated shaft. The acquisition system was similar to that specified in **Figure 3**. The aqueduct was supposed to cross the system at a distance of 80–90 m from the beginning of the lines. Imaging was performed with the velocity of 1200 m/s. The D-sections (**Figure 10b**) show a prominent anomaly located in the area which is close to the estimated extension of the aqueduct. The D-map (**Figure 10c**) displays an elongated anomaly whose inclination on the X-Y plane is in good agreement with the

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general direction of the aqueduct.

**Figure 11.** (a) Case 4: D-sections and (b) case 4: D-map.

**Figure 10.** (a) Ancient subsurface aqueduct, (b) case 3: D-sections and (c) case 3: D-map.

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**Figure 11.** (a) Case 4: D-sections and (b) case 4: D-map.

**Figure 10.** (a) Ancient subsurface aqueduct, (b) case 3: D-sections and (c) case 3: D-map.

14 Geophysics

of about 200 m from the nearest excavated shaft. The acquisition system was similar to that specified in **Figure 3**. The aqueduct was supposed to cross the system at a distance of 80–90 m from the beginning of the lines. Imaging was performed with the velocity of 1200 m/s. The D-sections (**Figure 10b**) show a prominent anomaly located in the area which is close to the estimated extension of the aqueduct. The D-map (**Figure 10c**) displays an elongated anomaly whose inclination on the X-Y plane is in good agreement with the general direction of the aqueduct.

#### **4.4. Modern operating aqueduct**

The fourth case is from a site located above a modern operating aqueduct which supplies water to a large part of Israel. The diameter of the aqueduct is 3 m. At the investigated site it is located at the depth of 27 m within the limestone. In this case our target object was quite a small one, since the ratio of its dimension (diameter) to the depth to its center is about 1/10, making it quite challenging.

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Efficient Use of Technology—Unlocking Potential. 2016

diffraction summation. First Break. 2005;**23**(January):39-42

The diffraction survey carried out at the site used the acquisition system including 2 receiver lines with 24 receivers on each line and 4 source lines with 24 source points on each line. The source spacing was 5 m in both the X and Y directions; the receiver spacing was 5 m in the X direction and 15 m in Y direction. The survey crossed the aqueduct at approximately the right angle at a distance of about 40 m from the beginning of the lines. Imaging was performed with the velocity of 1100 m/s. The D-sections obtained for the data (**Figure 11a**) show a distinct anomaly at X = 45 m. The estimated depth of the anomaly is about 24 m. Thus, the estimated spatial location of the target object corresponds fairly well with the actual location of the aqueduct. This is confirmed by the D-map (**Figure 11b**) which displays a quasi-linear anomaly whose location on the X-Y plane is close to the aqueduct location.

#### **5. Summary**

The main points of our work can be summarized as follows: a method for detecting and mapping localized near-surface inhomogeneites was presented.

The method is based on 3D subsurface imaging using spatial summation of diffracted waves along their time surfaces.

The method was successfully tested on synthetic data with a very low s/n ratio.

Application of the method to real data demonstrates that it can provide a reliable detection of relatively small subsurface sources located under different geographical conditions at a wide range of depths.

#### **Acknowledgements**

The authors are grateful to the Geophysical Institute of Israel for granting permission to publish the datasets.

#### **Author details**

Shemer Keydar1 \*, Vladimir Shtivelman1 and Avner Arzi<sup>2</sup>

\*Address all correspondence to: shemer@gii.co.il


#### **References**

**4.4. Modern operating aqueduct**

16 Geophysics

making it quite challenging.

**5. Summary**

range of depths.

lish the datasets.

**Author details**

Shemer Keydar1

along their time surfaces.

**Acknowledgements**

The fourth case is from a site located above a modern operating aqueduct which supplies water to a large part of Israel. The diameter of the aqueduct is 3 m. At the investigated site it is located at the depth of 27 m within the limestone. In this case our target object was quite a small one, since the ratio of its dimension (diameter) to the depth to its center is about 1/10,

The diffraction survey carried out at the site used the acquisition system including 2 receiver lines with 24 receivers on each line and 4 source lines with 24 source points on each line. The source spacing was 5 m in both the X and Y directions; the receiver spacing was 5 m in the X direction and 15 m in Y direction. The survey crossed the aqueduct at approximately the right angle at a distance of about 40 m from the beginning of the lines. Imaging was performed with the velocity of 1100 m/s. The D-sections obtained for the data (**Figure 11a**) show a distinct anomaly at X = 45 m. The estimated depth of the anomaly is about 24 m. Thus, the estimated spatial location of the target object corresponds fairly well with the actual location of the aqueduct. This is confirmed by the D-map (**Figure 11b**) which displays a quasi-linear anomaly

The main points of our work can be summarized as follows: a method for detecting and map-

The method is based on 3D subsurface imaging using spatial summation of diffracted waves

Application of the method to real data demonstrates that it can provide a reliable detection of relatively small subsurface sources located under different geographical conditions at a wide

The authors are grateful to the Geophysical Institute of Israel for granting permission to pub-

and Avner Arzi<sup>2</sup>

The method was successfully tested on synthetic data with a very low s/n ratio.

whose location on the X-Y plane is close to the aqueduct location.

ping localized near-surface inhomogeneites was presented.

\*, Vladimir Shtivelman1

\*Address all correspondence to: shemer@gii.co.il

1 Geophysical Institute of Israel, Lod, Israel 2 Geotechnical Consultant, Ramat Gan, Israel


**Chapter 2**

**Provisional chapter**

**Measurement of Rotational Events in Regions Prone to**

On the basis of the explanation of rotational seismology as an area of study, a modern approach to the seismic rotation in various continuum models is summarized. The aim of this chapter is to formulate the fundamental requirements for rotational seismometer. Consequently, a review of all existing technologies of rotational seismometers including mechanical, electrochemical, magnetohydrodynamical, as well as optical type solutions is discussed. The analysis of their parameters that considers technical requirements enforced by rotational seismology has indicated an optical instrument using a Sagnac interferometer as the best solution. Fibre-Optic System for Rotational Events & phenomena Monitoring (FOSREM) with its main parameters and features is described as an example of such solution. Moreover, the example of rotational events recorded in Książ observatory, Poland, using mechanical rotational seismometers and FOSREM is presented. There are data for M = 3.8 earthquake near Jarocin, Poland on the 2012.01.06 at 15:37:56 at a distance of about 200 km from Książ. Although the used devices have totally different designs, the results obtained using FOSREM and the results calculated by mechanical devices show compatibility in rotational signals. **Keywords:** theory of rotational events, rotational seismometers, rotational seismic data

**Measurement of Rotational Events in Regions Prone to** 

DOI: 10.5772/intechopen.72169

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Mutual rotation or twisting of monumental blocks around a vertical axis as a result of seismic activity has been observed for nearly 300 years. The distortion of the San Bruno obelisk after the February 5, 1783 Calabria earthquake, intensity XI-XII MCS, is cited as the first illustration of these phenomena [1, 2], and now it is a symbol of seismic rotational effects. Starting with that event, we can find a large number of other examples of observed rotation effects resulting

**Seismicity: A Review**

**Seismicity: A Review**

Leszek R. Jaroszewicz, Anna Kurzych,

Leszek R. Jaroszewicz, Anna Kurzych,

http://dx.doi.org/10.5772/intechopen.72169

**Abstract**

**1. Introduction**

Krzysztof P. Teisseyre and Zbigniew Krajewski

Krzysztof P. Teisseyre and Zbigniew Krajewski

Additional information is available at the end of the chapter

processing, rotational seismic data acquisition

Additional information is available at the end of the chapter

**Provisional chapter**

#### **Measurement of Rotational Events in Regions Prone to Seismicity: A Review Seismicity: A Review**

**Measurement of Rotational Events in Regions Prone to** 

DOI: 10.5772/intechopen.72169

Leszek R. Jaroszewicz, Anna Kurzych, Krzysztof P. Teisseyre and Zbigniew Krajewski Krzysztof P. Teisseyre and Zbigniew Krajewski Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72169

Leszek R. Jaroszewicz, Anna Kurzych,

#### **Abstract**

On the basis of the explanation of rotational seismology as an area of study, a modern approach to the seismic rotation in various continuum models is summarized. The aim of this chapter is to formulate the fundamental requirements for rotational seismometer. Consequently, a review of all existing technologies of rotational seismometers including mechanical, electrochemical, magnetohydrodynamical, as well as optical type solutions is discussed. The analysis of their parameters that considers technical requirements enforced by rotational seismology has indicated an optical instrument using a Sagnac interferometer as the best solution. Fibre-Optic System for Rotational Events & phenomena Monitoring (FOSREM) with its main parameters and features is described as an example of such solution. Moreover, the example of rotational events recorded in Książ observatory, Poland, using mechanical rotational seismometers and FOSREM is presented. There are data for M = 3.8 earthquake near Jarocin, Poland on the 2012.01.06 at 15:37:56 at a distance of about 200 km from Książ. Although the used devices have totally different designs, the results obtained using FOSREM and the results calculated by mechanical devices show compatibility in rotational signals.

**Keywords:** theory of rotational events, rotational seismometers, rotational seismic data processing, rotational seismic data acquisition

#### **1. Introduction**

Mutual rotation or twisting of monumental blocks around a vertical axis as a result of seismic activity has been observed for nearly 300 years. The distortion of the San Bruno obelisk after the February 5, 1783 Calabria earthquake, intensity XI-XII MCS, is cited as the first illustration of these phenomena [1, 2], and now it is a symbol of seismic rotational effects. Starting with that event, we can find a large number of other examples of observed rotation effects resulting

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

from historical earthquakes where the description of 12 majors ones (VII-XI MSC) can be found [3]. The shallow, catastrophic 2009 l'Aquila earthquake was a source of more than hundreds of evidenced rotational effects. Its analysis [4] revealed a tectonic dependence of their distribution and the influence of substrate. From the above, positive correlations have been found between rotation effects, damage and soft lithology of the site where buildings are located.

mechanical features such as rock mass and soil. In the first case, the continuous material can translate rectilinearly in its body. A mechanical impulse is translated in a medium as the elastic wave in two simultaneous ways: as compressional-dilatational deformations––the longitudinal wave and transverse shape distortions––the transverse wave. In the second case, both the continuous and grainy solid matter can also be translated into rotational motions in which we distinguish a rotation (named also rigid rotation, or simply a turn) and a symmetric-shape distortion––the shear. It should be underlined that in the elastic theory, there is no place for a rigid rotation, as it would introduce a complicated deformation state around the small body which turns. This theory explained so many phenomena; as a result, the idea of rotation was

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

http://dx.doi.org/10.5772/intechopen.72169

21

Recently, it becomes clear that the S-waves comprise rotations of axes perpendicular to the wave propagation. For the plane wave, a suitable relation was found by Igel et al. [21] joining this rotation velocity to transverse acceleration and phase velocity. Rotation curves were very similar to signals of a horizontal acceleration divided by twice the phase velocity (all measured in SI units). The relation was confirmed with a simple geometrical consideration of motions [22, 23]. The same results were found also in the seismic near field, where the spherical wave front was taken as a sufficient approximation [24, 25]. This aspect of the measured oscillations leads to one of the reasons to study rotations––the phase velocity may be easily assessed in this way. The same relation is valid for a love-type surface wave. Since measurements usually proceed on the Earth's surface, rotations about horizontal axis, as in Sv and Rayleigh waves, are not amenable to this method. Finally, various reasons can be found for the presence of rotations also in a P-waves' part of a seismic event trace. For instance, it must be noted that in reality, far from ideal conditions, P-waves are not entirely longitudinal, as

It must be noted that this geometrical aspect of rotation does not solve all the problems. Microscopic motions and deformations may not be uniform and not have the same sense. Possible modes of their propagation have been formulated within the vast area of micromorphic studies (including micropolar variant of theories) led by mathematicians and physicists [26]. This branch of science is also named the generalized continuum theory. This trend, initiated by Cosserat brothers in 1909 [27], started to flourish decades later with works of Eringen [28], Nowacki [29, 30], and others. In the micromorphic approach, solid material is taken consisting of numerous small (not infinitesimal) bodies, often called shells, which are capable of deformations and rotations. Various modes of passing them from one body to the other have been proposed [31], and this leads to the independent rotational waves' concept [32, 33]. Individual small body in the undeformed state is usually seen as a cube; each of its sides may react not only to a vector of stress but also to their couple. Couple stress denotes a noncentric interaction between small bodies: a pair of forces act on the body's surface and their moment "tries" to distort or rotate the body. This theoretical small body is treated, in some works, as anisotropic layered entity [34].

In some works, joints between small bodies are treated as important elements in the deformation/propagation process. Among the particle-based numerical studies, there are such in which neighboring particles (small bodies) are linked by elastic bonds "…which can transfer elastic forces, both attractive or repulsive" and break if the distance between the pair exceeds a certain threshold. Such model allows shearing, twisting, and bending interactions between two bonded particles. Used in simulating fracturing, this model facilitates realistic results [35].

well as S-waves bear not only shearing deformations.

not accepted.

However, the term 'rotation' has several meanings in seismology. Displacement of rocks, soils and various objects during an earthquake in the focal area and its vicinity, and reversible rotational oscillations in the seismic wave field are called 'seismic rotations.' The historical explanation of observed seismic rotations based on mechanical models can be found in [5, 6], whereas Section 2. summarizes their explanations on the basis of continuum models.

Recently, it is believed that rotational signals contain additional information, valuable for studies on wave propagation, and that the rotational ground motion is an important source of excitations in the engineering structures. Therefore, increasing interest in rotational motions' measurement has emerged. From seismological point of view, it is an area of a rotational seismology which according to [7] becomes an emerging field for the study of all aspects of a rotational ground motion induced by earthquakes, explosions, and ambient vibrations. This domain is very interesting for researchers from a wide range of geophysical disciplines, including broadband seismology, strong motion seismology [8], earthquake physics [9, 10], seismic hazards [11], seismotectonics [12], geodesy [13], and for physicists using Earth-based observatories for detecting gravitational waves generated by astronomical sources [14–16]. Additionally, it is interesting for researchers of earthquake engineering, where seismic behavior of different engineering structures is investigated [17] to search for their optimal seismic design [18].

However, rotational seismology needs a new methodology and new instruments for more reliable recordings. A rigorous analysis of existing classical solutions delivered from instruments for seismological investigation [19] shows their limited usefulness for rotational events recording, mainly because of their sensitivity to linear motions, as well. For the abovementioned reason, in Section 3, we have summarized the main types of rotational seismometers that now exist, with comments on their usefulness. This description shows that a new approach taking advantage of the von Laue-Sagnac effect [20] is the most promising one. Finally, in Section 4, recent results regarding rotational events' detection, which are obtained in Poland, based on such approach are presented and discussed.

This chapter presents the description, the principle of operation, and the comparison of main technical parameters regarding requirements of rotational seismology. This will help seismologists and earth scientists involved in seismic studies to choose the best method for analyzing problems related to seismic rotation.

#### **2. Seismic rotation in various continuum models**

In all continuum models mentioned in this section, the wave motion, possibly with rotations, comes from the integration of motions and deformations of numerous small bodies, which form the given continuum. Exterior conditions or forces play only a minor role with the exception of a discontinuous surface. There exists a tension between two types of solid material's mechanical features such as rock mass and soil. In the first case, the continuous material can translate rectilinearly in its body. A mechanical impulse is translated in a medium as the elastic wave in two simultaneous ways: as compressional-dilatational deformations––the longitudinal wave and transverse shape distortions––the transverse wave. In the second case, both the continuous and grainy solid matter can also be translated into rotational motions in which we distinguish a rotation (named also rigid rotation, or simply a turn) and a symmetric-shape distortion––the shear. It should be underlined that in the elastic theory, there is no place for a rigid rotation, as it would introduce a complicated deformation state around the small body which turns. This theory explained so many phenomena; as a result, the idea of rotation was not accepted.

from historical earthquakes where the description of 12 majors ones (VII-XI MSC) can be found [3]. The shallow, catastrophic 2009 l'Aquila earthquake was a source of more than hundreds of evidenced rotational effects. Its analysis [4] revealed a tectonic dependence of their distribution and the influence of substrate. From the above, positive correlations have been found between rotation effects, damage and soft lithology of the site where buildings are located.

However, the term 'rotation' has several meanings in seismology. Displacement of rocks, soils and various objects during an earthquake in the focal area and its vicinity, and reversible rotational oscillations in the seismic wave field are called 'seismic rotations.' The historical explanation of observed seismic rotations based on mechanical models can be found in [5, 6],

Recently, it is believed that rotational signals contain additional information, valuable for studies on wave propagation, and that the rotational ground motion is an important source of excitations in the engineering structures. Therefore, increasing interest in rotational motions' measurement has emerged. From seismological point of view, it is an area of a rotational seismology which according to [7] becomes an emerging field for the study of all aspects of a rotational ground motion induced by earthquakes, explosions, and ambient vibrations. This domain is very interesting for researchers from a wide range of geophysical disciplines, including broadband seismology, strong motion seismology [8], earthquake physics [9, 10], seismic hazards [11], seismotectonics [12], geodesy [13], and for physicists using Earth-based observatories for detecting gravitational waves generated by astronomical sources [14–16]. Additionally, it is interesting for researchers of earthquake engineering, where seismic behavior of different engineering structures is investigated [17] to search for their optimal seismic design [18].

However, rotational seismology needs a new methodology and new instruments for more reliable recordings. A rigorous analysis of existing classical solutions delivered from instruments for seismological investigation [19] shows their limited usefulness for rotational events recording, mainly because of their sensitivity to linear motions, as well. For the abovementioned reason, in Section 3, we have summarized the main types of rotational seismometers that now exist, with comments on their usefulness. This description shows that a new approach taking advantage of the von Laue-Sagnac effect [20] is the most promising one. Finally, in Section 4, recent results regarding rotational events' detection, which are obtained

This chapter presents the description, the principle of operation, and the comparison of main technical parameters regarding requirements of rotational seismology. This will help seismologists and earth scientists involved in seismic studies to choose the best method for analyzing

In all continuum models mentioned in this section, the wave motion, possibly with rotations, comes from the integration of motions and deformations of numerous small bodies, which form the given continuum. Exterior conditions or forces play only a minor role with the exception of a discontinuous surface. There exists a tension between two types of solid material's

in Poland, based on such approach are presented and discussed.

**2. Seismic rotation in various continuum models**

problems related to seismic rotation.

20 Geophysics

whereas Section 2. summarizes their explanations on the basis of continuum models.

Recently, it becomes clear that the S-waves comprise rotations of axes perpendicular to the wave propagation. For the plane wave, a suitable relation was found by Igel et al. [21] joining this rotation velocity to transverse acceleration and phase velocity. Rotation curves were very similar to signals of a horizontal acceleration divided by twice the phase velocity (all measured in SI units). The relation was confirmed with a simple geometrical consideration of motions [22, 23]. The same results were found also in the seismic near field, where the spherical wave front was taken as a sufficient approximation [24, 25]. This aspect of the measured oscillations leads to one of the reasons to study rotations––the phase velocity may be easily assessed in this way. The same relation is valid for a love-type surface wave. Since measurements usually proceed on the Earth's surface, rotations about horizontal axis, as in Sv and Rayleigh waves, are not amenable to this method. Finally, various reasons can be found for the presence of rotations also in a P-waves' part of a seismic event trace. For instance, it must be noted that in reality, far from ideal conditions, P-waves are not entirely longitudinal, as well as S-waves bear not only shearing deformations.

It must be noted that this geometrical aspect of rotation does not solve all the problems. Microscopic motions and deformations may not be uniform and not have the same sense. Possible modes of their propagation have been formulated within the vast area of micromorphic studies (including micropolar variant of theories) led by mathematicians and physicists [26]. This branch of science is also named the generalized continuum theory. This trend, initiated by Cosserat brothers in 1909 [27], started to flourish decades later with works of Eringen [28], Nowacki [29, 30], and others. In the micromorphic approach, solid material is taken consisting of numerous small (not infinitesimal) bodies, often called shells, which are capable of deformations and rotations. Various modes of passing them from one body to the other have been proposed [31], and this leads to the independent rotational waves' concept [32, 33]. Individual small body in the undeformed state is usually seen as a cube; each of its sides may react not only to a vector of stress but also to their couple. Couple stress denotes a noncentric interaction between small bodies: a pair of forces act on the body's surface and their moment "tries" to distort or rotate the body. This theoretical small body is treated, in some works, as anisotropic layered entity [34].

In some works, joints between small bodies are treated as important elements in the deformation/propagation process. Among the particle-based numerical studies, there are such in which neighboring particles (small bodies) are linked by elastic bonds "…which can transfer elastic forces, both attractive or repulsive" and break if the distance between the pair exceeds a certain threshold. Such model allows shearing, twisting, and bending interactions between two bonded particles. Used in simulating fracturing, this model facilitates realistic results [35].

The contemporary studies on generalized elasticity can be found in the works of Grekova [36] as well as in the works of Neff et al. [37], which finally concluded that the rotations that are treated as antisymmetric motions/deformations should also be presented. Review on the topic has been prepared by Hadjesfandiari and Dargush [38], which concluded that when an elastic wave propagates through the medium considered in accordance with generalized elasticity concepts, its elements undergo angular motions. Despite the fact that the micromorphic approach is more visible in acoustics or in the studies on various materials than in the geophysics, recent [39–41] search for laboratory confirmation of the micromorphic concepts of seismic rotation yielded sound results, as well.

were the same and only the last one differs in a measuring range containing amplitude up to

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

http://dx.doi.org/10.5772/intechopen.72169

23

A formulation of main requirements for rotational seismometers regarding the rotational seismology is useful for a review of available current solutions in this area. Generally, all used devices can be classified as mechanical, acoustical, electrochemical, and optical devices.

The mechanical systems were historically first used, and they can detect rotation in two ways: directly and nondirectly. The directly rotation detecting systems represent modern mechanical rotational sensors based on a highly miniaturized technique named micro electro-mechanical systems (MEMS). Originally, this technique was developed for manufacturing integrated accelerometers for airborne applications. Rotational seismometers in this technique, usually called MEMS gyro, resemble microelectronic systems in terms of size and production methods. MEMS gyros use the Coriolis effect, and each type of these sensors currently uses vibrating proof masses, which generally vibrate at a high frequency. If the sensor rotates in an inertial space, a Coriolis force is induced on the proof mass. The Coriolis effect generates a vibration in an orthogonal plane, and amplitude of the orthogonal motion can be detected. One can distinguish the following technological structures of MEMS gyros [54]: tuning fork gyros (TFG), hemispherical resonating gyro (HRG) or wine glass resonator gyro, vibrating-wheel gyros, and Foucault pendulum gyros. The biggest advantage of these devices is their mass production at low cost with a small form factor. Systron Donner Inertial (USA), using this technology, manufactured a compact, high reliability, solid-state angular rotation sensor named Horizon™ [55]. It uses vibrating quartz tuning tines to sense rate, acting as a Coriolis sensor, coupled to a similar fork as a pickup to produce the rate output signal (**Figure 1**). Aligned with their support fixtures and frames, these paired

Another company, Gladiator Technologies Inc., offers six models of MEMS gyros, which are very small, portable and of ultra-low power consumption (see **Figure 1c**) [56]. Nevertheless, the products by both abovementioned companies do not fulfill requirements for entirely rotational seismology as shown in the study, and their parameters are listed in **Table 1**. They are suited solutions as an additional device, which can be used for laboratory investigation, mainly for

**Figure 1.** MEMS gyros: (a) scheme of operation, (b) the Horizon™ MEMS angular rate sensor HZ1-100-100, and

tines are fabricated from thin wafers of single crystal piezoelectric quartz.

a rotational seismology engineering application (see example [57]).

(c) Gladiator Technologies Inc. model G200D [56].

a few rad/s at a frequency range up to 100 Hz [53].

Original theory of rotational components of a seismic field has been developed by Teisseyre. Starting from elastic continuum with defects [42], he constructed a model of rotations and shears' generation and propagation on the base of constitutional bonds between the antisymmetric part of stresses, density of self-rotation nuclei and the stress moments. Finally, a linear continuum theory, incorporating asymmetric (symmetric plus antisymmetric) stress field, as well as shears and rotations, was introduced [43–45]. In this theory, rotation and shear propel each other. Developing stages of abovementioned theories helped to popularize the rotational seismology in the sciences and resulted in the monographs by [9, 10]. Teisseyre works also accomplished field studies with the use of original microarray of sensors [46–49].

Near-field rotation effects were explained by the action of a nonlinear deformational bendrotation wave [50]. Several studies point to the possibility of rotational soliton waves (pulses) generated during an earthquake in the focal area, then propagating slowly along fault and triggering new events [51].

Beside verifications of theoretical concepts, dynamic measurements of a real earthquake wave field are urgently needed. These should be best done with special devices enabling detection and recording of rotational motions. Such devices generally named the rotational seismometers or seismographs appeared relatively not long ago, and description of their current state is given in the following section.

#### **3. Current state of rotational seismometers**

The main thing regarding the practical construction of a rotational seismometer is a proper description of the fundamental parameters required for such sensor. The general scope of such parameters for a rotational seismometer, which is used for recording signals connected with rotational seismic effects was formulated only 5 years ago in 2012 by [52] as the following four requirements: (1) independently; (2) assures portable size as well as stable work under changing ambient conditions (temperature, humidity, vibration, pressure,…); (3) uses independent power supply that assures autonomous work; and (4) protects measuring rotation rate with an amplitude of the order of 10−7 rad/s at a frequency range between 0.01 and 0.1 Hz. Moreover, (1) the device should be completely insensitive to linear motion or has possibility to measure linear and rotational movements, and the similar requirements were also described for an earthquake engineering area of rotational seismology interest; the first three were the same and only the last one differs in a measuring range containing amplitude up to a few rad/s at a frequency range up to 100 Hz [53].

The contemporary studies on generalized elasticity can be found in the works of Grekova [36] as well as in the works of Neff et al. [37], which finally concluded that the rotations that are treated as antisymmetric motions/deformations should also be presented. Review on the topic has been prepared by Hadjesfandiari and Dargush [38], which concluded that when an elastic wave propagates through the medium considered in accordance with generalized elasticity concepts, its elements undergo angular motions. Despite the fact that the micromorphic approach is more visible in acoustics or in the studies on various materials than in the geophysics, recent [39–41] search for laboratory confirmation of the micromorphic concepts

Original theory of rotational components of a seismic field has been developed by Teisseyre. Starting from elastic continuum with defects [42], he constructed a model of rotations and shears' generation and propagation on the base of constitutional bonds between the antisymmetric part of stresses, density of self-rotation nuclei and the stress moments. Finally, a linear continuum theory, incorporating asymmetric (symmetric plus antisymmetric) stress field, as well as shears and rotations, was introduced [43–45]. In this theory, rotation and shear propel each other. Developing stages of abovementioned theories helped to popularize the rotational seismology in the sciences and resulted in the monographs by [9, 10]. Teisseyre works also

Near-field rotation effects were explained by the action of a nonlinear deformational bendrotation wave [50]. Several studies point to the possibility of rotational soliton waves (pulses) generated during an earthquake in the focal area, then propagating slowly along fault and

Beside verifications of theoretical concepts, dynamic measurements of a real earthquake wave field are urgently needed. These should be best done with special devices enabling detection and recording of rotational motions. Such devices generally named the rotational seismometers or seismographs appeared relatively not long ago, and description of their current state

The main thing regarding the practical construction of a rotational seismometer is a proper description of the fundamental parameters required for such sensor. The general scope of such parameters for a rotational seismometer, which is used for recording signals connected with rotational seismic effects was formulated only 5 years ago in 2012 by [52] as the following four requirements: (1) independently; (2) assures portable size as well as stable work under changing ambient conditions (temperature, humidity, vibration, pressure,…); (3) uses independent power supply that assures autonomous work; and (4) protects measuring rotation rate with an amplitude of the order of 10−7 rad/s at a frequency range between 0.01 and 0.1 Hz. Moreover, (1) the device should be completely insensitive to linear motion or has possibility to measure linear and rotational movements, and the similar requirements were also described for an earthquake engineering area of rotational seismology interest; the first three

accomplished field studies with the use of original microarray of sensors [46–49].

of seismic rotation yielded sound results, as well.

triggering new events [51].

22 Geophysics

is given in the following section.

**3. Current state of rotational seismometers**

A formulation of main requirements for rotational seismometers regarding the rotational seismology is useful for a review of available current solutions in this area. Generally, all used devices can be classified as mechanical, acoustical, electrochemical, and optical devices.

The mechanical systems were historically first used, and they can detect rotation in two ways: directly and nondirectly. The directly rotation detecting systems represent modern mechanical rotational sensors based on a highly miniaturized technique named micro electro-mechanical systems (MEMS). Originally, this technique was developed for manufacturing integrated accelerometers for airborne applications. Rotational seismometers in this technique, usually called MEMS gyro, resemble microelectronic systems in terms of size and production methods. MEMS gyros use the Coriolis effect, and each type of these sensors currently uses vibrating proof masses, which generally vibrate at a high frequency. If the sensor rotates in an inertial space, a Coriolis force is induced on the proof mass. The Coriolis effect generates a vibration in an orthogonal plane, and amplitude of the orthogonal motion can be detected. One can distinguish the following technological structures of MEMS gyros [54]: tuning fork gyros (TFG), hemispherical resonating gyro (HRG) or wine glass resonator gyro, vibrating-wheel gyros, and Foucault pendulum gyros. The biggest advantage of these devices is their mass production at low cost with a small form factor. Systron Donner Inertial (USA), using this technology, manufactured a compact, high reliability, solid-state angular rotation sensor named Horizon™ [55]. It uses vibrating quartz tuning tines to sense rate, acting as a Coriolis sensor, coupled to a similar fork as a pickup to produce the rate output signal (**Figure 1**). Aligned with their support fixtures and frames, these paired tines are fabricated from thin wafers of single crystal piezoelectric quartz.

Another company, Gladiator Technologies Inc., offers six models of MEMS gyros, which are very small, portable and of ultra-low power consumption (see **Figure 1c**) [56]. Nevertheless, the products by both abovementioned companies do not fulfill requirements for entirely rotational seismology as shown in the study, and their parameters are listed in **Table 1**. They are suited solutions as an additional device, which can be used for laboratory investigation, mainly for a rotational seismology engineering application (see example [57]).

**Figure 1.** MEMS gyros: (a) scheme of operation, (b) the Horizon™ MEMS angular rate sensor HZ1-100-100, and (c) Gladiator Technologies Inc. model G200D [56].


**Table 1.** The main parameters of the rotational sensors in the MEMS technology.

The mechanical systems working in an indirect way use defined pairs of classical seismometers. The first of them named Rotaphone based on commercially available geophones arranged in parallel pairs has been mounted on a rigid frame. They have been applied to record seismic events induced by natural sources (weak earthquakes with measured rotation about 10−6 rad/s) and anthropogenic sources (blasts with measured rotation about 10−3 rad/s) [24, 59–61]. They can be described as a recording system of ground velocity and rotational rate at a point. In order to obtain the rotational rate accurately, special gradients of the ground velocity wave field have to be measured. In 2010, a system named 6DOF (six-degree-of-freedom, see **Figure 2a**) was developed containing eight horizontal and one vertical geophones SM-6 (Sensor Nederland, B.V.), and it was mounted onto a cubic-shaped metal frame. It gives the possibility of recording three Cartesian components of ground velocity and three rotation rate components about Cartesian axes. Finally, the system named Rotaphone-D used 16 (eight horizontal and eight vertical) SM-6 geophones mounted around disc with a separation of the paired geophones of 0.4 m, as shown in **Figure 2b** [58]. The separating distances were chosen to correlate with a specific wavelength of interest. Data from **Table 2** show that Rotaphone is close to fulfilling

the requirements for seismological applications. However, their frequency ranges are still too narrow, and they should be treated as short-period systems. The other type of mechanical

A/D converter (dynamic) Type (Bit) 4 × Tedia (28) 1 × EE & S (24)

The instrument generally operates in a high-frequency range (above the natural frequency of the sensors used).

**6DOF [24] D [58]**

http://dx.doi.org/10.5772/intechopen.72169

25

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

The electrochemical rotational seismometers use molecular electronic transfer (MET). One can point out R-1 and R-2 from Eentec (USA) as representative in this group. Sensor construction is based on the electrochemical transducer contained in a channel filled with an electrolytic solution [63]. It includes four fine platinum mesh electrodes separated by microporous spacers (**Figure 3**). The fluid motion is converted into an electrical signal by using the ions' convective diffusion in electrolyte. The rotational seismometer has a toroidal channel filled

**Figure 3.** The electrochemical rotational seismometer: (a) schematic diagram of the MET transducer and (b) the Eentec

rotational seismometer operating in an indirect way named TAPS is described later.

**Parameter Unit Rotaphone**

Understood as an expression for the smallest signal that can be resolved ([19] p. 79).

**Table 2.** The main parameters of Rotaphone rotational seismometers.

1

2

3

4

Data for geophone SM-6.

Disc diameter.

R-1 [62].

Frequency range Hz 2–601 2–801 Sampling frequency Hz 250 250 Sensitivity<sup>2</sup> rad/s 2.16 × 10−9 3.77 × 10−9 Maximum rate rad/s 2.87 × 10−1 3.17 × 10−2 Dynamic range dB 120 120 Operating temperature °C −20–40 −40–100<sup>3</sup> Weight kg 9.5 15.3 Dimensions (L × W × H) mm 350 × 350 × 430 445<sup>4</sup> × 112 Natural frequency Hz 4.5 4.5

**Figure 2.** Schematic and general view of Rotaphones: (a) 6DOF prototype II [24] and (b) Rotaphone-D [58].


1 The instrument generally operates in a high-frequency range (above the natural frequency of the sensors used).

3 Data for geophone SM-6.

4 Disc diameter.

The mechanical systems working in an indirect way use defined pairs of classical seismometers. The first of them named Rotaphone based on commercially available geophones arranged in parallel pairs has been mounted on a rigid frame. They have been applied to record seismic events induced by natural sources (weak earthquakes with measured rotation about 10−6 rad/s) and anthropogenic sources (blasts with measured rotation about 10−3 rad/s) [24, 59–61]. They can be described as a recording system of ground velocity and rotational rate at a point. In order to obtain the rotational rate accurately, special gradients of the ground velocity wave field have to be measured. In 2010, a system named 6DOF (six-degree-of-freedom, see **Figure 2a**) was developed containing eight horizontal and one vertical geophones SM-6 (Sensor Nederland, B.V.), and it was mounted onto a cubic-shaped metal frame. It gives the possibility of recording three Cartesian components of ground velocity and three rotation rate components about Cartesian axes. Finally, the system named Rotaphone-D used 16 (eight horizontal and eight vertical) SM-6 geophones mounted around disc with a separation of the paired geophones of 0.4 m, as shown in **Figure 2b** [58]. The separating distances were chosen to correlate with a specific wavelength of interest. Data from **Table 2** show that Rotaphone is close to fulfilling

Dimensions (L × W × H) mm 58.3 × 25.3 × 25.3 25.4 × 25.4 × 25.4

An output noise for SNR = 1 also defined as a resolution @ 1 Hz in (rad/s).

**Table 1.** The main parameters of the rotational sensors in the MEMS technology.

1

24 Geophysics

**Parameter Unit HZ1–200-100 [55] G200D [56]** Axial Uniaxial Triaxial Sensitivity<sup>1</sup> rad/s/√Hz 4.4 × 10−4 8.7 × 10−5 Maximum rate rad/s 3.49 5.23

Frequency band Hz >60 Bandwidth 200 Operating temperature °C −40 to +71 −40 to +85 Calibration (S.F. dev. from 20/22°C) %/°C <0.08 <0.05 Shock survival g 200 500 Power supply VDC 8–12 3.1–5.5 Supply current mA <20 <300 Power consumption W 0.24 0.30 Weight kg <0.06 <0.031

**Figure 2.** Schematic and general view of Rotaphones: (a) 6DOF prototype II [24] and (b) Rotaphone-D [58].

**Table 2.** The main parameters of Rotaphone rotational seismometers.

the requirements for seismological applications. However, their frequency ranges are still too narrow, and they should be treated as short-period systems. The other type of mechanical rotational seismometer operating in an indirect way named TAPS is described later.

The electrochemical rotational seismometers use molecular electronic transfer (MET). One can point out R-1 and R-2 from Eentec (USA) as representative in this group. Sensor construction is based on the electrochemical transducer contained in a channel filled with an electrolytic solution [63]. It includes four fine platinum mesh electrodes separated by microporous spacers (**Figure 3**). The fluid motion is converted into an electrical signal by using the ions' convective diffusion in electrolyte. The rotational seismometer has a toroidal channel filled

**Figure 3.** The electrochemical rotational seismometer: (a) schematic diagram of the MET transducer and (b) the Eentec R-1 [62].

<sup>2</sup> Understood as an expression for the smallest signal that can be resolved ([19] p. 79).

with electrolyte. If the sensor rotates, liquid is forced through the MET sensor placed across the channel, converting liquid motion into electrical output. The parameters of R-1 and R-2 (see **Table 3**) are very close to fulfilling all technical requirements for entirely rotational seismology for both seismological and engineering applications.

Nevertheless, measurements carried out in the last decade showed reasonable results only for higher frequencies. The test with model R-1 showed its linear sensitivity equal to 6 × 10−5 rad/s/ (m/s<sup>2</sup> ) and a 2% cross-axis sensitivity [65]. The calibration quality casts also doubt in lower frequency range (<1 Hz) [66] since the frequency response does not have a flat shape, and at frequencies above 1 Hz, the dynamic range is only 80 dB [56]. Moreover, the measurement [52] in a temperature range of 20–50°C revealed deviations in the scale factor from the nominal value equaling 27 and 18% for R-1 and R-2, respectively, which suggests that this technology needs to be improved. In spite of the abovementioned disadvantages of the electrochemical seismometers, the R-1 model has recorded several hundreds of local earthquakes and two explosions in Taiwan [67].

The sensors designed by Applied Technology Associates (USA) [68] represent another technology with fluid. These devices operate based on the physical principle named magnetohydrodynamics (MHD). The main part of the sensing is a rotational proof mass containing conducting fluid as well as a permanent magnet that is fixed to the sensor case (**Figure 4**). The case-fixed magnetic flux moves through the inertially fixed conducting fluid with relative velocity as the case is rotated with the angular velocity Ω. This relative velocity between the magnetic flux and the fluid conductor generates a radially oriented electric field. This interaction or the MHD effect produces a voltage difference between the electrode surfaces that may be amplified by a transformer or other active electronic amplifier configurations. The signal (voltage output) is proportional to the angular rate Ω [70].

At ATA website, one can find two models of angular rate sensors: ARS-14 and ARS-15 (**Figure 5a** and **b**), where ARS-14 is able to measure angular motions as low as 30 nanoradians. Nevertheless, it should be emphasized that the sensor construction in MHD technology limits the frequency bandpass because the lower corner frequency is a function of parameters such as conductive fluid and fluid proof geometry. The upper value of a frequency bandwidth is usually determined by a signal processing unit. The ATA model Proto-SMHD (**Figure 5c**) which can be found in [69] is interesting because it is the device suited for microseismic signal detection. Nevertheless, in the literature, there are no examples of these sensors application

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

http://dx.doi.org/10.5772/intechopen.72169

27

**Figure 4.** Principle of magnetohydrodynamics effect of a conductive fluid in the presence of a magnetic field [69].

The last group is the optical systems operating based on the Sagnac effect [72] (more precisely, the von Laue-Sagnac effect). They are interferometric devices which use light for rotation detection. For the abovementioned reason, they have nonfrequency dependence of an output signal. The optical rotational seismometer exists in laser (RLG) or fiber (FOG) technology.

The ring laser gyroscopes (RLGs) detect the Sagnac beat frequency of two counter-propagating laser beams, which are propagated along a rectangular or triangular perimeter (**Figure 6a**). In the RLG, two coherent laser beams of an equal wavelength are generated. They are introduced into the system, and they circulate around the closed cavity in opposite directions. If the whole

**Figure 5.** Various models of angular rate sensors by ATA: (a) ARS-14, (b) ARS-15 [69], and (c) Proto-SMHD [71].

for recording effects connected with rotational seismology.


1 An output noise for SNR = 1 also defined as a resolution @ 1 Hz in (rad/s).

2 Understood as the gain of the instrument ([19] p. 79).

**Table 3.** The main parameters of rotational seismometers R-1, R-2.

Measurement of Rotational Events in Regions Prone to Seismicity: A Review http://dx.doi.org/10.5772/intechopen.72169 27

with electrolyte. If the sensor rotates, liquid is forced through the MET sensor placed across the channel, converting liquid motion into electrical output. The parameters of R-1 and R-2 (see **Table 3**) are very close to fulfilling all technical requirements for entirely rotational seis-

Nevertheless, measurements carried out in the last decade showed reasonable results only for higher frequencies. The test with model R-1 showed its linear sensitivity equal to 6 × 10−5 rad/s/

) and a 2% cross-axis sensitivity [65]. The calibration quality casts also doubt in lower frequency range (<1 Hz) [66] since the frequency response does not have a flat shape, and at frequencies above 1 Hz, the dynamic range is only 80 dB [56]. Moreover, the measurement [52] in a temperature range of 20–50°C revealed deviations in the scale factor from the nominal value equaling 27 and 18% for R-1 and R-2, respectively, which suggests that this technology needs to be improved. In spite of the abovementioned disadvantages of the electrochemical seismometers, the R-1 model has recorded several hundreds of local earthquakes and two explosions in Taiwan [67]. The sensors designed by Applied Technology Associates (USA) [68] represent another technology with fluid. These devices operate based on the physical principle named magnetohydrodynamics (MHD). The main part of the sensing is a rotational proof mass containing conducting fluid as well as a permanent magnet that is fixed to the sensor case (**Figure 4**). The case-fixed magnetic flux moves through the inertially fixed conducting fluid with relative velocity as the case is rotated with the angular velocity Ω. This relative velocity between the magnetic flux and the fluid conductor generates a radially oriented electric field. This interaction or the MHD effect produces a voltage difference between the electrode surfaces that may be amplified by a transformer or other active electronic amplifier configurations. The

mology for both seismological and engineering applications.

signal (voltage output) is proportional to the angular rate Ω [70].

Operating temperature °C −15 to +55 (extended −45 to +55)

An output noise for SNR = 1 also defined as a resolution @ 1 Hz in (rad/s).

**Table 3.** The main parameters of rotational seismometers R-1, R-2.

Understood as the gain of the instrument ([19] p. 79).

Shock survival g 200 200 Power supply VDC 9–14 9–18 Power consumption W 0.28 0.54 Weight kg 1.0 1.5

**Parameter Unit R-1 [62] R-2 [64]** Axial Triaxial Triaxial Sensitivity<sup>1</sup> rad/s/√Hz 1.2 × 10−7 0.6 × 10−7 Maximum rate rad/s 0.10 0.40 Dynamic range dB 110 117

Frequency band (extended) Hz 0.05–20 (0.03–50) 0.03–50 (0.01–100)

Dimensions (L × W × H) mm 120 × 120 × 90 120 × 120 × 100

/optional V/rad/s 50/ 2 × 102 50/5–2 × 102

(m/s<sup>2</sup>

26 Geophysics

Scale factor<sup>2</sup>

1

2

**Figure 4.** Principle of magnetohydrodynamics effect of a conductive fluid in the presence of a magnetic field [69].

At ATA website, one can find two models of angular rate sensors: ARS-14 and ARS-15 (**Figure 5a** and **b**), where ARS-14 is able to measure angular motions as low as 30 nanoradians. Nevertheless, it should be emphasized that the sensor construction in MHD technology limits the frequency bandpass because the lower corner frequency is a function of parameters such as conductive fluid and fluid proof geometry. The upper value of a frequency bandwidth is usually determined by a signal processing unit. The ATA model Proto-SMHD (**Figure 5c**) which can be found in [69] is interesting because it is the device suited for microseismic signal detection. Nevertheless, in the literature, there are no examples of these sensors application for recording effects connected with rotational seismology.

The last group is the optical systems operating based on the Sagnac effect [72] (more precisely, the von Laue-Sagnac effect). They are interferometric devices which use light for rotation detection. For the abovementioned reason, they have nonfrequency dependence of an output signal. The optical rotational seismometer exists in laser (RLG) or fiber (FOG) technology.

The ring laser gyroscopes (RLGs) detect the Sagnac beat frequency of two counter-propagating laser beams, which are propagated along a rectangular or triangular perimeter (**Figure 6a**). In the RLG, two coherent laser beams of an equal wavelength are generated. They are introduced into the system, and they circulate around the closed cavity in opposite directions. If the whole

**Figure 5.** Various models of angular rate sensors by ATA: (a) ARS-14, (b) ARS-15 [69], and (c) Proto-SMHD [71].

**Figure 6.** The ring laser gyroscope: (a) principle of operation, (b) GEOSensor [73], and (c) ROMY project––schema of the construction [74].

system rotates, the effective cavity length between the counter-propagating laser differs and a frequency splitting of two counter-propagating optical waves is obtained. The Sagnac frequency, δf, is described as:

$$
\delta f = \frac{4A}{\lambda P} n \Omega \tag{1}
$$

low noise <20 nrad/s/√Hz, high dynamic range, Plug & Play, no calibration needed, mainte-

**) Sensitivity (rad/s/√Hz)**

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

http://dx.doi.org/10.5772/intechopen.72169

29

Finally, in this section, we compare results obtained from two rotational seismometer systems installed for a continuum measurement in Książ, Poland seismological observatory––the Fibre-Optic System for Rotational Events& phenomena Monitoring (FOSREM) based on a fiber-optic gyroscope and the Twin Antiparallel Pendulum Seismometers (TAPS) based on

FOSREM is a new version of Autonomous Fibre-Optic Rotational Seismometer (AFORS), which was used between 2007 and 2017 in Książ. Each FOSREM contains three basic parts, which work interdependently: rotational seismometers FOSREM-XX type, data transmission unit (DTU), and power communication unit (PCU), see **Figure 7a**. The heart of the FOSREM––the rotational seismometer FOSREM-XX type––contains an optical head for generating the phase shift proportional to the detected rotation rate as well as the electronic part for data processing (**Figure 7b**). The optical head is constructed according to a so-called minimum configuration of FOG [77]. The light beam emitted by the source SLED is halved by the coupler and propagated to the sensor loop where two beams are propagating in the opposite direction. The sensor loop has been constructed by winding of 5 km SMF-28e + fiber in a double-quadrupole mode on a 0.215 m duralumin circular frame with attenuation equal to 0.35 dB/km@1310 nm [78]. The two polarizers mounted in line between two couplers assure the same optical path for the both counter-propagating waves. In order to shift the operating point to quadrature point of operation, the phase modulator at the end of the sensors loop was applied. The detected rotation rate is obtained by a specially designed system of filters (see **Figure 7b**), which properly select and amplify the first (A1ω) and the second (A2ω) amplitude of harmonic detected output signal u(t). The electronic part calculates the rotation rate Ω. Applying the following equation [79]:

[*Se u*(*t*)

are optical and electronical constant of the interferometer, respectively.

] = *So tan*−1

[*Se*( \_\_\_ *A*1*<sup>ω</sup>*

*<sup>A</sup>*2*ω*)], (2)

**4. Comparison of results obtained from measurements using optical** 

nance-free, embedded digitizer, GNSS time stamping, and so on.

**Table 4.** The sensitivity of different RLG systems used for rotation detection.

C-II 1 7.2 × 10−10 G 16 9.0 × 10−11 UG1 367 4.7 × 10−12 GEOsensor 2.56 4.5 × 10−11

ROMY 249 (0.02–0.05) × 10−12

**and mechanical rotational seismometers**

microarray of mechanical seismometers.

**RLG name Area (m2**

*Ω*(*t*) = *So tan*−1

So and Se

where *A* and *P* are the area and perimeter enclosed by the beam path, respectively; λ is optical wavelength of the laser oscillation, *Ω* is vector of angular velocity at which the instrument is turning; *n* is normal vector to the laser beam plane.

The RLGs have been applied for the rotational seismic events recording since the 1990s. The first ring laser gyroscope named "C-I" was assembled in the University of Canterbury in New Zealand in 1988–1990, and their parameters can be found in [75]. The next version was the ring laser "C-II" [76]. Its cavity with an area of 1.0 m2 was equipped with an ultra-high vacuum between metal flanges and a solid piece of Zerodur (glass ceramic with a low thermal expansion coefficient). The ring laser gyro with an area of 16 m2 and named ring laser "G" was assembled at Wettzell, Germany in 1998–2001. The bigger ring laser gyro named "UG-1" is installed in Cashmere Cavern, New Zealand. Its laser cavity has an area of 367 m2 . Especially, for seismological application, the ring laser "GEOsensor" has been designed and assembled at Wettzell, Germany. The "ROtational Motions in seismologY (ROMY)" [74] is a big project under the leadership of Igel. During the project, an apparatus consisting of four individual triangular ring lasers arranged in the shape of a tetrahedron with 12 m of length on each side (**Figure 6c**) will be used. The ROMY's constructors expect sensitivity in the range between 0.02 and 0.05 × 10−12 rad/s [74]. **Table 4** summarizes the fundamental parameters of various RLG systems. As one can see, there are not so many installations of RLGs, mostly because of their high cost and high sophistication involved in installation. They are very sensitive to external local disorders such as temperature, noise or pressure. Due to their dimensions and special isolation, they are unable to be transported.

Regarding the practical application of the optic rotational seismometer in fiber technology, the authors have knowledge only about one, other than their solution described in the next section, from iXBlue (France) named blueSeis-3A. Its parameters are available on web page http://www.blueseis.com as: portable, three-component system with 0.01–100 Hz broadband,


**Table 4.** The sensitivity of different RLG systems used for rotation detection.

system rotates, the effective cavity length between the counter-propagating laser differs and a frequency splitting of two counter-propagating optical waves is obtained. The Sagnac fre-

**Figure 6.** The ring laser gyroscope: (a) principle of operation, (b) GEOSensor [73], and (c) ROMY project––schema of the

where *A* and *P* are the area and perimeter enclosed by the beam path, respectively; λ is optical wavelength of the laser oscillation, *Ω* is vector of angular velocity at which the instrument is

The RLGs have been applied for the rotational seismic events recording since the 1990s. The first ring laser gyroscope named "C-I" was assembled in the University of Canterbury in New Zealand in 1988–1990, and their parameters can be found in [75]. The next version was

vacuum between metal flanges and a solid piece of Zerodur (glass ceramic with a low thermal

assembled at Wettzell, Germany in 1998–2001. The bigger ring laser gyro named "UG-1" is

for seismological application, the ring laser "GEOsensor" has been designed and assembled at Wettzell, Germany. The "ROtational Motions in seismologY (ROMY)" [74] is a big project under the leadership of Igel. During the project, an apparatus consisting of four individual triangular ring lasers arranged in the shape of a tetrahedron with 12 m of length on each side (**Figure 6c**) will be used. The ROMY's constructors expect sensitivity in the range between 0.02 and 0.05 × 10−12 rad/s [74]. **Table 4** summarizes the fundamental parameters of various RLG systems. As one can see, there are not so many installations of RLGs, mostly because of their high cost and high sophistication involved in installation. They are very sensitive to external local disorders such as temperature, noise or pressure. Due to their dimensions and special

Regarding the practical application of the optic rotational seismometer in fiber technology, the authors have knowledge only about one, other than their solution described in the next section, from iXBlue (France) named blueSeis-3A. Its parameters are available on web page http://www.blueseis.com as: portable, three-component system with 0.01–100 Hz broadband,

installed in Cashmere Cavern, New Zealand. Its laser cavity has an area of 367 m2

*<sup>P</sup> <sup>n</sup>* (1)

was equipped with an ultra-high

and named ring laser "G" was

. Especially,

quency, δf, is described as:

construction [74].

28 Geophysics

*<sup>f</sup>* <sup>=</sup> \_\_\_ <sup>4</sup>*<sup>A</sup>*

turning; *n* is normal vector to the laser beam plane.

isolation, they are unable to be transported.

the ring laser "C-II" [76]. Its cavity with an area of 1.0 m2

expansion coefficient). The ring laser gyro with an area of 16 m2

low noise <20 nrad/s/√Hz, high dynamic range, Plug & Play, no calibration needed, maintenance-free, embedded digitizer, GNSS time stamping, and so on.

#### **4. Comparison of results obtained from measurements using optical and mechanical rotational seismometers**

Finally, in this section, we compare results obtained from two rotational seismometer systems installed for a continuum measurement in Książ, Poland seismological observatory––the Fibre-Optic System for Rotational Events& phenomena Monitoring (FOSREM) based on a fiber-optic gyroscope and the Twin Antiparallel Pendulum Seismometers (TAPS) based on microarray of mechanical seismometers.

FOSREM is a new version of Autonomous Fibre-Optic Rotational Seismometer (AFORS), which was used between 2007 and 2017 in Książ. Each FOSREM contains three basic parts, which work interdependently: rotational seismometers FOSREM-XX type, data transmission unit (DTU), and power communication unit (PCU), see **Figure 7a**. The heart of the FOSREM––the rotational seismometer FOSREM-XX type––contains an optical head for generating the phase shift proportional to the detected rotation rate as well as the electronic part for data processing (**Figure 7b**). The optical head is constructed according to a so-called minimum configuration of FOG [77]. The light beam emitted by the source SLED is halved by the coupler and propagated to the sensor loop where two beams are propagating in the opposite direction. The sensor loop has been constructed by winding of 5 km SMF-28e + fiber in a double-quadrupole mode on a 0.215 m duralumin circular frame with attenuation equal to 0.35 dB/km@1310 nm [78]. The two polarizers mounted in line between two couplers assure the same optical path for the both counter-propagating waves. In order to shift the operating point to quadrature point of operation, the phase modulator at the end of the sensors loop was applied. The detected rotation rate is obtained by a specially designed system of filters (see **Figure 7b**), which properly select and amplify the first (A1ω) and the second (A2ω) amplitude of harmonic detected output signal u(t). The electronic part calculates the rotation rate Ω. Applying the following equation [79]:

$$\mathcal{Q}(t) = S\_o \tan^{-1} [S\_\epsilon \,\mu(t)] \, \, = \,\, S\_o \tan^{-1} \left[ S\_\epsilon \left( \frac{A\_{\iota\omega}}{A\_{\omega\iota}} \right) \right] \,\,\tag{2}$$

So and Se are optical and electronical constant of the interferometer, respectively.

**Figure 7.** FOSREM: (a) from left: rotational seismometer FOSREM-SS, FOSREM-BB, data transmission unit (DTU), and power communication unit (PCU); (b) schematic diagram of FOSREM-XX, top––optical head, bottom––electronic part.

In order to continuously collect data, the special software has been applied which enables the recording of only values of signals, which gained the assumed level of event [79]. The DTU enables a synchronic data recording from up to three rotational seismometers with their collection on a local disc as well as a transfer to PCU via fiber link. The PCU transmits the recorded data using Internet or GSM/GPS to a dedicated server FOSREM with a rate up to 100 Mbps. Furthermore, PCU enables the device to run for a minimum of 12 h.

**Table 5** summarizes the main parameters of three fiber systems used by our team. They differ in sizes, mechanical protections, and measuring range. AFORS and FOSREM-SS are suited for seismological investigation, but they cannot be applied for an engineering application because they have limited detection of the maximum rotation rate. FOSREM-BB due to the optimized optical part and the special software solution allows for the rotation rate detection in a wider range of signal amplitude up to 10 rad/s.

AFORS and FOSREM may work even when tilted; moreover, when used in continuous mode, they may record the tilt. They are portable, easy to assemble, as well as fully remotely controlled via Internet. It makes them as suitable devices to work with in a continuous mode for a very long period of time (weeks, months, and even years). For these reasons, AFORS (in 2007) and two FOSREM-SS (in 2017) have been mounted in seismological observatory in Książ in order to gather data connected with rotational seismic events.

As a reference system, the TAPS has also been mounted in Książ. TAPS is a mechanical rotational sensor constructed by a group from Institute of Geophysics PAS, Poland [80]. It is a set of two antiparallel pendulum seismometers (SM-3 type, Russia) mounted at one axis and connected parallel with opposite orientations (**Figure 8**). If the ground motion includes the displacement *u*(*t*) and the only vertical rotation *Ω*(*t*), the electromotive force (EMF) *f*(*t*) recorded by each SM-3 contains the component of displacement ±*u(t)* and the rotational motion *Ω(t)* multiplied by the proper length of the pendulum *l* [80]:

$$f\_{l,\aleph}(t) = \pm \omega(t) + l \cdot \Omega(t),\tag{3}$$

**Unit**

Picture of the optical head

Optical losses Theoretical sensitivity

Frequency bandpass

Accuracy in bandpass

Angle Random Walk

Bias instability

Dimension

Weight Operating temperature

Measuring range

**Table 5.**

The main parameters of rotational seismometers AFORS and FOSREM type.

°C rad/s

4 × 10−9–6.4 × 10−3

2 × 10−8–0.06

2 × 10−8–10

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

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31

0–50

rad/s rad/√Hz

rad/s

mm

kg

~18

700 × ϕ = 160

1.1 × 10−8

1.2 × 10−8

(0.48–6.1) × 10−8

Hz

0.83–106.15

rad/√Hz

4 × 10−9

dB

14.47

16.89 2.18 × 10−8 DC–328.12

3 × 10−8–1.6 × 10−6

3.2 × 10−8 1.6 × 10−8 470 × 360 × 230

~10

4.9 × 10−8

0.8 × 10−8 360 × 360 × 160

16.37

2.06 × 10−8

**AFORS**

**FOSREM-SS**

**FOSREM-BB**

In order to continuously collect data, the special software has been applied which enables the recording of only values of signals, which gained the assumed level of event [79]. The DTU enables a synchronic data recording from up to three rotational seismometers with their collection on a local disc as well as a transfer to PCU via fiber link. The PCU transmits the recorded data using Internet or GSM/GPS to a dedicated server FOSREM with a rate up to

**Figure 7.** FOSREM: (a) from left: rotational seismometer FOSREM-SS, FOSREM-BB, data transmission unit (DTU), and power communication unit (PCU); (b) schematic diagram of FOSREM-XX, top––optical head, bottom––electronic part.

**Table 5** summarizes the main parameters of three fiber systems used by our team. They differ in sizes, mechanical protections, and measuring range. AFORS and FOSREM-SS are suited for seismological investigation, but they cannot be applied for an engineering application because they have limited detection of the maximum rotation rate. FOSREM-BB due to the optimized optical part and the special software solution allows for the rotation rate detection

AFORS and FOSREM may work even when tilted; moreover, when used in continuous mode, they may record the tilt. They are portable, easy to assemble, as well as fully remotely controlled via Internet. It makes them as suitable devices to work with in a continuous mode for a very long period of time (weeks, months, and even years). For these reasons, AFORS (in 2007) and two FOSREM-SS (in 2017) have been mounted in seismological observatory in Książ in

As a reference system, the TAPS has also been mounted in Książ. TAPS is a mechanical rotational sensor constructed by a group from Institute of Geophysics PAS, Poland [80]. It is a set of two antiparallel pendulum seismometers (SM-3 type, Russia) mounted at one axis and connected parallel with opposite orientations (**Figure 8**). If the ground motion includes the displacement *u*(*t*) and the only vertical rotation *Ω*(*t*), the electromotive force (EMF) *f*(*t*) recorded by each SM-3 contains the component of displacement ±*u(t)* and the rotational motion *Ω(t)*

(*t*) = ±*u*(*t*) + *l* ∙ *Ω*(*t*), (3)

100 Mbps. Furthermore, PCU enables the device to run for a minimum of 12 h.

in a wider range of signal amplitude up to 10 rad/s.

30 Geophysics

order to gather data connected with rotational seismic events.

multiplied by the proper length of the pendulum *l* [80]:

*L*,*R*

*f*

**Table 5.** The main parameters of rotational seismometers AFORS and FOSREM type.

**Figure 8.** The TAPS rotational seismometer: (a) scheme [81] and (b) general view. ϕ(t) is the angle of rotation for a given pendulum.

where the signs "+" and "−"represent right (R) and left (L) seismometers, respectively. From the above, the rotational and translational components can be obtained from the sum and difference of two recorded signals, respectively as:

$$
\Omega(\mathbf{t}) = \frac{1}{2l} [f\_k(\mathbf{t}) + f\_\perp(\mathbf{t})] \quad \text{and} \quad \mathbf{u}(\mathbf{t}) = \frac{1}{2l} [f\_k(\mathbf{t}) - f\_\perp(\mathbf{t})].\tag{4}
$$

**5. Conclusions**

were used.

area of rotational seismology.

Activity of the Military University of Technology PBS-654.

**Acknowledgements**

Several advanced technologies of rotational sensors began to develop due to rapid increasing interest of rotational seismology. Nevertheless, the strict requirements for this scientific discipline are not fulfilled in many cases. From the presented review, it is clear that probably technologies based on optical interferometer are the most promising ones. However, it can be concluded that theoretical and mainly experimental studies of the rotational seismology are still in the initial state of development. Future works should be channeled toward acquiring a large amount of reliable experimental data recorded by different devices regarding rotational events from long distance sources (earthquakes generated in natural ways) as well as from short distance sources (the shocks generated in an artificial way––the explosions in a mine region). Such data are very handy for the confirmation of any theoretical investigation in the

**Figure 9.** M = 3.8 earthquake near Jarocin, Poland, 2012.01.06, 15:37:56. The uppermost window shows a rotation signal obtained from the AFORS. Plots of the rotation labeled "from TAPS" were obtained with the array method––two TAPSs

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

http://dx.doi.org/10.5772/intechopen.72169

33

This work was carried out with the financial support of the Polish Ministry of Science and Higher Education project POIR.04.02.00-14-A003/16: "EPOS—System Obserwacji Płyty Europejskiej", the National Science Centre, Poland under project 2016/23/N/ST10/02508 as well as the Statutory

Due to the rotational rate determination from the sum of the measured signals, the inaccuracies and difficulties can be observed. If the two antiparallel seismometers are precisely the same, the sum of the signals is proportional to the rotation rate. Taking into account the practical aspects of the pendulums, they are never identical. There is a difference in measured signals, which is widely described in [81]. As a result, it causes noise in the measurements of one order of magnitude greater for TAPS than for SM-3. In practice, the attenuation characteristic differences of the pendulum seismometers equal to a few per cent can generate a false rotational signal, especially if the rotational component is small in comparison with the translation one. There are different solutions for eliminating this problem, unfortunately with limited efficiency. Nowadays, one can find the records obtained by TAPSs including rotational motions during earthquakes [46, 82, 83] and seismic activity connected with artificial detonation in mine regions [84–87]. Unfortunately, this system does not fulfill the requirements for seismological applications of the rotational seismology due to the limited frequency bandpass as well as the measuring range.

In order to illustrate the rotational phenomena in the seismic wave field, we present in **Figure 9** seismograms of seismic events recorded in Książ. This earthquake was felt around Jarocin town and radiated the seismic field with clean rotational components. The distance to the source was of about 200 km. We show the unfiltered diagrams of the whole waveforms, but with a low-pass filtration which cut the spectrum at about 12.5 Hz. We decided to use these analyses in order to remove a high-frequency noise. The presented data allow for the comparison of rotational signals obtained by two different devices––TAPS and AFORS which have totally different idea of design. The compatibility between these two sensors is disturbed by differences in their spectral characteristics [86]. Unfortunately, we have observed noncorrelation between TAPS and AFORS for the same set of recorded events. For this reason, we decided to install in Ksiaż two FOSREM-SS in order to obtain more precise data.

Measurement of Rotational Events in Regions Prone to Seismicity: A Review http://dx.doi.org/10.5772/intechopen.72169 33

**Figure 9.** M = 3.8 earthquake near Jarocin, Poland, 2012.01.06, 15:37:56. The uppermost window shows a rotation signal obtained from the AFORS. Plots of the rotation labeled "from TAPS" were obtained with the array method––two TAPSs were used.

#### **5. Conclusions**

where the signs "+" and "−"represent right (R) and left (L) seismometers, respectively. From the above, the rotational and translational components can be obtained from the sum and dif-

**Figure 8.** The TAPS rotational seismometer: (a) scheme [81] and (b) general view. ϕ(t) is the angle of rotation for a given

Due to the rotational rate determination from the sum of the measured signals, the inaccuracies and difficulties can be observed. If the two antiparallel seismometers are precisely the same, the sum of the signals is proportional to the rotation rate. Taking into account the practical aspects of the pendulums, they are never identical. There is a difference in measured signals, which is widely described in [81]. As a result, it causes noise in the measurements of one order of magnitude greater for TAPS than for SM-3. In practice, the attenuation characteristic differences of the pendulum seismometers equal to a few per cent can generate a false rotational signal, especially if the rotational component is small in comparison with the translation one. There are different solutions for eliminating this problem, unfortunately with limited efficiency. Nowadays, one can find the records obtained by TAPSs including rotational motions during earthquakes [46, 82, 83] and seismic activity connected with artificial detonation in mine regions [84–87]. Unfortunately, this system does not fulfill the requirements for seismological applications of the rotational seismology due to the limited frequency bandpass as well as the measuring range. In order to illustrate the rotational phenomena in the seismic wave field, we present in **Figure 9** seismograms of seismic events recorded in Książ. This earthquake was felt around Jarocin town and radiated the seismic field with clean rotational components. The distance to the source was of about 200 km. We show the unfiltered diagrams of the whole waveforms, but with a low-pass filtration which cut the spectrum at about 12.5 Hz. We decided to use these analyses in order to remove a high-frequency noise. The presented data allow for the comparison of rotational signals obtained by two different devices––TAPS and AFORS which have totally different idea of design. The compatibility between these two sensors is disturbed by differences in their spectral characteristics [86]. Unfortunately, we have observed noncorrelation between TAPS and AFORS for the same set of recorded events. For this reason,

we decided to install in Ksiaż two FOSREM-SS in order to obtain more precise data.

] and u(t) <sup>=</sup> \_\_<sup>1</sup>

2*l*[*f R* (t) − *f L* (*t*)

]. (4)

ference of two recorded signals, respectively as:

2*l*[*f R* (t) + *f L* (*t*)

Ω(t) = \_\_<sup>1</sup>

pendulum.

32 Geophysics

Several advanced technologies of rotational sensors began to develop due to rapid increasing interest of rotational seismology. Nevertheless, the strict requirements for this scientific discipline are not fulfilled in many cases. From the presented review, it is clear that probably technologies based on optical interferometer are the most promising ones. However, it can be concluded that theoretical and mainly experimental studies of the rotational seismology are still in the initial state of development. Future works should be channeled toward acquiring a large amount of reliable experimental data recorded by different devices regarding rotational events from long distance sources (earthquakes generated in natural ways) as well as from short distance sources (the shocks generated in an artificial way––the explosions in a mine region). Such data are very handy for the confirmation of any theoretical investigation in the area of rotational seismology.

#### **Acknowledgements**

This work was carried out with the financial support of the Polish Ministry of Science and Higher Education project POIR.04.02.00-14-A003/16: "EPOS—System Obserwacji Płyty Europejskiej", the National Science Centre, Poland under project 2016/23/N/ST10/02508 as well as the Statutory Activity of the Military University of Technology PBS-654.

#### **Author details**

Leszek R. Jaroszewicz<sup>1</sup> \*, Anna Kurzych<sup>1</sup> , Krzysztof P. Teisseyre2 and Zbigniew Krajewski1 [12] Presentation on Seismotectonics from the Department of Geophysics, University of Munich [Internet]. 2016. Available from: www.geophysik.uni-muenchen.de/~igel/Lectures/Sedi/

Measurement of Rotational Events in Regions Prone to Seismicity: A Review

http://dx.doi.org/10.5772/intechopen.72169

35

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\*Address all correspondence to: jarosz@wat.edu.pl

1 Military University of Technology, Warsaw, Poland

2 Institute of Geophysics Polish Academy of Sciences, Warsaw, Poland

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**Author details**

34 Geophysics

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[61] Brokešová J. Short-period seismic rotations and translations recorded by Rotaphone [Habilitation Thesis]. Appendix G. Prague: Department of Geophysics, Charles Uni-

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[64] Rotational Seismometers R-2, R3. AST LLC. In: Data Sheet Presented at 4th International Working Group on Rotational Seismology Meeting; 20-23 June 2016; Tutzing. 2016 [65] Nigbor RL, Evans RJ, Hutt C. Laboratory and field testing of commercial rotational seismometers. Bulletin of the Seismological Society of America. 2009;**99**(2B):1215-1227. DOI:

[66] Wassermann J, Lehendorfer S, Igel W, Schreiber U. Performance test of a commercial rotational motions sensor. Bulletin of the Seismological Society of America. 2009;**99**(2B):1449-

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[71] Applied Technology Associates. Seismic SMHD––Rotational Sensor Development and Deployment [Internet]. Available from: www.osti.gov/scitech/servlets/purl/1258768

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**Chapter 3**

Provisional chapter

**Inversion and Interpretation of Magnetic Anomaly in**

DOI: 10.5772/intechopen.71027

**the Presence of Significant Remanence and Self-**

Inversion and Interpretation of Magnetic Anomaly

Self-Demagnetization Based on Magnetic Amplitude

Remanent magnetization and self-demagnetization effects of high-susceptibility body distort the intensity and direction of internal magnetization and hence complicate the inversion and interpretation of magnetic anomaly. The magnitude magnetic anomaly, which is weakly sensitive to the magnetization direction, provides an indirect way to investigate these complex anomalies. We study the sensitivity characteristics of 2D magnitude magnetic anomaly to magnetization direction and source shapes, implement the magnetization intensity inversion, and further estimate the magnetization direction by inverting for the total field data. The magnetic amplitude inversion is tested by the use of synthetic data, which are caused by prism models with strong remanent magnetization and high susceptibility. It is also applied to the field data of an iron-ore deposit in South Australia. The primary advantage of magnitude anomaly inversion is that the magnetization directions are not assumed to parallel the geomagnetic field. The magnetization intensity inversion and magnetization direction estimation make full use of the amplitude and phase information of magnetic anomalies. Magnetic amplitude inversion including other amplitude quantities such as normalized source strength and analytic signal offers an effective approach to investigate and interpret the magnetic anomalies

Keywords: magnetic anomaly, inversion and interpretation, remanent magnetization,

Susceptibility is the primary parameter used to represent the magnetic property of rocks and ores. Thus, numerous studies of magnetic data inversion were devoted to recover the

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

affected by complicated remanence and self-demagnetization.

self-demagnetization, magnetic amplitudes, mineral resources

**Demagnetization Based on Magnetic Amplitude**

in the Presence of Significant Remanence and

Shuang Liu and Xiangyun Hu

Shuang Liu and Xiangyun Hu

Abstract

1. Introduction

http://dx.doi.org/10.5772/intechopen.71027

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Provisional chapter

#### **Inversion and Interpretation of Magnetic Anomaly in the Presence of Significant Remanence and Self-Demagnetization Based on Magnetic Amplitude** Inversion and Interpretation of Magnetic Anomaly in the Presence of Significant Remanence and

DOI: 10.5772/intechopen.71027

Self-Demagnetization Based on Magnetic Amplitude

Shuang Liu and Xiangyun Hu

Additional information is available at the end of the chapter Shuang Liu and Xiangyun Hu

http://dx.doi.org/10.5772/intechopen.71027 Additional information is available at the end of the chapter

#### Abstract

Remanent magnetization and self-demagnetization effects of high-susceptibility body distort the intensity and direction of internal magnetization and hence complicate the inversion and interpretation of magnetic anomaly. The magnitude magnetic anomaly, which is weakly sensitive to the magnetization direction, provides an indirect way to investigate these complex anomalies. We study the sensitivity characteristics of 2D magnitude magnetic anomaly to magnetization direction and source shapes, implement the magnetization intensity inversion, and further estimate the magnetization direction by inverting for the total field data. The magnetic amplitude inversion is tested by the use of synthetic data, which are caused by prism models with strong remanent magnetization and high susceptibility. It is also applied to the field data of an iron-ore deposit in South Australia. The primary advantage of magnitude anomaly inversion is that the magnetization directions are not assumed to parallel the geomagnetic field. The magnetization intensity inversion and magnetization direction estimation make full use of the amplitude and phase information of magnetic anomalies. Magnetic amplitude inversion including other amplitude quantities such as normalized source strength and analytic signal offers an effective approach to investigate and interpret the magnetic anomalies affected by complicated remanence and self-demagnetization.

Keywords: magnetic anomaly, inversion and interpretation, remanent magnetization, self-demagnetization, magnetic amplitudes, mineral resources

#### 1. Introduction

Susceptibility is the primary parameter used to represent the magnetic property of rocks and ores. Thus, numerous studies of magnetic data inversion were devoted to recover the

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

susceptibility distributions and to infer the positions and shapes of magnetic sources. For example, Li and Oldenburg presented the techniques of depth-weighted, wavelet-transform compression and joint inversion of surface and borehole magnetic data [1–3]; Pilkington utilized the preconditioned conjugate gradient algorithm to solve the matrix equation [4]; Portniaguine and Zhdanov presented the image focusing techniques based on the minimum gradient support functions [5, 6]; Fedi presented the depth from extreme point method based on upward continuation theory [7], and so on. Nonetheless, the remanent magnetization also is an important part of rocks' and ores' magnetic property. It originates from conditions at their time of formation and widely exists in many real examples. The remanence alters the strength and direction of internal magnetization and exhibits large extents of uncertainty and regionality, which complicates the interpretation of magnetic data. Apart from the remanence, the self-demagnetization effect of high-susceptibility field sources also changes the magnitude and direction of internal magnetization [8–11]. Inversion of magnetic anomaly in the presence of remanence and self-demagnetization has become a hot topic in recent years.

calculated the three components of magnetization in a Cartesian and spherical framework, which served more complicated scenarios and had widespread applications in magnetic data inversion under the influences of significant remanent magnetization [32]. Similarly, Ellis et al. established the matrix equations between the magnetization components and magnetic anomalies and then optimized the objective function to obtain three components of magnetization vector [33]. These proposed methods were more applied to the inversion in the presence of remanence, but seldom used to invert the high-susceptibility distributions when the self-demagnetization effect is considered. Liu et al. inverted the 2D magnetization vector distributions of a high-susceptibility prism model based on the borehole magnitude mag-

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 43

The physical principles of self-demagnetization are different with remanence, but they have similar response in that both change the strength and direction of internal magnetization vectors. In cases where susceptibility of magnet is <0.1 SI, the effects of demagnetization are insignificant and can be neglected in forward modeling. However, such effects are important when modeling bodies with high susceptibility [11]. It is demonstrated that the selfdemagnetization effect tends to reduce the magnitude and biases the direction of internal magnetization, thereby distorting the amplitudes and shapes of magnetic anomalies [34]. The self-demagnetization widely exists in magnetic exploration [10] and engineering prospecting [9, 35]. A large number of forward modeling studies in relation to self-demagnetization have been carried out [9, 36–50], but it is still difficult to invert the property distributions considering the implications of self-demagnetization. The earlier approaches dealing with this problem involve correcting the magnetic anomaly by the use of the demagnetization factors for some simple models such as the 3D sphere and 2D elliptic cylinder [10]. Obviously, this method is only suitable for some simple geological conditions. Being similar to the electrical methods, in addition, Lelièvre and Oldenburg directly solved the Maxwell's equations using a finite volume discretization to recover the 3D high susceptibility distributions [9]. This is an effective way to solve the self-demagnetization problem, but the algorithms for solving the partial differential equations are difficult to implement under the complicated boundary conditions and rugged topography. Krahenbuhl and Li proposed an amplitude inversion method, and the study gave good results under the influence of self-demagnetization at high magnetic susceptibility [35]. Liu et al. inverted the 2D magnetization magnitude and direction distributions of a high-susceptibility dike model using borehole magnetization vector inversion [8]. Krahenbuhl and Li implemented the inversion of multiple source bodies and complex structures exhibiting

strong self-demagnetization based on the magnetic amplitude data [50].

Taking the 2D magnetic anomaly as an example, we discuss the characteristics of magnitude magnetic anomaly to magnetization direction and shapes of magnetic sources, and introduce the computations of magnitude magnetic anomaly in frequency domain. We recover the magnetization intensity distributions from the magnitude magnetic anomaly. Then, the total field anomalies are computed to estimate the magnetization direction. We simulate the magnetic field responses of high-susceptibility source under the self-demagnetization effect using the finite element method (FEM) and use the synthetic prism models with significant remanent

netic anomalies [8].

Some strategies have been proposed to deal with the remanence problem as Clark [12] summarized. The first kind of approach is to estimate the magnetization direction before recovering the physical property distributions using a standard magnetic inversion. The methods of estimating the magnetization direction are many. For example, Fedi et al. proposed the maxmin method of reduced-to-the-pole (RTP) to obtain the magnetization direction [13]; Bilim and Ates estimated the magnetization direction by searching for the maximum correlation between pseudo-gravity and gravity anomalies [14]. Phillips used Helbig's integrals for estimating the vector components of the magnetic dipole moment from the first-order moments of the vector magnetic field components [15]. Nicolosi et al. computed the magnetization direction of crustal structures using an equivalent source algorithm [16]. Dannemiller and Li estimated the total magnetization direction based on the correlation between the vertical gradient and the total gradient of the RTP field [17]. Gerovska et al. inverted the magnetization direction by correlating RTP and the magnitude magnetic anomalies [18]. Li et al. estimated the magnetization direction of magnetic anomalies through the correlation between normalized source strength and RTP [19]. The above magnetization direction estimation approaches are more amenable for simple and isolated anomalies because usually a unique magnetization direction is achieved. Due to the fact that only an averaged magnetization direction can be achieved, the above methods are more applicable for some simple and isolated anomalies.

In addition, an alternative method is presented to directly invert for some kinds of amplitude anomalies which are low sensitive to magnetization directions such as the total gradient data [20], the magnitude magnetic anomaly [21–25], the normalized source strength [26–28], and the analytic signal [29, 30]. This approach is more effective when the magnetization direction is highly variable due to the factors such as structural changes. The third method is the magnetization vector inversion. Wang et al. recovered a three-component Cartesian magnetization model and inverted the three components of total magnetization. However, their approach was more applicable in determining the total magnetization of separated, homogeneous bodies [31]. Lelièvre and Oldenburg improved their methods and calculated the three components of magnetization in a Cartesian and spherical framework, which served more complicated scenarios and had widespread applications in magnetic data inversion under the influences of significant remanent magnetization [32]. Similarly, Ellis et al. established the matrix equations between the magnetization components and magnetic anomalies and then optimized the objective function to obtain three components of magnetization vector [33]. These proposed methods were more applied to the inversion in the presence of remanence, but seldom used to invert the high-susceptibility distributions when the self-demagnetization effect is considered. Liu et al. inverted the 2D magnetization vector distributions of a high-susceptibility prism model based on the borehole magnitude magnetic anomalies [8].

susceptibility distributions and to infer the positions and shapes of magnetic sources. For example, Li and Oldenburg presented the techniques of depth-weighted, wavelet-transform compression and joint inversion of surface and borehole magnetic data [1–3]; Pilkington utilized the preconditioned conjugate gradient algorithm to solve the matrix equation [4]; Portniaguine and Zhdanov presented the image focusing techniques based on the minimum gradient support functions [5, 6]; Fedi presented the depth from extreme point method based on upward continuation theory [7], and so on. Nonetheless, the remanent magnetization also is an important part of rocks' and ores' magnetic property. It originates from conditions at their time of formation and widely exists in many real examples. The remanence alters the strength and direction of internal magnetization and exhibits large extents of uncertainty and regionality, which complicates the interpretation of magnetic data. Apart from the remanence, the self-demagnetization effect of high-susceptibility field sources also changes the magnitude and direction of internal magnetization [8–11]. Inversion of magnetic anomaly in the presence

42 Geophysics

of remanence and self-demagnetization has become a hot topic in recent years.

above methods are more applicable for some simple and isolated anomalies.

In addition, an alternative method is presented to directly invert for some kinds of amplitude anomalies which are low sensitive to magnetization directions such as the total gradient data [20], the magnitude magnetic anomaly [21–25], the normalized source strength [26–28], and the analytic signal [29, 30]. This approach is more effective when the magnetization direction is highly variable due to the factors such as structural changes. The third method is the magnetization vector inversion. Wang et al. recovered a three-component Cartesian magnetization model and inverted the three components of total magnetization. However, their approach was more applicable in determining the total magnetization of separated, homogeneous bodies [31]. Lelièvre and Oldenburg improved their methods and

Some strategies have been proposed to deal with the remanence problem as Clark [12] summarized. The first kind of approach is to estimate the magnetization direction before recovering the physical property distributions using a standard magnetic inversion. The methods of estimating the magnetization direction are many. For example, Fedi et al. proposed the maxmin method of reduced-to-the-pole (RTP) to obtain the magnetization direction [13]; Bilim and Ates estimated the magnetization direction by searching for the maximum correlation between pseudo-gravity and gravity anomalies [14]. Phillips used Helbig's integrals for estimating the vector components of the magnetic dipole moment from the first-order moments of the vector magnetic field components [15]. Nicolosi et al. computed the magnetization direction of crustal structures using an equivalent source algorithm [16]. Dannemiller and Li estimated the total magnetization direction based on the correlation between the vertical gradient and the total gradient of the RTP field [17]. Gerovska et al. inverted the magnetization direction by correlating RTP and the magnitude magnetic anomalies [18]. Li et al. estimated the magnetization direction of magnetic anomalies through the correlation between normalized source strength and RTP [19]. The above magnetization direction estimation approaches are more amenable for simple and isolated anomalies because usually a unique magnetization direction is achieved. Due to the fact that only an averaged magnetization direction can be achieved, the The physical principles of self-demagnetization are different with remanence, but they have similar response in that both change the strength and direction of internal magnetization vectors. In cases where susceptibility of magnet is <0.1 SI, the effects of demagnetization are insignificant and can be neglected in forward modeling. However, such effects are important when modeling bodies with high susceptibility [11]. It is demonstrated that the selfdemagnetization effect tends to reduce the magnitude and biases the direction of internal magnetization, thereby distorting the amplitudes and shapes of magnetic anomalies [34]. The self-demagnetization widely exists in magnetic exploration [10] and engineering prospecting [9, 35]. A large number of forward modeling studies in relation to self-demagnetization have been carried out [9, 36–50], but it is still difficult to invert the property distributions considering the implications of self-demagnetization. The earlier approaches dealing with this problem involve correcting the magnetic anomaly by the use of the demagnetization factors for some simple models such as the 3D sphere and 2D elliptic cylinder [10]. Obviously, this method is only suitable for some simple geological conditions. Being similar to the electrical methods, in addition, Lelièvre and Oldenburg directly solved the Maxwell's equations using a finite volume discretization to recover the 3D high susceptibility distributions [9]. This is an effective way to solve the self-demagnetization problem, but the algorithms for solving the partial differential equations are difficult to implement under the complicated boundary conditions and rugged topography. Krahenbuhl and Li proposed an amplitude inversion method, and the study gave good results under the influence of self-demagnetization at high magnetic susceptibility [35]. Liu et al. inverted the 2D magnetization magnitude and direction distributions of a high-susceptibility dike model using borehole magnetization vector inversion [8]. Krahenbuhl and Li implemented the inversion of multiple source bodies and complex structures exhibiting strong self-demagnetization based on the magnetic amplitude data [50].

Taking the 2D magnetic anomaly as an example, we discuss the characteristics of magnitude magnetic anomaly to magnetization direction and shapes of magnetic sources, and introduce the computations of magnitude magnetic anomaly in frequency domain. We recover the magnetization intensity distributions from the magnitude magnetic anomaly. Then, the total field anomalies are computed to estimate the magnetization direction. We simulate the magnetic field responses of high-susceptibility source under the self-demagnetization effect using the finite element method (FEM) and use the synthetic prism models with significant remanent magnetization and high susceptibility to test the amplitude inversion, respectively. Finally, amplitude inversion is applied to the field data of an iron-ore deposit in Southern Australia.

#### 2. Methodology

#### 2.1. 2D magnitude magnetic anomaly

The magnitude magnetic anomaly (i.e., Ta) belongs to the magnitude transforms and has some differences compared with the total field anomaly (i.e., ΔT). The 2D magnitude magnetic anomaly is defined as

$$T\_a = \left(H\_{ax}^2 + Z\_a^2\right)^{\frac{1}{2}},\tag{1}$$

Ta <sup>¼</sup> <sup>H</sup><sup>2</sup>

mine the inclined direction of magnetic bodies.

where <sup>μ</sup>0Ms

ax <sup>þ</sup> <sup>Z</sup><sup>2</sup> a <sup>1</sup>

<sup>2</sup> <sup>¼</sup> <sup>μ</sup>0Ms 4πGσ

magnitude magnetic anomaly is not dependent on the magnetization orientation.

not to assume the magnetization inclination paralleling the Earth's magnetic field.

V2 xx <sup>þ</sup> <sup>V</sup><sup>2</sup> xz <sup>1</sup>

<sup>4</sup>πG<sup>σ</sup> is a constant, σ is the residual density, Ms is the effective magnetization intensity, and Vxx, Vzz, Vxz, and Vzx are the second-order partial derivatives of gravitational potential, none of which are dependent on the direction of magnetization. Eq. (6) demonstrates that the

Figure 1 shows the examples of total field anomalies and magnitude magnetic anomalies of a rectangular prism model magnetized by different magnetization inclinations (i.e., I = 0�, 30�, 60�, 90�, 135�), of which the magnetization intensity is M = 100 A/m and geomagnetic inclination and declination are I<sup>0</sup> = 45� and D<sup>0</sup> = 0�, respectively. For the different magnetization inclinations, the total field anomalies (colored solid lines) are different, but their corresponding magnitude magnetic anomalies (black solid line) are completely similar. In fact, the observed total field anomalies contain amplitude and phase information. The magnitude anomalies reflect their amplitude information, which is related to the intensity of magnetic bodies' magnetization or susceptibility. The phase information is related to the magnetization direction. Therefore, the primary advantage of using amplitude anomalies of total field anomalies to invert the magnetization intensity or susceptibility distributions is that it is not essential to input the magnetization inclination or

Besides, the magnitude magnetic anomalies show better discrimination to the occurrences of the magnetic bodies. As for tabular models with different inclinations, the shapes of magnitude magnetic anomalies are different. In Figure 2, the magnitude anomalies of vertical tabular bodies (i.e., α = 90�) are symmetrical with similar decrease rate at the two sides of the anomalies. As for dipping tabular bodies with inclinations α = 15�, 30�, 45�, 60� and 75�, the magnitude anomalies at inclined direction decrease slightly, while they are steep at another direction. Therefore, the magnitude magnetic anomalies are conveniently utilized to preliminarily deter-

Overall, magnitude magnetic anomaly has two advantages. First, it does not depend on the magnetization direction. The magnitude anomaly has the approximate resolution to recover

Figure 1. (a) The rectangular prism model (b) corresponding total field anomalies and magnitude magnetic anomalies.

<sup>2</sup> <sup>¼</sup> <sup>μ</sup>0Ms 4πGσ

V2 zz <sup>þ</sup> <sup>V</sup><sup>2</sup> zx <sup>1</sup>

2

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027

, (6)

45

where Hax and Za are the horizontal and vertical components of magnetic anomalies, respectively. Given that Hax and Za anomalies satisfy the linear superposition principle, Ta can be added by anomalies from each magnetic cell numbered i:

$$T\_d = \left[ \left( \sum\_i H\_{\text{air}} \right)^2 + \left( \sum\_i Z\_{\text{ai}} \right)^2 \right]^{\frac{1}{7}}. \tag{2}$$

For single magnetic cell, the magnitude anomaly can be written as

$$T\_{ai} = \left(H\_{axi}^2 + Z\_{ai}^2\right)^{\frac{1}{2}}.\tag{3}$$

Based on Eqs. (2) and (3), the following equation can be deduced:

$$T\_a \le \sum\_i T\_{ai} \tag{4}$$

which indicates that the magnitude magnetic anomaly, the first difference with total field, is nonlinear relative to the magnetization intensity. It complicates the forward modeling and inversion. For example, the magnitude magnetic anomalies cannot be computed by adding single mesh cell's anomalies. Also, their sensitivity matrix is more complex to calculate than that of total field anomalies.

According to the 2D Poisson formula of magnetic field, the horizontal and vertical component anomalies are given by:

$$\begin{cases} H\_{ax} = \frac{\mu\_0}{4\pi G\sigma} [M\_{\text{x}}V\_{xx} + M\_{\text{z}}V\_{zx}] \\\\ Z\_d = \frac{\mu\_0}{4\pi G\sigma} [M\_{\text{x}}V\_{xz} + M\_{\text{z}}V\_{zz}] \end{cases} \tag{5}$$

where V is the gravitational potential. Thus, Ta can be written as

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 45

$$T\_a = \left(H\_{ax}^2 + Z\_a^2\right)^{\frac{1}{2}} = \frac{\mu\_0 M\_s}{4\pi G\sigma} \left[V\_{xx}^2 + V\_{xx}^2\right]^{\frac{1}{2}} = \frac{\mu\_0 M\_s}{4\pi G\sigma} \left[V\_{zz}^2 + V\_{zx}^2\right]^{\frac{1}{2}}\tag{6}$$

where <sup>μ</sup>0Ms <sup>4</sup>πG<sup>σ</sup> is a constant, σ is the residual density, Ms is the effective magnetization intensity, and Vxx, Vzz, Vxz, and Vzx are the second-order partial derivatives of gravitational potential, none of which are dependent on the direction of magnetization. Eq. (6) demonstrates that the magnitude magnetic anomaly is not dependent on the magnetization orientation.

magnetization and high susceptibility to test the amplitude inversion, respectively. Finally, amplitude inversion is applied to the field data of an iron-ore deposit in Southern Australia.

The magnitude magnetic anomaly (i.e., Ta) belongs to the magnitude transforms and has some differences compared with the total field anomaly (i.e., ΔT). The 2D magnitude magnetic

where Hax and Za are the horizontal and vertical components of magnetic anomalies, respectively. Given that Hax and Za anomalies satisfy the linear superposition principle, Ta can be

ax <sup>þ</sup> <sup>Z</sup><sup>2</sup> a � �<sup>1</sup>

> <sup>þ</sup> <sup>X</sup> i Zai

2

� �<sup>2</sup> � �<sup>1</sup>

axi <sup>þ</sup> <sup>Z</sup><sup>2</sup> ai � �<sup>1</sup>

2

2

, (1)

: (2)

(5)

: (3)

Tai , (4)

Ta <sup>¼</sup> <sup>H</sup><sup>2</sup>

i Haxi � �<sup>2</sup>

Tai <sup>¼</sup> <sup>H</sup><sup>2</sup>

Ta ≤ X i

which indicates that the magnitude magnetic anomaly, the first difference with total field, is nonlinear relative to the magnetization intensity. It complicates the forward modeling and inversion. For example, the magnitude magnetic anomalies cannot be computed by adding single mesh cell's anomalies. Also, their sensitivity matrix is more complex to calculate than

According to the 2D Poisson formula of magnetic field, the horizontal and vertical component

<sup>4</sup>πG<sup>σ</sup> ½ � MxVxx <sup>þ</sup> MzVzx

MxVxz þ MzVzz ½ �

,

Hax <sup>¼</sup> <sup>μ</sup><sup>0</sup>

8 >><

>>:

where V is the gravitational potential. Thus, Ta can be written as

Za <sup>¼</sup> <sup>μ</sup><sup>0</sup> 4πGσ

2. Methodology

44 Geophysics

anomaly is defined as

that of total field anomalies.

anomalies are given by:

2.1. 2D magnitude magnetic anomaly

added by anomalies from each magnetic cell numbered i:

Ta <sup>¼</sup> <sup>X</sup>

For single magnetic cell, the magnitude anomaly can be written as

Based on Eqs. (2) and (3), the following equation can be deduced:

Figure 1 shows the examples of total field anomalies and magnitude magnetic anomalies of a rectangular prism model magnetized by different magnetization inclinations (i.e., I = 0�, 30�, 60�, 90�, 135�), of which the magnetization intensity is M = 100 A/m and geomagnetic inclination and declination are I<sup>0</sup> = 45� and D<sup>0</sup> = 0�, respectively. For the different magnetization inclinations, the total field anomalies (colored solid lines) are different, but their corresponding magnitude magnetic anomalies (black solid line) are completely similar. In fact, the observed total field anomalies contain amplitude and phase information. The magnitude anomalies reflect their amplitude information, which is related to the intensity of magnetic bodies' magnetization or susceptibility. The phase information is related to the magnetization direction. Therefore, the primary advantage of using amplitude anomalies of total field anomalies to invert the magnetization intensity or susceptibility distributions is that it is not essential to input the magnetization inclination or not to assume the magnetization inclination paralleling the Earth's magnetic field.

Besides, the magnitude magnetic anomalies show better discrimination to the occurrences of the magnetic bodies. As for tabular models with different inclinations, the shapes of magnitude magnetic anomalies are different. In Figure 2, the magnitude anomalies of vertical tabular bodies (i.e., α = 90�) are symmetrical with similar decrease rate at the two sides of the anomalies. As for dipping tabular bodies with inclinations α = 15�, 30�, 45�, 60� and 75�, the magnitude anomalies at inclined direction decrease slightly, while they are steep at another direction. Therefore, the magnitude magnetic anomalies are conveniently utilized to preliminarily determine the inclined direction of magnetic bodies.

Overall, magnitude magnetic anomaly has two advantages. First, it does not depend on the magnetization direction. The magnitude anomaly has the approximate resolution to recover

Figure 1. (a) The rectangular prism model (b) corresponding total field anomalies and magnitude magnetic anomalies.

Figure 2. The magnitude magnetic anomalies of the dipping prisms with different inclinations.

the magnetic sources as total field anomaly. Second, magnitude anomaly performs more accurately in estimating the occurrence of magnetic bodies. Owing to the influences of inclined magnetization, it is difficult to determine the dipping direction using total field anomaly.

#### 2.2. Computation of magnitude magnetic anomaly

Magnitude magnetic anomaly (i.e., Ta) belongs to the transformed quantity which is computed from observed total field anomaly (i.e., ΔT) in frequency domain [51]. Initially, we calculate the frequency spectrum of ΔT by implementing fast Fourier transform (FFT):

$$
\Delta T \xrightarrow{\text{FFT}} \mathcal{F}\_{\Delta T\_{\prime}} \tag{7}
$$

F Hax ¼ ω<sup>Δ</sup>T!HaxFΔT, (8)

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 47

FZa ¼ ω<sup>Δ</sup>T!ZaFΔT, (9)

, (10)

, (11)

IFFTHax, (12)

IFFTZa: (13)

T<sup>a</sup> ¼ TaðmÞ (14)

Δm (15)

where F Hax and FZa are the frequency spectrums of Hax and Za components; ω<sup>Δ</sup>T!Hax and ω<sup>Δ</sup>T!Za are the frequency factors transforming ΔT to Hax and Za components and

where I<sup>0</sup> and A<sup>0</sup> denote the inclination of the Earth's magnetic field and the azimuth of profile, and i is the imaginary number. Hence, the horizontal and vertical component anomalies are

<sup>F</sup> Hax !

<sup>F</sup>Za !

After obtaining the Hax and Za components, the magnitude anomalies are computed by the use

Eqs. (7)–(13) summarize the calculation processes of magnitude magnetic anomaly. The critical processes are based on the computations of Hax and Za components in frequency domain. Regardless of geomagnetic inclination and profile's azimuth, it does not need inputting

Eq. (4) indicates that the magnitude magnetic anomaly vector T<sup>a</sup> is nonlinearly related to the

where Ta(m) is a nonlinear function. Using first-order Taylor expansions on Eq. (14), we obtain

ΔT<sup>a</sup> ¼ JTa

i sinI<sup>0</sup> þ icosI0cosA<sup>0</sup>

1 sinI<sup>0</sup> þ icosI0cosA<sup>0</sup>

ω<sup>Δ</sup>T!Hax ð Þ¼ κ

ω<sup>Δ</sup>T!Za ð Þ¼ κ

obtained by carrying out the inverse frequent Fourier transform (IFFT):

another parameter during the whole calculation processes.

magnetization intensity vector m. Their relation is given by

2.3. Magnetization intensity inversion

the following matrix equation:

and

and

and

of Eq. (1).

expressed as:

where F<sup>Δ</sup><sup>T</sup> represents the frequency spectrum of ΔT. Then, the frequency spectrums of horizontal and vertical components (i.e., Hax and Za) are achieved by, respectively, multiplying a transformed factor on the ΔT frequency spectrum:

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 47

$$\mathcal{F}\_{H\_{\text{ax}}} = \omega\_{\Lambda \Gamma \to H\_{\text{ax}}} \mathcal{F}\_{\Lambda \Gamma \prime} \tag{8}$$

and

$$\mathcal{F}\_{\mathbb{Z}\_4} = \omega\_{\Lambda \mathcal{T} \to \mathbb{Z}\_4} \mathcal{F}\_{\Lambda \mathcal{T} \prime} \tag{9}$$

where F Hax and FZa are the frequency spectrums of Hax and Za components; ω<sup>Δ</sup>T!Hax and ω<sup>Δ</sup>T!Za are the frequency factors transforming ΔT to Hax and Za components and expressed as:

$$\omega\_{\Delta T \to H\_{\text{ar}}}(\kappa) = \frac{i}{\sin I\_0 + i \cos I\_0 \cos A\_0} \,\prime \tag{10}$$

and

$$\omega\_{\Delta T \to Z\_x}(\kappa) = \frac{1}{\sin I\_0 + i \cos I\_0 \cos A\_0},\tag{11}$$

where I<sup>0</sup> and A<sup>0</sup> denote the inclination of the Earth's magnetic field and the azimuth of profile, and i is the imaginary number. Hence, the horizontal and vertical component anomalies are obtained by carrying out the inverse frequent Fourier transform (IFFT):

$$\mathcal{F}\_{H\_{\text{av}}} \xrightarrow{\text{IFFT}} \mathcal{H}\_{\text{axv}} \tag{12}$$

and

the magnetic sources as total field anomaly. Second, magnitude anomaly performs more accurately in estimating the occurrence of magnetic bodies. Owing to the influences of inclined magnetization, it is difficult to determine the dipping direction using total field anomaly.

Magnitude magnetic anomaly (i.e., Ta) belongs to the transformed quantity which is computed from observed total field anomaly (i.e., ΔT) in frequency domain [51]. Initially, we calculate the

FFT <sup>F</sup>ΔT, (7)

<sup>Δ</sup><sup>T</sup>!

where F<sup>Δ</sup><sup>T</sup> represents the frequency spectrum of ΔT. Then, the frequency spectrums of horizontal and vertical components (i.e., Hax and Za) are achieved by, respectively, multiplying a

frequency spectrum of ΔT by implementing fast Fourier transform (FFT):

Figure 2. The magnitude magnetic anomalies of the dipping prisms with different inclinations.

2.2. Computation of magnitude magnetic anomaly

46 Geophysics

transformed factor on the ΔT frequency spectrum:

$$\mathcal{F}\_{\mathbb{Z}\_q} \xrightarrow{\text{IFFT}} \mathbb{Z}\_q. \tag{13}$$

After obtaining the Hax and Za components, the magnitude anomalies are computed by the use of Eq. (1).

Eqs. (7)–(13) summarize the calculation processes of magnitude magnetic anomaly. The critical processes are based on the computations of Hax and Za components in frequency domain. Regardless of geomagnetic inclination and profile's azimuth, it does not need inputting another parameter during the whole calculation processes.

#### 2.3. Magnetization intensity inversion

Eq. (4) indicates that the magnitude magnetic anomaly vector T<sup>a</sup> is nonlinearly related to the magnetization intensity vector m. Their relation is given by

$$\mathbf{T}\_a = T\_a(\mathbf{m}) \tag{14}$$

where Ta(m) is a nonlinear function. Using first-order Taylor expansions on Eq. (14), we obtain the following matrix equation:

$$
\Delta \mathbf{T}\_a = \mathbf{J}\_{T\_a} \Delta \mathbf{m} \tag{15}
$$

where ΔT<sup>a</sup> and Δm are corrections of T<sup>a</sup> and m, respectively, and JTa is named sensitivity matrix whose element JTað Þ <sup>i</sup>;<sup>j</sup> is the partial derivative of Ta at the ith observation point to the jth model parameter mj [23]. Thus,

$$J\_{T\_x(i,j)} = \frac{\partial T\_{\text{ai}}}{\partial m\_j} = \frac{\partial}{\partial m\_j} \left( H\_{\text{axi}}^2 + Z\_{\text{ai}}^2 \right)^{\frac{1}{2}} = \frac{1}{T\_{\text{ai}}} \left( H\_{\text{axi}} G\_{\text{H}\_{\text{ar}(i)}} + Z\_{\text{ai}} G\_{\text{Z}\_{\text{a}(i)}} \right), \tag{16}$$

where i (i = 1,2,…,m) denotes the ith observation point, j (j = 1,2,…,n) denotes the jth mesh cell, m and n are the total numbers of observation points and mesh cells, respectively, and GHax ið Þ;<sup>j</sup> and GZa ið Þ;<sup>j</sup> are the elements of GHax and GZa . Here, GHax and GZa are the constant sensitivity matrices of Hax and Za anomalies. This equation demonstrates that because of the nonlinearity relation between magnitude anomalies and magnetization intensity, it is more complicated to compute the sensitive matrix of Ta than that of Hax, Za, and ΔT anomalies. The sensitivity matrix of Ta is related to the sensitive matrices of Hax, Za and the calculated Hax, Za, and Ta anomalies.

The minimum error solution of Eq. (15) is equivalent to solving the symmetric positive definite equation:

$$\mathbf{J}\_{T\_s}^T \mathbf{J}\_{T\_s} \Delta \mathbf{m} = \mathbf{J}\_{T\_s}^T \Delta \mathbf{T}\_a. \tag{17}$$

R IðÞ¼ <sup>C</sup> <sup>Δ</sup>Tobs; <sup>Δ</sup>Tpre � �

get to the maximal values, it can be expressed as,

tization direction.

remanence

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>C</sup> <sup>Δ</sup>Tobs; <sup>Δ</sup>Tobs � �<sup>C</sup> <sup>Δ</sup>Tpre; <sup>Δ</sup>Tpre ½ � <sup>q</sup> <sup>0</sup>

where I is the magnetization inclination, R Ið Þ is the correlation coefficient between observed and predicted total field anomalies, ΔTobs is the observed total field anomalies, ΔTpre is the predicted total field anomalies when the magnetization inclination is set to be I, and <sup>C</sup> <sup>Δ</sup>Tobs; <sup>Δ</sup>Tobs � �, <sup>C</sup> <sup>Δ</sup>Tpre; <sup>Δ</sup>Tpre ½ � are the covariance of observed and predicted data, C ΔTobs; ΔTpre � � is the cross-covariance between observed and predicted data. Therefore, the most appropriate magnetization inclination is that when the correlation coefficients of Eq. (20)

Eqs. (20) and (21) are the principle formulas used to estimate the magnetization direction. Based on the recovered magnetization distributions, we calculate the predicted magnetic anomalies magnetized by different magnetization inclinations varied from 0 to 360�

magnetization inclination with the largest correlation coefficients between the observed and predicted anomalies is defined as the most appropriate magnetization direction. In essence, the method makes use of the phase information of total field anomalies to determine the magne-

3. Synthetic examples: magnetic amplitude inversion with significant

We firstly test the method by the use of the 2D rectangular prism in Figure 1a, of which the top buried depth is 150 m and the length and width are 150 and 200 m, respectively. The Earth's magnetic field intensity is T<sup>0</sup> = 50,000 nT, with inclination I<sup>0</sup> = 45� and declination D<sup>0</sup> = 0�. The rectangular prism is magnetized by a constant magnetization with intensity M = 100 A/m and declination D = 0�, but the magnetization inclinations are assumed to be I = 0�, 30�, 45�, 60�, 90�, and 135� under influence of remanent magnetization. The magnetic observation point spacing is 20 m, and there are 51 points in total. As shown in Figure 1b, the total field anomalies are changed for different magnetization inclinations. However, for different magnetization inclinations varied from 0 to 135�, their amplitude anomalies always are the black solid line of the Figure 1b. The 2D amplitude data are strictly invariant with the magnetization direction. Therefore, using the amplitude anomalies to recover the magnetization, intensity distributions reduces the errors resulting from the incorrect magnetization direction. When inverting for the total field data, it is necessary to input the correct magnetization direction.

We invert for the amplitude data of the rectangular prism model in Figure 1b. The subsurface is divided into 800 (20 rows � 40 columns) mesh cells with size of 25 � 25 m. The

3.1. Rectangular prism with different magnetization inclinations

� ≤ I ≤ 360 � ��

Ibest ¼ arg max R I ½ � ð Þ : (21)

, (20)

49

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027

. The

We multiply a matrix P at both sides of Eq. (17); hence,

$$\mathbf{P}\left(\mathbf{J}\_{T\_s}^T \mathbf{J}\_{T\_s} \Delta \mathbf{m}\right) = \mathbf{P}\left(\mathbf{J}\_{T\_s}^T \Delta \mathbf{T}\_a\right),\tag{18}$$

where P usually is a diagonal matrix named preconditioner, which is used to reduce the condition number of Eq. (17) and promote the convergence rate. When Pilkington [4] and Liu et al. [8] used preconditioned conjugate gradient method to invert the magnetic anomaly, the preconditioner is given by.

$$\mathbf{P} = \mathbf{z}^{\beta} \mathbf{I},\tag{19}$$

where z is the buried depth of mesh cells, β is a constant related to the magnetic anomalies' attenuation rate with the increase of distances between cells and observation point, and I is the unit matrix.

#### 2.4. Estimation of effective magnetization direction

After obtaining the magnetization intensity distributions, we can regard them as known information and then calculate the total field anomalies using different magnetization directions. Thus, if the magnetization direction is given appropriately, the computed total field anomalies should fit the observed total field anomalies and their correlation coefficients get to maximum. Therefore, we compute the correlation coefficients between the observed and predicted total field anomalies of which the magnetization inclinations rotate a cycle from 0 to 360� with a certain step:

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 49

$$R(I) = \frac{\mathbb{C}\left[\Delta T^{\text{obs}}, \Delta T^{\text{pre}}\right]}{\sqrt{\mathbb{C}\left[\Delta T^{\text{obs}}, \Delta T^{\text{obs}}\right] \mathbb{C}\left[\Delta T^{\text{pre}}, \Delta T^{\text{pre}}\right]}} \quad \text{(0 }^\circ \text{<} I \lesssim 360^\circ\text{)},\tag{20}$$

where I is the magnetization inclination, R Ið Þ is the correlation coefficient between observed and predicted total field anomalies, ΔTobs is the observed total field anomalies, ΔTpre is the predicted total field anomalies when the magnetization inclination is set to be I, and <sup>C</sup> <sup>Δ</sup>Tobs; <sup>Δ</sup>Tobs � �, <sup>C</sup> <sup>Δ</sup>Tpre; <sup>Δ</sup>Tpre ½ � are the covariance of observed and predicted data, C ΔTobs; ΔTpre � � is the cross-covariance between observed and predicted data. Therefore, the most appropriate magnetization inclination is that when the correlation coefficients of Eq. (20) get to the maximal values, it can be expressed as,

$$I\_{\text{best}} = \arg\max[\mathcal{R}(I)].\tag{21}$$

Eqs. (20) and (21) are the principle formulas used to estimate the magnetization direction. Based on the recovered magnetization distributions, we calculate the predicted magnetic anomalies magnetized by different magnetization inclinations varied from 0 to 360� . The magnetization inclination with the largest correlation coefficients between the observed and predicted anomalies is defined as the most appropriate magnetization direction. In essence, the method makes use of the phase information of total field anomalies to determine the magnetization direction.

#### 3. Synthetic examples: magnetic amplitude inversion with significant remanence

#### 3.1. Rectangular prism with different magnetization inclinations

where ΔT<sup>a</sup> and Δm are corrections of T<sup>a</sup> and m, respectively, and JTa is named sensitivity matrix whose element JTað Þ <sup>i</sup>;<sup>j</sup> is the partial derivative of Ta at the ith observation point to the

> <sup>2</sup> <sup>¼</sup> <sup>1</sup> Tai

where i (i = 1,2,…,m) denotes the ith observation point, j (j = 1,2,…,n) denotes the jth mesh cell, m and n are the total numbers of observation points and mesh cells, respectively, and GHax ið Þ;<sup>j</sup> and GZa ið Þ;<sup>j</sup> are the elements of GHax and GZa . Here, GHax and GZa are the constant sensitivity matrices of Hax and Za anomalies. This equation demonstrates that because of the nonlinearity relation between magnitude anomalies and magnetization intensity, it is more complicated to compute the sensitive matrix of Ta than that of Hax, Za, and ΔT anomalies. The sensitivity matrix of Ta is related to the sensitive matrices of Hax, Za and the calculated Hax, Za,

The minimum error solution of Eq. (15) is equivalent to solving the symmetric positive definite

Δm ¼ J T Ta

where P usually is a diagonal matrix named preconditioner, which is used to reduce the condition number of Eq. (17) and promote the convergence rate. When Pilkington [4] and Liu et al. [8] used preconditioned conjugate gradient method to invert the magnetic anomaly, the

where z is the buried depth of mesh cells, β is a constant related to the magnetic anomalies' attenuation rate with the increase of distances between cells and observation point, and I is the

After obtaining the magnetization intensity distributions, we can regard them as known information and then calculate the total field anomalies using different magnetization directions. Thus, if the magnetization direction is given appropriately, the computed total field anomalies should fit the observed total field anomalies and their correlation coefficients get to maximum. Therefore, we compute the correlation coefficients between the observed and predicted total field anomalies of which the magnetization inclinations rotate a cycle from 0

<sup>¼</sup> P J<sup>T</sup> Ta ΔT<sup>a</sup> 

HaxiGHax ið Þ;<sup>j</sup> þ ZaiGZa ið Þ;<sup>j</sup> 

ΔTa: (17)

<sup>P</sup> <sup>¼</sup> <sup>z</sup><sup>β</sup>I, (19)

, (18)

, (16)

jth model parameter mj [23]. Thus,

and Ta anomalies.

preconditioner is given by.

with a certain step:

unit matrix.

to 360�

equation:

48 Geophysics

JTað Þ <sup>i</sup>;<sup>j</sup> <sup>¼</sup> <sup>∂</sup>Tai ∂mj

¼ ∂ ∂mj

H2 axi <sup>þ</sup> <sup>Z</sup><sup>2</sup> ai <sup>1</sup>

> J T Ta JTa

P J<sup>T</sup> Ta JTa Δm 

We multiply a matrix P at both sides of Eq. (17); hence,

2.4. Estimation of effective magnetization direction

We firstly test the method by the use of the 2D rectangular prism in Figure 1a, of which the top buried depth is 150 m and the length and width are 150 and 200 m, respectively. The Earth's magnetic field intensity is T<sup>0</sup> = 50,000 nT, with inclination I<sup>0</sup> = 45� and declination D<sup>0</sup> = 0�. The rectangular prism is magnetized by a constant magnetization with intensity M = 100 A/m and declination D = 0�, but the magnetization inclinations are assumed to be I = 0�, 30�, 45�, 60�, 90�, and 135� under influence of remanent magnetization. The magnetic observation point spacing is 20 m, and there are 51 points in total. As shown in Figure 1b, the total field anomalies are changed for different magnetization inclinations. However, for different magnetization inclinations varied from 0 to 135�, their amplitude anomalies always are the black solid line of the Figure 1b. The 2D amplitude data are strictly invariant with the magnetization direction. Therefore, using the amplitude anomalies to recover the magnetization, intensity distributions reduces the errors resulting from the incorrect magnetization direction. When inverting for the total field data, it is necessary to input the correct magnetization direction.

We invert for the amplitude data of the rectangular prism model in Figure 1b. The subsurface is divided into 800 (20 rows � 40 columns) mesh cells with size of 25 � 25 m. The preconditioned conjugate gradient algorithm converges stably after hundreds of iterations, and the predicted amplitude data accurately fit the observed data. The recovered magnetization distributions including the position and shape of magnetic sources yield a good approximation with the true model (Figure 3a). The magnitude anomalies show similar resolution to the recovery of physical property distributions compared with the total field anomalies (Figure 3b).

point, and the position of the maximum point represents the optimal magnetization direction. For example, for the red solid curve when the magnetization direction is horizontal (i.e., I = 0), the maximal peak locates at I = 0.5 with maximal correlation R = 0.9986, and therefore, the estimated optimal magnetization is Ibest = 0.5. The results of magnetization direction determination for the six synthetic magnetization inclinations are shown in Table 1. The synthetic magnetization inclinations are 0, 30, 45, 60, 90, and 135, and their corresponding estimated magnetization inclinations are 0.5, 30.0, 45.0, 60.0, 90.0, and 135.0. The maximal correlations resulted to 0.9986. The estimated magnetization inclinations are in agreement with

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 51

We design four 2D prism models, of which the cross sections are the dipping tabular, syncline tabular, cut tabular, and reproduction tabular (Figure 5). The Earth's magnetic field intensity is T<sup>0</sup> = 50,000 nT, with inclination I<sup>0</sup> = 45 and declination D<sup>0</sup> = 0. The models are magnetized by a constant magnetization magnitude M = 100 A/m with inclination I = 60 and declination D = 0. The magnetic observation point spacing is 20 m, and there are 51 points in total. The observed total field anomalies and the transformed magnitude anomalies are shown in Figure 6. Being similar to amplitude inversion of the Figure 3, the subsurface is divided into

Synthetic (degree) 0 30 45 60 90 135 Estimated (degree) 0.5 30.0 45.0 60.0 90.0 135.0 Correlation 0.9987 0.9987 0.9988 0.9987 0.9987 0.9986

Figure 5. The magnetization intensity inversion results using magnitude magnetic anomalies for the synthetic prism

model: (a) dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

Table 1. The estimated magnetization inclinations for rectangular model using correlation method.

3.2. Complicated prisms with the same magnetization inclination

the true values (error < 0.5).

With the known magnetization intensity distribution of Figure 3a, subsequently, the total field anomalies are computed of which the magnetization inclinations are varied a cycle from 0 to 360 by a step of 0.5. Then, we calculate the correlations between the observed and predicted total field anomalies for each magnetization inclination. As shown in Figure 4, the six colored solid lines, respectively, represent the correlation curves of the six synthetic magnetization inclinations (i.e., I = 0, 30, 45, 60, 90, and 135), of which the horizontal and vertical axes denote the magnetization inclination and the value of correlation. The correlation curve fluctuates between 1 and 1 shaped as the sine or cosine function. Each curve has one maximum

Figure 3. The magnetization intensity inversion results of the rectangular model using (a) magnitude magnetic anomalies and (b) total field anomalies.

Figure 4. The correlation curves of the rectangular model with different magnetization inclinations. The positions of maximal values reflect the magnetization directions.

point, and the position of the maximum point represents the optimal magnetization direction. For example, for the red solid curve when the magnetization direction is horizontal (i.e., I = 0), the maximal peak locates at I = 0.5 with maximal correlation R = 0.9986, and therefore, the estimated optimal magnetization is Ibest = 0.5. The results of magnetization direction determination for the six synthetic magnetization inclinations are shown in Table 1. The synthetic magnetization inclinations are 0, 30, 45, 60, 90, and 135, and their corresponding estimated magnetization inclinations are 0.5, 30.0, 45.0, 60.0, 90.0, and 135.0. The maximal correlations resulted to 0.9986. The estimated magnetization inclinations are in agreement with the true values (error < 0.5).

#### 3.2. Complicated prisms with the same magnetization inclination

preconditioned conjugate gradient algorithm converges stably after hundreds of iterations, and the predicted amplitude data accurately fit the observed data. The recovered magnetization distributions including the position and shape of magnetic sources yield a good approximation with the true model (Figure 3a). The magnitude anomalies show similar resolution to the recovery of physical property distributions compared with the total field anomalies

With the known magnetization intensity distribution of Figure 3a, subsequently, the total field anomalies are computed of which the magnetization inclinations are varied a cycle from 0 to 360 by a step of 0.5. Then, we calculate the correlations between the observed and predicted total field anomalies for each magnetization inclination. As shown in Figure 4, the six colored solid lines, respectively, represent the correlation curves of the six synthetic magnetization inclinations (i.e., I = 0, 30, 45, 60, 90, and 135), of which the horizontal and vertical axes denote the magnetization inclination and the value of correlation. The correlation curve fluctuates between 1 and 1 shaped as the sine or cosine function. Each curve has one maximum

Figure 3. The magnetization intensity inversion results of the rectangular model using (a) magnitude magnetic anomalies

0 30 60 120 90 150 180 210 240 270 300 330 360 Magnetization inclination (Degree)

Figure 4. The correlation curves of the rectangular model with different magnetization inclinations. The positions of

(Figure 3b).

50 Geophysics


and (b) total field anomalies.

I=0° I=30° I=45°

maximal values reflect the magnetization directions.

I=60° I=90° I=135° We design four 2D prism models, of which the cross sections are the dipping tabular, syncline tabular, cut tabular, and reproduction tabular (Figure 5). The Earth's magnetic field intensity is T<sup>0</sup> = 50,000 nT, with inclination I<sup>0</sup> = 45 and declination D<sup>0</sup> = 0. The models are magnetized by a constant magnetization magnitude M = 100 A/m with inclination I = 60 and declination D = 0. The magnetic observation point spacing is 20 m, and there are 51 points in total. The observed total field anomalies and the transformed magnitude anomalies are shown in Figure 6. Being similar to amplitude inversion of the Figure 3, the subsurface is divided into


Table 1. The estimated magnetization inclinations for rectangular model using correlation method.

Figure 5. The magnetization intensity inversion results using magnitude magnetic anomalies for the synthetic prism model: (a) dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

800 (20 rows 40 columns) rectangular cells. The preconditioned conjugate gradient converges after 100 iterations on average, and simultaneously, the predicted magnitude anomalies accurately fit the observed magnitude data (Figure 7). The recovered magnetization intensity distributions are shown in Figure 5. The inversion results are basically in accordance with the synthetic models. Owing to the lower resolution due to deep-buried magnetic sources, the deeper sources of combinational models including the cut prisms (Figure 5c) and reproduction

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 53

After recovering the magnetization intensity distributions (Figure 5), we estimated the magnetization directions based on the known magnetization intensity distributions. The correlation curves and the estimated magnetization inclination are shown in Figure 7 and Table 2. Except the syncline prism model with error of 12, other determined magnetization inclinations are close to 60. The amplitude data do not clearly distinguish the closed magnetic bodies leading to the predicted total field data not fitting the observed total field data accurately for combinational syncline and cut prisms. Besides, compared with the traditional correlation methods for estimating the magnetization direction [14, 15–18], this method considers magnetic sources' shapes and

positions, which improves the precision of magnetization direction determination.

Model a B c D Synthetic (degree) 60 60 60 60 Estimated (degree) 63.0 59.5 72.0 62.0 Correlation 0.9978 0.8717 0.9446 0.9994

Table 2. The magnetization inclination determination results for four prism models: (a) dipping prism, (b) syncline

Figure 8. The magnetization intensity inversion results for the total field anomalies of the dipping prism model using

different magnetization inclinations: (a) I = 0, (b) I = 45, (c) I = 90, and (d) I = 135.

prisms (Figure 5d) are not clearly distinguished.

prism, (c) cut prism, and (d) reproduction prism.

Figure 6. The observed and predicted total field anomalies and magnitude magnetic anomalies of the synthetic prism models: (a) dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

Figure 7. The correlation coefficient curves and the computed magnetization directions of the synthetic prism model: (a) dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

800 (20 rows 40 columns) rectangular cells. The preconditioned conjugate gradient converges after 100 iterations on average, and simultaneously, the predicted magnitude anomalies accurately fit the observed magnitude data (Figure 7). The recovered magnetization intensity distributions are shown in Figure 5. The inversion results are basically in accordance with the synthetic models. Owing to the lower resolution due to deep-buried magnetic sources, the deeper sources of combinational models including the cut prisms (Figure 5c) and reproduction prisms (Figure 5d) are not clearly distinguished.

After recovering the magnetization intensity distributions (Figure 5), we estimated the magnetization directions based on the known magnetization intensity distributions. The correlation curves and the estimated magnetization inclination are shown in Figure 7 and Table 2. Except the syncline prism model with error of 12, other determined magnetization inclinations are close to 60. The amplitude data do not clearly distinguish the closed magnetic bodies leading to the predicted total field data not fitting the observed total field data accurately for combinational syncline and cut prisms. Besides, compared with the traditional correlation methods for estimating the magnetization direction [14, 15–18], this method considers magnetic sources' shapes and positions, which improves the precision of magnetization direction determination.


Table 2. The magnetization inclination determination results for four prism models: (a) dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

Figure 6. The observed and predicted total field anomalies and magnitude magnetic anomalies of the synthetic prism

Figure 7. The correlation coefficient curves and the computed magnetization directions of the synthetic prism model: (a)

dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

models: (a) dipping prism, (b) syncline prism, (c) cut prism, and (d) reproduction prism.

52 Geophysics

Figure 8. The magnetization intensity inversion results for the total field anomalies of the dipping prism model using different magnetization inclinations: (a) I = 0, (b) I = 45, (c) I = 90, and (d) I = 135.

Taking the dipping prism as an example, we invert for the magnetization distributions from total field anomalies (true magnetization inclination is 45�) by giving different magnetization inclinations (i.e., I = 0�, 45�, 90�, 135�), assuming that we do not know the real magnetization direction of prism model. Only when the magnetization direction is given to be correct (true magnetization inclination is I = 45�), the inversion results coincide with the true model (Figure 8b). Otherwise, the inversion results have large errors compared with the true model (Figure 8a, c, and d). And even some of the iterations cannot be converged. Therefore, it is essential to give the correct magnetization inclination when using total field anomalies to recover the magnetization distributions. Otherwise, the inversion results may be distorted by the inaccurate magnetization direction.

strike northeast-southwest direction with amplitudes from 1000 to 5000 nT (Figure 9a). We use the data of Line 6 that traverses the center of mining area to test the method. The point

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 55

First, we divided the subsurface into 1060 (20 rows 53 columns) square cells with size of 40 m. The recovered magnetization intensity distributions indicate that the magnetic bodies are inclined to northwest about 60 and extend downward around 300 m (Figure 9b). Besides, the correlation curve demonstrates that the magnetization inclination is 264.0 (Figure 9c). The declination and inclination of the Earth's magnetic field in the mining area are NE6.8 and 67.1. In the profile of Line 6, the effective magnetization inclination increases to 72.4. Therefore, the magnetization

We design a 2D dike model with high susceptibility = 10.0 SI, of which the four vertices' coordinates are A (350–300 m), B (450–300 m), C (550–100 m), and D (450–100 m) (Figure 10). The geomagnetic field intensity is T<sup>0</sup> = 50,000 nT with an inclination of 45. First, the finite element method (FEM) is used to simulate the surface total field anomalies (i.e., ΔT), the

Figure 10. The magnetization inversion results of the high-susceptibility (κ = 10.0 SI) dike model: (a) the real internal magnetization intensity, (b) direction distributions when the self-demagnetization effect is not negligible, (c) the inverted magnetization intensity distributions using magnetic amplitude inversion, and (d) the estimated magnetization inclina-

spacing of this profile is 20 m, and there are 107 observation points in total.

direction deflects 23.6 (i.e., 360–264 72.4) from Earth's magnetic field.

5. Synthetic example: magnetic amplitude inversion of

high-susceptibility body

tion using correlation coefficient method.

#### 4. Field examples: Brennand iron-ore deposit, Eyre peninsula, South Australia

The Brennand iron-ore deposit lies in the Eyre Peninsula, South Australia, located at longitude: 135� 52<sup>0</sup> 00<sup>00</sup> E and latitude: 34� 24<sup>0</sup> 00<sup>00</sup> S. The banded iron formation (BIF) ore bodies have high magnetic susceptibility and produce strong magnetic anomalies. The aeromagnetic anomalies

Figure 9. The magnetization intensity and direction inversion results for the Line 6 of the Brennand iron-ore deposit, Eyre Peninsula, South Australia: (a) the contour map of total field anomalies, (b) the recovered magnetization intensity distributions, and (c) the estimated magnetization direction.

strike northeast-southwest direction with amplitudes from 1000 to 5000 nT (Figure 9a). We use the data of Line 6 that traverses the center of mining area to test the method. The point spacing of this profile is 20 m, and there are 107 observation points in total.

First, we divided the subsurface into 1060 (20 rows 53 columns) square cells with size of 40 m. The recovered magnetization intensity distributions indicate that the magnetic bodies are inclined to northwest about 60 and extend downward around 300 m (Figure 9b). Besides, the correlation curve demonstrates that the magnetization inclination is 264.0 (Figure 9c). The declination and inclination of the Earth's magnetic field in the mining area are NE6.8 and 67.1. In the profile of Line 6, the effective magnetization inclination increases to 72.4. Therefore, the magnetization direction deflects 23.6 (i.e., 360–264 72.4) from Earth's magnetic field.

#### 5. Synthetic example: magnetic amplitude inversion of high-susceptibility body

Taking the dipping prism as an example, we invert for the magnetization distributions from total field anomalies (true magnetization inclination is 45�) by giving different magnetization inclinations (i.e., I = 0�, 45�, 90�, 135�), assuming that we do not know the real magnetization direction of prism model. Only when the magnetization direction is given to be correct (true magnetization inclination is I = 45�), the inversion results coincide with the true model (Figure 8b). Otherwise, the inversion results have large errors compared with the true model (Figure 8a, c, and d). And even some of the iterations cannot be converged. Therefore, it is essential to give the correct magnetization inclination when using total field anomalies to recover the magnetization distributions. Otherwise, the inversion results may be distorted by

The Brennand iron-ore deposit lies in the Eyre Peninsula, South Australia, located at longitude: 135� 52<sup>0</sup> 00<sup>00</sup> E and latitude: 34� 24<sup>0</sup> 00<sup>00</sup> S. The banded iron formation (BIF) ore bodies have high magnetic susceptibility and produce strong magnetic anomalies. The aeromagnetic anomalies

Figure 9. The magnetization intensity and direction inversion results for the Line 6 of the Brennand iron-ore deposit, Eyre Peninsula, South Australia: (a) the contour map of total field anomalies, (b) the recovered magnetization intensity

4. Field examples: Brennand iron-ore deposit, Eyre peninsula,

the inaccurate magnetization direction.

distributions, and (c) the estimated magnetization direction.

South Australia

54 Geophysics

We design a 2D dike model with high susceptibility = 10.0 SI, of which the four vertices' coordinates are A (350–300 m), B (450–300 m), C (550–100 m), and D (450–100 m) (Figure 10). The geomagnetic field intensity is T<sup>0</sup> = 50,000 nT with an inclination of 45. First, the finite element method (FEM) is used to simulate the surface total field anomalies (i.e., ΔT), the

Figure 10. The magnetization inversion results of the high-susceptibility (κ = 10.0 SI) dike model: (a) the real internal magnetization intensity, (b) direction distributions when the self-demagnetization effect is not negligible, (c) the inverted magnetization intensity distributions using magnetic amplitude inversion, and (d) the estimated magnetization inclination using correlation coefficient method.

magnitude magnetic anomaly (i.e., Ta), the true internal magnetization intensity, and the inclination distributions. Theoretical simulation reveals that the internal magnetization distribution is inhomogeneous with average strength (50–60 A/m) (Figure 10a), which is far less than 397 A/m (i.e., M ¼ κH<sup>0</sup> ¼ κT0=μ0) when demagnetization is not considered. The selfdemagnetization effect decreases the internal magnetization intensity. Moreover, the internal magnetization inclination ranges from 50 to 65� with average of 60� (Figure 10b). The selfdemagnetization effect deflects the magnetization direction about 15� (i.e., 60–45�) to the longaxis direction of the dike model. The computed total field anomaly and magnitude anomaly are shown with red and blue solid curves in Figure 11. The point spacing is 3 m.

6. Weak sensitivity of 3D magnitude magnetic anomaly to

Ta <sup>¼</sup> <sup>H</sup><sup>2</sup>

[21, 52]. For 3D cases, magnitude magnetic anomaly is written as

The 2D magnitude magnetic anomaly is totally independent of the magnetization direction and has high centricity with the magnetic source's position, which provides an idea of magnitude magnetic transform to investigate the inversion and interpretation of magnetic anomaly

ax <sup>þ</sup> <sup>H</sup><sup>2</sup>

Which, however, has low sensitivity to the direction of magnetization. Stavrev and Gerovska [52] and Pilkington and Beiki [26] used a variable to evaluate the sensitivity of magnitude magnetic transform to magnetization direction by comparing with the field of vertical magne-

j j F Ið Þ� ; D F Ið Þ <sup>b</sup>; Db dxdy=

where F is the magnitude magnetic transform; I and D are inclination and declination of

Figure 12. Sensitivities of (a, c) magnitude magnetic anomaly and (b, d) total field anomaly to the total magnetization direction. Plot (a) shows the sensitivity of magnitude magnetic anomaly to magnetization inclination and declination. Plot (b) shows the sensitivity of total field anomaly to magnetization inclination and declination. Plot (c) shows the sensitivity of magnitude magnetic anomaly to magnetization inclination (i.e., cross section at declination = 50� in plot (a)). Plot (d) shows the sensitivity of total field anomaly to magnetization inclination (i.e., cross section at declination = 50� in plot (b)).

� �<sup>1</sup>

ay <sup>þ</sup> <sup>Z</sup><sup>2</sup> a

2

ðð

, (22)

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 57

j j F Ið Þ <sup>b</sup>; Db dxdy, (23)

magnetization direction

tization direction, expressed as

S Ið Þ¼ ; D

ðð

magnetization direction, respectively; I<sup>b</sup> = 90� and D<sup>b</sup> = 90�.

We inverted for the magnitude magnetic anomaly (i.e., blue curve in Figure 11), and the cross section was divided into 40 � 20 square cells with size of 25 m. The preconditioned conjugate gradient method was converged after 200 times of iterations, and the predicted magnitude anomaly fit the observed anomaly accurately (Figure 11). The inverted magnetization intensity distributions are shown in Figure 10c. The range of the inverted magnetization intensity is (40–65 A/m), of which the amplitudes and shapes are in accordance with the real distribution of magnetization in the presence of demagnetization (Figure 10a). The correlation coefficients (with step of 0.2� varied from 0 to 90�) between the observed and predicted data reach the maximum at A (I = 52.0�, R = 0. 997,696). Hence, for this high-susceptibility prism, the estimated internal magnetization inclination is 52� (Figure 10d). This result is in good agreement with the theoretical distributions of magnetization inclination (Figure 10b). Therefore, from the magnetization vector inversion results, it can be concluded that the demagnetization effect biases the magnetization direction to the dike's long-axis direction 7� (i.e., 52–45�). They reduce the magnetization intensity and magnetic anomalies by about seven times (i.e., 397/ 60). The relative error of magnetic anomalies caused by demagnetization effects reaches 85% (i.e., (397–60)/397). Theoretically, for high-susceptibility magnetic bodies of which the susceptibility is 10 SI, the magnetic anomalies' error caused by demagnetization effects reaches 83% [8].

Figure 11. The observed and predicted total field anomalies and magnitude magnetic anomalies.

#### 6. Weak sensitivity of 3D magnitude magnetic anomaly to magnetization direction

magnitude magnetic anomaly (i.e., Ta), the true internal magnetization intensity, and the inclination distributions. Theoretical simulation reveals that the internal magnetization distribution is inhomogeneous with average strength (50–60 A/m) (Figure 10a), which is far less than 397 A/m (i.e., M ¼ κH<sup>0</sup> ¼ κT0=μ0) when demagnetization is not considered. The selfdemagnetization effect decreases the internal magnetization intensity. Moreover, the internal magnetization inclination ranges from 50 to 65� with average of 60� (Figure 10b). The selfdemagnetization effect deflects the magnetization direction about 15� (i.e., 60–45�) to the longaxis direction of the dike model. The computed total field anomaly and magnitude anomaly

We inverted for the magnitude magnetic anomaly (i.e., blue curve in Figure 11), and the cross section was divided into 40 � 20 square cells with size of 25 m. The preconditioned conjugate gradient method was converged after 200 times of iterations, and the predicted magnitude anomaly fit the observed anomaly accurately (Figure 11). The inverted magnetization intensity distributions are shown in Figure 10c. The range of the inverted magnetization intensity is (40–65 A/m), of which the amplitudes and shapes are in accordance with the real distribution of magnetization in the presence of demagnetization (Figure 10a). The correlation coefficients (with step of 0.2� varied from 0 to 90�) between the observed and predicted data reach the maximum at A (I = 52.0�, R = 0. 997,696). Hence, for this high-susceptibility prism, the estimated internal magnetization inclination is 52� (Figure 10d). This result is in good agreement with the theoretical distributions of magnetization inclination (Figure 10b). Therefore, from the magnetization vector inversion results, it can be concluded that the demagnetization effect biases the magnetization direction to the dike's long-axis direction 7� (i.e., 52–45�). They reduce the magnetization intensity and magnetic anomalies by about seven times (i.e., 397/ 60). The relative error of magnetic anomalies caused by demagnetization effects reaches 85% (i.e., (397–60)/397). Theoretically, for high-susceptibility magnetic bodies of which the susceptibility is

are shown with red and blue solid curves in Figure 11. The point spacing is 3 m.

56 Geophysics

10 SI, the magnetic anomalies' error caused by demagnetization effects reaches 83% [8].

Figure 11. The observed and predicted total field anomalies and magnitude magnetic anomalies.

The 2D magnitude magnetic anomaly is totally independent of the magnetization direction and has high centricity with the magnetic source's position, which provides an idea of magnitude magnetic transform to investigate the inversion and interpretation of magnetic anomaly [21, 52]. For 3D cases, magnitude magnetic anomaly is written as

$$T\_a = \left(H\_{ax}^2 + H\_{ay}^2 + Z\_a^2\right)^{\frac{1}{2}},\tag{22}$$

Which, however, has low sensitivity to the direction of magnetization. Stavrev and Gerovska [52] and Pilkington and Beiki [26] used a variable to evaluate the sensitivity of magnitude magnetic transform to magnetization direction by comparing with the field of vertical magnetization direction, expressed as

$$S(I, D) = \iint |F(I, D) - F(I\_b, D\_b)| dxdy / \iint |F(I\_b, D\_b)| dxdy,\tag{23}$$

where F is the magnitude magnetic transform; I and D are inclination and declination of magnetization direction, respectively; I<sup>b</sup> = 90� and D<sup>b</sup> = 90�.

Figure 12. Sensitivities of (a, c) magnitude magnetic anomaly and (b, d) total field anomaly to the total magnetization direction. Plot (a) shows the sensitivity of magnitude magnetic anomaly to magnetization inclination and declination. Plot (b) shows the sensitivity of total field anomaly to magnetization inclination and declination. Plot (c) shows the sensitivity of magnitude magnetic anomaly to magnetization inclination (i.e., cross section at declination = 50� in plot (a)). Plot (d) shows the sensitivity of total field anomaly to magnetization inclination (i.e., cross section at declination = 50� in plot (b)).

Figure 12 shows the sensitivities of magnitude magnetic anomaly and total field anomaly to the magnetization inclination and declination. It is revealed that both the magnitude magnetic anomaly and total field anomaly are mainly sensitive to magnetization inclination. And the magnitude magnetic anomaly shows far weaker sensitivity than total field. The sensitivity value in Eq. (23) of total field is up to 1.3 when the magnetization direction is horizontal, while it is only 0.3 for magnitude magnetic anomaly. When the magnetization direction is horizontal, for magnitude magnetic data and total field data, the sensitivity reaches a maximal value.

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 59

The weak sensitivity feature of 3D magnitude magnetic anomaly to magnetization direction impacts the magnetization intensity inversion results. Figure 13a and b shows the total field anomaly and magnitude magnetic anomaly of the 3D synthetic model when the total magnetization direction is horizontal (magnetization intensity M = 1 A/m, inclination I = 0, declination = 30; geomagnetic inclination I<sup>0</sup> = 45, declination D<sup>0</sup> = 0). The total fields include positive and negative anomalies showing a relatively complicated feature. The magnitude magnetic anomaly only has positive values, and its extreme points show some offsets from the horizontal centers of magnetic source (Figure 13b). When inverting the magnitude magnetic anomaly, as shown in Figure 13(c–f), the recovered magnetization distributions also have some offsets to north compared with the true models. The deep shapes of recovered magnetization intensity distributions in particularly for sources A and C have big differences with the true models, which also would increase the error of magnetization direction estimation.

Remanent magnetization is prevalent in many mining areas, but their directions usually are unknown because of the difficulty in collecting the oriented samples. For high-susceptibility source, the influence of self-demagnetization effect also cannot be ignored. The magnitude anomalies are frequently transformed from the observed total field anomalies. The primary advantage of magnitude anomalies inversion is that the magnetization directions are not assumed to parallel the geomagnetic field, or it is not necessary to input the magnetization directions as the total field data inversion. The magnitude anomalies have similar resolution to the recovery of physical property distributions and perform higher sensitivity to the occurrences of magnetic bodies compared with the total field anomaly. Based on the known magnetization intensity distributions, the total field anomalies are computed by the use of different magnetization directions. Thus, the magnetization direction of maximal correlation with the observed total field anomaly is deemed as the most appropriate magnetization direction. This strategy considers the influences of magnetic sources' shapes and obtains an average magnetization direction compared with another correlation approaches. The inverted magnetization intensity and direction help to study the influences of remanence and self-demagnetization. The method makes full use of the amplitude and phase information of total field anomaly to determine the magnetization intensity and direction, respectively. The amplitude anomaly is more related to the intensity of magnetization vector, while the phase is mainly dependent on the direction of magnetization vector. The 2D magnitude magnetic anomaly provides an idea of magnitude magnetic transform to implement the amplitude data inversion, but in 3D case, magnitude magnetic anomaly is weakly sensitive to magnetization direction, which brings some errors for the inversion of magnetization intensity. Other magnetic anomaly quantities such as analytic signal and normalized source strength have weak sensitivity to magnetization

7. Conclusions

Figure 13. Magnetization inversion results of magnitude magnetic anomaly of a 3D synthetic model with horizontal total magnetization direction: (a) total field anomaly, (b) magnitude magnetic anomaly, (c) horizontal cross section at depth = 175 m, and vertical cross sections at northing = (d) 725 m, (e) 525 m, and (f) 275 m.

magnitude magnetic anomaly shows far weaker sensitivity than total field. The sensitivity value in Eq. (23) of total field is up to 1.3 when the magnetization direction is horizontal, while it is only 0.3 for magnitude magnetic anomaly. When the magnetization direction is horizontal, for magnitude magnetic data and total field data, the sensitivity reaches a maximal value.

The weak sensitivity feature of 3D magnitude magnetic anomaly to magnetization direction impacts the magnetization intensity inversion results. Figure 13a and b shows the total field anomaly and magnitude magnetic anomaly of the 3D synthetic model when the total magnetization direction is horizontal (magnetization intensity M = 1 A/m, inclination I = 0, declination = 30; geomagnetic inclination I<sup>0</sup> = 45, declination D<sup>0</sup> = 0). The total fields include positive and negative anomalies showing a relatively complicated feature. The magnitude magnetic anomaly only has positive values, and its extreme points show some offsets from the horizontal centers of magnetic source (Figure 13b). When inverting the magnitude magnetic anomaly, as shown in Figure 13(c–f), the recovered magnetization distributions also have some offsets to north compared with the true models. The deep shapes of recovered magnetization intensity distributions in particularly for sources A and C have big differences with the true models, which also would increase the error of magnetization direction estimation.

#### 7. Conclusions

Figure 12 shows the sensitivities of magnitude magnetic anomaly and total field anomaly to the magnetization inclination and declination. It is revealed that both the magnitude magnetic anomaly and total field anomaly are mainly sensitive to magnetization inclination. And the

58 Geophysics

Figure 13. Magnetization inversion results of magnitude magnetic anomaly of a 3D synthetic model with horizontal total magnetization direction: (a) total field anomaly, (b) magnitude magnetic anomaly, (c) horizontal cross section at

depth = 175 m, and vertical cross sections at northing = (d) 725 m, (e) 525 m, and (f) 275 m.

Remanent magnetization is prevalent in many mining areas, but their directions usually are unknown because of the difficulty in collecting the oriented samples. For high-susceptibility source, the influence of self-demagnetization effect also cannot be ignored. The magnitude anomalies are frequently transformed from the observed total field anomalies. The primary advantage of magnitude anomalies inversion is that the magnetization directions are not assumed to parallel the geomagnetic field, or it is not necessary to input the magnetization directions as the total field data inversion. The magnitude anomalies have similar resolution to the recovery of physical property distributions and perform higher sensitivity to the occurrences of magnetic bodies compared with the total field anomaly. Based on the known magnetization intensity distributions, the total field anomalies are computed by the use of different magnetization directions. Thus, the magnetization direction of maximal correlation with the observed total field anomaly is deemed as the most appropriate magnetization direction. This strategy considers the influences of magnetic sources' shapes and obtains an average magnetization direction compared with another correlation approaches. The inverted magnetization intensity and direction help to study the influences of remanence and self-demagnetization. The method makes full use of the amplitude and phase information of total field anomaly to determine the magnetization intensity and direction, respectively. The amplitude anomaly is more related to the intensity of magnetization vector, while the phase is mainly dependent on the direction of magnetization vector. The 2D magnitude magnetic anomaly provides an idea of magnitude magnetic transform to implement the amplitude data inversion, but in 3D case, magnitude magnetic anomaly is weakly sensitive to magnetization direction, which brings some errors for the inversion of magnetization intensity. Other magnetic anomaly quantities such as analytic signal and normalized source strength have weak sensitivity to magnetization direction, so they also can be inverted to study the remanent magnetization and selfdemagnetization. The amplitude data inversion provides an effective approach to investigate the complex remanence and self-demagnetization.

[9] Lelièvre PG, Oldenburg DW. Magnetic forward modelling and inversion for high suscep-

Inversion and Interpretation of Magnetic Anomaly… http://dx.doi.org/10.5772/intechopen.71027 61

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#### Acknowledgements

This work was financially supported by the National Natural Sciences Foundation of China (41604087, 41630317), the Natural Sciences Foundation of Hubei Province (2016CFB122), the China Postdoctoral Science Foundation (2016M590132), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGL170407, CUG160609).

#### Author details

Shuang Liu\* and Xiangyun Hu

\*Address all correspondence to: lius@cug.edu.cn

Institute of Geophysics and Geomatics, China University of Geosciences (Wuhan), Wuhan, China

#### References


[9] Lelièvre PG, Oldenburg DW. Magnetic forward modelling and inversion for high susceptibility. Geophysical Journal International. 2006;166(1):76-90

direction, so they also can be inverted to study the remanent magnetization and selfdemagnetization. The amplitude data inversion provides an effective approach to investigate

This work was financially supported by the National Natural Sciences Foundation of China (41604087, 41630317), the Natural Sciences Foundation of Hubei Province (2016CFB122), the China Postdoctoral Science Foundation (2016M590132), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGL170407, CUG160609).

Institute of Geophysics and Geomatics, China University of Geosciences (Wuhan), Wuhan,

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**Chapter 4**

**Provisional chapter**

**Basement Tectonics and Fault Reactivation in Alberta**

Injection-induced seismicity in Western Canada and elsewhere in North America has drawn considerable recent interest. Current models indicate that induced earthquakes occur on reactivated basement faults, which can be challenging to detect using seismic-reflection data. Here we use regional gravity and magnetic datasets, together with LITHOPROBE crustal seismic profiles, to investigate basement tectonics and crustal structure in an area of Western Canada that is prone to induced seismicity. Previously mapped basement faults that were active during the Paleozoic can be recognized on the basis of pronounced curvature, truncations and/or offsets of stratigraphic marker horizons. Within the Precambrian crystalline basement, however, brittle faults are poorly imaged by seismic data due to various factors such as the obscuring effect of multiples. Regional potential-field fabrics are critical to establish the tectonic setting of basement domains, with complementary information provided by magnetic, Bouguer and isostatic residual gravity anomalies based on 2D modelling constrained by seismic profiles. However, individual faults appear to lack diagnostic expression in regional potential-field anomaly data, since the anomalies are dominated by the effects of larger-scale crustal structures. We show evidence that large-scale basement faults can potentially be recognized on the basis of truncation and offset of distinct horizons within the Winagami Reflection Sequence (WRS), which is interpreted as a regionally-extensive mid-crustal sill complex emplaced during a Proterozoic magmatic pulse. An abundance of caution is necessary to interpret these features, due to complications arising from out-of-plane reflections at long reflection times.

**Basement Tectonics and Fault Reactivation in Alberta** 

DOI: 10.5772/intechopen.72766

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

During the last decade, exploitation of unconventional resources, including low-permeability hydrocarbons, has been a major focus of oil and gas development in North America. One

**Keywords:** magnetics, gravity, seismic, basement reactivation, induced seismicity

**Based on Seismic and Potential Field Data**

**Based on Seismic and Potential Field Data**

Eneanwan Ekpo, David Eaton and Ronald Weir

Eneanwan Ekpo, David Eaton and Ronald Weir

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72766

**Abstract**

**1. Introduction**

**Provisional chapter**

#### **Basement Tectonics and Fault Reactivation in Alberta Based on Seismic and Potential Field Data Based on Seismic and Potential Field Data**

**Basement Tectonics and Fault Reactivation in Alberta** 

DOI: 10.5772/intechopen.72766

Eneanwan Ekpo, David Eaton and Ronald Weir Eneanwan Ekpo, David Eaton and Ronald Weir Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72766

#### **Abstract**

Injection-induced seismicity in Western Canada and elsewhere in North America has drawn considerable recent interest. Current models indicate that induced earthquakes occur on reactivated basement faults, which can be challenging to detect using seismic-reflection data. Here we use regional gravity and magnetic datasets, together with LITHOPROBE crustal seismic profiles, to investigate basement tectonics and crustal structure in an area of Western Canada that is prone to induced seismicity. Previously mapped basement faults that were active during the Paleozoic can be recognized on the basis of pronounced curvature, truncations and/or offsets of stratigraphic marker horizons. Within the Precambrian crystalline basement, however, brittle faults are poorly imaged by seismic data due to various factors such as the obscuring effect of multiples. Regional potential-field fabrics are critical to establish the tectonic setting of basement domains, with complementary information provided by magnetic, Bouguer and isostatic residual gravity anomalies based on 2D modelling constrained by seismic profiles. However, individual faults appear to lack diagnostic expression in regional potential-field anomaly data, since the anomalies are dominated by the effects of larger-scale crustal structures. We show evidence that large-scale basement faults can potentially be recognized on the basis of truncation and offset of distinct horizons within the Winagami Reflection Sequence (WRS), which is interpreted as a regionally-extensive mid-crustal sill complex emplaced during a Proterozoic magmatic pulse. An abundance of caution is necessary to interpret these features, due to complications arising from out-of-plane reflections at long reflection times.

**Keywords:** magnetics, gravity, seismic, basement reactivation, induced seismicity

#### **1. Introduction**

During the last decade, exploitation of unconventional resources, including low-permeability hydrocarbons, has been a major focus of oil and gas development in North America. One

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

emerging area of concern is induced seismicity, which has led to a renewed interest in faults as well as the structural architecture of Precambrian basement. Recent studies of injectioninduced seismicity in parts of Western Canada [1–3] have highlighted the probable role of pre-existing basement faults in controlling the distribution of induced earthquakes. Although some basement-related faults in this region have been identified using seismic-reflection images (for example, see [4–6]), faults that may control the location of induced earthquakes are often challenging to detect using seismic-reflection images alone. Problematic cases include faults with a geometry that is unfavourable for seismic mapping in horizontally stratified rocks, such as sub horizontal thrust faults or vertical strike-slip faults, or brittle faults hosted within crystalline basement rocks that lack clear marker reflections. The latter is particularly true in the shallow crystalline basement in Western Canada, where basement structure may be difficult to discern in the presence of strong multiple reflections [7].

(**Figure 1**). Southern Alberta is dominated by Archean domains, bounded to the north by the Vulcan Low; central Alberta consists of the domains of the Hearne Province that surround the Snowbird Tectonic Zone (STZ); and, northern Alberta consists of the domains that surround the early Proterozoic Great Slave Lake shear zone (GSLsz). Basement domains that are the focus of this study occur between the STZ and GSLsz and have Paleoproterozoic crystalliza-

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Subdivision of the crystalline basement underlying the WCSB into tectonic domains is based on sparse drillcore samples from hydrocarbon exploration wells, coupled with potential-field interpretation [14, 15]. The drillcore samples are described by [15] in terms of location, rock type, mineralogy and crystallization age based on U-Pb geochronology. Our study area is underlain by basement rocks of the Ksituan, Chinchaga, Buffalo Head and Wabumum domains (**Figure 1**), which are composed of igneous, metaigneous and less commonly metasedimentary rocks of Paleoproterozoic age (2.4–1.9 Ga). The 1.90–1.98 Ga Ksituan domain is defined by its strong, positive magnetic expression, which is typical of calc-alkaline magmatic belts due to the presence of magnetite as an accessory mineral phase [15]. Crustal imbrication

**Figure 1.** Location map showing tectonic domains of the Precambrian basement from [15]. Black lines show LITHOPROBE

from January 2014 to January 2017 (*MW* ≥ 2.5). Abbreviations and generalized ages of basement domain names are indicated in the legend. In addition, GSLsz denotes Great Slave Lake shear zone, STZ denotes Snowbird Tectonic Zone,

N, 116–118o

W,

seismic profiles from the ABT-PRAISE transect. Yellow dots show seismicity from within the region 54–56<sup>o</sup>

SCD and NCD denotes southern and northern Chinchaga domain.

tion ages (1.9–2.4 Ga).

Modelling and interpretation of regional gravity and magnetic data can provide valuable insights for understanding crustal structure beneath sedimentary basins [8, 9] including constraints for understanding geological risk factors for induced seismicity [10]. Models derived from magnetic and gravity data, due to their non-uniqueness, are usually combined with other geological and geophysical information (e.g. seismic and well data), to provide insights into the geometry of the subsurface [9]. The Western Canada Sedimentary Basin (WCSB) is a mature hydrocarbon basin, where extensive public-domain datasets are available, including regional-scale gravity and magnetic anomaly data as well as crustal seismic profiles. To complement the potential field data, this study uses crustal seismic-reflection data from the Alberta Basement Transects (ABT) Peace River Arch Industry Seismic Experiment (PRAISE) project [11], part of Canada's LITHOPROBE program [12].

The objective of this contribution is to present new insights arising from geophysical imaging and mapping of representative basement fault structures, together with a discussion of how they may be significant as a framework for understanding induced seismicity. The LITHOPROBE seismic profiles intersect structural boundaries that are seen on the regional aeromagnetic and gravity mapping. Our interpretation approach involves mapping and identification of basement structures, followed by 2D gravity and magnetic modelling for selected features. Since the gravity and aeromagnetic data span a large geographical area they are useful to characterize large-scale trends, whereas the 2D seismic lines give detailed constraints for building a model, such as fault throw and timing. Potential field data thus give a more complete tectonic picture of the area by filling in the gaps between areas of seismic coverage, providing an opportunity to improve our understanding of the structural framework.

#### **2. Regional geological setting**

The Precambrian basement beneath Alberta was formed by amalgamation of disparate domains that were assembled by the plate-tectonic processes of subduction and collision [13–15]. The crystalline basement in Alberta can be subdivided into three broad regions (**Figure 1**). Southern Alberta is dominated by Archean domains, bounded to the north by the Vulcan Low; central Alberta consists of the domains of the Hearne Province that surround the Snowbird Tectonic Zone (STZ); and, northern Alberta consists of the domains that surround the early Proterozoic Great Slave Lake shear zone (GSLsz). Basement domains that are the focus of this study occur between the STZ and GSLsz and have Paleoproterozoic crystallization ages (1.9–2.4 Ga).

emerging area of concern is induced seismicity, which has led to a renewed interest in faults as well as the structural architecture of Precambrian basement. Recent studies of injectioninduced seismicity in parts of Western Canada [1–3] have highlighted the probable role of pre-existing basement faults in controlling the distribution of induced earthquakes. Although some basement-related faults in this region have been identified using seismic-reflection images (for example, see [4–6]), faults that may control the location of induced earthquakes are often challenging to detect using seismic-reflection images alone. Problematic cases include faults with a geometry that is unfavourable for seismic mapping in horizontally stratified rocks, such as sub horizontal thrust faults or vertical strike-slip faults, or brittle faults hosted within crystalline basement rocks that lack clear marker reflections. The latter is particularly true in the shallow crystalline basement in Western Canada, where basement structure may

Modelling and interpretation of regional gravity and magnetic data can provide valuable insights for understanding crustal structure beneath sedimentary basins [8, 9] including constraints for understanding geological risk factors for induced seismicity [10]. Models derived from magnetic and gravity data, due to their non-uniqueness, are usually combined with other geological and geophysical information (e.g. seismic and well data), to provide insights into the geometry of the subsurface [9]. The Western Canada Sedimentary Basin (WCSB) is a mature hydrocarbon basin, where extensive public-domain datasets are available, including regional-scale gravity and magnetic anomaly data as well as crustal seismic profiles. To complement the potential field data, this study uses crustal seismic-reflection data from the Alberta Basement Transects (ABT) Peace River Arch Industry Seismic Experiment (PRAISE)

The objective of this contribution is to present new insights arising from geophysical imaging and mapping of representative basement fault structures, together with a discussion of how they may be significant as a framework for understanding induced seismicity. The LITHOPROBE seismic profiles intersect structural boundaries that are seen on the regional aeromagnetic and gravity mapping. Our interpretation approach involves mapping and identification of basement structures, followed by 2D gravity and magnetic modelling for selected features. Since the gravity and aeromagnetic data span a large geographical area they are useful to characterize large-scale trends, whereas the 2D seismic lines give detailed constraints for building a model, such as fault throw and timing. Potential field data thus give a more complete tectonic picture of the area by filling in the gaps between areas of seismic coverage, providing an opportunity to improve our understanding of the structural

The Precambrian basement beneath Alberta was formed by amalgamation of disparate domains that were assembled by the plate-tectonic processes of subduction and collision [13–15]. The crystalline basement in Alberta can be subdivided into three broad regions

be difficult to discern in the presence of strong multiple reflections [7].

project [11], part of Canada's LITHOPROBE program [12].

framework.

66 Geophysics

**2. Regional geological setting**

Subdivision of the crystalline basement underlying the WCSB into tectonic domains is based on sparse drillcore samples from hydrocarbon exploration wells, coupled with potential-field interpretation [14, 15]. The drillcore samples are described by [15] in terms of location, rock type, mineralogy and crystallization age based on U-Pb geochronology. Our study area is underlain by basement rocks of the Ksituan, Chinchaga, Buffalo Head and Wabumum domains (**Figure 1**), which are composed of igneous, metaigneous and less commonly metasedimentary rocks of Paleoproterozoic age (2.4–1.9 Ga). The 1.90–1.98 Ga Ksituan domain is defined by its strong, positive magnetic expression, which is typical of calc-alkaline magmatic belts due to the presence of magnetite as an accessory mineral phase [15]. Crustal imbrication

**Figure 1.** Location map showing tectonic domains of the Precambrian basement from [15]. Black lines show LITHOPROBE seismic profiles from the ABT-PRAISE transect. Yellow dots show seismicity from within the region 54–56<sup>o</sup> N, 116–118o W, from January 2014 to January 2017 (*MW* ≥ 2.5). Abbreviations and generalized ages of basement domain names are indicated in the legend. In addition, GSLsz denotes Great Slave Lake shear zone, STZ denotes Snowbird Tectonic Zone, SCD and NCD denotes southern and northern Chinchaga domain.

and pervasive ductile deformation of the Ksituan domain is evident from well-developed seismic-reflection fabrics, in the form of panels of dipping reflections in the upper and middle crust [4]. To the east, the slightly older (2.0–2.32 Ga) Buffalo Head Terrane is characterized by sinuous aeromagnetic patterns and discrete subdomains, composed of metaplutonic and subordinate felsic metavolcanic rocks [14]. The eastern edge of the Buffalo Head is defined by the Kimiwan anomaly, a linear magnetic high ~250 km in length. The origin of this magnetic anomaly has been interpreted as either a decapitated calc-alkaline pluton, or a broad zone of hydrothermal alteration and enhanced susceptibility above a crustal-scale extensional fault [9]. The former interpretation is more consistent with oxygen isotope signature of basement samples [16].

**3. Geophysical data**

velocity of 6 km/s.

In the 1990s, the Canadian LITHOPROBE program acquired a series of long 2D seismic-reflection transects as part of the Alberta Basement Transects program, with the objective of identifying structures present in the sedimentary basin and deeper levels of the crust [11]. The data were acquired using vibroseis sources and recorded to 18 s two-way time (TWT). In the case of the ABT-PRAISE program, acquisition parameters included a 25-m receiver group interval, 480 channels and unusually long offsets (>6 km) that are conducive to attenuation of multiple reverberations [4]. A representative 2D migrated data example is shown in **Figure 2**, where the approximate depth in the crystalline basement is calculated assuming an average P-wave

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69

Terrestrial gravity data used in this study were compiled on a 1 km grid by the Canadian Geodetic Survey and made available through the Geoscience Data Repository for Geophysical Data. Although the grid is sampled at 1 km, the raw data were acquired using an irregular distribution of stations with an average inter-station spacing of >5 km. Despite dense sampling along LITHOPROBE profiles [9], anomaly wavelengths that can be resolved without aliasing (based on the Nyquist criterion) are thus greater than 10 km. A Bouguer gravity anomaly map of Western Canada derived from this dataset contains a conspicuous gravity low (~ −200 mGal) associated with the isostatic root coincident with areas of high elevations in the Rocky Mountains (**Figure 3a**). This anomaly obscures most of the basement domains that are of interest in this study. One exception is the Snowbird Tectonic Zone (STZ), which is almost perpendicular to the deformation front and forms the southern boundary of basement domains in our study area. The isostatic residual gravity anomaly map (see [24]) is plotted in **Figure 3b**. By removing most of the gravitational effects of the isostatic root, the isostatic anomaly map reveals a distinct basement fabric parallel to the STZ that is truncated by orogen-parallel anomalies. A residual positive isostatic anomaly with an amplitude of ~25 mGal

**Figure 2.** Representative seismic expression of the Winagami Reflection Sequence (WRS) from LITHOPROBE deep seismic profiles. The WRS is comprised of subparallel high-amplitude reflections that form an anastomosing fan that

converges toward the southeast [18]. The location of this section is marked in **Figure 4**.

To the south, the Chinchaga domain overlaps in age with the Buffalo Head Terrane and is delineated by a negative magnetic anomaly pattern that reflects the absence of calc-alkaline granitic rocks. As discussed below, we distinguish between the northern and southern Chinchaga domains based on potential-field evidence. The southern Chinchaga domain is of particular interest as it underlies the Kaybob-Duvernay region where induced seismicity is concentrated. Finally, the Wabamun domain is interpreted as a structurally bound wedgeshaped block that is enclosed by strands of the Snowbird Tectonic Zone (STZ; [14]), possibly analogous (in terms of structural style) to Archean crustal-scale lozenges formed by annealed mylonites where the STZ is exposed at the surface [17].

Throughout the study area, dipping reflection fabrics observed on LITHOPROBE profiles in the upper and middle crust are cross-cut by the Winagami Reflection Sequence (WRS), a set of prominent, sub-horizontal reflections with an estimated areal extent of ~120,000 km<sup>2</sup> [18]. These reflections are interpreted as sheet-like mafic intrusions that record a ca. 1.8 Ga magmatic event. At several locations, the reflections can be followed around perpendicular bends in survey lines with no change in apparent dip, confirming that the reflectors are approximately horizontal [18]. As illustrated in **Figure 2**, at some locations individual reflections appear to be truncated and offset, suggestive of post-intrusive fault displacement [9].

Sedimentary units in this part of the WCSB are broadly divisible into three major stratigraphic successions that were deposited in three distinct phases [19]. From Cambrian to mid-Devonian time this region was situated near a passive margin, with non-deposition in the emergent Peace River Arch over a large region in the northern part of this study area [4]. During the Devonian, extensive carbonate shelf complexes formed, locally capped by linear reef chains, isolated reefs or reef complexes [20]. It has been suggested that sedimentation patterns, including abrupt facies changes, the development of fracture porosity and the orientation of reef trends or clastic strandlines, may have been influenced by small topographic features on the basement surface [21] that were transferred up section through a process of tectonic inheritance [20]. During the next major phase, the topographic expression of the Peace River Arch reversed to form the Peace River Embayment. Within the embayment, the formation of a network of satellite grabens caused localized subsidence during the Carboniferous, followed by more widespread subsidence during Permian and Triassic time [22]. The final major depositional phase was characterized by enhanced Mesozoic subsidence within a foreland basin in front of advancing Laramide thrust sheets [23].

## **3. Geophysical data**

and pervasive ductile deformation of the Ksituan domain is evident from well-developed seismic-reflection fabrics, in the form of panels of dipping reflections in the upper and middle crust [4]. To the east, the slightly older (2.0–2.32 Ga) Buffalo Head Terrane is characterized by sinuous aeromagnetic patterns and discrete subdomains, composed of metaplutonic and subordinate felsic metavolcanic rocks [14]. The eastern edge of the Buffalo Head is defined by the Kimiwan anomaly, a linear magnetic high ~250 km in length. The origin of this magnetic anomaly has been interpreted as either a decapitated calc-alkaline pluton, or a broad zone of hydrothermal alteration and enhanced susceptibility above a crustal-scale extensional fault [9]. The former interpretation is more consistent with oxygen isotope signature of basement

To the south, the Chinchaga domain overlaps in age with the Buffalo Head Terrane and is delineated by a negative magnetic anomaly pattern that reflects the absence of calc-alkaline granitic rocks. As discussed below, we distinguish between the northern and southern Chinchaga domains based on potential-field evidence. The southern Chinchaga domain is of particular interest as it underlies the Kaybob-Duvernay region where induced seismicity is concentrated. Finally, the Wabamun domain is interpreted as a structurally bound wedgeshaped block that is enclosed by strands of the Snowbird Tectonic Zone (STZ; [14]), possibly analogous (in terms of structural style) to Archean crustal-scale lozenges formed by annealed

Throughout the study area, dipping reflection fabrics observed on LITHOPROBE profiles in the upper and middle crust are cross-cut by the Winagami Reflection Sequence (WRS), a set of prominent, sub-horizontal reflections with an estimated areal extent of ~120,000 km<sup>2</sup>

These reflections are interpreted as sheet-like mafic intrusions that record a ca. 1.8 Ga magmatic event. At several locations, the reflections can be followed around perpendicular bends in survey lines with no change in apparent dip, confirming that the reflectors are approximately horizontal [18]. As illustrated in **Figure 2**, at some locations individual reflections

Sedimentary units in this part of the WCSB are broadly divisible into three major stratigraphic successions that were deposited in three distinct phases [19]. From Cambrian to mid-Devonian time this region was situated near a passive margin, with non-deposition in the emergent Peace River Arch over a large region in the northern part of this study area [4]. During the Devonian, extensive carbonate shelf complexes formed, locally capped by linear reef chains, isolated reefs or reef complexes [20]. It has been suggested that sedimentation patterns, including abrupt facies changes, the development of fracture porosity and the orientation of reef trends or clastic strandlines, may have been influenced by small topographic features on the basement surface [21] that were transferred up section through a process of tectonic inheritance [20]. During the next major phase, the topographic expression of the Peace River Arch reversed to form the Peace River Embayment. Within the embayment, the formation of a network of satellite grabens caused localized subsidence during the Carboniferous, followed by more widespread subsidence during Permian and Triassic time [22]. The final major depositional phase was characterized by enhanced Mesozoic subsidence within a foreland basin in

appear to be truncated and offset, suggestive of post-intrusive fault displacement [9].

[18].

mylonites where the STZ is exposed at the surface [17].

front of advancing Laramide thrust sheets [23].

samples [16].

68 Geophysics

In the 1990s, the Canadian LITHOPROBE program acquired a series of long 2D seismic-reflection transects as part of the Alberta Basement Transects program, with the objective of identifying structures present in the sedimentary basin and deeper levels of the crust [11]. The data were acquired using vibroseis sources and recorded to 18 s two-way time (TWT). In the case of the ABT-PRAISE program, acquisition parameters included a 25-m receiver group interval, 480 channels and unusually long offsets (>6 km) that are conducive to attenuation of multiple reverberations [4]. A representative 2D migrated data example is shown in **Figure 2**, where the approximate depth in the crystalline basement is calculated assuming an average P-wave velocity of 6 km/s.

Terrestrial gravity data used in this study were compiled on a 1 km grid by the Canadian Geodetic Survey and made available through the Geoscience Data Repository for Geophysical Data. Although the grid is sampled at 1 km, the raw data were acquired using an irregular distribution of stations with an average inter-station spacing of >5 km. Despite dense sampling along LITHOPROBE profiles [9], anomaly wavelengths that can be resolved without aliasing (based on the Nyquist criterion) are thus greater than 10 km. A Bouguer gravity anomaly map of Western Canada derived from this dataset contains a conspicuous gravity low (~ −200 mGal) associated with the isostatic root coincident with areas of high elevations in the Rocky Mountains (**Figure 3a**). This anomaly obscures most of the basement domains that are of interest in this study. One exception is the Snowbird Tectonic Zone (STZ), which is almost perpendicular to the deformation front and forms the southern boundary of basement domains in our study area. The isostatic residual gravity anomaly map (see [24]) is plotted in **Figure 3b**. By removing most of the gravitational effects of the isostatic root, the isostatic anomaly map reveals a distinct basement fabric parallel to the STZ that is truncated by orogen-parallel anomalies. A residual positive isostatic anomaly with an amplitude of ~25 mGal

**Figure 2.** Representative seismic expression of the Winagami Reflection Sequence (WRS) from LITHOPROBE deep seismic profiles. The WRS is comprised of subparallel high-amplitude reflections that form an anastomosing fan that converges toward the southeast [18]. The location of this section is marked in **Figure 4**.

is caused by flexural support of the Rocky Mountain front ranges, which is not accounted for by the isostatic correction [2].

which produce overall weak NE–SW fabric wavelengths in the ranges of 25–50 km. The only basement tectonic domain boundary that is clearly expressed in this map is the boundary between the southern Chinchaga domain, characterized by positive isostatic gravity residual,

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The aeromagnetic dataset used in this study is a 200-m residual total-field intensity grid obtained from the national aeromagnetic database (Geoscience Data Repository for Geophysical Data). This grid was compiled from different vintages of survey data, including public-domain and industry surveys flown over several decades [9]. **Figure 4b** shows an aeromagnetic anomaly map of the study area derived from this dataset. In contrast to the gravity anomaly map (**Figure 4b**), basement domain boundaries are prominently expressed in the aeromagnetic map. This is expected, since at a regional scale, the shape and intensity of the magnetic anomalies is primarily controlled by the magnetic susceptibility of the basement domains [15]. Apart from the loss of short-wavelength content toward the southwest due to thickening of the sediment cover, short-wavelength basement topography is muted by the high flexural strength of the lithosphere [21] and thus has a relatively minor influence on the

There are a number of prominent magnetic features in **Figure 4b**. The Ksituan domain (K) is characterized by elongate positive magnetic anomalies with wavelengths ~5–10 km that converge northwards toward the GSLsz, located in the northwest corner of the map. An abrupt rectilinear high-gradient zone separates the Ksituan domain from the southern Chinchaga

**Figure 4.** (a) Enlargement of isostatic residual gravity anomaly map within the area outlined in **Figure 3**. K, B, W and SCD denote Ksituan, Buffalo Head, Wabamun and Southern Chinchaga Domain, respectively. Dashed line indicates boundary between SCD and W, which may be a northern splay of the Snowbird Tectonic Zone. (b) Aeromagnetic anomaly map of the same area. Red stars show locations of basement drillcore and yellow circles show seismicity from **Figure 1**. SCD is bounded to the north and south by similar rectilinear edges, as shown by the dashed white lines. Short-

wavelength features of magnetic anomalies diminish to the southwest due to increasing basement depth.

and the Wabamun domain which has a weakly negative character.

magnetic anomalies.

An enlargement of the isostatic gravity map for our study area is shown in **Figure 4a**. The area is characterized by positive anomalies with ovoid shape and peak amplitudes of ~10 mGal,

**Figure 3.** (a) Bouguer gravity anomaly map of Western Canada, showing a −200 mGal anomaly associated with the isostatic root beneath high elevations in the Rocky Mountains as well as a linear anomaly along the Snowbird Tectonic Zone (STZ). (b) Isostatic gravity anomaly map, highlighting a positive residual associated with lithospheric flexural support for high topography [2]. Black lines show ABT-PRAISE transect and white box shows area of **Figure 4**.

which produce overall weak NE–SW fabric wavelengths in the ranges of 25–50 km. The only basement tectonic domain boundary that is clearly expressed in this map is the boundary between the southern Chinchaga domain, characterized by positive isostatic gravity residual, and the Wabamun domain which has a weakly negative character.

is caused by flexural support of the Rocky Mountain front ranges, which is not accounted for

An enlargement of the isostatic gravity map for our study area is shown in **Figure 4a**. The area is characterized by positive anomalies with ovoid shape and peak amplitudes of ~10 mGal,

**Figure 3.** (a) Bouguer gravity anomaly map of Western Canada, showing a −200 mGal anomaly associated with the isostatic root beneath high elevations in the Rocky Mountains as well as a linear anomaly along the Snowbird Tectonic Zone (STZ). (b) Isostatic gravity anomaly map, highlighting a positive residual associated with lithospheric flexural support for high topography [2]. Black lines show ABT-PRAISE transect and white box shows area of **Figure 4**.

by the isostatic correction [2].

70 Geophysics

The aeromagnetic dataset used in this study is a 200-m residual total-field intensity grid obtained from the national aeromagnetic database (Geoscience Data Repository for Geophysical Data). This grid was compiled from different vintages of survey data, including public-domain and industry surveys flown over several decades [9]. **Figure 4b** shows an aeromagnetic anomaly map of the study area derived from this dataset. In contrast to the gravity anomaly map (**Figure 4b**), basement domain boundaries are prominently expressed in the aeromagnetic map. This is expected, since at a regional scale, the shape and intensity of the magnetic anomalies is primarily controlled by the magnetic susceptibility of the basement domains [15]. Apart from the loss of short-wavelength content toward the southwest due to thickening of the sediment cover, short-wavelength basement topography is muted by the high flexural strength of the lithosphere [21] and thus has a relatively minor influence on the magnetic anomalies.

There are a number of prominent magnetic features in **Figure 4b**. The Ksituan domain (K) is characterized by elongate positive magnetic anomalies with wavelengths ~5–10 km that converge northwards toward the GSLsz, located in the northwest corner of the map. An abrupt rectilinear high-gradient zone separates the Ksituan domain from the southern Chinchaga

**Figure 4.** (a) Enlargement of isostatic residual gravity anomaly map within the area outlined in **Figure 3**. K, B, W and SCD denote Ksituan, Buffalo Head, Wabamun and Southern Chinchaga Domain, respectively. Dashed line indicates boundary between SCD and W, which may be a northern splay of the Snowbird Tectonic Zone. (b) Aeromagnetic anomaly map of the same area. Red stars show locations of basement drillcore and yellow circles show seismicity from **Figure 1**. SCD is bounded to the north and south by similar rectilinear edges, as shown by the dashed white lines. Shortwavelength features of magnetic anomalies diminish to the southwest due to increasing basement depth.

domain, which is characterized by muted, longer-wavelength negative magnetic anomalies. A "conjugate" rectilinear boundary, geometrically identical to the northern rectilinear boundary, marks the southern edge of the Chinchaga magnetic low. The Kimiwan anomaly (KA) is a NW-trending positive magnetic anomaly that merges with the arcuate western margin of the Buffalo Head high (B). Unlike other parts of the WCSB [9, 24], there is remarkably little correlation between the anomaly fabrics evident in the gravity and magnetic maps. The Kaybob-Duvernay region, where a high-concentration of induced seismicity exists, is underlain by basement rocks of the southern Chinchaga domain. Although the epicentral distribution in **Figure 4b** reveals a diffuse cloud that is elongate in an east-west direction, the location uncertainty for individual events is ~20 km. In contrast, recent studies that feature high-resolution epicentre locations [2] and well-resolved focal mechanisms [3] indicate that individual fault planes are approximately vertical with a likely north-south strike direction. Thus, local potential-field anomaly fabrics in this region with a roughly north-south trend may be of particular relevance for understanding induced seismicity.

who argued that curvature attributes derived from seismic data are well suited to identify subtle faults in the Kaybob-Duvernay region. In addition to the main Tangent fault, an antithetic

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**Figure 6** shows a simple gravity model for the Tangent fault, based on geometrical constraints derived from the seismic profile (**Figure 5**). The 2D gravity modelling method is based on the computed gravitational response of polygonal prisms of uniform density [25]. The model comprises three lithostratigraphic successions: Carboniferous-Mississippian (Debolt and Banff), Devonian (Wabamum) and Precambrian (Top of the crystalline basement). An average density was used from the available density log in the area as a constraint. The density of each layer is indicated on the profile. A good fit between observed and modelled gravity was achieved; however, the faults in this profile have a very small gravitational response. While this may reflect the coarse sampling of the raw gravity data, it demonstrates that the publicdomain gravity data are primarily useful for regional interpretations, rather than investigation of small-scale structures such as individual faults. This can be observed with the gravity

The well-documented basement faulting illustrated above provides an interpretative template for basement faults in the Kaybob-Duvernay region. **Figure 7** shows a 1.7–2.4 s time

**Figure 6.** 2D gravity model across the Tangent fault as well as a smaller fault to the east. Layer boundaries are defined

based on seismic profile data (**Figure 5**). These faults appear to have a subtle gravity response.

anomaly profile replicating the topmost layer of the crystalline basement.

fault and a smaller fault are visible in the profile.

#### **4. Modelling and interpretation**

The first example that we consider is the Tangent fault, a Carboniferous normal fault that bounds a half-graben within the Peace River Embayment [4]. This fault has not generated any induced seismicity, but it provides a useful template for interpretation of the geophysical expression of other faults. **Figure 5** shows a LITHOPROBE profile across the Tangent fault, which is characterized by a clearly defined down-to-the-east displacement of the top of the Precambrian basement. After correlating stratigraphic picks using a well tie, it is evident that overlying Paleozoic marker reflections (Wabamun, Banff, Debolt) exhibit a folded (or draped) character across the Tangent fault. This deformation style is consistent with a case study by [6],

**Figure 5.** Seismic profile across the Tangent fault as well as a smaller fault to the west, showing the density well log used to obtain a stratigraphic tie. This section was used to build the 2D model in **Figure 6**.

who argued that curvature attributes derived from seismic data are well suited to identify subtle faults in the Kaybob-Duvernay region. In addition to the main Tangent fault, an antithetic fault and a smaller fault are visible in the profile.

domain, which is characterized by muted, longer-wavelength negative magnetic anomalies. A "conjugate" rectilinear boundary, geometrically identical to the northern rectilinear boundary, marks the southern edge of the Chinchaga magnetic low. The Kimiwan anomaly (KA) is a NW-trending positive magnetic anomaly that merges with the arcuate western margin of the Buffalo Head high (B). Unlike other parts of the WCSB [9, 24], there is remarkably little correlation between the anomaly fabrics evident in the gravity and magnetic maps. The Kaybob-Duvernay region, where a high-concentration of induced seismicity exists, is underlain by basement rocks of the southern Chinchaga domain. Although the epicentral distribution in **Figure 4b** reveals a diffuse cloud that is elongate in an east-west direction, the location uncertainty for individual events is ~20 km. In contrast, recent studies that feature high-resolution epicentre locations [2] and well-resolved focal mechanisms [3] indicate that individual fault planes are approximately vertical with a likely north-south strike direction. Thus, local potential-field anomaly fabrics in this region with a roughly north-south trend may be of particular

The first example that we consider is the Tangent fault, a Carboniferous normal fault that bounds a half-graben within the Peace River Embayment [4]. This fault has not generated any induced seismicity, but it provides a useful template for interpretation of the geophysical expression of other faults. **Figure 5** shows a LITHOPROBE profile across the Tangent fault, which is characterized by a clearly defined down-to-the-east displacement of the top of the Precambrian basement. After correlating stratigraphic picks using a well tie, it is evident that overlying Paleozoic marker reflections (Wabamun, Banff, Debolt) exhibit a folded (or draped) character across the Tangent fault. This deformation style is consistent with a case study by [6],

**Figure 5.** Seismic profile across the Tangent fault as well as a smaller fault to the west, showing the density well log used

to obtain a stratigraphic tie. This section was used to build the 2D model in **Figure 6**.

relevance for understanding induced seismicity.

**4. Modelling and interpretation**

72 Geophysics

**Figure 6** shows a simple gravity model for the Tangent fault, based on geometrical constraints derived from the seismic profile (**Figure 5**). The 2D gravity modelling method is based on the computed gravitational response of polygonal prisms of uniform density [25]. The model comprises three lithostratigraphic successions: Carboniferous-Mississippian (Debolt and Banff), Devonian (Wabamum) and Precambrian (Top of the crystalline basement). An average density was used from the available density log in the area as a constraint. The density of each layer is indicated on the profile. A good fit between observed and modelled gravity was achieved; however, the faults in this profile have a very small gravitational response. While this may reflect the coarse sampling of the raw gravity data, it demonstrates that the publicdomain gravity data are primarily useful for regional interpretations, rather than investigation of small-scale structures such as individual faults. This can be observed with the gravity anomaly profile replicating the topmost layer of the crystalline basement.

The well-documented basement faulting illustrated above provides an interpretative template for basement faults in the Kaybob-Duvernay region. **Figure 7** shows a 1.7–2.4 s time

**Figure 6.** 2D gravity model across the Tangent fault as well as a smaller fault to the east. Layer boundaries are defined based on seismic profile data (**Figure 5**). These faults appear to have a subtle gravity response.

window of data from the ABT-PRAISE transect in this region, which is prone to induced seismicity. The profile is plotted with a vertical exaggeration of ~8:1. There are several interpreted basement faults in this profile, as marked by the black lines. These faults are interpreted based on observed reflection discontinuities. These features share some characteristics with the Tangent fault, including similar, albeit lower amplitude, expression of folding/drape within the sedimentary layers. One of the inferred basement faults is in close proximity to the edge of the Bigstone Leduc reef, while another inferred fault appears to correlate with a positive topographic feature that coincides with a downlap reflection termination (Z-marker) in the Upper Devonian Ireton formation [26]. Due to the effects of contamination by multiple reverberations below the top of basement at ~2100 ms, it is not clear if these interpreted faults merge at depth in the crystalline basement.

**Figure 8** shows the same seismic profile as in **Figure 7b**, but for a larger time window of 1.5–6.25 s, plotted with a vertical exaggeration of ~1.4. This profile contains strong but discontinuous WRS reflections, with a gentle southwest apparent dip within an approximate depth extent of 11–16 km (based on an assumed average basement velocity of 6.0 km/s). Individual WRS reflection show apparent truncations as they approach a listric corridor where these midcrustal reflections are absent. This pattern of disrupted WRS reflections resembles a similar disrupted pattern described by [9] for a crustal seismic profile across the Kimiwan Anomaly. Based on this reflection geometry, a crustal-scale reverse fault is tentatively interpreted that extends to the top of crystalline basement, at a point where faulting is seen in **Figure 7**. The

apparent fault offsets of Paleozoic reflections are considerably smaller in amplitude than the apparent offset evident in the middle crust. The interpreted crustal geometry in **Figure 8** was used to develop a gravity and magnetic model (**Figure 9**), with layer parameters in **Table 1**. Like the gravity modelling, the magnetic modelling was performed using a 2D algorithm based on uniformly magnetized polygonal prisms. Only induced magnetization was considered, based on local parameters for the geomagnetic field. The 2D gravity and magnetic modelling depicted in **Figure 8** shows that a good fit can be achieved between measured and observed potential-field profiles, using polygon vertices derived from the seismic interpretation. Following [9], no regional-residual separation was applied to permit assessment of the influence of features at various crustal levels. The dominant wavelength of the anomalies (>20 km) implies that the depth of features that give rise to the anomalies is considerably deeper than the top of the crystalline basement (~4 km). In this model, the sedimentary package overlaying the crystalline basement (light brown) was treated as one uniform unit with no magnetic susceptibility (k = 0 SI). Hence, the magnetic sources were attributed only to the crystalline basement. The model showed the structure of the basement on a regional scale. Hence, high-frequency anomalies were not modelled. This example also demonstrates

**Figure 8.** LITHOPROBE seismic data from the same spatial location as in **Figure 6**, showing crustal-scale structure of Winagami Reflection Sequence (WRS). Disruption of the WRS reflections is interpreted here as evidence for post-

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intrusion basement faulting.

**Figure 7.** LITHOPROBE seismic profile showing sedimentary layers (vertical exaggeration ~8:1) from the Kaybob-Duvernay region, where induced seismicity has occurred. Several basement faults are evident, as indicated by the black lines. Circle highlights a Leduc reef (Bigstone). Previous workers have suggested that basement faulting may have been influenced the locations of Leduc reefs [7, 20].

Basement Tectonics and Fault Reactivation in Alberta Based on Seismic and Potential Field Data http://dx.doi.org/10.5772/intechopen.72766 75

window of data from the ABT-PRAISE transect in this region, which is prone to induced seismicity. The profile is plotted with a vertical exaggeration of ~8:1. There are several interpreted basement faults in this profile, as marked by the black lines. These faults are interpreted based on observed reflection discontinuities. These features share some characteristics with the Tangent fault, including similar, albeit lower amplitude, expression of folding/drape within the sedimentary layers. One of the inferred basement faults is in close proximity to the edge of the Bigstone Leduc reef, while another inferred fault appears to correlate with a positive topographic feature that coincides with a downlap reflection termination (Z-marker) in the Upper Devonian Ireton formation [26]. Due to the effects of contamination by multiple reverberations below the top of basement at ~2100 ms, it is not clear if these interpreted faults

**Figure 8** shows the same seismic profile as in **Figure 7b**, but for a larger time window of 1.5–6.25 s, plotted with a vertical exaggeration of ~1.4. This profile contains strong but discontinuous WRS reflections, with a gentle southwest apparent dip within an approximate depth extent of 11–16 km (based on an assumed average basement velocity of 6.0 km/s). Individual WRS reflection show apparent truncations as they approach a listric corridor where these midcrustal reflections are absent. This pattern of disrupted WRS reflections resembles a similar disrupted pattern described by [9] for a crustal seismic profile across the Kimiwan Anomaly. Based on this reflection geometry, a crustal-scale reverse fault is tentatively interpreted that extends to the top of crystalline basement, at a point where faulting is seen in **Figure 7**. The

**Figure 7.** LITHOPROBE seismic profile showing sedimentary layers (vertical exaggeration ~8:1) from the Kaybob-Duvernay region, where induced seismicity has occurred. Several basement faults are evident, as indicated by the black lines. Circle highlights a Leduc reef (Bigstone). Previous workers have suggested that basement faulting may have been

merge at depth in the crystalline basement.

74 Geophysics

influenced the locations of Leduc reefs [7, 20].

**Figure 8.** LITHOPROBE seismic data from the same spatial location as in **Figure 6**, showing crustal-scale structure of Winagami Reflection Sequence (WRS). Disruption of the WRS reflections is interpreted here as evidence for postintrusion basement faulting.

apparent fault offsets of Paleozoic reflections are considerably smaller in amplitude than the apparent offset evident in the middle crust. The interpreted crustal geometry in **Figure 8** was used to develop a gravity and magnetic model (**Figure 9**), with layer parameters in **Table 1**.

Like the gravity modelling, the magnetic modelling was performed using a 2D algorithm based on uniformly magnetized polygonal prisms. Only induced magnetization was considered, based on local parameters for the geomagnetic field. The 2D gravity and magnetic modelling depicted in **Figure 8** shows that a good fit can be achieved between measured and observed potential-field profiles, using polygon vertices derived from the seismic interpretation. Following [9], no regional-residual separation was applied to permit assessment of the influence of features at various crustal levels. The dominant wavelength of the anomalies (>20 km) implies that the depth of features that give rise to the anomalies is considerably deeper than the top of the crystalline basement (~4 km). In this model, the sedimentary package overlaying the crystalline basement (light brown) was treated as one uniform unit with no magnetic susceptibility (k = 0 SI). Hence, the magnetic sources were attributed only to the crystalline basement. The model showed the structure of the basement on a regional scale. Hence, high-frequency anomalies were not modelled. This example also demonstrates

trending positive magnetic anomaly within the southern Chinchaga domain. The Kimiwan Anomaly has a positive magnetic signature (**Figure 4**) about 40 km in width with a northwest orientation. In the isostatic gravity map, this feature is difficult to map. The observed magnetic profile was extracted from the total field intensity magnetic map by getting a profile perpendicular to the two features of interest. Since no seismic constraint is available along this profile, the purpose of this simple forward model is to examine the applicability of the alteration-zone model for the Kimiwan Anomaly [9] to the north-south trending magnetic anomaly from the southern Chinchaga domain. The data was fitted with the anomalous regions situated in the middle crust (**Figure 10**). The observed gravity profile is included for reference. It is not modelled, as the gravity anomaly has a different and non-orthogonal strike direction from the magnetic anomaly so the 2D modelling assumptions would be violated. This example shows that the north-south trending Chinchaga magnetic anomaly, near the region of induced seismicity, can be fit using an anomalous region in the middle crust with susceptibility, depth extent and geometry that is similar to (albeit with a narrower than) the

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**Figure 10.** Magnetic model and observed gravity along profile A-A' (location shown in **Figure 4**). The profile crosses the Kimiwan Anomaly (KA), which forms the boundary between the Southern Chinchaga Domain (SCD) and the Buffalo Head Terrain. A smaller magnetic anomaly at *x* ~ 30 km is located within the SCD with a trend that is parallel with the KA as well as fault-plane solutions in the Duvernay region. Total magnetic field parameters used: inclination 74.80°N,

declination 16°N and magnitude 56,930 nT. Magnetic susceptibility values (K) are in SI units.

alteration-zone model for the Kimiwan Anomaly [9].

**Figure 9.** Gravity and magnetic model constructed based on seismic data in **Figures 6** and **7**. Layer densities and magnetic susceptibilities are given in **Table 1**. Total magnetic field parameters used for the 2D magnetic modelling: inclination 68.80°N, declination 2°N and magnitude 49,738 nT.


**Table 1.** Density and magnetic susceptibility values for **Figure 9**.

that the seismic structural interpretation is consistent with the observed gravity and magnetic anomalies.

A final modelling example is presented in **Figure 10**. Here, magnetic and gravity profiles are extracted from the total-intensity aeromagnetic and isostatic gravity anomaly grids, along profile A-A' (**Figure 4**). This profile cross-cuts the Kimiwan Anomaly as well as a north-south trending positive magnetic anomaly within the southern Chinchaga domain. The Kimiwan Anomaly has a positive magnetic signature (**Figure 4**) about 40 km in width with a northwest orientation. In the isostatic gravity map, this feature is difficult to map. The observed magnetic profile was extracted from the total field intensity magnetic map by getting a profile perpendicular to the two features of interest. Since no seismic constraint is available along this profile, the purpose of this simple forward model is to examine the applicability of the alteration-zone model for the Kimiwan Anomaly [9] to the north-south trending magnetic anomaly from the southern Chinchaga domain. The data was fitted with the anomalous regions situated in the middle crust (**Figure 10**). The observed gravity profile is included for reference. It is not modelled, as the gravity anomaly has a different and non-orthogonal strike direction from the magnetic anomaly so the 2D modelling assumptions would be violated. This example shows that the north-south trending Chinchaga magnetic anomaly, near the region of induced seismicity, can be fit using an anomalous region in the middle crust with susceptibility, depth extent and geometry that is similar to (albeit with a narrower than) the alteration-zone model for the Kimiwan Anomaly [9].

**Figure 10.** Magnetic model and observed gravity along profile A-A' (location shown in **Figure 4**). The profile crosses the Kimiwan Anomaly (KA), which forms the boundary between the Southern Chinchaga Domain (SCD) and the Buffalo Head Terrain. A smaller magnetic anomaly at *x* ~ 30 km is located within the SCD with a trend that is parallel with the KA as well as fault-plane solutions in the Duvernay region. Total magnetic field parameters used: inclination 74.80°N, declination 16°N and magnitude 56,930 nT. Magnetic susceptibility values (K) are in SI units.

that the seismic structural interpretation is consistent with the observed gravity and mag-

**Figure 9.** Gravity and magnetic model constructed based on seismic data in **Figures 6** and **7**. Layer densities and magnetic susceptibilities are given in **Table 1**. Total magnetic field parameters used for the 2D magnetic modelling:

**Modelled layers Density (g/cc) Magnetic susceptibility (SI)**

inclination 68.80°N, declination 2°N and magnitude 49,738 nT.

Sedimentary package 2.17 0 Leduc reef (pink) 2.08 0.00017 WRS (blue) 2.64 0.02 Basement (brown) 2.82 −0.027 WRS (green) 2.64 0.063 Basement (red) 2.79 0.05

**Table 1.** Density and magnetic susceptibility values for **Figure 9**.

A final modelling example is presented in **Figure 10**. Here, magnetic and gravity profiles are extracted from the total-intensity aeromagnetic and isostatic gravity anomaly grids, along profile A-A' (**Figure 4**). This profile cross-cuts the Kimiwan Anomaly as well as a north-south

netic anomalies.

76 Geophysics

#### **5. Discussion and conclusions**

In this study, potential-field methods are combined with seismic and well data to investigate basement structure in Alberta. Our analysis shows that regional gravity anomaly patterns primarily reflect large-scale crustal features, such as a Bouguer gravity low that marks the isostatic root beneath the Rocky Mountains (**Figure 3a**), an isostatic gravity high that reflects a flexurally supported topographic load in the Rock Mountain front ranges of Alberta (**Figure 3b**), and NE-SW linear fabrics associated with the Snowbird Tectonic Zone (STZ). On the other hand, magnetic-anomaly maps provide the primary method for delineating the extent of basement tectonic domains [14]. Isostatic-residual gravity anomalies (**Figure 4a**) are characterized by longer wavelength than magnetic anomalies (**Figure 4b**). While the magnetic anomalies predominantly reflect the magnetic susceptibility of the uppermost basement [15], due to the wavelength difference the gravity anomalies are primarily sensitive to deeper crustal levels. This difference in depth sensitivity may explain why the observed isostatic gravity and magnetic intensity fabrics are poorly correlated (**Figure 4**). Moreover, based on the available regional datasets the (likely subtle) magnetic and gravity expression of basement faults appears to be overwhelmed by anomalies produced by large-scale crustal features. This suggests that a good strategy to improve the sensitivity of potential-field methods to detect and constrain basement faults is to acquire densely sampled data and apply a well-characterized regional-residual separation.

reflections represent mafic sills that were originally more laterally continuous than at present, such that observed offsets can be reasonably interpreted as post-intrusion fault deformation. Extrapolation to the top of basement of the tentatively interpreted crustal-scale reverse fault (**Figures 6** and **7**) would bring this fault to the base of the WCSB close to several interpreted

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We are grateful for support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and Chevron for the Industrial Research Chair (IRC) in Microseismic System Dynamics. Warner Miles is thanked for helping with access to gridded aeromagnetic data, and Brian Roberts is thanked for providing LITHOPROBE data. CGG is gratefully acknowledged for licensing of the Geoview suite and LCT software through CGG's worldwide university program. Patrick Quist CGG Houston is thanked for help with answering questions relating to the LCT software and troubleshooting of the seismic and magnetic data. Geosoft software was also used for visualization and interpretation of potential field data. Lydia Dicaprio and Andrew Poulin are thanked for help with GMT and ArcGIS softwares.

and Ronald Weir<sup>2</sup>

[1] Schultz R, Corlett H, Haug K, Kocon K, MacCormack K, Stern V, Shipman T. Linking fossil reefs with earthquakes: Geologic insight to where induced seismicity occurs in

[2] Bao X, Eaton DW.Large variations in lithospheric thickness of western Laurentia: Tectonic inheritance or collisional reworking? Precambrian Research. 2015 Sep 30;**266**:579-586 [3] Schultz R, Wang R, Gu YJ, Haug K, Atkinson G. A seismological overview of the induced earthquakes in the Duvernay play near Fox Creek, Alberta. Journal of Geophysical

[4] Eaton DW, Ross GM, Hope J. The rise and fall of a cratonic arch: A regional seismic perspective on the Peace River Arch, Alberta. Bulletin of Canadian Petroleum Geology.

Alberta. Geophysical Research Letters. 2016 Mar 28;**43**(6):2534-2542

faults in close proximity to a major Leduc reef edge.

\*, David Eaton<sup>1</sup>

1 MIC, University of Calgary, Calgary, Canada

2 CREWES, University of Calgary, Calgary, Canada

Research: Solid Earth. 2017 Jan 1;**122**(1):492-505

\*Address all correspondence to: eneanwan.ekpo@ucalgary.ca

**Acknowledgements**

**Author details**

Eneanwan Ekpo<sup>1</sup>

**References**

1999;**47**(4):346-361

There is evidence to suggest that the southern Chinchaga domain is a distinct block from the northern Chinchaga domain, although basement drillcore samples are too sparse to either validate or falsify this interpretation. The Chinchaga domain has primarily negative magnetic anomaly values throughout its north-south extent, but there are distinct characteristics of the magnetic anomalies in the southern part that are dissimilar from magnetic-anomaly characteristics in the north. Specifically, the southern Chinchaga domain has a more muted negative character, with distinct internal positive anomalies that are absent in the north. In contrast, the northern Chinchaga domain is characterized by high-amplitude negative anomalies. In addition, the southern Chinchaga domain has strikingly rectilinear boundaries, in contrast to the arcuate nature of internal and bounding fabrics in the north. There are north-south trending magnetic anomalies in the southern Chinchaga domain that have an orientation consistent with observed induced-seismicity focal mechanisms, so this distinction may be important in terms of fully understanding the relationships of magnetic anomalies to induced seismicity.

As indicated by a LITHOPROBE seismic profile across the Tangent fault in the Peace River Embayment, despite a sharp offset at the top of crystalline basement, the seismic expression of faulting of Paleozoic layers is dominated by folding. This draped seismic expression supports the use of seismic curvature attribute analysis [6] for mapping potential fault structures. In the shallow basement, faults in the WCSB are difficult to map due to the lack of coherent reflections and the obscuring effects of multiple reverberations. On the other hand, disruption and offset of reflections within the Winagami Reflection Sequence (WRS) provides a potential opportunity to pinpoint loci of crustal-scale faulting at depth as an aid in the interpretation of basement faults. This interpretation approach relies on an assumption that these bright reflections represent mafic sills that were originally more laterally continuous than at present, such that observed offsets can be reasonably interpreted as post-intrusion fault deformation. Extrapolation to the top of basement of the tentatively interpreted crustal-scale reverse fault (**Figures 6** and **7**) would bring this fault to the base of the WCSB close to several interpreted faults in close proximity to a major Leduc reef edge.

## **Acknowledgements**

**5. Discussion and conclusions**

78 Geophysics

ized regional-residual separation.

lies to induced seismicity.

In this study, potential-field methods are combined with seismic and well data to investigate basement structure in Alberta. Our analysis shows that regional gravity anomaly patterns primarily reflect large-scale crustal features, such as a Bouguer gravity low that marks the isostatic root beneath the Rocky Mountains (**Figure 3a**), an isostatic gravity high that reflects a flexurally supported topographic load in the Rock Mountain front ranges of Alberta (**Figure 3b**), and NE-SW linear fabrics associated with the Snowbird Tectonic Zone (STZ). On the other hand, magnetic-anomaly maps provide the primary method for delineating the extent of basement tectonic domains [14]. Isostatic-residual gravity anomalies (**Figure 4a**) are characterized by longer wavelength than magnetic anomalies (**Figure 4b**). While the magnetic anomalies predominantly reflect the magnetic susceptibility of the uppermost basement [15], due to the wavelength difference the gravity anomalies are primarily sensitive to deeper crustal levels. This difference in depth sensitivity may explain why the observed isostatic gravity and magnetic intensity fabrics are poorly correlated (**Figure 4**). Moreover, based on the available regional datasets the (likely subtle) magnetic and gravity expression of basement faults appears to be overwhelmed by anomalies produced by large-scale crustal features. This suggests that a good strategy to improve the sensitivity of potential-field methods to detect and constrain basement faults is to acquire densely sampled data and apply a well-character-

There is evidence to suggest that the southern Chinchaga domain is a distinct block from the northern Chinchaga domain, although basement drillcore samples are too sparse to either validate or falsify this interpretation. The Chinchaga domain has primarily negative magnetic anomaly values throughout its north-south extent, but there are distinct characteristics of the magnetic anomalies in the southern part that are dissimilar from magnetic-anomaly characteristics in the north. Specifically, the southern Chinchaga domain has a more muted negative character, with distinct internal positive anomalies that are absent in the north. In contrast, the northern Chinchaga domain is characterized by high-amplitude negative anomalies. In addition, the southern Chinchaga domain has strikingly rectilinear boundaries, in contrast to the arcuate nature of internal and bounding fabrics in the north. There are north-south trending magnetic anomalies in the southern Chinchaga domain that have an orientation consistent with observed induced-seismicity focal mechanisms, so this distinction may be important in terms of fully understanding the relationships of magnetic anoma-

As indicated by a LITHOPROBE seismic profile across the Tangent fault in the Peace River Embayment, despite a sharp offset at the top of crystalline basement, the seismic expression of faulting of Paleozoic layers is dominated by folding. This draped seismic expression supports the use of seismic curvature attribute analysis [6] for mapping potential fault structures. In the shallow basement, faults in the WCSB are difficult to map due to the lack of coherent reflections and the obscuring effects of multiple reverberations. On the other hand, disruption and offset of reflections within the Winagami Reflection Sequence (WRS) provides a potential opportunity to pinpoint loci of crustal-scale faulting at depth as an aid in the interpretation of basement faults. This interpretation approach relies on an assumption that these bright We are grateful for support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and Chevron for the Industrial Research Chair (IRC) in Microseismic System Dynamics. Warner Miles is thanked for helping with access to gridded aeromagnetic data, and Brian Roberts is thanked for providing LITHOPROBE data. CGG is gratefully acknowledged for licensing of the Geoview suite and LCT software through CGG's worldwide university program. Patrick Quist CGG Houston is thanked for help with answering questions relating to the LCT software and troubleshooting of the seismic and magnetic data. Geosoft software was also used for visualization and interpretation of potential field data. Lydia Dicaprio and Andrew Poulin are thanked for help with GMT and ArcGIS softwares.

#### **Author details**

Eneanwan Ekpo<sup>1</sup> \*, David Eaton<sup>1</sup> and Ronald Weir<sup>2</sup> \*Address all correspondence to: eneanwan.ekpo@ucalgary.ca 1 MIC, University of Calgary, Calgary, Canada 2 CREWES, University of Calgary, Calgary, Canada

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80 Geophysics


**Section 2**

**Geo-Hazard: Seismicity and Geoelectric**

**Geo-Hazard: Seismicity and Geoelectric**

**Chapter 5**

**Provisional chapter**

**Characterization of Hydrocarbon-Contaminated Sites**

Electrical methods are effective tools for the characterization of oil-contaminated sites and are applied in defining the geometry of the contaminated plume and in designing the remedial process. The optimal methodology integrates geoelectric methods, data processing, and interpretation techniques. Electromagnetic profiling is a reliable and fast method used to provide the configuration of oil-contaminated plume from apparent resistivity map and used to guide the subsequent electrical resistivity tomography survey. From advanced field work methods, data processing, and interpretation procedures, electrical resistivity tomography survey provides the three-dimensional (3D) configuration of the contaminated plume, migration pathways, location of active contaminated sources, and information about lithology. For separate contaminated and clean zones, a petrophysical modeling is used for the calculation of soil resistivity based on groundwater salinity. Taking the pore-water salinity value into account, an inversion algorithm recalculates resistivity maps into maps of clay content, porosity, and cation exchange capacity, allowing a more accurate determination of the volume of contaminated soil. From clay content data, hydraulic conductivity values are calculated for determining the groundwater vulnerability due to vertical migration of contaminants from upper layers. The optimal geoelectric methodology is an efficient procedure to assess hydrocarbon-contaminated

**Sites Based on Geoelectrical Methods of Geophysical** 

DOI: 10.5772/intechopen.73103

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

sites, with emphasis on large sites with deeper groundwater table.

modeling, contaminated plume, OGEOMET

**Keywords:** oil-contaminated soil, geoelectrical characterization, petrophysical

**Based on Geoelectrical Methods of Geophysical**

**Characterization of Hydrocarbon-Contaminated** 

Omar Delgado-Rodríguez, Vladimir Shevnin,

Omar Delgado-Rodríguez, Vladimir Shevnin,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Héctor Peinado-Guevara and María Ladrón de Guevara-Torres

Héctor Peinado-Guevara and María Ladrón de Guevara-Torres

http://dx.doi.org/10.5772/intechopen.73103

**Exploration**

**Abstract**

**Exploration**

**Provisional chapter**

#### **Characterization of Hydrocarbon-Contaminated Sites Based on Geoelectrical Methods of Geophysical Exploration Sites Based on Geoelectrical Methods of Geophysical Exploration**

**Characterization of Hydrocarbon-Contaminated** 

DOI: 10.5772/intechopen.73103

Omar Delgado-Rodríguez, Vladimir Shevnin, Héctor Peinado-Guevara and María Ladrón de Guevara-Torres Héctor Peinado-Guevara and María Ladrón de Guevara-Torres Additional information is available at the end of the chapter

Omar Delgado-Rodríguez, Vladimir Shevnin,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73103

#### **Abstract**

Electrical methods are effective tools for the characterization of oil-contaminated sites and are applied in defining the geometry of the contaminated plume and in designing the remedial process. The optimal methodology integrates geoelectric methods, data processing, and interpretation techniques. Electromagnetic profiling is a reliable and fast method used to provide the configuration of oil-contaminated plume from apparent resistivity map and used to guide the subsequent electrical resistivity tomography survey. From advanced field work methods, data processing, and interpretation procedures, electrical resistivity tomography survey provides the three-dimensional (3D) configuration of the contaminated plume, migration pathways, location of active contaminated sources, and information about lithology. For separate contaminated and clean zones, a petrophysical modeling is used for the calculation of soil resistivity based on groundwater salinity. Taking the pore-water salinity value into account, an inversion algorithm recalculates resistivity maps into maps of clay content, porosity, and cation exchange capacity, allowing a more accurate determination of the volume of contaminated soil. From clay content data, hydraulic conductivity values are calculated for determining the groundwater vulnerability due to vertical migration of contaminants from upper layers. The optimal geoelectric methodology is an efficient procedure to assess hydrocarbon-contaminated sites, with emphasis on large sites with deeper groundwater table.

**Keywords:** oil-contaminated soil, geoelectrical characterization, petrophysical modeling, contaminated plume, OGEOMET

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

#### **1. Introduction**

In many countries, the growth of oil industry has been accompanied by the contamination of environment owing to exploitation, transportation, refining, and distribution of hydrocarbons. Over the years, great interest has been focused on the study of the environmental impact from oil industry. The spill of oil products can be a devastating event, with obvious consequences. Oil spills have a wide range of negative effects on the environment and economy. The spillage damages waterways, animal life, and plants. Determining the presence and concentration of hydrocarbon contaminants in the subsurface is performed by drilling and chemical analysis of soil samples collected from wells. The steps involved before the results of chemical analyses are obtained are very boring, expensive, and time-consuming. Moreover, in most geological situations, the oil contaminants are concentrated above the water table, implying that it is necessary to drill up to the aquifer, thereby increasing its vulnerability by the infiltration of contaminants from the surface. In most cases, geological conditions such as the presence of hard formations and deeper groundwater table make the drilling works more complicated, expensive, and time-consuming. The location of drilling points without prior knowledge of the spatial distribution of contaminants in subsoil ("blind" selection of drilling points) decreases the efficiency of this procedure.

boundary between contaminated and clean zones. It is also possible to obtain cross sections and maps of clay content, porosity, and CEC, using interpreted resistivity data from ERT survey and groundwater salinity information [11]. For uncontaminated soil, these parameters (clay content, porosity, and cation exchange capacity) are close to true petrophysical parameters, estimated with traditional methods in the laboratory. In contaminated soils, petrophysical param-

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87

This chapter presents an optimal geoelectric methodology for the characterization of hydrocarbon-contaminated sites that include the application of EMP and ERT methods with advanced petrophysical inversion of the geoelectrical data in order to define the geoelectric boundary

The optimal geoelectric methodology (OGEOMET) integrates the field and laboratory methods for measuring the soil and water resistivity in situ and on samples, respectively. OGEOMET also includes advanced petrophysical interpretation of the geoelectric data in order to define the geoelectric boundary between clean and contaminated soil and to estimate some soil petrophysical parameters. The field operations include EMP and ERT methods to obtain the spatial distribution of the soil resistivity and the groundwater resistivity measurements (WRMs). In addition, we perform the resistivity measurements in soil samples (RMSSs) to determine clay content, porosity, CEC, and hydraulic conductivity required for the characterization of the contaminated site. **Figure 1** shows the flowchart of field operations, process-

EMP is a reliable and fast method to provide the configuration of the surface contaminated by oil plume from apparent resistivity map. The application of the EMP method involves measuring the response of the subsurface in an induced electromagnetic field. Using the EM31-MK2 equipment [12] (**Figure 2**), an electromagnetic field is generated by a transmitter antenna, inducing eddy currents within the ground. These induced currents generate a secondary magnetic field. Both primary and secondary magnetic fields are measured in a receiver antenna. The ground conductivity (mS/m) is calculated from the ratio of the secondary and primary magnetic fields, and it is affected by a number of factors including clay content, moisture and salinity of pore water, conductive (metal) objects, and conductive contaminants. The EMP results, although not providing detailed stratigraphic information (layers and their thicknesses), can offer the horizontal changes in soil apparent conductivity.

In **Figure 3**, an example of EMP application on one rural site is presented [4]. The depth of the local aquifer is 4 m. The resistivity map has been constructed from the EMP data obtained using EM31-MK2 equipment [12] for the vertical polarization of the magnetic field, ensuring a maximal depth of investigation of 6 m. Twenty-two EMP profiles were performed on the

eters reach anomalous values. This helps in defining the contaminated plume.

**2. Optimal geoelectric methodology (OGEOMET)**

ing, and representation of results obtained from the OGEOMET.

**2.1. Application of the electromagnetic profiling (EMP) method**

between clean and contaminated soil and to estimate soil petrophysical parameters.

The resistivity contrast between clean and contaminated rocks depends on the age of the spill. In the case of recent spills, the presence of high-resistivity anomalies is expected. A low-resistivity anomaly arises in contaminated zones between 4 and 6 months after the spill has occurred, depending on the lithological and weather condition of the study area. Sauck [1] proposed that the low-resistivity anomaly is created by the intense action of bacteria on hydrocarbons in the lower part of the vadose zone. The organic and inorganic acids yielded during biodegradation process increase the dissolution of minerals, releasing ions that increase the total dissolved solids (TDSs) in the pore water. Abdel-Aal et al. [2] found some important details of this biodegradation process and changes in the electrical properties of contaminated zones. They demonstrated that the increase of soil conductivity contaminated by hydrocarbons due to the biodegradation process is mainly related to high-surface conductivity of biofilms between solid and liquid components created by bacteria in the pores of the affected rocks. Thus, the application of geoelectric methods is very useful for characterizing both recent and matured oil-contaminated zones [1–3].

Several investigations have demonstrated the successful application of the surface resistivity methods for configuration (in plan and depth) of the hydrocarbon-contaminated zones. Electrical resistivity tomography (ERT) and electromagnetic profiling (EMP) methods are useful for the delimitation of the resistivity anomalies caused by different types of hydrocarbon contaminants and rocks in rural [4, 5], industrial [6], and urban [7] sites. Soil resistivity depends mainly on water content and its salinity, clay content, and porosity. There are many models describing the dependence of soil resistivity on these factors (e.g., [8, 9]). The methodology shown in this chapter includes the use of the petrophysical model explained in detail by Shevnin et al. [10]. In the laboratory, the behavior of soil resistivity versus water salinity in clean soil samples is measured, and clay content, porosity, and cation exchange capacity (CEC) are determined. The knowledge of these petrophysical parameters is used to define the geoelectric boundary between contaminated and clean zones. It is also possible to obtain cross sections and maps of clay content, porosity, and CEC, using interpreted resistivity data from ERT survey and groundwater salinity information [11]. For uncontaminated soil, these parameters (clay content, porosity, and cation exchange capacity) are close to true petrophysical parameters, estimated with traditional methods in the laboratory. In contaminated soils, petrophysical parameters reach anomalous values. This helps in defining the contaminated plume.

This chapter presents an optimal geoelectric methodology for the characterization of hydrocarbon-contaminated sites that include the application of EMP and ERT methods with advanced petrophysical inversion of the geoelectrical data in order to define the geoelectric boundary between clean and contaminated soil and to estimate soil petrophysical parameters.

## **2. Optimal geoelectric methodology (OGEOMET)**

**1. Introduction**

86 Geophysics

In many countries, the growth of oil industry has been accompanied by the contamination of environment owing to exploitation, transportation, refining, and distribution of hydrocarbons. Over the years, great interest has been focused on the study of the environmental impact from oil industry. The spill of oil products can be a devastating event, with obvious consequences. Oil spills have a wide range of negative effects on the environment and economy. The spillage damages waterways, animal life, and plants. Determining the presence and concentration of hydrocarbon contaminants in the subsurface is performed by drilling and chemical analysis of soil samples collected from wells. The steps involved before the results of chemical analyses are obtained are very boring, expensive, and time-consuming. Moreover, in most geological situations, the oil contaminants are concentrated above the water table, implying that it is necessary to drill up to the aquifer, thereby increasing its vulnerability by the infiltration of contaminants from the surface. In most cases, geological conditions such as the presence of hard formations and deeper groundwater table make the drilling works more complicated, expensive, and time-consuming. The location of drilling points without prior knowledge of the spatial distribution of contaminants in subsoil

The resistivity contrast between clean and contaminated rocks depends on the age of the spill. In the case of recent spills, the presence of high-resistivity anomalies is expected. A low-resistivity anomaly arises in contaminated zones between 4 and 6 months after the spill has occurred, depending on the lithological and weather condition of the study area. Sauck [1] proposed that the low-resistivity anomaly is created by the intense action of bacteria on hydrocarbons in the lower part of the vadose zone. The organic and inorganic acids yielded during biodegradation process increase the dissolution of minerals, releasing ions that increase the total dissolved solids (TDSs) in the pore water. Abdel-Aal et al. [2] found some important details of this biodegradation process and changes in the electrical properties of contaminated zones. They demonstrated that the increase of soil conductivity contaminated by hydrocarbons due to the biodegradation process is mainly related to high-surface conductivity of biofilms between solid and liquid components created by bacteria in the pores of the affected rocks. Thus, the application of geoelectric methods is very useful for characterizing

Several investigations have demonstrated the successful application of the surface resistivity methods for configuration (in plan and depth) of the hydrocarbon-contaminated zones. Electrical resistivity tomography (ERT) and electromagnetic profiling (EMP) methods are useful for the delimitation of the resistivity anomalies caused by different types of hydrocarbon contaminants and rocks in rural [4, 5], industrial [6], and urban [7] sites. Soil resistivity depends mainly on water content and its salinity, clay content, and porosity. There are many models describing the dependence of soil resistivity on these factors (e.g., [8, 9]). The methodology shown in this chapter includes the use of the petrophysical model explained in detail by Shevnin et al. [10]. In the laboratory, the behavior of soil resistivity versus water salinity in clean soil samples is measured, and clay content, porosity, and cation exchange capacity (CEC) are determined. The knowledge of these petrophysical parameters is used to define the geoelectric

("blind" selection of drilling points) decreases the efficiency of this procedure.

both recent and matured oil-contaminated zones [1–3].

The optimal geoelectric methodology (OGEOMET) integrates the field and laboratory methods for measuring the soil and water resistivity in situ and on samples, respectively. OGEOMET also includes advanced petrophysical interpretation of the geoelectric data in order to define the geoelectric boundary between clean and contaminated soil and to estimate some soil petrophysical parameters. The field operations include EMP and ERT methods to obtain the spatial distribution of the soil resistivity and the groundwater resistivity measurements (WRMs). In addition, we perform the resistivity measurements in soil samples (RMSSs) to determine clay content, porosity, CEC, and hydraulic conductivity required for the characterization of the contaminated site. **Figure 1** shows the flowchart of field operations, processing, and representation of results obtained from the OGEOMET.

#### **2.1. Application of the electromagnetic profiling (EMP) method**

EMP is a reliable and fast method to provide the configuration of the surface contaminated by oil plume from apparent resistivity map. The application of the EMP method involves measuring the response of the subsurface in an induced electromagnetic field. Using the EM31-MK2 equipment [12] (**Figure 2**), an electromagnetic field is generated by a transmitter antenna, inducing eddy currents within the ground. These induced currents generate a secondary magnetic field. Both primary and secondary magnetic fields are measured in a receiver antenna. The ground conductivity (mS/m) is calculated from the ratio of the secondary and primary magnetic fields, and it is affected by a number of factors including clay content, moisture and salinity of pore water, conductive (metal) objects, and conductive contaminants. The EMP results, although not providing detailed stratigraphic information (layers and their thicknesses), can offer the horizontal changes in soil apparent conductivity.

In **Figure 3**, an example of EMP application on one rural site is presented [4]. The depth of the local aquifer is 4 m. The resistivity map has been constructed from the EMP data obtained using EM31-MK2 equipment [12] for the vertical polarization of the magnetic field, ensuring a maximal depth of investigation of 6 m. Twenty-two EMP profiles were performed on the study site. Each measured conductivity value (mS/m) was converted to a resistivity (Ohm-m) value. The low-resistivity anomalies (blue zones, **Figure 3**) indicate the presence of hydrocarbon contaminants affected by biodegradation process ("mature" contamination). This result is useful to plan the ERT survey (see flowchart in **Figure 1**).

**2.2. Water resistivity measurements (WRMs)**

**Figure 3.** Resistivity map obtained by EMP in a rural site.

increases the values of TDS in pore water of the affected soil.

The procedure for WRM is simple and includes the collection of water samples (~250 ml) in previously selected sampling points (e.g., wells, lagoons, swamps, etc.) using a plastic or a glass container (do not use metal container). A portable tester (e.g., HI98130) is placed in a container, and water conductivity (mS/cm) and temperature (°C) are measured. The water temperature variations are corrected using a reference temperature of 20°C. In some sites, the number of sampling points and their spatial distribution allow the production of water resistivity map. This map gives the preliminary delimitation of main contaminated zones. For example, **Figure 4** shows the water resistivity map obtained in the same rural site where the EMP method was applied (**Figure 3**). Forty-four water samples were collected from wells and pit. The water resistivity map shows low-resistivity anomalies (blue zones in **Figure 4**) as potentially contaminated zones, corresponding to the main low-resistivity anomalies determined by the EMP method (see **Figure 3**). The decrease of the water resistivity in the contaminated zones demonstrates that the biodegradation process of hydrocarbon contaminants

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Frequently, a water resistivity map is not obtained due to lack of water-sampling points. In this case, clean groundwater must be collected, in at least one sampling point, for the calculation of water resistivity and salinity values, useful for the petrophysical inversion procedure

and the determination of geoelectric boundary between clean and contaminated soils.

**Figure 1.** Flowchart of the OGEOMET for the characterization of hydrocarbon-contaminated sites.

**Figure 2.** EM31-MK2 ground conductivity meter in field operations [12].

Characterization of Hydrocarbon-Contaminated Sites Based on Geoelectrical Methods… http://dx.doi.org/10.5772/intechopen.73103 89

**Figure 3.** Resistivity map obtained by EMP in a rural site.

study site. Each measured conductivity value (mS/m) was converted to a resistivity (Ohm-m) value. The low-resistivity anomalies (blue zones, **Figure 3**) indicate the presence of hydrocarbon contaminants affected by biodegradation process ("mature" contamination). This result

is useful to plan the ERT survey (see flowchart in **Figure 1**).

88 Geophysics

**Figure 1.** Flowchart of the OGEOMET for the characterization of hydrocarbon-contaminated sites.

**Figure 2.** EM31-MK2 ground conductivity meter in field operations [12].

#### **2.2. Water resistivity measurements (WRMs)**

The procedure for WRM is simple and includes the collection of water samples (~250 ml) in previously selected sampling points (e.g., wells, lagoons, swamps, etc.) using a plastic or a glass container (do not use metal container). A portable tester (e.g., HI98130) is placed in a container, and water conductivity (mS/cm) and temperature (°C) are measured. The water temperature variations are corrected using a reference temperature of 20°C. In some sites, the number of sampling points and their spatial distribution allow the production of water resistivity map. This map gives the preliminary delimitation of main contaminated zones. For example, **Figure 4** shows the water resistivity map obtained in the same rural site where the EMP method was applied (**Figure 3**). Forty-four water samples were collected from wells and pit. The water resistivity map shows low-resistivity anomalies (blue zones in **Figure 4**) as potentially contaminated zones, corresponding to the main low-resistivity anomalies determined by the EMP method (see **Figure 3**). The decrease of the water resistivity in the contaminated zones demonstrates that the biodegradation process of hydrocarbon contaminants increases the values of TDS in pore water of the affected soil.

Frequently, a water resistivity map is not obtained due to lack of water-sampling points. In this case, clean groundwater must be collected, in at least one sampling point, for the calculation of water resistivity and salinity values, useful for the petrophysical inversion procedure and the determination of geoelectric boundary between clean and contaminated soils.

values are corrected to reference temperature (e.g., 20°C). Thus, we have five soil electrical resistivity values (one for each soil box) depending on the salinity of the pore water (ρexp(C)) [11]. The soil resistivity obtained as a function of the pore water salinity is used for the petro-

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From WRM and RMSS, and resistivity data obtained by ERT, it is possible to determine parameters such as clay content, porosity, and cation exchange capacity (CEC), which are important in determining the geoelectric boundary between clean and contaminated soil, and

The experimental resistivity versus salinity curve (ρexp(C)) and electrical resistivity values calculated (ρth(C)) using the theoretical model developed by [10, 11] were subjected to a curve-fitting process to calculate the different geological parameters. The theoretical model considers the geometrical microstructure of the components as well as electrochemical processes occurring in the soil for a wide range of the pore-water salinity and clay content. Different parameters are used for petrophysical modeling, including the following: water salinity (including types of anions and cations with their valence, hydration number, sorption constant, and mobility), porosity, capillary radii, humidity, cementation exponent *m*, the CEC for each component of soil, including sand and clay, and the temperature of the soil. The result of the modeling is the calculated soil resistivity as a function of water salinity. We need to estimate three soil parameters: clay content, porosity, and CEC. Once local groundwater (or salinity) and soil resistivity are known, the clay content and porosity are estimated for clean soils of the study site, and the geoelectric boundary is defined. *K* was calculated based on the clay content using the empirical formula proposed by Shevnin

K = 7.2.10− 4<sup>∗</sup> C−<sup>2</sup> (1)

where K is the saturated soil hydraulic conductivity (m\*day−1), and C is the clay content in

A practical example from **Figure 5** shows the results of the petrophysical modeling for the same rural site depicted in **Figures 2** and **4**, where a soil sample was collected from a clean zone. According to priori information, the collected soil belongs to the layer with a higher clay content. Applying the procedure explained earlier, the modeled sample (dashed curve C) gives the clay content of 43%. A value of resistivity of 27 Ohm-m (salinity of 0.22 g/l) was determined for noncontaminated groundwater. Lithologies from pure sand (curve 0) to sand clay with 40% of clay (curve 40, **Figure 5**) are in the range of 14–120 Ohm-m (vertical line A). The clay content for this resistivity interval is between 4 and 40%. Taking into account that the maximum clay content for the site is 43%, then the resistivity values less than 14 Ohm-m correspond to the contaminated soil (gray rectangle B), the resistivity value of the geoelectric boundary being used on the delineation of contaminated zones in resistiv-

the hydraulic conductivity (K), useful for the assessment of the aquifer vulnerability.

physical inversion.

et al. [13]

relative units between 0.01 and 1.

ity sections and maps.

**2.4. Petrophysical inversion**

**Figure 4.** Water resistivity map obtained by the application of WRM in a rural hydrocarbon-contaminated site.

#### **2.3. Resistivity measurements of soil samples (RMSSs)**

The soil samples should represent different soil types of the site. For this purpose, a drilling point, outside the contaminated area, is selected, and some soil samples are collected at different depths. A laboratory procedure that gives the characteristics of soil resistivity versus pore water salinity is applied. Each soil sample is dried and homogenized and, then, divided into five similar parts (subsamples) and placed into five soil boxes. Each soil box consists of a rectangular plastic (insulated) container with four electrodes (two to inject current and two to measure voltage). Once the subsample is placed into soil box, the water of known salinity (different for each soil box) in the range between 0.1 and 70 g/l is added to completely saturate each subsample. Taking into account that the electrokinetic process requires significant time (especially for clayed sediments) to achieve an equilibrium, we perform the resistivity measurements 1 h after water deposition. The measurements are performed in the low-frequency range to avoid problem with the electrode polarization and induction effect. The resistivity values are corrected to reference temperature (e.g., 20°C). Thus, we have five soil electrical resistivity values (one for each soil box) depending on the salinity of the pore water (ρexp(C)) [11]. The soil resistivity obtained as a function of the pore water salinity is used for the petrophysical inversion.

#### **2.4. Petrophysical inversion**

**2.3. Resistivity measurements of soil samples (RMSSs)**

90 Geophysics

The soil samples should represent different soil types of the site. For this purpose, a drilling point, outside the contaminated area, is selected, and some soil samples are collected at different depths. A laboratory procedure that gives the characteristics of soil resistivity versus pore water salinity is applied. Each soil sample is dried and homogenized and, then, divided into five similar parts (subsamples) and placed into five soil boxes. Each soil box consists of a rectangular plastic (insulated) container with four electrodes (two to inject current and two to measure voltage). Once the subsample is placed into soil box, the water of known salinity (different for each soil box) in the range between 0.1 and 70 g/l is added to completely saturate each subsample. Taking into account that the electrokinetic process requires significant time (especially for clayed sediments) to achieve an equilibrium, we perform the resistivity measurements 1 h after water deposition. The measurements are performed in the low-frequency range to avoid problem with the electrode polarization and induction effect. The resistivity

**Figure 4.** Water resistivity map obtained by the application of WRM in a rural hydrocarbon-contaminated site.

From WRM and RMSS, and resistivity data obtained by ERT, it is possible to determine parameters such as clay content, porosity, and cation exchange capacity (CEC), which are important in determining the geoelectric boundary between clean and contaminated soil, and the hydraulic conductivity (K), useful for the assessment of the aquifer vulnerability.

The experimental resistivity versus salinity curve (ρexp(C)) and electrical resistivity values calculated (ρth(C)) using the theoretical model developed by [10, 11] were subjected to a curve-fitting process to calculate the different geological parameters. The theoretical model considers the geometrical microstructure of the components as well as electrochemical processes occurring in the soil for a wide range of the pore-water salinity and clay content. Different parameters are used for petrophysical modeling, including the following: water salinity (including types of anions and cations with their valence, hydration number, sorption constant, and mobility), porosity, capillary radii, humidity, cementation exponent *m*, the CEC for each component of soil, including sand and clay, and the temperature of the soil. The result of the modeling is the calculated soil resistivity as a function of water salinity. We need to estimate three soil parameters: clay content, porosity, and CEC. Once local groundwater (or salinity) and soil resistivity are known, the clay content and porosity are estimated for clean soils of the study site, and the geoelectric boundary is defined. *K* was calculated based on the clay content using the empirical formula proposed by Shevnin et al. [13]

$$\mathbf{K} = 7.2.10^{-4} \,\mathrm{C}^{-2} \tag{1}$$

where K is the saturated soil hydraulic conductivity (m\*day−1), and C is the clay content in relative units between 0.01 and 1.

A practical example from **Figure 5** shows the results of the petrophysical modeling for the same rural site depicted in **Figures 2** and **4**, where a soil sample was collected from a clean zone. According to priori information, the collected soil belongs to the layer with a higher clay content. Applying the procedure explained earlier, the modeled sample (dashed curve C) gives the clay content of 43%. A value of resistivity of 27 Ohm-m (salinity of 0.22 g/l) was determined for noncontaminated groundwater. Lithologies from pure sand (curve 0) to sand clay with 40% of clay (curve 40, **Figure 5**) are in the range of 14–120 Ohm-m (vertical line A). The clay content for this resistivity interval is between 4 and 40%. Taking into account that the maximum clay content for the site is 43%, then the resistivity values less than 14 Ohm-m correspond to the contaminated soil (gray rectangle B), the resistivity value of the geoelectric boundary being used on the delineation of contaminated zones in resistivity sections and maps.

**Figure 5.** Petrophysical modeling of the rural contaminated site using soil, groundwater, and ERT information.

#### **2.5. Application of the electrical resistivity tomography (ERT) method**

ERT uses short spacing for measurements along profiles for two-dimensional (2D) study of inhomogeneous media, and a great number of electrodes are reconnected manually or automatically. The ERT survey has specially selected measuring and current points to obtain high resolution and low distortion caused by near-surface inhomogeneity [14]. In this method, different electrode arrays can be used (pole-dipole, dipole-dipole, and Wenner, Schlumberger).

The 2D inversion of filtered apparent resistivity data provides the high-quality cross sections of the true resistivity distribution. The application of the ERT method allows us to find the depth of contaminated zones and, finally, the 3D configuration of hydrocarbon-contaminated plume. Based on the resistivity cross sections and adding geological information, it is possible to make up lithostratigraphic sections. **Figure 6** shows the interpreted resistivity section of ERT profile 6 (see **Figure 7**) conducted at the same rural site (**Figures 2** and **4**), whose petrophysical modeling (**Figure 5**) defined a geoelectric boundary between clean and contaminated soils of 14 Ohm-m (red contour, **Figure 6**). The contaminated zones are defined in depth accurately allowing a direct soil sampling, reducing the number of soil samples needed for their quantification, and increasing the accuracy of results. For inversion of the apparent resistivity, the software RES2DINV [14] was used.

low-resistivity anomalies are related to high contaminated zones. The dashed line shows

**Figure 6.** Geoelectric section of profile 6. Contaminated zones are delimited in depth optimizing the soil-sampling work.

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Soil resistivity maps, determined by ERT and groundwater salinity information, were converted into petrophysical (clay content, porosity, and CEC) maps. The petrophysical parameters estimated for clean soil correspond to their true values, while values of clay content, porosity, and CEC calculated for contaminated soils do not match with their true values;

**2.6. Estimation of petrophysical parameters: determination of the volume of** 

the pit outline (**Figure 7**).

**Figure 7.** Resistivity map for target layer.

**contaminated soil**

From 11 interpreted resistivity sections, it was possible to obtain a resistivity map for "target layer." The target layer, where hydrocarbon contaminants are accumulated, is located in the lower part of the vadose zone. **Figure 7** shows the resistivity map for the target layer with a depth interval of 2–4 m, defining the contaminated plumes according to the geoelectric boundary (14 Ohm-m) defined from petrophysical modeling process. Two main Characterization of Hydrocarbon-Contaminated Sites Based on Geoelectrical Methods… http://dx.doi.org/10.5772/intechopen.73103 93

**Figure 6.** Geoelectric section of profile 6. Contaminated zones are delimited in depth optimizing the soil-sampling work.

**Figure 7.** Resistivity map for target layer.

**2.5. Application of the electrical resistivity tomography (ERT) method**

resistivity, the software RES2DINV [14] was used.

Schlumberger).

92 Geophysics

ERT uses short spacing for measurements along profiles for two-dimensional (2D) study of inhomogeneous media, and a great number of electrodes are reconnected manually or automatically. The ERT survey has specially selected measuring and current points to obtain high resolution and low distortion caused by near-surface inhomogeneity [14]. In this method, different electrode arrays can be used (pole-dipole, dipole-dipole, and Wenner,

**Figure 5.** Petrophysical modeling of the rural contaminated site using soil, groundwater, and ERT information.

The 2D inversion of filtered apparent resistivity data provides the high-quality cross sections of the true resistivity distribution. The application of the ERT method allows us to find the depth of contaminated zones and, finally, the 3D configuration of hydrocarbon-contaminated plume. Based on the resistivity cross sections and adding geological information, it is possible to make up lithostratigraphic sections. **Figure 6** shows the interpreted resistivity section of ERT profile 6 (see **Figure 7**) conducted at the same rural site (**Figures 2** and **4**), whose petrophysical modeling (**Figure 5**) defined a geoelectric boundary between clean and contaminated soils of 14 Ohm-m (red contour, **Figure 6**). The contaminated zones are defined in depth accurately allowing a direct soil sampling, reducing the number of soil samples needed for their quantification, and increasing the accuracy of results. For inversion of the apparent

From 11 interpreted resistivity sections, it was possible to obtain a resistivity map for "target layer." The target layer, where hydrocarbon contaminants are accumulated, is located in the lower part of the vadose zone. **Figure 7** shows the resistivity map for the target layer with a depth interval of 2–4 m, defining the contaminated plumes according to the geoelectric boundary (14 Ohm-m) defined from petrophysical modeling process. Two main low-resistivity anomalies are related to high contaminated zones. The dashed line shows the pit outline (**Figure 7**).

#### **2.6. Estimation of petrophysical parameters: determination of the volume of contaminated soil**

Soil resistivity maps, determined by ERT and groundwater salinity information, were converted into petrophysical (clay content, porosity, and CEC) maps. The petrophysical parameters estimated for clean soil correspond to their true values, while values of clay content, porosity, and CEC calculated for contaminated soils do not match with their true values; however, its high contrast (anomalous values—background) allows delineation of the contaminated zones with a high resolution. The contaminated zones are more clearly observed in petrophysical maps, with emphasis on clay content (clay content of >43%, **Figure 8**), than those in resistivity maps (**Figure 7**) for the target layer. In **Figure 8**, three main highly contaminated areas are observed in the pit zone. An additional small anomalous area is defined in the central part of the site (**Figure 8**). Using information about target layer (thicknesses from sections and areas from map), a total volume of hydrocarbon-contaminated soil of 4728 m3 was obtained.

from ERT profile 1 (see **Figure 9**). The intermediate layer corresponds to high-resistivity sandy aquifer with a maximum clay content of 2%. The portion of the aquifer with a lower resistivity (marked by a dashed line, **Figure 9**) indicates the possible presence of matured

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After determining the clay content values in each layer, the values of K can be estimated using expression (1). The clay content map for the aquitard of the site allows the estimation of a hydraulic conductivity map, which defines the areas where the aquifer is more vulnerable to infiltration of contaminants from upper layers. In **Figure 11**, four areas of the aquitard, near to spill point, with the lowest clay content (**Figure 11A**) or the highest hydraulic conductivity (**Figure 11B**) values, correspond to high aquifer vulnerability zones by infiltration (hydrogeo-

Using the information from different ERT sections, an aquifer resistivity map is obtained, showing the main plume associated with a detected pipe leakage point (red diamond, **Figure 12**). Note that another small contaminated zone close to another pipeline is observed in the eastern

**Figure 13** shows an industrial-contaminated site, where the presence of mature contamination was evident. An oil-contaminated industrial site was studied using the ERT method [15]. Based on resistivity range, the configuration of the contaminated plumes and the degree of contamination were defined. The minimal anomalous resistivity values are associated with the maximum oil contamination, which is in correspondence with biodegradation process and the presence of conductive biofilm. The configuration of the surface of the maximum zone of contamination helps to locate the unknown active sources of contamination (**Figure 13**). Zoning of

**2.8. Estimation of migration pathways of contaminants and location of sources of** 

part of the site (**Figure 12**), although this claim needs to be investigated.

contamination.

**contamination**

**Figure 9.** Scheme of the site.

logical windows) of gasoline from the aquitard.

#### **2.7. Determination of the aquifer vulnerability**

The rural site discussed earlier did not require the analysis of vulnerability of the aquifer to hydrocarbons infiltration from the upper layers because there are no active contaminated sources and the oil spill happened over 20 years ago. Therefore, we take another rural site as an example, where 8 months after a gasoline spill caused by pipeline leakage occurred, an ERT survey was performed [5] (**Figure 9**).

A total of 174 ERT points were distributed in six profiles (**Figure 9**). A Schlumberger array with AB/2 spacing from 2 to 20 m was used. **Figure 10** shows the geoelectric section obtained

**Figure 8.** Clay content map for target layer of the rural site.

from ERT profile 1 (see **Figure 9**). The intermediate layer corresponds to high-resistivity sandy aquifer with a maximum clay content of 2%. The portion of the aquifer with a lower resistivity (marked by a dashed line, **Figure 9**) indicates the possible presence of matured contamination.

After determining the clay content values in each layer, the values of K can be estimated using expression (1). The clay content map for the aquitard of the site allows the estimation of a hydraulic conductivity map, which defines the areas where the aquifer is more vulnerable to infiltration of contaminants from upper layers. In **Figure 11**, four areas of the aquitard, near to spill point, with the lowest clay content (**Figure 11A**) or the highest hydraulic conductivity (**Figure 11B**) values, correspond to high aquifer vulnerability zones by infiltration (hydrogeological windows) of gasoline from the aquitard.

Using the information from different ERT sections, an aquifer resistivity map is obtained, showing the main plume associated with a detected pipe leakage point (red diamond, **Figure 12**). Note that another small contaminated zone close to another pipeline is observed in the eastern part of the site (**Figure 12**), although this claim needs to be investigated.

#### **2.8. Estimation of migration pathways of contaminants and location of sources of contamination**

**Figure 13** shows an industrial-contaminated site, where the presence of mature contamination was evident. An oil-contaminated industrial site was studied using the ERT method [15]. Based on resistivity range, the configuration of the contaminated plumes and the degree of contamination were defined. The minimal anomalous resistivity values are associated with the maximum oil contamination, which is in correspondence with biodegradation process and the presence of conductive biofilm. The configuration of the surface of the maximum zone of contamination helps to locate the unknown active sources of contamination (**Figure 13**). Zoning of

**Figure 9.** Scheme of the site.

however, its high contrast (anomalous values—background) allows delineation of the contaminated zones with a high resolution. The contaminated zones are more clearly observed in petrophysical maps, with emphasis on clay content (clay content of >43%, **Figure 8**), than those in resistivity maps (**Figure 7**) for the target layer. In **Figure 8**, three main highly contaminated areas are observed in the pit zone. An additional small anomalous area is defined in the central part of the site (**Figure 8**). Using information about target layer (thicknesses from sections and

The rural site discussed earlier did not require the analysis of vulnerability of the aquifer to hydrocarbons infiltration from the upper layers because there are no active contaminated sources and the oil spill happened over 20 years ago. Therefore, we take another rural site as an example, where 8 months after a gasoline spill caused by pipeline leakage occurred, an

A total of 174 ERT points were distributed in six profiles (**Figure 9**). A Schlumberger array with AB/2 spacing from 2 to 20 m was used. **Figure 10** shows the geoelectric section obtained

was obtained.

areas from map), a total volume of hydrocarbon-contaminated soil of 4728 m3

**2.7. Determination of the aquifer vulnerability**

94 Geophysics

ERT survey was performed [5] (**Figure 9**).

**Figure 8.** Clay content map for target layer of the rural site.

**Figure 10.** Resistivity section of ERT profile 1.

the contaminated plume (contaminated and maximum zones of contamination) and location of sources of contamination, including information on the regional trend of groundwater flow and topographical characteristics of the site, allow the estimation of the migration pathways of contaminants in the subsurface. Two active sources of contamination, related to minor oil

**Figure 13.** Determination of pathways of contaminants flow and location of sources of contamination in an industrial

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97

leakage from pipelines, were located.

site.

**Figure 12.** Resistivity map for the aquifer.

**Figure 11.** (A) Clay content map and (B) hydraulic conductivity map for the aquitard.

Characterization of Hydrocarbon-Contaminated Sites Based on Geoelectrical Methods… http://dx.doi.org/10.5772/intechopen.73103 97

**Figure 12.** Resistivity map for the aquifer.

**Figure 10.** Resistivity section of ERT profile 1.

96 Geophysics

**Figure 11.** (A) Clay content map and (B) hydraulic conductivity map for the aquitard.

**Figure 13.** Determination of pathways of contaminants flow and location of sources of contamination in an industrial site.

the contaminated plume (contaminated and maximum zones of contamination) and location of sources of contamination, including information on the regional trend of groundwater flow and topographical characteristics of the site, allow the estimation of the migration pathways of contaminants in the subsurface. Two active sources of contamination, related to minor oil leakage from pipelines, were located.

## **3. Conclusions**

The OGEOMTE effectively integrates the application of different methods and techniques such as the EMP, ERT, WRM, MRSS, and petrophysical modeling.

[4] Shevnin V, Delgado-Rodríguez O, Fernández-Linares L, Zegarra-Martinez H, Mousatov A, Ryjov AA. Geoelectrical characterization of an oil-contaminated site in Tabasco,

Characterization of Hydrocarbon-Contaminated Sites Based on Geoelectrical Methods…

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99

[5] Delgado-Rodríguez O, Shevnin V, Ochoa-Valdés J, Ryjov AA. Geoelectrical characterization of a site with hydrocarbon contamination caused by pipeline leakage. Geofísica

[6] Delgado-Rodríguez O, Shevnin V, Ochoa-Valdés J, Ryjov A. Using electrical techniques for planning the remediation process in a hydrocarbon contaminated site. Revista

[7] Delgado-Rodríguez O, Flores-Hernández D, Amezcua-Allieri MA, Shevnin V, Rosas-Molina A, Marin-Córdova S. Joint interpretation of geoelectrical and volatile organic compounds data: A case study in a hydrocarbons contaminated urban site. Geofísica

[8] Archie GE. The electric resistivity logs as an aid in determining some reservoir charac-

[9] Waxman MH, Smits LJM. Electrical conductivities in oil-bearing shaly sands. Journal of

[10] Shevnin V, Mousatov A, Ryjov A, Delgado-Rodríguez O. Estimation of clay content in soil based on resistivity modeling and laboratory measurements. Geophysical Prospecting.

[11] Delgado-Rodríguez O, Ladrón de Guevara-Torres M, Shevnin V, Ryjov A. Estimation of soil petrophysical parameters based on electrical resistivity values obtained from lab

[12] Geonics Limited. Catalogue: Geophysical instrumentation for exploration & environment. 2012. 12 pp. Available from: http://www.geonics.com/pdfs/downloads/catalogue.

[13] Shevnin V, Delgado-Rodríguez O, Mousatov A, Ryjov AA. Estimation of hydraulic conductivity on clay content in soil determined from resistivity data. Geofísica Internacional.

[14] Loke MH, Barker RD. Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method. Geophysical Prospecting. 1996;**44**:131-152

[15] Shevnin V, Delgado-Rodríguez O, Mousatov A, Nakamura-Labastida E, Mejía-Aguilar A. Oil pollution detection using resistivity sounding. Geofísica Internacional. 2003;**42**(4):613-622

and in-field measurements. Geofísica Internacional. 2012;**51**(1):5-15

Mexico. Geofísica Internacional. 2005;**44**(3):251-263

Internacional de Contaminación Ambiental. 2006;**22**(4):157-163

Internacional. 2006;**45**(1):63-72

Internacional. 2014;**53**(2):183-198

2007;**55**:265-275

2006;**45**(3):195-207

pdf

teristics. SPE-AIME Transactions. 1942;**146**:54-62

the Society of Petroleum Engineering. 1968;**8**:107-122

These methods are efficient tools for the assessment of hydrocarbons of contaminated sites. Useful results have been obtained in sites with different geological-geographical environments, including rural, urban, and industrial sites.

The application of the OGEOMET reduces the number of drillings and soil samples for chemical analysis. Based on our experience, the application of the OGEOMET can reduce the number of drills from ten to five times and the number of soil samples from 20 to 10 times.

The advantages of the application of the OGEOMET are more evident as the size and complexity of the grade of the study site increase. The whole or partial application of the OGEOMET depends on the characteristics and requirements of the study site.

#### **Author details**

Omar Delgado-Rodríguez<sup>1</sup> \*, Vladimir Shevnin<sup>2</sup> , Héctor Peinado-Guevara3 and María Ladrón de Guevara-Torres4

\*Address all correspondence to: omar.delgado@ipicyt.edu.mx

1 Division of Applied Geosciences, Potosine Institute of Scientific and Technological Research, San Luis Potosí, SLP, Mexico

2 Department of Geophysics, Moscow State University Geological Faculty, Moscow, Russia

3 Faculty of Economics and Administrative Sciences, Autonomous University of Sinaloa, Guasave, Sinaloa, Mexico

4 National Polytechnical Institute, CIIDIR-Oaxaca, Oaxaca, Mexico

#### **References**


[4] Shevnin V, Delgado-Rodríguez O, Fernández-Linares L, Zegarra-Martinez H, Mousatov A, Ryjov AA. Geoelectrical characterization of an oil-contaminated site in Tabasco, Mexico. Geofísica Internacional. 2005;**44**(3):251-263

**3. Conclusions**

98 Geophysics

**Author details**

Omar Delgado-Rodríguez<sup>1</sup>

Guasave, Sinaloa, Mexico

**References**

María Ladrón de Guevara-Torres4

Research, San Luis Potosí, SLP, Mexico

The OGEOMTE effectively integrates the application of different methods and techniques

These methods are efficient tools for the assessment of hydrocarbons of contaminated sites. Useful results have been obtained in sites with different geological-geographical environ-

The application of the OGEOMET reduces the number of drillings and soil samples for chemical analysis. Based on our experience, the application of the OGEOMET can reduce the number of drills from ten to five times and the number of soil samples from 20 to 10 times.

The advantages of the application of the OGEOMET are more evident as the size and complexity of the grade of the study site increase. The whole or partial application of the OGEOMET

, Héctor Peinado-Guevara3

and

such as the EMP, ERT, WRM, MRSS, and petrophysical modeling.

depends on the characteristics and requirements of the study site.

\*Address all correspondence to: omar.delgado@ipicyt.edu.mx

4 National Polytechnical Institute, CIIDIR-Oaxaca, Oaxaca, Mexico

sandy sediments. Applied Geophysics. 2000;**44**:151-165

Research Letters. 2004;**31**(12):L12505:1-4

\*, Vladimir Shevnin<sup>2</sup>

1 Division of Applied Geosciences, Potosine Institute of Scientific and Technological

2 Department of Geophysics, Moscow State University Geological Faculty, Moscow, Russia

[1] Sauck WA. A model for the resistivity structure of LNAPL plumes and their environs in

[2] Abdel-Aal G, Atekwana E, Slater L, Atekwana EA. Effects of microbial processes on electrolytic and interfacial electrical properties of unconsolidated sediments. Geophysical

[3] Atekwana EA, Cassidy DP, Magnuson C, Endres AL, Werkema Jr DD, Sauck WA. Changes in geoelectrical properties accompanying microbial degradation of LNAPL. Proceedings of SAGEEP (Symposium on the Application of Geophysics to Environment and Engineering Problems) 2001. pp. OCS1-OCS10. https://doi.org/10.4133/1.2922929

3 Faculty of Economics and Administrative Sciences, Autonomous University of Sinaloa,

ments, including rural, urban, and industrial sites.


**Chapter 6**

**Provisional chapter**

**Characterization of Seismic Responses in Mexico City**

In this investigation, we present the Hilbert-Huang transform (HHT) as an alternative technique, which has advantage over other methods for extracting useful data of seismic ground response. The HHT, integrated with the empirical mode decomposition (EMD) and the Hilbert transformation (HT), enables engineers to analyze data from nonlinear and nonstationary processes. The product of the transformation is a detailed description of time-varying frequency diagrams. The recordings of accelerations of soft-soil deposits in Mexico City are studied under this technique. Results of the analysis of accelerograms indicate that this adaptive decomposition permits the extraction motion characteristics, which cannot be effectively unraveled by other conventional data processing techniques. The findings and conclusions derived from studies such as the one presented here con-

**Keywords:** Hilbert-Huang transform, empirical mode decomposition, time series analysis, ground motions, fundamental frequency, peak ground acceleration

The assessment of ground motions due to potential earthquakes is perhaps the most challenging problem in geotechnical earthquake engineering. Analysis of available behavioral data collected during seismic phenomena is the natural first step to approach this demand. During any seismic event, there are variations of the intensity of the ground motion with time (acceleration, velocity or displacement). After the arrival of the first seismic wave, the intensity accumulates quickly till a maximum value is sustained (for some seconds) and later diminishes gradually until it gets vanished. Additionally exists a variation of the frequency content with time with a tendency to move to lower frequencies as time progresses, what is known as "frequency dependent dispersive effect" [1].

**Characterization of Seismic Responses in Mexico City** 

DOI: 10.5772/intechopen.73034

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Using Hilbert-Huang Transform**

**Using Hilbert-Huang Transform**

Additional information is available at the end of the chapter

tribute to a better understanding of seismic response patterns.

Additional information is available at the end of the chapter

Silvia Raquel García Benítez and Leonardo Alcántara Nolasco

Silvia Raquel García Benítez and Leonardo Alcántara Nolasco

http://dx.doi.org/10.5772/intechopen.73034

**Abstract**

**1. Introduction**

**Provisional chapter**

#### **Characterization of Seismic Responses in Mexico City Using Hilbert-Huang Transform Using Hilbert-Huang Transform**

**Characterization of Seismic Responses in Mexico City** 

DOI: 10.5772/intechopen.73034

Silvia Raquel García Benítez and Leonardo Alcántara Nolasco Leonardo Alcántara Nolasco Additional information is available at the end of the chapter

Silvia Raquel García Benítez and

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73034

#### **Abstract**

In this investigation, we present the Hilbert-Huang transform (HHT) as an alternative technique, which has advantage over other methods for extracting useful data of seismic ground response. The HHT, integrated with the empirical mode decomposition (EMD) and the Hilbert transformation (HT), enables engineers to analyze data from nonlinear and nonstationary processes. The product of the transformation is a detailed description of time-varying frequency diagrams. The recordings of accelerations of soft-soil deposits in Mexico City are studied under this technique. Results of the analysis of accelerograms indicate that this adaptive decomposition permits the extraction motion characteristics, which cannot be effectively unraveled by other conventional data processing techniques. The findings and conclusions derived from studies such as the one presented here contribute to a better understanding of seismic response patterns.

**Keywords:** Hilbert-Huang transform, empirical mode decomposition, time series analysis, ground motions, fundamental frequency, peak ground acceleration

#### **1. Introduction**

The assessment of ground motions due to potential earthquakes is perhaps the most challenging problem in geotechnical earthquake engineering. Analysis of available behavioral data collected during seismic phenomena is the natural first step to approach this demand. During any seismic event, there are variations of the intensity of the ground motion with time (acceleration, velocity or displacement). After the arrival of the first seismic wave, the intensity accumulates quickly till a maximum value is sustained (for some seconds) and later diminishes gradually until it gets vanished. Additionally exists a variation of the frequency content with time with a tendency to move to lower frequencies as time progresses, what is known as "frequency dependent dispersive effect" [1].

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

Recognized that linear transformed domain and response spectral analysis be ill with shortcomings when applied to ground motions [2–5], this study proposes the use of the Hilbert-Huang transform (HHT) [6, 7] as an alternative for finding useful features into seismic recordings, granted its well-supported validity for dealing with nonstationary random processes [8–11]. The subject under analysis is a well-known soft-clay deposit in Mexico City, the SCT site [12–14]. The seismic response of this location is examined in order to achieve detailed information about behaviors that could not be discovered with restrictive tools. The well-defined descriptions of the time-frequency-amplitude content obtained using the HHT better describe the *nature* of the ground motions. The HHT applied to seismic phenomena results in helpful data for safer designs and improved practical earthquake engineering.

*A*(*t*) and *θ*(*t*) are the instantaneous amplitudes and phase functions, respectively [15]. The instantaneous frequency can then be written as the time derivative of the phase, as shown in

Characterization of Seismic Responses in Mexico City Using Hilbert-Huang Transform

Note that the analytic function *z*(*t*) is the mathematical approximation to the original signal *x*(*t*). Due to the fact that amplitude and frequency functions are expressed as functions of time, the Hilbert spectrum, which displays the relative amplitude or energy (square of amplitude) contributions for a certain frequency at a specific time, can be constructed as *H*(*ω*,*t*). **Figure 1** shows the complete block diagram of the HHT. Researchers seeking for deeper knowledge in

The EMD is the first stage in the HHT method. The algorithm starts to decompose almost any signal into a finite set of functions. The resulting functions are called intrinsic mode functions

*dt* (4)

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103

Eq. (4).

*<sup>ω</sup>* <sup>=</sup> *<sup>d</sup>*(*t*) \_\_\_\_

this subject should refer to the works of [7, 16, 17].

**Figure 1.** Hilbert-Huang transform operating diagram (modified from [18]).

**2.3. Empirical mode decomposition**

#### **2. Hilbert-Huang transform**

#### **2.1. Overview of Hilbert-Huang transform**

The HHT was proposed by Huang and coworkers [6] and consists of two parts: (1) empirical mode decomposition (EMD) and (2) Hilbert spectral analysis. Signals to be analyzed are decomposed into a finite number of intrinsic mode functions or IMFs in what is called the EMD process, the crucial part of the transformation. An IMF is described as a function satisfying the following conditions: (1) the number of extrema and zero-crossings must either equal or differ at most by one; (2) at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero [6]. An IMF permits directly Hilbert transforms.

#### **2.2. Hilbert spectral analysis**

The Hilbert transform allows the computation of instantaneous frequencies and amplitudes and describes the signal more locally. Eq. (1) displays the Hilbert transform ŷ which can be written for any function *x*(*t*) of Lp class (the Lp *spaces* are function spaces described by a natural generalization of the p-norm for finite-dimensional vector spaces) [5]. The PV denotes Cauchy's principle value integral.

$$H[\mathbf{x}(t)] \equiv \hat{y}(t) = \frac{1}{\pi} PV \int\_{-\omega}^{\omega} \frac{\mathbf{x}(\tau)}{t - \tau} d\tau \tag{1}$$

Huang et al. [6] and Attoh-Okine et al. [7] determined that an analytic function can be formed with the Hilbert transform pair as shown in Eq. (2).

$$z(t) = x(t) + \dot{\mathfrak{H}}(t) \tag{2}$$

where

$$A(t) = \left\{ \mathbf{x}^2 + \hat{y}^2 \right\}^{12}, \quad \theta(t) = \tan^{-1} \left( \frac{\hat{y}}{\overline{x}} \right) \quad \text{and} \quad i = \sqrt{-1} \tag{3}$$

*A*(*t*) and *θ*(*t*) are the instantaneous amplitudes and phase functions, respectively [15]. The instantaneous frequency can then be written as the time derivative of the phase, as shown in Eq. (4).

$$
\omega = \frac{d\theta(t)}{dt} \tag{4}
$$

Note that the analytic function *z*(*t*) is the mathematical approximation to the original signal *x*(*t*). Due to the fact that amplitude and frequency functions are expressed as functions of time, the Hilbert spectrum, which displays the relative amplitude or energy (square of amplitude) contributions for a certain frequency at a specific time, can be constructed as *H*(*ω*,*t*). **Figure 1** shows the complete block diagram of the HHT. Researchers seeking for deeper knowledge in this subject should refer to the works of [7, 16, 17].

#### **2.3. Empirical mode decomposition**

Recognized that linear transformed domain and response spectral analysis be ill with shortcomings when applied to ground motions [2–5], this study proposes the use of the Hilbert-Huang transform (HHT) [6, 7] as an alternative for finding useful features into seismic recordings, granted its well-supported validity for dealing with nonstationary random processes [8–11]. The subject under analysis is a well-known soft-clay deposit in Mexico City, the SCT site [12–14]. The seismic response of this location is examined in order to achieve detailed information about behaviors that could not be discovered with restrictive tools. The well-defined descriptions of the time-frequency-amplitude content obtained using the HHT better describe the *nature* of the ground motions. The HHT applied to seismic phenomena results in helpful data for safer designs and improved practical earthquake

The HHT was proposed by Huang and coworkers [6] and consists of two parts: (1) empirical mode decomposition (EMD) and (2) Hilbert spectral analysis. Signals to be analyzed are decomposed into a finite number of intrinsic mode functions or IMFs in what is called the EMD process, the crucial part of the transformation. An IMF is described as a function satisfying the following conditions: (1) the number of extrema and zero-crossings must either equal or differ at most by one; (2) at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero [6]. An IMF permits directly

The Hilbert transform allows the computation of instantaneous frequencies and amplitudes and describes the signal more locally. Eq. (1) displays the Hilbert transform ŷ which can be written for any function *x*(*t*) of Lp class (the Lp *spaces* are function spaces described by a natural generalization of the p-norm for finite-dimensional vector spaces) [5]. The PV denotes

> (*t*) = \_\_1 *<sup>π</sup> PV* ∫

Huang et al. [6] and Attoh-Okine et al. [7] determined that an analytic function can be formed

, *θ*(*t*) = tan<sup>−</sup><sup>1</sup>

−∞ <sup>∞</sup> *x*(*τ*) \_\_\_\_

( *y*̂ \_\_

*<sup>x</sup>*) and *i* = √

*<sup>t</sup>* <sup>−</sup> *<sup>τ</sup> d* (1)

(*t*) = *A*(*t*) e*<sup>i</sup>*(*t*) (2)

\_\_\_

−1 (3)

engineering.

102 Geophysics

Hilbert transforms.

where

**2.2. Hilbert spectral analysis**

Cauchy's principle value integral.

*A*(*t*) = (*x*<sup>2</sup> + *y*̂

*H*[*x*(*t*)] ≡ *y*̂

with the Hilbert transform pair as shown in Eq. (2).

2 )1/2

*z*(*t*) = *x*(*t*) + *iy*̂

**2. Hilbert-Huang transform**

**2.1. Overview of Hilbert-Huang transform**

The EMD is the first stage in the HHT method. The algorithm starts to decompose almost any signal into a finite set of functions. The resulting functions are called intrinsic mode functions

**Figure 1.** Hilbert-Huang transform operating diagram (modified from [18]).

(IMFs) whose Hilbert transformation gives physical instantaneous frequency values. The algorithm employs an iterative sifting process which successively subtracts the local mean from a signal, as follows:


These six steps are repeated until the produced signal converges to the definition of an IMF, which is a signal with a zero mean and whose number of extrema and zero-crossings differs by at most one, considered as monocomponent functions with no riding waves [5]. Then, the IMF is subtracted from the original signal, and the sifting process is repeated on the remainder. This is iterated until the final residue is a monotonic function. The ultimate extracted IMF is the lowest frequency component of the signal, better known as the trend. The characterization of an IMF was created to guarantee that the signal gives physical frequency values when using the Hilbert transform.

Once a signal has been fully decomposed, the signal *D*(*t*) can be written as the finite sum of the IMFs and a final residue, as shown in Eq. (5).

$$D(t) = R\_u(t) + \sum\_{j=1}^{n} IMF\_j(t) \tag{5}$$

where earthquake-related damages have concentrated recurrently in the past. The data set selected for this investigation consisted of a set of 22 acceleration time series recorded during earthquakes that happened from 1985 to 2011. The characteristics of these events are enlisted in **Table 1**. The signals are of 150 s length (on average) at a measuring rate of 0.01 s. Magnitudes go from M3 to M8.1, and epicenters are from the Pacific subduction zone (in front of the Guerrero and Michoacán coasts) and normal intraplate earthquakes (located in central

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105

The formation is a sequence of soft clay strata interspersed with layers of harder clayey silts with sands (**Figure 2a**). The evolution of pore pressures, measured over a 12-year period (1990–2002) [19], illustrates a gradual depletion of pressures from 0.014 to 0.002 kPa/year at different depths. The water content, volumetric weight and undrained strength profiles at two different dates (1952 and 1986) are shown in **Figure 2b**. These profiles show that (1) thicknesses of the relevant clay strata have decreased as a consequence of regional subsidence; (2) water content reductions are especially significant below 15 m approximately which is consistent with the fact that pumping-induced consolidation propagates upwards from the base of the clayey soils to the surface; and (3) changes in soil density (volumetric weight) confirm that

Concerning the dynamic properties, the evolution on shear wave propagation velocities is presented through the field evidence given in **Figure 2d** (suspension logging tests performed

soil strata have densified as the clay masses consolidate.

**Table 1.** Characteristics of seismic events.

Mexico).

Using Eqs. (5) and (7), the analytic function can be formed as shown in Eq. (2).

$$D(t) - \mathbb{R}\_{\boldsymbol{\eta}}(t) = \operatorname{Re} \left[ \sum\_{j=1}^{n} A\_j(t) \, e^{(\boldsymbol{\mu})\boldsymbol{\eta} t} \right] \tag{6}$$

Also, for reference, Eq. (6) shows the Fourier decomposition of a signal, *x*(*t*).

$$D(t) = \operatorname{Re} \left[ \sum\_{i=1}^{n} A\_{\rangle} e^{i\omega\_{i}t} \right] \tag{7}$$

The EMD decomposition can be considered a generalized Fourier decomposition, because it describes a signal in terms of amplitude and basis functions whose amplitudes and frequencies may fluctuate with time [5, 16]. Detailed examples of EMD can be found in [16].

#### **3. Hilbert-Huang transformation of seismic response**

#### **3.1. Geotechnical database**

To illustrate the HHT for studying seismic response of clayey soils, data recorded in the SCT site, a location in Mexico City, are analyzed. SCT is located within a densely urbanized zone, where earthquake-related damages have concentrated recurrently in the past. The data set selected for this investigation consisted of a set of 22 acceleration time series recorded during earthquakes that happened from 1985 to 2011. The characteristics of these events are enlisted in **Table 1**. The signals are of 150 s length (on average) at a measuring rate of 0.01 s. Magnitudes go from M3 to M8.1, and epicenters are from the Pacific subduction zone (in front of the Guerrero and Michoacán coasts) and normal intraplate earthquakes (located in central Mexico).

The formation is a sequence of soft clay strata interspersed with layers of harder clayey silts with sands (**Figure 2a**). The evolution of pore pressures, measured over a 12-year period (1990–2002) [19], illustrates a gradual depletion of pressures from 0.014 to 0.002 kPa/year at different depths. The water content, volumetric weight and undrained strength profiles at two different dates (1952 and 1986) are shown in **Figure 2b**. These profiles show that (1) thicknesses of the relevant clay strata have decreased as a consequence of regional subsidence; (2) water content reductions are especially significant below 15 m approximately which is consistent with the fact that pumping-induced consolidation propagates upwards from the base of the clayey soils to the surface; and (3) changes in soil density (volumetric weight) confirm that soil strata have densified as the clay masses consolidate.

Concerning the dynamic properties, the evolution on shear wave propagation velocities is presented through the field evidence given in **Figure 2d** (suspension logging tests performed


**Table 1.** Characteristics of seismic events.

(IMFs) whose Hilbert transformation gives physical instantaneous frequency values. The algorithm employs an iterative sifting process which successively subtracts the local mean

**2.** Link the maxima with an interpolation function, producing an upper envelope of the

**3.** Link the minima with an interpolation function, producing a lower envelope of the signal.

These six steps are repeated until the produced signal converges to the definition of an IMF, which is a signal with a zero mean and whose number of extrema and zero-crossings differs by at most one, considered as monocomponent functions with no riding waves [5]. Then, the IMF is subtracted from the original signal, and the sifting process is repeated on the remainder. This is iterated until the final residue is a monotonic function. The ultimate extracted IMF is the lowest frequency component of the signal, better known as the trend. The characterization of an IMF was created to guarantee that the signal gives physical frequency values when using the Hilbert transform.

Once a signal has been fully decomposed, the signal *D*(*t*) can be written as the finite sum of

(*t*) + ∑ *j*=1 *n IMFj*

> ∑ *j*=1 *n Aj* (*t*)*ei*∫*ωj* (*t*)*dt*

∑ *j*=1 *n Aj ei<sup>ω</sup><sup>j</sup> t*

The EMD decomposition can be considered a generalized Fourier decomposition, because it describes a signal in terms of amplitude and basis functions whose amplitudes and frequen-

To illustrate the HHT for studying seismic response of clayey soils, data recorded in the SCT site, a location in Mexico City, are analyzed. SCT is located within a densely urbanized zone,

cies may fluctuate with time [5, 16]. Detailed examples of EMD can be found in [16].

Using Eqs. (5) and (7), the analytic function can be formed as shown in Eq. (2).

Also, for reference, Eq. (6) shows the Fourier decomposition of a signal, *x*(*t*).

**3. Hilbert-Huang transformation of seismic response**

(*t*) <sup>=</sup> Re[

(*t*) (5)

] (7)

] (6)

**4.** Calculate the local mean as half the difference between the upper and lower envelopes.

**1.** Settle on the local extrema (maxima, minima) of the signal.

from a signal, as follows:

**6.** Iterate on the residual.

**5.** Locate the local mean from the signal.

the IMFs and a final residue, as shown in Eq. (5).

*D*(*t*) = *Rn*

*<sup>D</sup>*(*t*) <sup>=</sup> Re[

*D*(*t*) − *Rn*

**3.1. Geotechnical database**

signal.

104 Geophysics

**Figure 2.** Stratigraphic column in SCT site, the evolution of water content W, volumetric weight ɣ, undrained strength qc and shear wave velocity Vs profiles. (a) Description (b) W, % (c) ɣ, kN/m3 (d) qc , kPa (e) Vs, (m/s).

in 1986 and 2001 [20]). The expected stiffening of the clay strata over the 15 years that lapsed between dates is more evident for greater depths.

#### **3.2. Decomposition of accelerograms**

According to the procedure described above (EMD algorithm), the selected accelerograms were decomposed into their IMF components. The results are like those shown, by way of example, in **Figure 3** (IMFs obtained from the September 30, 1999 event). For this accelerogram, the algorithm yielded nine components and a residue.

The best tactics to establish *f*

frequency will be called *f*

response.

*n*

puted values occur in the neighborhood of *f*

**Figure 3.** IMFs obtained from September 30, 1999, event.

are to compute it using an abstract method and then compare

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*n*

*IMF* corresponding to each mode

= 0.5 Hz. Using

this value with that shown by recorded data. Theoretically, fundamental frequency for SCT

microtremors [23, 24] and multi-degree-of-freedom system (MDOF) methods [25], the com-

Attempting to relate the intrinsic oscillations with this important deposit parameter, the predominant frequency of each IMF in data set is analyzed. What follows this predominant

are depicted. The first (IMF1) and last modes (IMF6 to IMF10) are not in the graph. The IMF1s have flat spectra where it is not possible to determine a predominant frequency. The last modes (from IMF6 to IMF10) have very short box sections with exceptionally low frequency values (near to zero). These modes, in terms of their fundamental frequency, are considered irrelevant, that is, they do not have effect on the analysis of the measured

~0.47 Hz.

*n*

*IMF*. In **Figure 4**, boxplots of the *f*

(clay deposit ≈ 40 m thick) calculated using average of shear wave velocity is *f*

To discriminate between the IMFs, they will be studied under two geotechnical-seismological parameters that are crucial for anti-seismic designs: fundamental frequency *f n* and peak ground acceleration (PGA).

In Mexico City, several past earthquakes have resulted in devastating failures of built environment, which in most of the cases were attributed to strong amplification of seismic waves. For analyzing the phenomena of resonance, it is necessary to determine *f n* of a soil deposit. *f n* is dependent on its thickness, low strain stiffness and density. Assessment of these characteristics has been the subject of several research studies, yet inconsistencies and uncertainties associated with their estimation have not been resolved conclusively [21, 22]. Hence, many researchers tend to corroborate their calculations by using data recorded on surface during earthquake events.

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**Figure 3.** IMFs obtained from September 30, 1999, event.

in 1986 and 2001 [20]). The expected stiffening of the clay strata over the 15 years that lapsed

**Figure 2.** Stratigraphic column in SCT site, the evolution of water content W, volumetric weight ɣ, undrained strength qc

(d) qc

, kPa (e) Vs, (m/s).

According to the procedure described above (EMD algorithm), the selected accelerograms were decomposed into their IMF components. The results are like those shown, by way of example, in **Figure 3** (IMFs obtained from the September 30, 1999 event). For this accelero-

To discriminate between the IMFs, they will be studied under two geotechnical-seismolog-

In Mexico City, several past earthquakes have resulted in devastating failures of built environment, which in most of the cases were attributed to strong amplification of seismic waves.

 is dependent on its thickness, low strain stiffness and density. Assessment of these characteristics has been the subject of several research studies, yet inconsistencies and uncertainties associated with their estimation have not been resolved conclusively [21, 22]. Hence, many researchers tend to corroborate their calculations by using data recorded on surface during

*n*

of a soil deposit.

*n*

and peak

ical parameters that are crucial for anti-seismic designs: fundamental frequency *f*

For analyzing the phenomena of resonance, it is necessary to determine *f*

between dates is more evident for greater depths.

and shear wave velocity Vs profiles. (a) Description (b) W, % (c) ɣ, kN/m3

gram, the algorithm yielded nine components and a residue.

**3.2. Decomposition of accelerograms**

ground acceleration (PGA).

earthquake events.

*f n*

106 Geophysics

The best tactics to establish *f n* are to compute it using an abstract method and then compare this value with that shown by recorded data. Theoretically, fundamental frequency for SCT (clay deposit ≈ 40 m thick) calculated using average of shear wave velocity is *f n* = 0.5 Hz. Using microtremors [23, 24] and multi-degree-of-freedom system (MDOF) methods [25], the computed values occur in the neighborhood of *f n* ~0.47 Hz.

Attempting to relate the intrinsic oscillations with this important deposit parameter, the predominant frequency of each IMF in data set is analyzed. What follows this predominant frequency will be called *f IMF*. In **Figure 4**, boxplots of the *f IMF* corresponding to each mode are depicted. The first (IMF1) and last modes (IMF6 to IMF10) are not in the graph. The IMF1s have flat spectra where it is not possible to determine a predominant frequency. The last modes (from IMF6 to IMF10) have very short box sections with exceptionally low frequency values (near to zero). These modes, in terms of their fundamental frequency, are considered irrelevant, that is, they do not have effect on the analysis of the measured response.

**Figure 4.** Boxplot of IMF, excluding the corrupting and irrelevant modes.

Despite the range of magnitudes, epicentral depths, generating mechanisms, directivity and dates, the *f IMF* of IMF5 is closely related to the natural frequency of SCT site. The *f IMF* of IMF5 practically does not change, and this is noticeable in the condensed box. The dispersion is minimal, and it should be noted that this graph includes minor events (M < 4) and the extreme earthquake of 1985 (M8.1). On the other hand, the median of the *f IMF* of IMF3 is comparable to the second vibrate mode *f* 2 (using the MDOF method [23], *f* 2 is ~1.4 Hz). Its boxplot is taller than the IMF5 and has evident dispersion in lower and upper whiskers.

1/*f n*

by *f*

of 1/*f n*

rement of the 1/*f*

**Figure 5.** Evolution of *f*

possible to verify using the *f*

of the earthquake itself [30].

*n*

*n*

*n*

devastating 1985 Michoacán earthquake (M8.1).

the registered motion of the soil deposit.

= 2.0. This finding reinforces the hypothesis about stiffening of the clayey strata that are not

, continuous line results from [26]. Dashed line represents the behavioral trend of *f*

*IMF*-IMF5 could drive to two stages of the evolution: the first one with a more dramatic dec-

frequencies change more slowly to the present day. The model's tendency that drops the values

PGA, as the maximum ground acceleration that occurred during earthquake shaking at a location [28], is used as an intensity measurement, and the design-basis-earthquake ground motion is often defined in terms of PGA [29]. Even damage to buildings and infrastructure is more closely related to ground motion, of which PGA is a measure, rather than the magnitude

The boxplots of the maximum instant amplitudes, associated with each IMF, are shown in **Figure 6a**. The most extreme points (marked with the numbers 2 and 15) are two of the most intense seismic events registered in Mexico City (M > 7.0), being the extreme value the

Isolating the M8.1 event to properly observe the characteristics of each box (**Figure 6b**), it is evident that last modes have very small boxes. Considering this minor amplitudes and their fundamental frequencies (very close to zero), we conclude that they are irrelevant modes. Examining the relatively small box of the IMF1 maximum amplitudes, it was found that the extraordinary earthquake of 1985 is found inside the rectangle. It seems that this first oscillation does not respond to the input energy as the other modes do, so it is inferred that a mechanism, other than the ground motion itself, is the one that controls this oscillation. Based on this observation and their flat Fourier spectra, the IMF1 is labeled as a mode that "corrupts"

less dramatically over time is clearly illustrated with the aligned values of *f*

from registered data. Actually, a deep analysis of the path shown

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*IMF*-IMF3.

*IMF*-IMF5.

since 1985 (or before) and toward the year 2000, and a second one where the

Mexico City's seismic response has changed over the years. The numerous efforts made to analyze this phenomenon showed that the response may be due to land subsidence (consequence of water extraction) [19, 20]. Since the pumping and the capacity of the clay strata to expel water are quite different at each geotechnical zone of the city, the effect on seismic response is a complex problem.

To guarantee safe structural designs, the most significant aspect to be demonstrated is the effect of the subsidence on the spectral ordinates (with respect to the current values specified for design purposes) and the relative values of the structures and site periods. With specific geotechnical and geological information, Avilés et al. [26] presented an incremental procedure to evaluate the progressive evolution of *f n* over time, in order to evaluate the effects of these changes on the earthquake ground response. The adjustments expected in selected values of *f n* , from 1980 to 2020, can be appreciated in **Figure 5**. What can be anticipated, as the evolution of this phenomenon, is that after the initial reference year the parameter decreases monotonically as the times span increases [27].

Observe what occurred when the values of *f n* , from original data, are superimposed in the graph. The frequencies obtained from the recorded accelerograms hardly follow the trend set by [26]. Most events do not fit the specific curve for SCT (1/*f n* = 2), and the expected drop patterns of *f n* cannot be verified. However, the behavior shown by the IMF3 and IMF5 fits very well to the decrement curves obtained with the iterative model. The *f IMF* of IMF5 fits the theoretical curve of

**Figure 5.** Evolution of *f n* , continuous line results from [26]. Dashed line represents the behavioral trend of *f IMF*-IMF5.

Despite the range of magnitudes, epicentral depths, generating mechanisms, directivity and

*IMF* of IMF5 is closely related to the natural frequency of SCT site. The *f*

practically does not change, and this is noticeable in the condensed box. The dispersion is minimal, and it should be noted that this graph includes minor events (M < 4) and the extreme

(using the MDOF method [23], *f*

Mexico City's seismic response has changed over the years. The numerous efforts made to analyze this phenomenon showed that the response may be due to land subsidence (consequence of water extraction) [19, 20]. Since the pumping and the capacity of the clay strata to expel water are quite different at each geotechnical zone of the city, the effect on seismic response is a complex problem. To guarantee safe structural designs, the most significant aspect to be demonstrated is the effect of the subsidence on the spectral ordinates (with respect to the current values specified for design purposes) and the relative values of the structures and site periods. With specific geotechnical and geological information, Avilés et al. [26] presented an incremental proce-

*n*

, from 1980 to 2020, can be appreciated in **Figure 5**. What can be anticipated, as the

*n*

of these changes on the earthquake ground response. The adjustments expected in selected

evolution of this phenomenon, is that after the initial reference year the parameter decreases

The frequencies obtained from the recorded accelerograms hardly follow the trend set by [26].

cannot be verified. However, the behavior shown by the IMF3 and IMF5 fits very well to the

*n*

2

earthquake of 1985 (M8.1). On the other hand, the median of the *f*

than the IMF5 and has evident dispersion in lower and upper whiskers.

2

**Figure 4.** Boxplot of IMF, excluding the corrupting and irrelevant modes.

dure to evaluate the progressive evolution of *f*

monotonically as the times span increases [27].

Most events do not fit the specific curve for SCT (1/*f*

decrement curves obtained with the iterative model. The *f*

Observe what occurred when the values of *f*

*IMF* of IMF5

*n*

*IMF* of IMF3 is comparable

is ~1.4 Hz). Its boxplot is taller

over time, in order to evaluate the effects

, from original data, are superimposed in the graph.

= 2), and the expected drop patterns of *f*

*IMF* of IMF5 fits the theoretical curve of

dates, the *f*

108 Geophysics

values of *f*

*n*

to the second vibrate mode *f*

1/*f n* = 2.0. This finding reinforces the hypothesis about stiffening of the clayey strata that are not possible to verify using the *f n* from registered data. Actually, a deep analysis of the path shown by *f IMF*-IMF5 could drive to two stages of the evolution: the first one with a more dramatic decrement of the 1/*f n* since 1985 (or before) and toward the year 2000, and a second one where the frequencies change more slowly to the present day. The model's tendency that drops the values of 1/*f n* less dramatically over time is clearly illustrated with the aligned values of *f IMF*-IMF3.

PGA, as the maximum ground acceleration that occurred during earthquake shaking at a location [28], is used as an intensity measurement, and the design-basis-earthquake ground motion is often defined in terms of PGA [29]. Even damage to buildings and infrastructure is more closely related to ground motion, of which PGA is a measure, rather than the magnitude of the earthquake itself [30].

The boxplots of the maximum instant amplitudes, associated with each IMF, are shown in **Figure 6a**. The most extreme points (marked with the numbers 2 and 15) are two of the most intense seismic events registered in Mexico City (M > 7.0), being the extreme value the devastating 1985 Michoacán earthquake (M8.1).

Isolating the M8.1 event to properly observe the characteristics of each box (**Figure 6b**), it is evident that last modes have very small boxes. Considering this minor amplitudes and their fundamental frequencies (very close to zero), we conclude that they are irrelevant modes. Examining the relatively small box of the IMF1 maximum amplitudes, it was found that the extraordinary earthquake of 1985 is found inside the rectangle. It seems that this first oscillation does not respond to the input energy as the other modes do, so it is inferred that a mechanism, other than the ground motion itself, is the one that controls this oscillation. Based on this observation and their flat Fourier spectra, the IMF1 is labeled as a mode that "corrupts" the registered motion of the soil deposit.

**Figure 6.** Boxplot of MIAs according to the IMF, (a) the whole set, including 19/09/85 Michoacán earthquake and (b) events with M ≤ 7.5.

It can be seen that the energy is concentrated mainly on fourth and fifth oscillations. These modes most react to the extreme earthquake of 1985. The dispersion is minimal, and the atypical event (M8.1) is certainly at a distance, which does not happen with the other oscillations. It appears that the recognized amplification potential of this soft-clay site [20] is mainly evident for the central modes.

The "corrupted" (IMF1) and the irrelevant modes (IMF6 to IMF10) were removed from the registered accelerograms. The response spectra of accelerations from both sets of signals, the original and the "cleaned," are calculated. Some selected responses are depicted in **Figure 7**. These are examples of responses that can be reproduced with the IMF3 or IMF5 with adequate approximation. The energy-frequency content of the original response spectra is represented

**Figure 7.** Examples of spectra evaluated using original signals and selected IMFs, (a) events better represented with

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IMF5 and (b) events better represented with IMF3.

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**Figure 7.** Examples of spectra evaluated using original signals and selected IMFs, (a) events better represented with IMF5 and (b) events better represented with IMF3.

It can be seen that the energy is concentrated mainly on fourth and fifth oscillations. These modes most react to the extreme earthquake of 1985. The dispersion is minimal, and the atypical event (M8.1) is certainly at a distance, which does not happen with the other oscillations. It appears that the recognized amplification potential of this soft-clay site [20] is mainly evident

**Figure 6.** Boxplot of MIAs according to the IMF, (a) the whole set, including 19/09/85 Michoacán earthquake and (b) events

The "corrupted" (IMF1) and the irrelevant modes (IMF6 to IMF10) were removed from the registered accelerograms. The response spectra of accelerations from both sets of signals, the original and the "cleaned," are calculated. Some selected responses are depicted in **Figure 7**. These are examples of responses that can be reproduced with the IMF3 or IMF5 with adequate approximation. The energy-frequency content of the original response spectra is represented

for the central modes.

with M ≤ 7.5.

110 Geophysics

with one intrinsic mode, the one with a MIA near to the PGA registered. It has been found that the most intense events from the Pacific subduction zone tend to be related mainly with the *fifth* mode, while for minor and intraplate events, the ground motion can be represented using only the *third* mode. Deep examinations are necessary to clarify this finding, but the advantages of EMD when analyzing complex responses are clear.

It should be emphasized that the "cleaned" signals represent simpler and easier time series, with desirable density for minimizing computational costs (when running complex groundmotion models).

#### **3.3. Hilbert spectra of ground motions**

The nonrecommended practice of using Fourier for studying nonstationary-nonlinear data is revealed as a limitative tool for these kinds of analyses since it cannot show the detailed information about the peculiarities of the energy-frequency distribution, aspect that is utilized, for example, to conclude about site effects.

From the Hilbert spectra, events in the database have direct important characteristics such as the arrival time and the duration of intense phase of the earthquakes can be detected. In addition to the well-defined zone of maximum accelerations, the huge variations of the response frequencies between the beginning (the maximum amplitude cycles) and the end of the event can be clearly detected and quantified

**Figure 8.** The HS for selected intraplate and interplate events. Significant frequency deviation during the strong motion

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**Figure 9.** The historical 1985 earthquake (M8.1) and the responses registered during September 8, 2017 (M8.2) and

showed that the energy is concentrated below 1 Hz.

devastating September 19, 2017 (M7.1).

(see, for example, the HS events in **Figure 8**). Although most of the events found in the database have disseminated energy in the high-frequency range, this is minor compared to the highest levels recorded in the entire time series. The persistent energy resides along horizontal packets below 1 Hz. It is easy to detect the peak accelerations of each response (in addition to the concentric energy surrounding these maxima), the fundamental frequencies, and the duration of the arrival packets. The "corrupted" oscillations can be distinguished, with low frequencies and low constant amplitudes that are maintained from the beginning to the end of the record.

The difficulty of transforming signals from near-field motions (time series of short duration) to Fourier spectra is not a problem using HS (see, for example, the HS of the June 15, 1999 event). The frequency distribution clearly shows the energy content along the frequency axis (from 0.4 to 0.8 Hz), and it is quite easy to determine the resonant frequency of the site (at ≈0.55 Hz) and the associated energy density.

In **Figure 9**, three of the most intense earthquakes registered in Mexico City are shown. They are the well-known 1985 and the most recent devastating events, September 8, 2017, and September 19, 2017. While the responses to minor earthquakes have a much wider energy distribution, the content for these events is quite different. The spikes are more evident, and they can be located around the PGA. Although these Hilbert spectra have the decreasing trend in energy density as a function of frequency, as the other events, these spectra show a visible lack of energy in the low-frequency range (less than 0.2 Hz).

Consider the HS of September 19, 2017 earthquake, the one that hit the city and collapsed a large number of buildings, houses and underground facilities. It is well defined at the lowfrequency range (from 0.4 to below 1 Hz) where maximum amplitudes were present, a serious situation for the high-rise structures. The peak of energy, located at a very narrow frequency Characterization of Seismic Responses in Mexico City Using Hilbert-Huang Transform http://dx.doi.org/10.5772/intechopen.73034 113

with one intrinsic mode, the one with a MIA near to the PGA registered. It has been found that the most intense events from the Pacific subduction zone tend to be related mainly with the *fifth* mode, while for minor and intraplate events, the ground motion can be represented using only the *third* mode. Deep examinations are necessary to clarify this finding, but the

It should be emphasized that the "cleaned" signals represent simpler and easier time series, with desirable density for minimizing computational costs (when running complex ground-

The nonrecommended practice of using Fourier for studying nonstationary-nonlinear data is revealed as a limitative tool for these kinds of analyses since it cannot show the detailed information about the peculiarities of the energy-frequency distribution, aspect that is utilized, for

From the Hilbert spectra, events in the database have direct important characteristics such as the arrival time and the duration of intense phase of the earthquakes can be detected. In addition to the well-defined zone of maximum accelerations, the huge variations of the response frequencies between the beginning (the maximum amplitude cycles) and the end of the event

(see, for example, the HS events in **Figure 8**). Although most of the events found in the database have disseminated energy in the high-frequency range, this is minor compared to the highest levels recorded in the entire time series. The persistent energy resides along horizontal packets below 1 Hz. It is easy to detect the peak accelerations of each response (in addition to the concentric energy surrounding these maxima), the fundamental frequencies, and the duration of the arrival packets. The "corrupted" oscillations can be distinguished, with low frequencies and low constant amplitudes that are maintained from the beginning to the end of the record. The difficulty of transforming signals from near-field motions (time series of short duration) to Fourier spectra is not a problem using HS (see, for example, the HS of the June 15, 1999 event). The frequency distribution clearly shows the energy content along the frequency axis (from 0.4 to 0.8 Hz), and it is quite easy to determine the resonant frequency of the site (at ≈0.55 Hz)

In **Figure 9**, three of the most intense earthquakes registered in Mexico City are shown. They are the well-known 1985 and the most recent devastating events, September 8, 2017, and September 19, 2017. While the responses to minor earthquakes have a much wider energy distribution, the content for these events is quite different. The spikes are more evident, and they can be located around the PGA. Although these Hilbert spectra have the decreasing trend in energy density as a function of frequency, as the other events, these spectra show a

Consider the HS of September 19, 2017 earthquake, the one that hit the city and collapsed a large number of buildings, houses and underground facilities. It is well defined at the lowfrequency range (from 0.4 to below 1 Hz) where maximum amplitudes were present, a serious situation for the high-rise structures. The peak of energy, located at a very narrow frequency

visible lack of energy in the low-frequency range (less than 0.2 Hz).

advantages of EMD when analyzing complex responses are clear.

motion models).

112 Geophysics

**3.3. Hilbert spectra of ground motions**

example, to conclude about site effects.

can be clearly detected and quantified

and the associated energy density.

**Figure 8.** The HS for selected intraplate and interplate events. Significant frequency deviation during the strong motion showed that the energy is concentrated below 1 Hz.

**Figure 9.** The historical 1985 earthquake (M8.1) and the responses registered during September 8, 2017 (M8.2) and devastating September 19, 2017 (M7.1).

range (0.5–0.8 Hz), could be responsible for the huge number of damaged buildings in a defined geotechnical area of the city. Similarly, to the spatial variation of the destruction at Mexico City during the 1985 earthquake, for this event some areas have been recognized, with special stratigraphies, which presented amplification potentials never seen before. As many investigators have concluded, any linear model could not predict this kind of ground responses.

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2003;**32**(10):1533-1554

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de Desastres Naturales, Accidentes e Infraestructura Civil. 2006;**6**(2):111

#### **4. Conclusions**

The decomposed components, namely IMFs, contain observable, physical information about the ground motion. Owing to the fact that the intrinsic oscillations can be related to the phenomena without restrictive hypothesis, the conclusions obtained from the behavior of each mode are more *natural* than those achieved from theoretical positions faraway the system, which generates the signal.

Despite the fact that the soil properties in the SCT site have changed because of regional subsidence, the recorded accelerations do not seem to exhibit the expected stiffening effect. What is shown in this research is that the time series, which serve as a basis for showing the soils hardening, are *corrupted* by external oscillations that mask actual responses. It was recognized that IMF5 and IMF3 actually showed the decrease in rate of the frequencies postulated in theoretical models. By detecting the oscillations that do mainly correspond to the *real* ground motion, the EMD is presented as an alternative tool for finding directly the frequencies related with the highest energy concentrations.

The usefulness of these finding points to the need for further investigation in evaluating the competency of tools for analyzing the recordings and for obtaining conclusions, since they are the basis of the process of calibration of all the theoretical, geotechnical and seismological models.

The Hilbert spectral transformation permits the recognition of oscillation modes that would have been masked by Fourier spectral analysis.

#### **Acknowledgements**

The accelerogram records for this research were provided by the Unidad de Instrumentación Sísmica, Instituto de Ingeniería, UNAM.

#### **Author details**

Silvia Raquel García Benítez\* and Leonardo Alcántara Nolasco

\*Address all correspondence to: sgab@pumas.iingen.unam.mx

Researcher, Geotechnical Department, Instituto de Ingeniería, Universidad Nacional Autónoma de México, México City, México

### **References**

range (0.5–0.8 Hz), could be responsible for the huge number of damaged buildings in a defined geotechnical area of the city. Similarly, to the spatial variation of the destruction at Mexico City during the 1985 earthquake, for this event some areas have been recognized, with special stratigraphies, which presented amplification potentials never seen before. As many investigators

The decomposed components, namely IMFs, contain observable, physical information about the ground motion. Owing to the fact that the intrinsic oscillations can be related to the phenomena without restrictive hypothesis, the conclusions obtained from the behavior of each mode are more *natural* than those achieved from theoretical positions faraway the system,

Despite the fact that the soil properties in the SCT site have changed because of regional subsidence, the recorded accelerations do not seem to exhibit the expected stiffening effect. What is shown in this research is that the time series, which serve as a basis for showing the soils hardening, are *corrupted* by external oscillations that mask actual responses. It was recognized that IMF5 and IMF3 actually showed the decrease in rate of the frequencies postulated in theoretical models. By detecting the oscillations that do mainly correspond to the *real* ground motion, the EMD is presented as an alternative tool for finding directly the frequencies related

The usefulness of these finding points to the need for further investigation in evaluating the competency of tools for analyzing the recordings and for obtaining conclusions, since they are the basis of the process of calibration of all the theoretical, geotechnical and seismological models. The Hilbert spectral transformation permits the recognition of oscillation modes that would

The accelerogram records for this research were provided by the Unidad de Instrumentación

Researcher, Geotechnical Department, Instituto de Ingeniería, Universidad Nacional

have concluded, any linear model could not predict this kind of ground responses.

**4. Conclusions**

114 Geophysics

which generates the signal.

**Acknowledgements**

**Author details**

with the highest energy concentrations.

have been masked by Fourier spectral analysis.

Sísmica, Instituto de Ingeniería, UNAM.

Autónoma de México, México City, México

Silvia Raquel García Benítez\* and Leonardo Alcántara Nolasco \*Address all correspondence to: sgab@pumas.iingen.unam.mx


[15] Yangkang C, Chao Z, Jiang Y, Zhaoyu J. Application of empirical mode decomposition in random noise attenuation of seismic data. Journal of Seismic Exploration. 2014;**23**:481-495

**Section 3**

**Earth Planetary System**


## **Earth Planetary System**

[15] Yangkang C, Chao Z, Jiang Y, Zhaoyu J. Application of empirical mode decomposition in random noise attenuation of seismic data. Journal of Seismic Exploration. 2014;**23**:481-495

[16] Huang NE, Wu Z. A review on Hilbert-Huang transform: Method and its applications to

[17] Huang NE, Shen SSP. Hilbert-Huang Transform and Its Applications. London: World

[18] Lee MH, Shyu KK, Lee PL. Hardware implementation of EMD using DSP and FPGA for online signal processing. IEEE Transactions on Industrial Electronics. 2011;**58**(6):

[19] Ovando-Shelley E, Romo MP, Contreras N, Giralt A. Effects on soil properties of future settlements in downtown Mexico City due to ground water extraction. Geofísica

[20] Ovando-Shelley E, Ossa A, Romo MP. The sinking of Mexico City: Its effects on soil properties and seismic response. Soil Dynamics and Earthquake Engineering. 2007;**27**:333-343

[21] Pando M, Cano L, Suárez L, Ritta R, Montejo L. Comparison of site fundamental period estimates using weak-motion earthquakes and microtremors. In: The 14th World Conference on Earthquake Engineering. 2008. http://www.iitk.ac.in/nicee/wcee/article/14\_02-0142.pdf

[22] Demetriu S, Trandafir R. Time-frequency representations of earthquake motion records.

[23] Lermo J, Chávez-García F. Are microtremors useful in site response evaluation? Bulletin

[24] Ordaz M, Miranda E, Avilés J. Proposal for seismic design spectra for Mexico's Federal

[25] Bozorgnia Y, Bertero V. Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering. Boca Raton: CRC Press; 2004. p. 976. ISBN: 0-8493-

[26] Avilés J, Pérez-Rocha L. Regional subsidence of Mexico City and its effects on seismic

[27] Yin JH, Graham J. Elastic visco-plastic modelling of one dimensional consolidation.

[28] Douglas J. An investigation of analysis of variance as a tool for exploring regional differ-

[29] Noeggerath J, Geller RJ, Gusiakov VK. Fukushima: The myth of safety, the reality of

[30] Campbell KW, Bozorgnia Y. Updated near-source groundmotion (attenuation) relations for the horizontal and vertical components of peak ground acceleration and acceleration response spectra. Bulletin of the Seismological Society of America. 2003;**93**:314-331

response. Soil Dynamics and Earthquake Engineering. 2010;**30**:981-989

ences in strong ground motions. Journal of Seismology. 2004;**8**(4):485-496

Analele Stiintifice ale Universitatii Ovidius Constanta. 2003;**11**(2):57-68

of the Seismological Society of America. 1994;**84**(5):1350-1364

District. Ingeniería de Estructuras. 2003;**8**(2):189-207

geoscience. Bulletin of the Atomic Scientists. 2011;**67**:37

geophysical studies. Reviews of Geophysics. 2008;**46**(2):1-23

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Internacional. 2003;**42**(2):185-204

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Geotechnique. 1996;**46**(3):515-527

**Chapter 7**

**Provisional chapter**

**Dynamics of the Early Stage of Formation of the**

**Dynamics of the Early Stage of Formation of the** 

DOI: 10.5772/intechopen.72641

In previous studies it was shown that the energy release during the decay of short-living radioactive elements in small bodies is sufficient for the temperature inside such a protoplanetary core to become larger than the melting temperature of iron. This ensures the realization of the process of differentiation of matter and the development of convection in the inner envelopes. At all stages of proto-Earth's formation, convective heat and mass transfer is the most important factor in the dynamics of the planet. However, the release of heat due to friction in the viscous liquid of the outer regions of the core so far has not been taken into account at all or was taken into account only in the formed envelopes of a planet of constant radius. In this chapter, we present the results of a numerical simulation of the thermal evolution of a 3D spherical segment of a protoplanet of an increasing radius, taking into account the accidental falling of bodies and particles. An algorithm for the numerical solution of the problem is given, taking into account the dissipation of tidal

energy in the Earth-Moon system at the stage of planetary accumulation.

tides, numerical solution of the differential system of equations

**Keywords:** stage of Earth-Moon forming, temperature distribution, energy of Moon

It is a paradox, but there are no significant differences regarding the earliest stages of the forming of the universe and its structure. The basis of modern concepts is the law of gravitation of Einstein A [1]. Unlike Newton's law of gravitation, this potential explicitly takes into account the time dependence and the finite velocity of the gravitational interaction distribution. The initial condition for the Einstein equation is a point singularity in which the mass of the entire substance of the universe is concentrated. Friedman A [2] for the first time obtained

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Yurie Khachay, Olga Hachay and Alexander Antipin

Yurie Khachay, Olga Hachay and Alexander Antipin

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Earth's-Moon System**

**Earth's-Moon System**

http://dx.doi.org/10.5772/intechopen.72641

**Abstract**

**1. Introduction**

**Provisional chapter**

#### **Dynamics of the Early Stage of Formation of the Earth's-Moon System Earth's-Moon System**

**Dynamics of the Early Stage of Formation of the** 

DOI: 10.5772/intechopen.72641

Yurie Khachay, Olga Hachay and Alexander Antipin Yurie Khachay, Olga Hachay and Alexander Antipin Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72641

#### **Abstract**

In previous studies it was shown that the energy release during the decay of short-living radioactive elements in small bodies is sufficient for the temperature inside such a protoplanetary core to become larger than the melting temperature of iron. This ensures the realization of the process of differentiation of matter and the development of convection in the inner envelopes. At all stages of proto-Earth's formation, convective heat and mass transfer is the most important factor in the dynamics of the planet. However, the release of heat due to friction in the viscous liquid of the outer regions of the core so far has not been taken into account at all or was taken into account only in the formed envelopes of a planet of constant radius. In this chapter, we present the results of a numerical simulation of the thermal evolution of a 3D spherical segment of a protoplanet of an increasing radius, taking into account the accidental falling of bodies and particles. An algorithm for the numerical solution of the problem is given, taking into account the dissipation of tidal energy in the Earth-Moon system at the stage of planetary accumulation.

**Keywords:** stage of Earth-Moon forming, temperature distribution, energy of Moon tides, numerical solution of the differential system of equations

#### **1. Introduction**

It is a paradox, but there are no significant differences regarding the earliest stages of the forming of the universe and its structure. The basis of modern concepts is the law of gravitation of Einstein A [1]. Unlike Newton's law of gravitation, this potential explicitly takes into account the time dependence and the finite velocity of the gravitational interaction distribution. The initial condition for the Einstein equation is a point singularity in which the mass of the entire substance of the universe is concentrated. Friedman A [2] for the first time obtained

Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons

no stationary solutions of the gravitational equation had been published. After Hubble's experiment on installed "red shift" [3] in the spectra of stars and galaxies, and then of "relict" radiation [4], the idea of the universe expanding was established. At the same time, our universe is understood as a region, about 13.8 billion light-years in radius, filled with matter formed after the "Big Explosion."

However, new questions arise. What is beyond the boundaries of our universe? Is the Universe only one? Are there any measurable physical fields and processes that will allow us to detect real objects external to our universe? A singular point has arisen in the already existing universe, and can we then trace the development of the instability leading to the 'Big Explosion" of this singular object? Are the laws of physics established in our universe in the outer universes preserved? Clearly, this is only a small part of the issues related to the problems of cosmic physics and planetology.

It is believed now that the most justified are ideas about the formation of stars and planets in protoplanetary clouds inside spiral arms of galaxies. **Figures 1** and **2** show an example of such galaxies.

The evolution of our solar protoplanetary cloud has been studied in detail. This is a vivid example of how complex are the processes of formation of the inner shells of the Earth and its natural moon satellite are insufficiently researched. Despite significant achievements, until recently, it has not been possible to obtain a quantitative explanation of the results obtained on the basis of the analysis of W-Hf and Al-Mg isotope systems, which are interpreted as evidence of the very early separation of chemical reservoirs of the core and mantle in time less than 10 million years [5–7]. While on the basis of the results on the uranium-lead system, the formation of these structures lasted about 100 million years, that is, the separation of their chemical reservoirs occurred long before the end of the growth of the structures themselves.

**2. Modeling of early stage of formation of the Earth and Moon**

**Figure 2.** Star RS Korma ESO/G. Bono and CTIO. http://www.eso.org/public/images/potw1126a/

**2.1. The main physical results and mathematical formulation of the problem**

of their accumulation (**Figure 3**).

Initially, a one-dimensional model was used to solve the problem of early stage of the Earth's formation [8, 9]. Adiabatic stresses and three-dimensional effects due to the location of bodies on the surface of a growing planet have not been taken into account. The main source of internal energy of the protoplanet at this stage of its formation was the release of heat due to the natural radioactive decay of long-living uranium and thorium. The contribution due to the release of heat from the impact of small particles and bodies of the protoplanetary cloud on the surface of the growing planet had been known to be very small, since most of their energy, according to Stefan's law, was released into space. As a result, sufficiently low estimates of the temperature of the inner regions of the protoplanet were obtained by the end of the process

Dynamics of the Early Stage of Formation of the Earth's-Moon System

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121

As can be seen from these results, the temperature estimates obtained turned out to be lower than the melting point of iron at a given depth. From this it follows that since the values of the iron coefficient in a solid silicate substance are very small, then for the entire age of the Earth, the separation of a predominantly iron core from a predominantly silicate mantle could not occur. In order for such separation to be realized, the molten state of the substance and the

A new model for the accumulation of terrestrial planets was proposed in the work of [11, 12], which uses modern results of isotope geochemical analyses and allowed obtaining reliable estimates of the concentration of short-living naturally radioactive isotopes and, above all, 26Al in the matter of the protoplanetary cloud. On the basis of these data, new estimates of

convective heat and mass transfer of the components in the melt are required.

**Figure 1.** Impacted galaxies.

**Figure 2.** Star RS Korma ESO/G. Bono and CTIO. http://www.eso.org/public/images/potw1126a/

no stationary solutions of the gravitational equation had been published. After Hubble's experiment on installed "red shift" [3] in the spectra of stars and galaxies, and then of "relict" radiation [4], the idea of the universe expanding was established. At the same time, our universe is understood as a region, about 13.8 billion light-years in radius, filled with matter

However, new questions arise. What is beyond the boundaries of our universe? Is the Universe only one? Are there any measurable physical fields and processes that will allow us to detect real objects external to our universe? A singular point has arisen in the already existing universe, and can we then trace the development of the instability leading to the 'Big Explosion" of this singular object? Are the laws of physics established in our universe in the outer universes preserved? Clearly, this is only a small part of the issues related to the problems of

It is believed now that the most justified are ideas about the formation of stars and planets in protoplanetary clouds inside spiral arms of galaxies. **Figures 1** and **2** show an example of

The evolution of our solar protoplanetary cloud has been studied in detail. This is a vivid example of how complex are the processes of formation of the inner shells of the Earth and its natural moon satellite are insufficiently researched. Despite significant achievements, until recently, it has not been possible to obtain a quantitative explanation of the results obtained on the basis of the analysis of W-Hf and Al-Mg isotope systems, which are interpreted as evidence of the very early separation of chemical reservoirs of the core and mantle in time less than 10 million years [5–7]. While on the basis of the results on the uranium-lead system, the formation of these structures lasted about 100 million years, that is, the separation of their chemical reservoirs occurred long before the end of the growth

formed after the "Big Explosion."

cosmic physics and planetology.

of the structures themselves.

**Figure 1.** Impacted galaxies.

such galaxies.

120 Geophysics

#### **2. Modeling of early stage of formation of the Earth and Moon**

#### **2.1. The main physical results and mathematical formulation of the problem**

Initially, a one-dimensional model was used to solve the problem of early stage of the Earth's formation [8, 9]. Adiabatic stresses and three-dimensional effects due to the location of bodies on the surface of a growing planet have not been taken into account. The main source of internal energy of the protoplanet at this stage of its formation was the release of heat due to the natural radioactive decay of long-living uranium and thorium. The contribution due to the release of heat from the impact of small particles and bodies of the protoplanetary cloud on the surface of the growing planet had been known to be very small, since most of their energy, according to Stefan's law, was released into space. As a result, sufficiently low estimates of the temperature of the inner regions of the protoplanet were obtained by the end of the process of their accumulation (**Figure 3**).

As can be seen from these results, the temperature estimates obtained turned out to be lower than the melting point of iron at a given depth. From this it follows that since the values of the iron coefficient in a solid silicate substance are very small, then for the entire age of the Earth, the separation of a predominantly iron core from a predominantly silicate mantle could not occur. In order for such separation to be realized, the molten state of the substance and the convective heat and mass transfer of the components in the melt are required.

A new model for the accumulation of terrestrial planets was proposed in the work of [11, 12], which uses modern results of isotope geochemical analyses and allowed obtaining reliable estimates of the concentration of short-living naturally radioactive isotopes and, above all, 26Al in the matter of the protoplanetary cloud. On the basis of these data, new estimates of

the content of 26Al in the protoplanetary matter of the Earth. The results are presented in **Figures 4** and **5**. To describe the growth of the mass of the protoplanet and the nearest satel-

<sup>∂</sup>*<sup>t</sup>* <sup>=</sup> 2(1 <sup>+</sup> <sup>2</sup>*θ*)*<sup>r</sup>* <sup>2</sup> *<sup>ω</sup>*(<sup>1</sup> <sup>−</sup> \_\_*<sup>m</sup>*

where *m* is the current mass of the growing body, *M* is the final mass of the planet, *r* is the radius of the growing protoplanet, *θ* is the statistical parameter that takes into account the distribution of bodies and particles by mass and velocity in the protoplanetary supply zone, *σ* is the surface density of the protoplanetary cloud's matter in the orbit of the growing body, and *ω* is the angular velocity of the orbital rotation. The change of the temperature in the inner

) = −∇*P* + *μ*Δ*V*

**Figure 4.** The distribution of the temperature in the growing pre-planetary body. Its radius is 1—400 km, 2—300 km,

<sup>→</sup> + 2*ρV*

<sup>→</sup> × Ω

<sup>→</sup>(∇*T*) <sup>=</sup> *<sup>χ</sup>*Δ*<sup>T</sup>* <sup>+</sup> *<sup>Q</sup>*<sup>1</sup> (3)

Dynamics of the Early Stage of Formation of the Earth's-Moon System

<sup>→</sup> = 0 (4)

parts of the growing planets was described by a system of equations:

<sup>∂</sup>*<sup>t</sup>* <sup>+</sup> *<sup>V</sup>*

*<sup>M</sup>*)*σ* (1)

http://dx.doi.org/10.5772/intechopen.72641

123

<sup>→</sup> − *ρ*∇*W* (2)

lite, the Safronov equation was used [8, 10]:

*ρ*( ∂*V* → \_\_\_ <sup>∂</sup>*<sup>t</sup>* <sup>+</sup> *<sup>V</sup>* <sup>→</sup>(∇*V* →)

*divV*

\_\_\_ <sup>∂</sup>*<sup>T</sup>*

and 3—250 km.

\_\_\_ <sup>∂</sup>*<sup>m</sup>*

**Figure 3.** The Earth's temperature distribution after the end of accumulation. 1—The temperature of full mantle material melting, 2—the temperature of the solid mantle, 3—the melting iron temperature, 4—the temperature distribution into the Earth by Safronov [8] (lower curve) and the temperature distribution into the Earth by Lubimova (upper curve) [10].

the temperature distribution in the growing pre-planetary bodies of the planet in the "feeding" zone of the Earth were obtained. It was shown in the work of [11] that the energy release during the decay of short-living radioactive elements in small bodies is sufficient for the temperature inside such a protoplanetary core to become greater than the melting temperature of iron. This ensures the realization of **Table 1** which illustrates the processes of matter density differentiation and the development of convection in the inner envelopes. Originally, a one-dimensional model was used to numerically solve that problem, based on new data on


**Table 1.** The dependence of the temperature in the center of the pre-planetary body from the content of Al2 O3 [12]. the content of 26Al in the protoplanetary matter of the Earth. The results are presented in **Figures 4** and **5**. To describe the growth of the mass of the protoplanet and the nearest satellite, the Safronov equation was used [8, 10]:

$$\frac{\partial m}{\partial t} = \mathcal{Z}(1 + \mathcal{Z}\theta) \, r^2 \, \omega \left(1 - \frac{m}{M}\right) \sigma \tag{1}$$

where *m* is the current mass of the growing body, *M* is the final mass of the planet, *r* is the radius of the growing protoplanet, *θ* is the statistical parameter that takes into account the distribution of bodies and particles by mass and velocity in the protoplanetary supply zone, *σ* is the surface density of the protoplanetary cloud's matter in the orbit of the growing body, and *ω* is the angular velocity of the orbital rotation. The change of the temperature in the inner parts of the growing planets was described by a system of equations:

$$\rho \left( \frac{\partial \vec{V}}{\partial t} + \vec{V} (\nabla \vec{V}) \right) = -\nabla P + \mu \Delta \vec{V} + 2\rho \vec{V} \times \vec{\Omega} - \rho \nabla W \tag{2}$$

$$\frac{\partial T}{\partial t} + \vec{V} (\nabla T) = \chi \Delta T + Q\_1 \tag{3}$$

$$d\vec{v}\vec{V} = \mathbf{0} \tag{4}$$

the temperature distribution in the growing pre-planetary bodies of the planet in the "feeding" zone of the Earth were obtained. It was shown in the work of [11] that the energy release during the decay of short-living radioactive elements in small bodies is sufficient for the temperature inside such a protoplanetary core to become greater than the melting temperature of iron. This ensures the realization of **Table 1** which illustrates the processes of matter density differentiation and the development of convection in the inner envelopes. Originally, a one-dimensional model was used to numerically solve that problem, based on new data on

**Figure 3.** The Earth's temperature distribution after the end of accumulation. 1—The temperature of full mantle material melting, 2—the temperature of the solid mantle, 3—the melting iron temperature, 4—the temperature distribution into the Earth by Safronov [8] (lower curve) and the temperature distribution into the Earth by Lubimova (upper curve) [10].

**Concentration of Аl<sup>2</sup>**

**O3 mass. %**

 1240 1701 1734 1825 1676 1752 1812 1978 1690 1793 1876 2104 1701 1828 1928 2206 1711 1856 1972 2290 1718 1878 2006 2359 1730 1912 2059 2461

**Table 1.** The dependence of the temperature in the center of the pre-planetary body from the content of Al2

**Теmperature into the pre-planetary body center, K**

**1.0 3.0 4.6 9.0**

O3 [12].

**Radius of the pre-planetary** 

**body, km**

122 Geophysics

**Figure 4.** The distribution of the temperature in the growing pre-planetary body. Its radius is 1—400 km, 2—300 km, and 3—250 km.

of thermal radiation, depending on its composition and density. As can be seen from the results presented in **Figure 5**, the temperature of the growing surface sharply decreases as the transparency of the atmosphere increases, due to the increase of the gravitational radius of

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In the work of [12–14], it was shown that successively changing with the growth of the emerging Earth and the Moon, the main contribution of heat generation in the inner regions of growing bodies is provided first by radioactive sources and, after that, heated from above by the arrival of kinetic energy during a collision with the growing Earth and the Moon. At all stages of the Earth's formation, convective heat and mass transfer is the most important factor in the dynamics of the planet. For the numerical solution of the boundary value problem (Eqs. (1)–(5)), the through-count method proposed in [15, 16] was used. However the one-dimensional model of the thermal structure of the interior regions does not allow one to understand

the protoplanet and the possibility of retaining the silicate content of the cloud.

the occurrence of the largest surface structures of continents and oceans.

**system**

at a radius of 100 km is shown.

100 km was inserted a comma.

**2.2. New results of 3D modeling of the early stage formation of the Earth-Moon** 

In addition, the release of heat due to friction in the viscous melt of the inner envelopes has either not been taken into account at all or has been taken into account only in the already formed envelopes of a planet of constant radius. In this chapter, the first results of numerical modeling of the thermal evolution of the 3D spherical segment of a protoplanet of an increasing radius are considered, taking into account the accidental falling of bodies and particles. In **Figure 6**, the nonuniform temperature distribution on the surface of the growing proto-Earth

**Figure 6.** The variant of temperature distribution, stipulated by the random distribution of the accumulated bodies by their values and kinetic energy on the planet's surface at the radius R = 100 km, λ and θ-spherical angles in radians. After

**Figure 5.** Possible variants of the temperature distributions to the moment, when the Earth has the size 6300 km [12]. 1—The accumulation from little particles. The generation of heat by short-living radioactive elements is not taken into account: ε = 0.001 for growing core and ε = 0.001 for mantle. 2 and 3—The generation of heat by short-living radioactive elements is taken into account: 2—ε = 0.3 for growing core and ε = 0.02 for mantle and 3—ε = 0.4 for growing core and ε = 0.01 for mantle. 4—ε = 04 for growing core and ε = 0.02 for mantle and 5—ε = 0.5 for growing core and ε = 0.05 for mantle. 6—The dependence of the core's melting temperature from pressure.

Here *ρ* is the density of the medium, *V* <sup>→</sup> the volume velocity of the flow, *P* the pressure, *μ* the kinematic viscosity of the medium, Ω <sup>→</sup> the angular velocity of diurnal rotation, *W* the potential of the rotating body, *T* the medium temperature at a given point and time, *Q*<sup>1</sup> the normalized cumulative power of the release of the specific internal energy, and *χ* the thermal diffusivity.

Using the Boussinesq approximation for "incompressible fluid" greatly simplifies the consideration of Eqs. ((2)–(4)) [15, 16]. In the energy balance equation, adiabatic heating and energy release of radioactive sources *Q*<sup>1</sup> are taken into account here, but the contribution of energy dissipation of viscous friction was not taken into account:

$$k\rho \frac{\gamma M}{r} \frac{dr}{dt} = \left[\varepsilon \sigma \left[T^4 - T\_1^4\right] + \rho c\_p \left[T - T\_1\right] \frac{dr}{dt}\right] \tag{5}$$

The system of Eqs. ((1)–(5)) in the spherical sector is solved numerically, and the conditions of periodicity are given on the lateral boundaries, while the conditions (Eq. (5)) are calculated on the outer surface of the growing radius [12].

where *ρ* is the density of the medium; *γ* is the gravitational constant; *M* is the mass of the growing planet; *r* is its radius; *T* and *T*<sup>1</sup> are, respectively, the surface temperature of the body and the external medium; *ε* is the permeability coefficient and *cP* the specific heat; and *k* is the fraction of the conversion of the potential energy into thermal energy.

The results of the work by [12] show various options for estimating the temperature of the interior regions of the planet by the time of completing its accumulation for numerical models that take into account the difference in transmission *ε* from the boundary conditions (Eq. (5)) of thermal radiation, depending on its composition and density. As can be seen from the results presented in **Figure 5**, the temperature of the growing surface sharply decreases as the transparency of the atmosphere increases, due to the increase of the gravitational radius of the protoplanet and the possibility of retaining the silicate content of the cloud.

In the work of [12–14], it was shown that successively changing with the growth of the emerging Earth and the Moon, the main contribution of heat generation in the inner regions of growing bodies is provided first by radioactive sources and, after that, heated from above by the arrival of kinetic energy during a collision with the growing Earth and the Moon. At all stages of the Earth's formation, convective heat and mass transfer is the most important factor in the dynamics of the planet. For the numerical solution of the boundary value problem (Eqs. (1)–(5)), the through-count method proposed in [15, 16] was used. However the one-dimensional model of the thermal structure of the interior regions does not allow one to understand the occurrence of the largest surface structures of continents and oceans.

#### **2.2. New results of 3D modeling of the early stage formation of the Earth-Moon system**

**Figure 5.** Possible variants of the temperature distributions to the moment, when the Earth has the size 6300 km [12]. 1—The accumulation from little particles. The generation of heat by short-living radioactive elements is not taken into account: ε = 0.001 for growing core and ε = 0.001 for mantle. 2 and 3—The generation of heat by short-living radioactive elements is taken into account: 2—ε = 0.3 for growing core and ε = 0.02 for mantle and 3—ε = 0.4 for growing core and ε = 0.01 for mantle. 4—ε = 04 for growing core and ε = 0.02 for mantle and 5—ε = 0.5 for growing core and ε = 0.05 for

cumulative power of the release of the specific internal energy, and *χ* the thermal diffusivity. Using the Boussinesq approximation for "incompressible fluid" greatly simplifies the consideration of Eqs. ((2)–(4)) [15, 16]. In the energy balance equation, adiabatic heating and energy

4

The system of Eqs. ((1)–(5)) in the spherical sector is solved numerically, and the conditions of periodicity are given on the lateral boundaries, while the conditions (Eq. (5)) are calculated on

where *ρ* is the density of the medium; *γ* is the gravitational constant; *M* is the mass of the

and the external medium; *ε* is the permeability coefficient and *cP* the specific heat; and *k* is the

The results of the work by [12] show various options for estimating the temperature of the interior regions of the planet by the time of completing its accumulation for numerical models that take into account the difference in transmission *ε* from the boundary conditions (Eq. (5))

] + *ρcP*[*T* − *T*1]

<sup>→</sup> the volume velocity of the flow, *P* the pressure, *μ* the

the normalized

*dt* (5)

<sup>→</sup> the angular velocity of diurnal rotation, *W* the potential

are taken into account here, but the contribution of energy

\_\_*dr*

are, respectively, the surface temperature of the body

mantle. 6—The dependence of the core's melting temperature from pressure.

dissipation of viscous friction was not taken into account:

*M <sup>r</sup>* \_\_*dr*

fraction of the conversion of the potential energy into thermal energy.

of the rotating body, *T* the medium temperature at a given point and time, *Q*<sup>1</sup>

*dt* <sup>=</sup> [*T*<sup>4</sup> <sup>−</sup> *<sup>T</sup>*<sup>1</sup>

Here *ρ* is the density of the medium, *V*

kinematic viscosity of the medium, Ω

124 Geophysics

release of radioactive sources *Q*<sup>1</sup>

*k* \_\_\_

the outer surface of the growing radius [12].

growing planet; *r* is its radius; *T* and *T*<sup>1</sup>

In addition, the release of heat due to friction in the viscous melt of the inner envelopes has either not been taken into account at all or has been taken into account only in the already formed envelopes of a planet of constant radius. In this chapter, the first results of numerical modeling of the thermal evolution of the 3D spherical segment of a protoplanet of an increasing radius are considered, taking into account the accidental falling of bodies and particles. In **Figure 6**, the nonuniform temperature distribution on the surface of the growing proto-Earth at a radius of 100 km is shown.

**Figure 6.** The variant of temperature distribution, stipulated by the random distribution of the accumulated bodies by their values and kinetic energy on the planet's surface at the radius R = 100 km, λ and θ-spherical angles in radians. After 100 km was inserted a comma.

In **Figures 7**–**9**, the temperature distributions in the inner areas Earth are presented in the form of cross sections of spherical sectors.

In Ref. [13] proposed an algorithm for numerical solution of the problem with allowance for the dissipation of tidal energy in the Earth-Moon system at the stage of planet accumulation. The results obtained showed that the contribution of this source of heat could at times be very significant.

In Ref. [12] showed that the energy release during the decay of short-living radioactive elements in small area, over 50 km in size, is sufficient for the temperature inside such a pre-planetary body to become larger than the melting temperature of iron. This ensures the realization of the process of matter density differentiation and the development of convection in the interior regions of the growing planet. As the Earth grew, the forming area of the outer core remained in the molten state. The use of the 3D model in solving the system of Eqs. ((2)–(4)) with the boundary condition (Eq. (5)) at the stage of formation of the Earth and the Moon made it possible to trace the occurrence and development of thermal heterogeneities in the growing internal areas of the Earth. Similar results were obtained also for the Moon. As can be seen from the results presented in **Figures 7** and **8**, formed due to a random distribution of falling bodies on the forming planet, near-surface thermal heterogeneities do not have time to homogenize and cause a complex structure of distribution of concentration and thermal heterogeneities. However, the Earth and the Moon form a tight double system. Therefore, the thermal evolution of these bodies at the accumulation stage must be analyzed together. The need to take into account the release of heat due to the attenuation of tides during the accumulation of the Earth was noted in the work of [17, 18]. For the mathematical description of the thermal evolution of proto-Earth and proto-Moon growing in the process of accumulation as a close binary system, it is necessary to take into account the evolution of the Moon's orbit due to the tidal interaction and the dissipation of viscous fluid friction energy excited by this tidal interaction.

**Figure 7.** An example of the temperature distribution and initial thermal heterogeneities in the protoplanet up to the end of its accumulation, without taking into account the heat of tidal friction.

In contrast to the model, for which the Businesque approximation—an incompressible viscous fluid—is still applicable, we can no longer use the incompressibility approximation in Eqs. (2) and (4). In the model under consideration, the tidal interaction between the Sun and the planets will be neglected, which will allow us to use the results of an analysis of the close

**Figure 9.** The temperature distribution in the inner areas of the proto-Earth for various values of the achieved radius:

**Figure 8.** The temperature distribution of the Earth's interior to the end of accumulation along the section of the 3D

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127

sector (without taking into account the heat dissipation energy of tidal friction).

1-R = 1930 km, 2-R = 3670 km, 3-R = 5220 km, and 4-R = 6680 km.

In **Figures 7**–**9**, the temperature distributions in the inner areas Earth are presented in the

In Ref. [13] proposed an algorithm for numerical solution of the problem with allowance for the dissipation of tidal energy in the Earth-Moon system at the stage of planet accumulation. The results obtained showed that the contribution of this source of heat could at times be very

In Ref. [12] showed that the energy release during the decay of short-living radioactive elements in small area, over 50 km in size, is sufficient for the temperature inside such a pre-planetary body to become larger than the melting temperature of iron. This ensures the realization of the process of matter density differentiation and the development of convection in the interior regions of the growing planet. As the Earth grew, the forming area of the outer core remained in the molten state. The use of the 3D model in solving the system of Eqs. ((2)–(4)) with the boundary condition (Eq. (5)) at the stage of formation of the Earth and the Moon made it possible to trace the occurrence and development of thermal heterogeneities in the growing internal areas of the Earth. Similar results were obtained also for the Moon. As can be seen from the results presented in **Figures 7** and **8**, formed due to a random distribution of falling bodies on the forming planet, near-surface thermal heterogeneities do not have time to homogenize and cause a complex structure of distribution of concentration and thermal heterogeneities. However, the Earth and the Moon form a tight double system. Therefore, the thermal evolution of these bodies at the accumulation stage must be analyzed together. The need to take into account the release of heat due to the attenuation of tides during the accumulation of the Earth was noted in the work of [17, 18]. For the mathematical description of the thermal evolution of proto-Earth and proto-Moon growing in the process of accumulation as a close binary system, it is necessary to take into account the evolution of the Moon's orbit due to the tidal interaction and the dissipa-

**Figure 7.** An example of the temperature distribution and initial thermal heterogeneities in the protoplanet up to the end

tion of viscous fluid friction energy excited by this tidal interaction.

of its accumulation, without taking into account the heat of tidal friction.

form of cross sections of spherical sectors.

significant.

126 Geophysics

**Figure 8.** The temperature distribution of the Earth's interior to the end of accumulation along the section of the 3D sector (without taking into account the heat dissipation energy of tidal friction).

**Figure 9.** The temperature distribution in the inner areas of the proto-Earth for various values of the achieved radius: 1-R = 1930 km, 2-R = 3670 km, 3-R = 5220 km, and 4-R = 6680 km.

In contrast to the model, for which the Businesque approximation—an incompressible viscous fluid—is still applicable, we can no longer use the incompressibility approximation in Eqs. (2) and (4). In the model under consideration, the tidal interaction between the Sun and the planets will be neglected, which will allow us to use the results of an analysis of the close binary system. For the Earth-Moon system, one can use the approximation for the law of conservation of momentum in the form (Eq. (6)) [17], (**Figure 10**). It does not take into account the interaction with the Sun, which ensures the solar tide:

$$I\,\Omega + \frac{M\_i \cdot m\_i}{M\_i + m\_i}L^2\,\omega = \text{const} \tag{6}$$

*Ф* = 2*μ*[(

+ \_\_1 2 ( ∂ *u* \_\_\_\_\_\_\_\_\_*<sup>z</sup>* <sup>∂</sup> *<sup>x</sup>* <sup>+</sup> ∂ *u* \_\_\_\_\_\_\_\_\_\_\_\_\_ *<sup>x</sup>* <sup>∂</sup> *<sup>z</sup>* ) 2

jections of the velocity in Cartesian coordinates.

*Q*<sup>−</sup><sup>1</sup> = \_\_\_\_\_\_\_\_\_ *<sup>δ</sup> <sup>E</sup>*

as a source term in Eq. (8).

**3. Conclusions**

∂ *u* \_\_\_\_\_\_\_\_\_*<sup>x</sup>* <sup>∂</sup> *<sup>x</sup>* ) 2 ( <sup>∂</sup> *uy* \_\_\_\_\_\_\_\_\_ ∂ *y* ) 2 + ( ∂ *u* \_\_\_\_\_\_\_\_\_*<sup>z</sup>* <sup>∂</sup> *<sup>z</sup>* ) 2 + \_\_1 2 ( ∂ *u* \_\_\_\_\_\_\_\_\_*<sup>x</sup>* ∂ *y* + ∂ *uy* \_\_\_\_\_\_\_\_\_\_\_\_\_ ∂ *x* ) 2 + \_\_1 2 ( <sup>∂</sup> *uy* \_\_\_\_\_\_\_\_\_ <sup>∂</sup> *<sup>z</sup>* <sup>+</sup> ∂ *u* \_\_\_\_\_\_\_\_\_\_\_\_\_ *<sup>z</sup>* ∂ *y* ) 2

> ] <sup>+</sup> *<sup>λ</sup>* 〈<sup>∂</sup> *<sup>u</sup>* \_\_\_\_\_\_\_\_\_*<sup>x</sup>* <sup>∂</sup> *<sup>x</sup>* <sup>+</sup> <sup>∂</sup> *uy* \_\_\_\_\_\_\_\_\_ ∂ *y* + ∂ *u* \_\_\_\_\_\_\_\_\_*<sup>z</sup>* ∂ *z* 〉 2

The algorithm for solving this nonlinear system of equations is as follows. For each moment of time, using Eq. (1), new values of the Earth's and Moon's masses and the time step are found at a fixed step along the coordinate r. New boundary conditions for the proto-Earth and like for the proto-Moon are calculated (Eq. (5)). A direct problem is solved in the body of the increased radius, for which the temperature, velocity, and pressure fields are used as the initial conditions from the previous time step (Eqs. (2), (8), (4)), respectively. New distributions of the melting temperature and the function Ф in (Eq. (9)) are computed from the new temperature and pressure distribution. Since the system of equations is nonlinear, the solution is sought using the iteration method, which provides a given relative error. The number of iterations is carried out until the specified accuracy of the solution is achieved. Then the system (Eqs. (6) and (7)) is solved, and new parameters of the satellite orbit are determined. After this, the next step is taken along the spatial grid. But the solution of this nonlinear boundary value problem with the necessary number of iterations at each time step and the necessity of calculating the dissipative function (Eq. (8)) requires very large computational powers. In this case, there are very rough estimates of the viscosity dependences on temperature and pressure, which lead to computational difficulties. Therefore, we confine ourselves to an estimate that can be obtained using the phenomenological approach and using the Q-factor approximation of the interior regions of the Earth and the Moon, based on the results of [17, 18]. We use the quality factor as the fraction of the energy E dissipating into heat during one oscillation period (Eq. (10)):

This function is estimated by modern seismic results on the attenuation of the Earth's natural oscillations for the model hydrostatic pressure and available estimates of the current temperature [18]. Tidal interaction redistributes the moments of momentum between the bodies forming a closed system, and its modern value is a well-known value. On the contrary, the total amount of energy in the open system Earth-Moon is not conserved. The value of the rotational energy is not conserved but partially dissipates into heat, and this part of it must be taken into account

Newton's law, with sufficient accuracy, described the gravitational interaction of material bodies on the scales of individual stars and their planetary systems. It is not applicable to describing processes in the universe as a whole. In this case, it is already necessary to use the

general theory of relativity and the law of gravitational interaction of Einstein.

where *μ* and *λ* are the coefficients of the first and second viscosities: *ux*

(9)

129

are the pro-

, *uy*

Dynamics of the Early Stage of Formation of the Earth's-Moon System

<sup>2</sup>*π<sup>E</sup>* (10)

, and *uz*

http://dx.doi.org/10.5772/intechopen.72641

where *I* is the inertial moment of the growing Earth, *Ω*(*t*) is the angular velocity of its rotation about its own axis at time *t*, ω(*t*) is the angular velocity of the orbital motion of the Moon around the Earth for the same moment of time, *M1* is the mass of the proto-Earth for the time moment (*t*), *m*<sup>1</sup> is the proto-Moon mass at the same time moment (*t*), and *L*(*t*) is the distance between the centers of mass of the Earth and the Moon.

For the energy of the Earth's own motion and the total energy of the Moon's orbital motion, one can use the expressions (Eq. (7)):

$$E\_{\Omega} = I \frac{\Omega^2}{2} \quad E\_{\omega} = -\gamma \frac{M\_i(t)}{2L} \tag{7}$$

To describe the dynamics of the Earth-Moon system, it is necessary to replace Eq. (3) by Eq. (8):

$$
\rho c \left( \frac{\partial T}{\partial t} + \vec{V} (\nabla T) \right) = \lambda \Lambda T + Q\_i + \Phi \tag{8}
$$

where *Ф* is the dissipative function in each of the melt regions, as can be seen from the results of the simpler model, shown in **Figures 7** and **8** for each time point. The function *Ф* describing the energy dissipation in a viscous fluid in a Cartesian coordinate system has the form [19, 20]:

**Figure 10.** Temperature distribution in the interior areas of the Moon up to the completion of its accumulation.

$$\begin{split} \clubsuit \spadesuit &= 2\mu \Big[ \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{z}}}{\partial \boldsymbol{x}} \right)^{2} \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{y}}}{\partial \boldsymbol{y}} \right)^{2} + \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{z}}}{\partial \boldsymbol{z}} \right)^{2} + \frac{1}{2} \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{x}}}{\partial \boldsymbol{y}} + \frac{\partial \boldsymbol{u}\_{\boldsymbol{y}}}{\partial \boldsymbol{x}} \right)^{2} + \frac{1}{2} \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{y}}}{\partial \boldsymbol{z}} + \frac{\partial \boldsymbol{u}\_{\boldsymbol{z}}}{\partial \boldsymbol{y}} \right)^{2} \\ &+ \frac{1}{2} \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{z}}}{\partial \boldsymbol{x}} + \frac{\partial \boldsymbol{u}\_{\boldsymbol{x}}}{\partial \boldsymbol{z}} \right)^{2} \Bigg] + \lambda \left( \frac{\partial \boldsymbol{u}\_{\boldsymbol{z}}}{\partial \boldsymbol{x}} + \frac{\partial \boldsymbol{u}\_{\boldsymbol{y}}}{\partial \boldsymbol{y}} + \frac{\partial \boldsymbol{u}\_{\boldsymbol{z}}}{\partial \boldsymbol{z}} \right)^{2} \end{split} \tag{9}$$

where *μ* and *λ* are the coefficients of the first and second viscosities: *ux* , *uy* , and *uz* are the projections of the velocity in Cartesian coordinates.

The algorithm for solving this nonlinear system of equations is as follows. For each moment of time, using Eq. (1), new values of the Earth's and Moon's masses and the time step are found at a fixed step along the coordinate r. New boundary conditions for the proto-Earth and like for the proto-Moon are calculated (Eq. (5)). A direct problem is solved in the body of the increased radius, for which the temperature, velocity, and pressure fields are used as the initial conditions from the previous time step (Eqs. (2), (8), (4)), respectively. New distributions of the melting temperature and the function Ф in (Eq. (9)) are computed from the new temperature and pressure distribution. Since the system of equations is nonlinear, the solution is sought using the iteration method, which provides a given relative error. The number of iterations is carried out until the specified accuracy of the solution is achieved. Then the system (Eqs. (6) and (7)) is solved, and new parameters of the satellite orbit are determined. After this, the next step is taken along the spatial grid. But the solution of this nonlinear boundary value problem with the necessary number of iterations at each time step and the necessity of calculating the dissipative function (Eq. (8)) requires very large computational powers. In this case, there are very rough estimates of the viscosity dependences on temperature and pressure, which lead to computational difficulties. Therefore, we confine ourselves to an estimate that can be obtained using the phenomenological approach and using the Q-factor approximation of the interior regions of the Earth and the Moon, based on the results of [17, 18]. We use the quality factor as the fraction of the energy E dissipating into heat during one oscillation period (Eq. (10)):

$$Q^{-1} = \frac{\delta E}{2\pi E} \tag{10}$$

This function is estimated by modern seismic results on the attenuation of the Earth's natural oscillations for the model hydrostatic pressure and available estimates of the current temperature [18].

Tidal interaction redistributes the moments of momentum between the bodies forming a closed system, and its modern value is a well-known value. On the contrary, the total amount of energy in the open system Earth-Moon is not conserved. The value of the rotational energy is not conserved but partially dissipates into heat, and this part of it must be taken into account as a source term in Eq. (8).

#### **3. Conclusions**

binary system. For the Earth-Moon system, one can use the approximation for the law of conservation of momentum in the form (Eq. (6)) [17], (**Figure 10**). It does not take into account the

where *I* is the inertial moment of the growing Earth, *Ω*(*t*) is the angular velocity of its rotation about its own axis at time *t*, ω(*t*) is the angular velocity of the orbital motion of the Moon

For the energy of the Earth's own motion and the total energy of the Moon's orbital motion,

<sup>2</sup> *E<sup>ω</sup>* = −*γ*

To describe the dynamics of the Earth-Moon system, it is necessary to replace Eq. (3) by Eq. (8):

where *Ф* is the dissipative function in each of the melt regions, as can be seen from the results of the simpler model, shown in **Figures 7** and **8** for each time point. The function *Ф* describing the energy dissipation in a viscous fluid in a Cartesian coordinate system has the form [19, 20]:

**Figure 10.** Temperature distribution in the interior areas of the Moon up to the completion of its accumulation.

is the proto-Moon mass at the same time moment (*t*), and *L*(*t*) is the distance

*M*1 (*t*) *m*<sup>1</sup> (*t*) \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

*L*<sup>2</sup> *ω* = *const* (6)

is the mass of the proto-Earth for the time

<sup>2</sup>*<sup>L</sup>* (7)

) = *λ*Δ*T* + *Q*<sup>1</sup> + *Ф* (8)

*M*<sup>1</sup> \_\_\_\_\_\_\_ ⋅ *m*<sup>1</sup> *M*<sup>1</sup> + *m*<sup>1</sup>

interaction with the Sun, which ensures the solar tide:

around the Earth for the same moment of time, *M1*

between the centers of mass of the Earth and the Moon.

\_\_\_ ∂*T* <sup>∂</sup>*<sup>t</sup>* <sup>+</sup> *<sup>V</sup>* <sup>→</sup>(∇*T*)

*I* Ω +

one can use the expressions (Eq. (7)):

*c*(

*<sup>E</sup>*<sup>Ω</sup> <sup>=</sup> *<sup>I</sup>* <sup>Ω</sup><sup>2</sup> \_\_\_

moment (*t*), *m*<sup>1</sup>

128 Geophysics

Newton's law, with sufficient accuracy, described the gravitational interaction of material bodies on the scales of individual stars and their planetary systems. It is not applicable to describing processes in the universe as a whole. In this case, it is already necessary to use the general theory of relativity and the law of gravitational interaction of Einstein.

To simulate the conditions for the evolution of the protoplanetary solar disk, the law of gravitation in the Newton approximation is quite sufficient. The obtained numerical results of the solution of the boundary value problem in the body of the increasing radius of the system of nonlinear equations for modeling the thermal conditions for the formation of the Earth and the Moon in one-dimensional and three-dimensional models were analyzed. It is shown that effects can be revealed in the three-dimensional model of the numerical solution of the problem, which could not be detected in a spherically symmetric model, and they significantly influence on the dynamical evolution of the binary system Earth-Moon.

[2] Friedman A. Über die Krümmung des. Raumes. Zeitschrift fur Physik. 1922;**10**:377-386

Dynamics of the Early Stage of Formation of the Earth's-Moon System

http://dx.doi.org/10.5772/intechopen.72641

131

[3] Hubble E. The relationship between the distance and the radial velocity of extragalactic nebulae. In: Proceedings of the USA National Academy of Sciences. 1929;**15**(3):168-173

[5] Jacobsen S. The Hf-W isotopic system and the origin of the Earth and Moon. Annual

[6] Krot A, Amelin Y, Bland P, Ciesla F, Connelly J, et al. Origin and chronology of chondritic components: A review. Geokhimica et Cosmokhimica Acta. 2009;**73**:4963-4997 [7] Nyquist L, Kleine T, Shih C-Y, Reese Y. The distribution of short-living radioisotopes in the early solar system and the chronology of asteroid accretion, differentiation, and

secondary mineralization. Geokhimica et Cosmokhimica Acta. 2009;**73**:5115-5136

[8] Safronov V. Evolution of the Protoplanetary Cloud and Formation of the Earth and the

[9] Maeva S. About the thermal history of the Earth. Izvestija AN USSR. Physika Zemli.

[11] Anfilogov V, Khachay Y. A possible scenario of material differentiation at initial stage of

[12] Anfilogov V, Khachay Y. Some aspects of the solar system formation. Briefs of the Earth Sciences. Cham, Heidelberg, New York, Dordrecht, London: Springer; 2015. 75p

[13] Khachay Y, Hachay O, Antipin A. Heat production by the viscous dissipation of energy

[14] Pechernikova G, Vitjasev A. Catastrophic influences of cosmic bodies. Moscow: IKZ

[15] Samarskiy A, Moiseenko B. The economic scheme of transparent account of Stefan problem. Journal of Computational Mathematics and Mathematical Physics. 1965;

[16] Tikhonov A, Lubimova E, Vlasov V. About the evolution of melting zones in the Earth's

[18] Zharkov V, Trubitsin V. Physics of the Planetary Interior. Moscow: Nauka; 1980. 448 p.

[19] Landau L, Lifshitz E. Theoretical physics. Hydrodynamics. 3rd ed. Main edition of phys-

[20] Schubert G, Turcotte D, Olson P. Mantle Convection in the Earth and Planets. Melburn, Australia, Madrid, Spain, Cape Town, South Africa: Cambridge University Press; 2001.

[10] Lubimova E. Thermal Earth and Moon. Moscow: Nauka; 1968. 280 p (in Russian)

the earth formation. Doclady Earth Siences. 2005;**403A**:954-947 (in Russian)

at the stage of accumulation of the earth. Geoinformatika. 2017;**4**:5-9

thermal history. Dokladi AN USSR. 1969;**188**(2):338-341 (in Russian) [17] Ruskol E. Origin of the Moon. Moscow: Nauka; 1975. 188 p. (in Russian)

math literature. Moscow: Nauka; 1986. 736 p. (in Russian)

[4] Penzias A. The origin of the Elements. 1979;**129**:581-593

Planets. Moscow: Nauka; 1969; 168 p (in Russian)

Akadembook; 2005. pp. 251-265 (in Russian)

1967;**3**:3-17 (in Russian)

**5**(5):816-827 (in Russian)

(in Russian)

940 p

Review of Earth and Planetary Sciences. 2005;**33**:531-570

As the mass increases, the distance between their centers of mass and the speed of the orbital rotation of the Moon around the Earth change. From the law of conservation of angular momentum (Eq. (6)), it follows that the tidal interaction as the mass of the central body increases provides the transfer of the orbital angular momentum of the satellite to the central massive body. At the same time, part of the rotational energy was converted into thermal energy due to viscous friction. Losing the orbital moment, the satellite should approach the central body right up to the orbit of Rosh. The problem of the behavior of the satellite at the Rosh limit requires a careful mathematical study. The power of additional thermal energy and the volume of molten inclusions should increase with the growth of the Earth. Due to the continued transfer of the satellite's orbital moment to the central body, its own angular velocity continued to grow. This should lead to an increase in the orbital angular velocity of the satellite and an increase in the radius of its orbit, which is observed up to the present time.

Thus, the effect of dissipation of viscous friction most significantly manifests itself at the initial stage of the formation of the Earth. The results obtained depend on the parameters, primarily the viscosity versus temperature and pressure, the values of which are known with a high degree of uncertainty. They are to be verified from the results of further research in the areas of physical-mathematical and geological exploration.

#### **Acknowledgements**

The work was carried out with the RFBR grant No. 16-05-00540.

#### **Author details**

Yurie Khachay, Olga Hachay\* and Alexander Antipin

\*Address all correspondence to: olgakhachay@yandex.ru

Institute of Geophysics UB RAS, Ekaterinburg, Russian Federation

#### **References**

[1] Einstein A. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik. 1916;**354**(7):769-822


To simulate the conditions for the evolution of the protoplanetary solar disk, the law of gravitation in the Newton approximation is quite sufficient. The obtained numerical results of the solution of the boundary value problem in the body of the increasing radius of the system of nonlinear equations for modeling the thermal conditions for the formation of the Earth and the Moon in one-dimensional and three-dimensional models were analyzed. It is shown that effects can be revealed in the three-dimensional model of the numerical solution of the problem, which could not be detected in a spherically symmetric model, and they significantly

As the mass increases, the distance between their centers of mass and the speed of the orbital rotation of the Moon around the Earth change. From the law of conservation of angular momentum (Eq. (6)), it follows that the tidal interaction as the mass of the central body increases provides the transfer of the orbital angular momentum of the satellite to the central massive body. At the same time, part of the rotational energy was converted into thermal energy due to viscous friction. Losing the orbital moment, the satellite should approach the central body right up to the orbit of Rosh. The problem of the behavior of the satellite at the Rosh limit requires a careful mathematical study. The power of additional thermal energy and the volume of molten inclusions should increase with the growth of the Earth. Due to the continued transfer of the satellite's orbital moment to the central body, its own angular velocity continued to grow. This should lead to an increase in the orbital angular velocity of the satellite and an increase in the radius of its orbit, which is observed up to the present time. Thus, the effect of dissipation of viscous friction most significantly manifests itself at the initial stage of the formation of the Earth. The results obtained depend on the parameters, primarily the viscosity versus temperature and pressure, the values of which are known with a high degree of uncertainty. They are to be verified from the results of further research in the

influence on the dynamical evolution of the binary system Earth-Moon.

areas of physical-mathematical and geological exploration.

The work was carried out with the RFBR grant No. 16-05-00540.

Yurie Khachay, Olga Hachay\* and Alexander Antipin

\*Address all correspondence to: olgakhachay@yandex.ru

Institute of Geophysics UB RAS, Ekaterinburg, Russian Federation

[1] Einstein A. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik.

**Acknowledgements**

**Author details**

130 Geophysics

**References**

1916;**354**(7):769-822


**Section 4**

**Electrical Resistivity Surveying**

**Electrical Resistivity Surveying**

**Chapter 8**

**Provisional chapter**

**Geoelectrical Sounding and Imaging over the Central**

**Geoelectrical Sounding and Imaging over the Central** 

Electrical properties of rocks and geoelectrical resistivity method have been discussed in this chapter, in which the results of an electrical survey over the sedimentary terrain of the central zone of Panama (Central America) are presented. This study therefore includes (i) a petrophysical study with the aim of relating its electrical resistivity values with the volumetric water contents, (ii) an electrical resistivity imaging (2D inversion), and (iii) an electrical sounding (1D inversion) for detecting the water table and its corresponding stratigraphy and variation with time. Two datasets for these last methods have been developed with the aim of monitoring the percentage changes in model resistivity. Petrophysical tests show good fits between resistivity and volumetric water content and known parameters for rocks and soils. 1D and 2D inversions show a significant reliability with the stratigraphic information obtained from a borehole and strong changes caused

**Keywords:** electrical sounding, electrical resistivity imaging, petrophysical,

In geophysical studies, resistivity method can be used in fault zone detection and stratigraphic characterization, in hydrology for tracing water transport during a given period of irrigation studies, and for archeological and agriculture purposes. Resistivity is controlled by water content, soil texture and its geochemical properties, lithology, organic matter content, and thermodynamic parameters. The electrical properties of the materials that make up part of the outermost layers of the crust can be studied either electrically or electromagnetically from the response produced by the flow of electrical current in the subsurface. Geoelectrical methods

sedimentary rocks, geophysical inversion, time-lapse imaging

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.74210

**Zone of Panama**

**Zone of Panama**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74210

by rainy season in this tropical zone.

Alexis Mojica

Alexis Mojica

**Abstract**

**1. Introduction**

#### **Geoelectrical Sounding and Imaging over the Central Zone of Panama Geoelectrical Sounding and Imaging over the Central Zone of Panama**

DOI: 10.5772/intechopen.74210

#### Alexis Mojica Alexis Mojica

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.74210

#### **Abstract**

Electrical properties of rocks and geoelectrical resistivity method have been discussed in this chapter, in which the results of an electrical survey over the sedimentary terrain of the central zone of Panama (Central America) are presented. This study therefore includes (i) a petrophysical study with the aim of relating its electrical resistivity values with the volumetric water contents, (ii) an electrical resistivity imaging (2D inversion), and (iii) an electrical sounding (1D inversion) for detecting the water table and its corresponding stratigraphy and variation with time. Two datasets for these last methods have been developed with the aim of monitoring the percentage changes in model resistivity. Petrophysical tests show good fits between resistivity and volumetric water content and known parameters for rocks and soils. 1D and 2D inversions show a significant reliability with the stratigraphic information obtained from a borehole and strong changes caused by rainy season in this tropical zone.

**Keywords:** electrical sounding, electrical resistivity imaging, petrophysical, sedimentary rocks, geophysical inversion, time-lapse imaging

#### **1. Introduction**

In geophysical studies, resistivity method can be used in fault zone detection and stratigraphic characterization, in hydrology for tracing water transport during a given period of irrigation studies, and for archeological and agriculture purposes. Resistivity is controlled by water content, soil texture and its geochemical properties, lithology, organic matter content, and thermodynamic parameters. The electrical properties of the materials that make up part of the outermost layers of the crust can be studied either electrically or electromagnetically from the response produced by the flow of electrical current in the subsurface. Geoelectrical methods

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

take into account these electrical and electromagnetic aspects whose physical parameters, such as electrical current, electrical potential, and electromagnetic fields can be measured naturally or artificially. In 1830 a self-potential method based on the natural electrical response of the subsurface was used [1]. In his work, low-intensity electrical currents generated by some minerals were identified. Later, this methodology underwent certain changes in terms of using a natural source, and Schlumberger, during the second decade of the last century, decided to use artificial sources by injecting electrical current into the subsoil.

Geoelectrical methods have been used extensively in groundwater studies and stratigraphic characterization. Several authors have carried out studies of samples in the laboratory using petrophysical relationships [8] in which the volumetric water content is obtained by the measurement of dry bulk density and the gravimetric water content, for example, see [9, 10] in leachate recirculation studies, [11, 12] for root-zone moisture interactions and watershed

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137

This chapter gives a short description of electrical properties of rocks, basic principles of the geoelectrical resistivity method, and a case study of sedimentary rocks of central zone of Panama (Central America) that include petrophysical soil analysis and 1D and 2D inversion methodology. This study has been developed with the aim: (i) to obtain a relationship between electrical resistivity with volumetric water content and correlation with the empirical equation of Archie's law and (ii) to define a 1D and 2D electrical models for two datasets obtained in different seasons (dry and rainy) and relate the results to the stratigraphy and in

The study area is located in an open test zone of the extension of the Technological University of Panama, 19 km East-Northeast of Panama City in the central zone of Isthmus of Panama, Central America; see **Figure 1(a)**. Panama has a rainy and dry seasons, with a tropical maritime

addition monitor the percentage changes of calculated resistivity values.

**Figure 1.** (a) Location map and (b) geological setting of study area and environs [18].

characterization, and [13] in rainfall simulations.

**2. Study area and geology**

The electrical resistivity of rocks is a physical property that is characterized by very large variations in their values; most rocks and soil can be classified as highly resistive or insulating, and only metallic minerals and some of their salts can be classified as conductors. There are three ways in which electrical current can propagate through the subsurface: ohmic or electronic, electrolytic, and dielectric. The first is related to normal type of flow of charges through materials with free electrons such as metals; for electrolytic conduction, almost all soils and rocks have pores that could be saturated with water; thus, for those types of soils and rocks that have high ranges of electrical resistivity, the circulation of electrical current is carried out exclusively through electrolytic conduction due to the presence of water contained in the pores and fissures of the material. This means that the value of the electrical resistivity depends on the concentration and degree of dissociation and mobility of ions [2]. Electrolytic conduction is produced by the slow movement of the ions within the electrolyte; therefore, the rocks are electrolytic conductors where the flow of electrical charge occurs through the conduction of ions. Dielectric conduction occurs only in materials with high electrical resistivity (insulators). According to [3], in this class of materials, the electrons can experience a slight displacement with respect to their atomic nucleus in the presence of a variable external electric field.

Geoelectrical methods include a wide variety of techniques that are adapted to the objectives of the investigation, the dimensions and topography of the area of interest, and the electrical properties of the soil and rocks that make up the study area and whether these properties undergo large variations. Techniques such as self-potential, telluric and magnetotellurics, electrical resistivity (which we will deal with in more detail in this chapter), electromagnetism, and induced polarization allow a rapid measurement of the electrical properties of the soil, such as electrical resistivity, or its opposite, electrical conductivity. These noninvasive techniques essentially involve the interpretation of these physical parameters of the soil, which quantify the degree of difficulty or ease in which a certain volume of soil responds to the passing of electric charges, respectively; for more details about these methods, see [1, 3–7].

The electrical resistivity method is one of the most common geoelectrical methods for the prior evaluation of soil in civil, environmental, archeological, geological, and agricultural projects. Its noninvasive nature and the rapid data acquisition make this method an inexpensive and effective tool in the detailed evaluation of soil. Then, the determination of the geochemical and geophysical properties of soil is essential to the development of civil and agricultural engineering projects. In archeology, for example, the resistivity method constitutes an additional tool of remarkable value when evaluating in advance the presence and/ or absence of buried archeological features, thus optimizing resources and time spent in the field, with significant economic impact. Conventional methods of soil analysis directly affect the soil because the samples must be taken and analyzed in a laboratory.

Geoelectrical methods have been used extensively in groundwater studies and stratigraphic characterization. Several authors have carried out studies of samples in the laboratory using petrophysical relationships [8] in which the volumetric water content is obtained by the measurement of dry bulk density and the gravimetric water content, for example, see [9, 10] in leachate recirculation studies, [11, 12] for root-zone moisture interactions and watershed characterization, and [13] in rainfall simulations.

This chapter gives a short description of electrical properties of rocks, basic principles of the geoelectrical resistivity method, and a case study of sedimentary rocks of central zone of Panama (Central America) that include petrophysical soil analysis and 1D and 2D inversion methodology. This study has been developed with the aim: (i) to obtain a relationship between electrical resistivity with volumetric water content and correlation with the empirical equation of Archie's law and (ii) to define a 1D and 2D electrical models for two datasets obtained in different seasons (dry and rainy) and relate the results to the stratigraphy and in addition monitor the percentage changes of calculated resistivity values.

#### **2. Study area and geology**

take into account these electrical and electromagnetic aspects whose physical parameters, such as electrical current, electrical potential, and electromagnetic fields can be measured naturally or artificially. In 1830 a self-potential method based on the natural electrical response of the subsurface was used [1]. In his work, low-intensity electrical currents generated by some minerals were identified. Later, this methodology underwent certain changes in terms of using a natural source, and Schlumberger, during the second decade of the last century,

The electrical resistivity of rocks is a physical property that is characterized by very large variations in their values; most rocks and soil can be classified as highly resistive or insulating, and only metallic minerals and some of their salts can be classified as conductors. There are three ways in which electrical current can propagate through the subsurface: ohmic or electronic, electrolytic, and dielectric. The first is related to normal type of flow of charges through materials with free electrons such as metals; for electrolytic conduction, almost all soils and rocks have pores that could be saturated with water; thus, for those types of soils and rocks that have high ranges of electrical resistivity, the circulation of electrical current is carried out exclusively through electrolytic conduction due to the presence of water contained in the pores and fissures of the material. This means that the value of the electrical resistivity depends on the concentration and degree of dissociation and mobility of ions [2]. Electrolytic conduction is produced by the slow movement of the ions within the electrolyte; therefore, the rocks are electrolytic conductors where the flow of electrical charge occurs through the conduction of ions. Dielectric conduction occurs only in materials with high electrical resistivity (insulators). According to [3], in this class of materials, the electrons can experience a slight displacement

with respect to their atomic nucleus in the presence of a variable external electric field.

Geoelectrical methods include a wide variety of techniques that are adapted to the objectives of the investigation, the dimensions and topography of the area of interest, and the electrical properties of the soil and rocks that make up the study area and whether these properties undergo large variations. Techniques such as self-potential, telluric and magnetotellurics, electrical resistivity (which we will deal with in more detail in this chapter), electromagnetism, and induced polarization allow a rapid measurement of the electrical properties of the soil, such as electrical resistivity, or its opposite, electrical conductivity. These noninvasive techniques essentially involve the interpretation of these physical parameters of the soil, which quantify the degree of difficulty or ease in which a certain volume of soil responds to the passing of electric charges, respectively; for more details about these methods, see [1, 3–7].

The electrical resistivity method is one of the most common geoelectrical methods for the prior evaluation of soil in civil, environmental, archeological, geological, and agricultural projects. Its noninvasive nature and the rapid data acquisition make this method an inexpensive and effective tool in the detailed evaluation of soil. Then, the determination of the geochemical and geophysical properties of soil is essential to the development of civil and agricultural engineering projects. In archeology, for example, the resistivity method constitutes an additional tool of remarkable value when evaluating in advance the presence and/ or absence of buried archeological features, thus optimizing resources and time spent in the field, with significant economic impact. Conventional methods of soil analysis directly affect

the soil because the samples must be taken and analyzed in a laboratory.

decided to use artificial sources by injecting electrical current into the subsoil.

136 Geophysics

The study area is located in an open test zone of the extension of the Technological University of Panama, 19 km East-Northeast of Panama City in the central zone of Isthmus of Panama, Central America; see **Figure 1(a)**. Panama has a rainy and dry seasons, with a tropical maritime

**Figure 1.** (a) Location map and (b) geological setting of study area and environs [18].

climate with a hot, humid, rainy season (May → December) and a short dry season (January → May). According to [14] the transition at the end of the dry season to the beginning of rainy season is linked with the disappearance of trade winds.

According to [15–18], the study area is characterized by a dense sequence of sediments and volcanic rocks. The site is influenced by the geological elements of the Panama Formation (marine facies) of early to late Oligocene; these elements consist of tuffaceous sandstone, tuffaceous siltstone, and algal and foraminiferal limestone [18]. **Figure 1(b)** shows the geological map and study area and environs.

### **3. Methodology**

#### **3.1. Site layout and profile**

To obtain a distribution of electrical resistivity values in lateral and vertical directions, and its variations for a period of three and half months, we have defined a North-South profile of 47 m long; this profile is superimposed on a borehole drilled in 2011 with a piezometer to monitor groundwater dynamics linked with dry and wet seasons. **Figure 2(a)** and **(b)** show the area with profile, electrical sounding, and borehole positions and **Figure 2(c)** a geotechnical scheme of the borehole.

#### **3.2. Petrophysical relationship**

A total of five soil samples were collected from the site to a depth of 20 cm. To obtain a relationship between resistivity and volumetric water content, we have used the ASTM standard G57-06, where the samples are homogenized inside a box of insulating materials as shown in **Figure 3**.

In this box, two metal plates with an equal surface (S) are placed; we connected these plates to the source of electrical current or resistivity meter; see **Figure 3**. On the surface of the soil sample, two metal pins are inserted and separated by distance (*l*) to measure the voltage generated when the electric current passes through this sample. The value of electrical resistivity

**Figure 3.** LandMapper of Landviser and Miller soil box used for the measurement of the electrical resistivity of each soil

sample in laboratory, according to ASTM standard G57-06 (photo courtesy of 3P Soc. Ltda).

*ρ* = *RS/l* (1)

where *R* is the electrical resistance (in Ω). Volumetric water content (θ) and dry bulk density were obtained by weight difference (dried at 105°C for 24 hours) and calculating the gravimetric water content. The relationship between ρ-θ of these samples can be demonstrated and

where *a* is the tortuosity factor, ρ*w* is the electrical resistivity of the fluid filling the pores,

sample (volume of fluid/volume of void-space), and *m* and *n* correspond to the cementation and saturation exponents of the rock, respectively. Under certain special conditions, it is possible to approximate these last parameters and to obtain the volumetric water content

<sup>−</sup>*<sup>n</sup>* (2)

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is the saturation of the

(ρ) of the soil sample is given by:

then fit it into Archie's law [8]:

.

from Φ and *Sa*

*ρ* = *aρ<sup>w</sup>* Φ−*<sup>m</sup> Sa*

Φ is the porosity (volume of void-space/bulk volume of the soil), *Sa*

**Figure 2.** (a) Details of the study area with North-South profile and electrical sounding and borehole location, (b) panoramic of the field site, and (c) description of borehole log.

climate with a hot, humid, rainy season (May → December) and a short dry season (January → May). According to [14] the transition at the end of the dry season to the beginning of rainy

According to [15–18], the study area is characterized by a dense sequence of sediments and volcanic rocks. The site is influenced by the geological elements of the Panama Formation (marine facies) of early to late Oligocene; these elements consist of tuffaceous sandstone, tuffaceous siltstone, and algal and foraminiferal limestone [18]. **Figure 1(b)** shows the geological

To obtain a distribution of electrical resistivity values in lateral and vertical directions, and its variations for a period of three and half months, we have defined a North-South profile of 47 m long; this profile is superimposed on a borehole drilled in 2011 with a piezometer to monitor groundwater dynamics linked with dry and wet seasons. **Figure 2(a)** and **(b)** show the area with profile, electrical sounding, and borehole positions and **Figure 2(c)** a geotechnical scheme of the borehole.

A total of five soil samples were collected from the site to a depth of 20 cm. To obtain a relationship between resistivity and volumetric water content, we have used the ASTM standard G57-06, where the samples are homogenized inside a box of insulating materials as shown in **Figure 3**.

**Figure 2.** (a) Details of the study area with North-South profile and electrical sounding and borehole location, (b)

panoramic of the field site, and (c) description of borehole log.

season is linked with the disappearance of trade winds.

map and study area and environs.

**3. Methodology**

138 Geophysics

**3.1. Site layout and profile**

**3.2. Petrophysical relationship**

**Figure 3.** LandMapper of Landviser and Miller soil box used for the measurement of the electrical resistivity of each soil sample in laboratory, according to ASTM standard G57-06 (photo courtesy of 3P Soc. Ltda).

In this box, two metal plates with an equal surface (S) are placed; we connected these plates to the source of electrical current or resistivity meter; see **Figure 3**. On the surface of the soil sample, two metal pins are inserted and separated by distance (*l*) to measure the voltage generated when the electric current passes through this sample. The value of electrical resistivity (ρ) of the soil sample is given by:

$$
\rho = RSl \tag{1}
$$

where *R* is the electrical resistance (in Ω). Volumetric water content (θ) and dry bulk density were obtained by weight difference (dried at 105°C for 24 hours) and calculating the gravimetric water content. The relationship between ρ-θ of these samples can be demonstrated and then fit it into Archie's law [8]:

$$
\rho = a \rho\_u \Phi^{-u} \mathcal{S}\_u^{-u} \tag{2}
$$

where *a* is the tortuosity factor, ρ*w* is the electrical resistivity of the fluid filling the pores, Φ is the porosity (volume of void-space/bulk volume of the soil), *Sa* is the saturation of the sample (volume of fluid/volume of void-space), and *m* and *n* correspond to the cementation and saturation exponents of the rock, respectively. Under certain special conditions, it is possible to approximate these last parameters and to obtain the volumetric water content from Φ and *Sa* .

#### **3.3. Electrical sounding and 2D electrical resistivity imaging acquisition and processing**

The electrical resistivity methods generate three-dimensional patterns of electric current and electric potential flows within the subsurface [19]. In the case of two electrodes inserted in the surface of a homogeneous and isotropic half soil and separated by a short distance, it is possible to see a symmetrical pattern in the equipotential lines and in the electric flow lines; this means that at any point in the vicinity of the system, the electrical potential can be affected by the current electrodes (*A* and *B*). In situ, the voltage (Δ*V*) between two points (*M* and *N*) due to the two electrical sources is measured, and the electrical resistivity value is given by:

$$
\rho = k \,\Delta V \text{l/i} \tag{3}
$$

The apparent resistivity value corresponding to each distance AB/2 is plotted logarithmically, resulting in a curvilinear tendency and, subsequently, with the resolution of the 1D inverse problem. This dataset is fitted to a curve that obeys the number of layers with their respective values of calculated electrical resistivity and thickness. The aim of inverse problem is to reconstruct a model from apparent electrical resistivity values. Two resistivity datasets were collected using a Schlumberger electrode configuration on the 16th of February, 2012, and 31st of May, 2012.

**Figure 5.** Distribution of apparent electrical resistivity data points for (a) the electrical sounding with a Schlumberger

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array and (b) a pseudo-section for imaging analysis with a Wenner-Schlumberger array.

The second method consists of obtaining a high-resolution 2D image of the distribution of the electrical resistivity both laterally and vertically. The process consists of obtaining a set of apparent electrical resistivity values through a finite number of electrodes aligned along a profile with a constant distance between them (1 m for this study). The data can be obtained by varying the distances between the pairs of transmitter-receiver electrodes by multiples of a value with a computer-controlled multielectrode system. **Figure 5(b)** shows the electrode

Measurements (for electrical sounding and 2D electrical resistivity imaging) were performed with a Syscal R1 Switch-48 (IRIS Instruments), in a simple mode for the first and a multielectrode mode for the second. In respect of the acquisition setting, the maximum value allowed standard deviation of the measurement was fixed at 1%; minimum and maximum number of stacks per measurement and the current time per cycle were fixed at 3 and 6 and 500 ms, respectively. To obtain a realistic 2D image of electrical resistivity distribution in the soil, we used a cell-based inversion method; this method subdivided the subsurface into a number of rectangular cells whose positions and sizes can be fixed [20]. The aim is to use an inversion algorithm to calculate the electrical resistivity of the cells that provides a model response that agrees with the apparent electrical resistivity values obtained in the field. In this study we used the regularized least-square optimization method [20–22]. This optimization method has two different constraints: the smoothness-constrained method [21] and the robust method [23]; the first is used when the subsurface exhibits a smooth variation in resistivity distribution and the second in regions that are piecewise constant and separated by sharp boundaries [20, 24].

location along the profile and the measured points.

where *k* corresponds to geometrical factor, which only depends on electrode position and *i* the electrical current.

In the case of an inhomogeneous medium, the measurements of the electrical resistivity of the subsurface tend to change when the set of four electrodes or quadrupole is moved along a profile. Another important aspect is that the value of electrical resistivity defined in the last equation will depend on the geometrical configuration of the electrodes and not on the intensity of the electric current. Therefore, the value obtained in this equation will correspond to a kind of average values of resistivity of the subsurface, from which we get the apparent electrical resistivity (ρ*<sup>a</sup>* ). It is important to note that the value of the apparent electrical resistivity of the soil will be its real value only if the soil is homogeneous. In practice there are different types of quadrupole arrays whose use will depend on the objectives of the research. Each of them is characterized by different geometric constants (*k*); **Figure 4** presents the most common arrangements used in soil exploration.

For each of the linear arrays of **Figure 4**, the record of the apparent electrical resistivity value of the subsoil is taken at the center of the internal electrodes; the measurement point is located at the center of the four electrodes. These quadrupole arrays allow the development of several modalities which are closely related to the objectives of the research. In this work we used the electrical sounding and 2D electrical resistivity imaging. The first method consists of keeping the position of the potential electrodes fixed (1 m apart for this study) and moving the current electrodes by 1 m. This procedure, illustrated in **Figure 5(a)**, allows defining a tabular model of the subsurface based on the geometrical distribution of the strata that have different electrical properties.

**Figure 4.** Some common quadrupole arrays: (a) Schlumberger, (b) Wenner, and (c) dipole–dipole and geometric constant.

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**3.3. Electrical sounding and 2D electrical resistivity imaging acquisition and** 

is measured, and the electrical resistivity value is given by:

The electrical resistivity methods generate three-dimensional patterns of electric current and electric potential flows within the subsurface [19]. In the case of two electrodes inserted in the surface of a homogeneous and isotropic half soil and separated by a short distance, it is possible to see a symmetrical pattern in the equipotential lines and in the electric flow lines; this means that at any point in the vicinity of the system, the electrical potential can be affected by the current electrodes (*A* and *B*). In situ, the voltage (Δ*V*) between two points (*M* and *N*) due to the two electrical sources

*ρ* = *k* Δ *V/i* (3)

where *k* corresponds to geometrical factor, which only depends on electrode position and *i*

In the case of an inhomogeneous medium, the measurements of the electrical resistivity of the subsurface tend to change when the set of four electrodes or quadrupole is moved along a profile. Another important aspect is that the value of electrical resistivity defined in the last equation will depend on the geometrical configuration of the electrodes and not on the intensity of the electric current. Therefore, the value obtained in this equation will correspond to a kind of average values of resistivity of the subsurface, from which we get the apparent electri-

of the soil will be its real value only if the soil is homogeneous. In practice there are different types of quadrupole arrays whose use will depend on the objectives of the research. Each of them is characterized by different geometric constants (*k*); **Figure 4** presents the most com-

For each of the linear arrays of **Figure 4**, the record of the apparent electrical resistivity value of the subsoil is taken at the center of the internal electrodes; the measurement point is located at the center of the four electrodes. These quadrupole arrays allow the development of several modalities which are closely related to the objectives of the research. In this work we used the electrical sounding and 2D electrical resistivity imaging. The first method consists of keeping the position of the potential electrodes fixed (1 m apart for this study) and moving the current electrodes by 1 m. This procedure, illustrated in **Figure 5(a)**, allows defining a tabular model of the subsurface based on the geometrical distribution of the strata that have different electrical properties.

**Figure 4.** Some common quadrupole arrays: (a) Schlumberger, (b) Wenner, and (c) dipole–dipole and geometric constant.

). It is important to note that the value of the apparent electrical resistivity

**processing**

140 Geophysics

the electrical current.

cal resistivity (ρ*<sup>a</sup>*

mon arrangements used in soil exploration.

**Figure 5.** Distribution of apparent electrical resistivity data points for (a) the electrical sounding with a Schlumberger array and (b) a pseudo-section for imaging analysis with a Wenner-Schlumberger array.

The apparent resistivity value corresponding to each distance AB/2 is plotted logarithmically, resulting in a curvilinear tendency and, subsequently, with the resolution of the 1D inverse problem. This dataset is fitted to a curve that obeys the number of layers with their respective values of calculated electrical resistivity and thickness. The aim of inverse problem is to reconstruct a model from apparent electrical resistivity values. Two resistivity datasets were collected using a Schlumberger electrode configuration on the 16th of February, 2012, and 31st of May, 2012.

The second method consists of obtaining a high-resolution 2D image of the distribution of the electrical resistivity both laterally and vertically. The process consists of obtaining a set of apparent electrical resistivity values through a finite number of electrodes aligned along a profile with a constant distance between them (1 m for this study). The data can be obtained by varying the distances between the pairs of transmitter-receiver electrodes by multiples of a value with a computer-controlled multielectrode system. **Figure 5(b)** shows the electrode location along the profile and the measured points.

Measurements (for electrical sounding and 2D electrical resistivity imaging) were performed with a Syscal R1 Switch-48 (IRIS Instruments), in a simple mode for the first and a multielectrode mode for the second. In respect of the acquisition setting, the maximum value allowed standard deviation of the measurement was fixed at 1%; minimum and maximum number of stacks per measurement and the current time per cycle were fixed at 3 and 6 and 500 ms, respectively. To obtain a realistic 2D image of electrical resistivity distribution in the soil, we used a cell-based inversion method; this method subdivided the subsurface into a number of rectangular cells whose positions and sizes can be fixed [20]. The aim is to use an inversion algorithm to calculate the electrical resistivity of the cells that provides a model response that agrees with the apparent electrical resistivity values obtained in the field. In this study we used the regularized least-square optimization method [20–22]. This optimization method has two different constraints: the smoothness-constrained method [21] and the robust method [23]; the first is used when the subsurface exhibits a smooth variation in resistivity distribution and the second in regions that are piecewise constant and separated by sharp boundaries [20, 24].

As in the electrical sounding, two resistivity datasets were collected using a Wenner-Schlumberger array for the electrical resistivity imaging on the 16th of February, 2012, and 31st of May, 2012.

#### **3.4. Time-lapse inversion**

To monitor the changes in subsurface resistivity values during the period defined in the study area, we used the Res2Dinv inversion software (Geotomo); the time-lapse dataset can be interpreted through the time-lapse method proposed by [25]. In this software, the initial dataset for the inversion model is used as a reference model in the inversion of the later time-lapse datasets [26]. For our first dataset, we used the robust method; regarding another inversion parameter, we used an initial damping factor of 0.15, minimum damping factor = 0.030, and a simultaneous inversion.

#### **4. Results and interpretation**

#### **4.1. Resistivity: volumetric water content derived from soil samples**

**Figure 6** presents a plot of electrical resistivity versus the volumetric water content of the soil samples obtained in the surveyed area. The fit was done using a power function with a good coefficient of determination, *R*<sup>2</sup> of 0.950; high values of resistivity of this type of soil (weathered rock) can be linked to 26% of volumetric water content, while the low values of electrical resistivity of the samples are related to 49% of water content.

**Figure 7.** (a) Logarithmic representation of the two datasets as a function of distance AB/2, (b) tabular earth model

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**Figure 8.** Electrical resistivity tomography obtained for a (a) reference test – February 16, 2012 – and (b) second test, May

31, 2102. (c) Percentage changes in model resistivity obtained in this study.

obtained from the inversion, and (c) borehole performed on site.

#### **4.2. Electrical sounding**

**Figure 7(a)** represents the two datasets obtained with a Schlumberger array in the given periods; subsequently, with the resolution of the inverse problem 1D, these datasets were fitted to a curve (for each one) that obeys the number of layers with their respective values

**Figure 6.** Relationship between the electrical resistivity and the volumetric water content obtained in the surveyed area.

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As in the electrical sounding, two resistivity datasets were collected using a Wenner-Schlumberger array for the electrical resistivity imaging on the 16th of February, 2012, and

To monitor the changes in subsurface resistivity values during the period defined in the study area, we used the Res2Dinv inversion software (Geotomo); the time-lapse dataset can be interpreted through the time-lapse method proposed by [25]. In this software, the initial dataset for the inversion model is used as a reference model in the inversion of the later time-lapse datasets [26]. For our first dataset, we used the robust method; regarding another inversion parameter, we used an initial damping factor of 0.15, minimum damping factor = 0.030, and a simultaneous inversion.

**Figure 6** presents a plot of electrical resistivity versus the volumetric water content of the soil samples obtained in the surveyed area. The fit was done using a power function with a good

ered rock) can be linked to 26% of volumetric water content, while the low values of electrical

**Figure 7(a)** represents the two datasets obtained with a Schlumberger array in the given periods; subsequently, with the resolution of the inverse problem 1D, these datasets were fitted to a curve (for each one) that obeys the number of layers with their respective values

**Figure 6.** Relationship between the electrical resistivity and the volumetric water content obtained in the surveyed area.

of 0.950; high values of resistivity of this type of soil (weath-

31st of May, 2012.

142 Geophysics

**3.4. Time-lapse inversion**

**4. Results and interpretation**

coefficient of determination, *R*<sup>2</sup>

**4.2. Electrical sounding**

**4.1. Resistivity: volumetric water content derived from soil samples**

resistivity of the samples are related to 49% of water content.

**Figure 7.** (a) Logarithmic representation of the two datasets as a function of distance AB/2, (b) tabular earth model obtained from the inversion, and (c) borehole performed on site.

**Figure 8.** Electrical resistivity tomography obtained for a (a) reference test – February 16, 2012 – and (b) second test, May 31, 2102. (c) Percentage changes in model resistivity obtained in this study.

of calculated electrical resistivity and thickness. After solving the inverse problem for each dataset, the errors obtained were not greater than 2.1%. **Figure 7(b)** shows a three-layer model for each test.

**Acknowledgements**

**Conflict of interest**

**Author details**

Alexis Mojica1,2\*

of Panama, Panama

**References**

429 p

s10712-005-1759-6

Verlag; 1995. 173 p

9780511810305

Chichester: Wiley; 2011. 710 p

2007. 390 p. DOI: 10.1017/CBO9780511807107

Author discloses no potential conflicts of interest.

\*Address all correspondence to: alexis.mojica@utp.ac.pa

observations.

I am grateful to the Technological University of Panama and National Research System of SENACYT for all their support. I would like to thank the reviewers for their constructive

Geoelectrical Sounding and Imaging over the Central Zone of Panama

http://dx.doi.org/10.5772/intechopen.74210

145

1 Research Laboratory in Engineering and Applied Sciences, CEI, Technological University

[1] Parasnis DS. Principles of Applied Geophysics. 5th ed. London: Chapman & Hall; 1997.

[2] Nover G. Electrical properties of crustal and mantle rocks – A review of laboratory measurements and their explanation. Surveys in Geophysics. 2005;**26**:593-651. DOI: 10.1007/

[3] Telford WM, Geldart LP, Sheriff RE. Applied Geophysics. 2nd ed. New York: Cambridge

[4] Vogelsang D. Environmental Geophysics. A Practical Guide. 1st ed. Germany: Springer-

[5] Reynolds JM. An Introduction to Applied and Environmental Geophysics. 2nd ed.

[6] Mussett AE, Khan MA. Looking into the Earth. An Introduction to Geological Geophysics. 1st ed. New York: Cambridge University Press; 2000. 470 p. DOI: 10.1017/CBO

[7] Lowrie W. Fundamentals of Geophysics. 2nd ed. New York: Cambridge University Press;

2 Tocumen Extension and National Research System, SENACYT, Panama

University Press; 1990. 770 p. DOI: 10.1017/CBO9781139167932

In both cases, the resolution of the inverse problem suggests the existence of a first layer of 14.5–19.7 Ω.m and a variation of thickness from 0.6 m to 1.6; this effect is linked to the change from dry to rainy season. Water-table elevation obtained from a piezometer has shown variation between 1.57 and 0.61 m for each date, followed by a second layer of 8.9 and 9.6 Ω.m and 5.4 and 6.4 m thick for each season, respectively. Finally, there is a last layer with 16.2 and 16.5 Ω.m; the results of this last layer do not show significant changes in their electrical properties and thicknesses. In accordance with the borehole at the site, the two first layers are linked to weathered and fractured sedimentary rock, while the last layer reported for both analyses is linked to hard sedimentary rock.

#### **4.3. Electrical resistivity imaging and time-lapse results**

**Figure 8(a)** and **(b)** show the results of inverse problem solution; in these electrical tomographies, it is possible to identify a first horizon related to weathered rocks and clay (13–27 Ω.m) with tones in brown, red, and yellow. The changes in calculated resistivity values are related to the beginning of rainy season; saturation of surface horizons can produce a decrease in calculated resistivity value. At depth, it is possible to identify a low resistivity (6–13 Ω.m) horizon from the result of **Figure 8(a)**. However, these low values are also revealed at shallow depth; see **Figure 8(b)**. About **Figure 8(c)**, high negative percentage changes are linked to increase of water content in subsoil produced by rains which occurred on May 31, 2012. At depth, the percentage changes are close to 0. Positive percentage changes in model resistivity are related to inversion artifacts. It is possible that these unrealistic changes can be linked to the removal electrode after the first test or inversion scheme used in this analysis.

#### **5. Conclusions**

The results of this study show the value of petrophysical relationship of soil samples in understanding the potential function between the electrical properties of rocks and its volumetric water content. These functions can help to understand the evolution of vadose zone moisture in response to seasonal changes in the tropics. Electrical sounding and electrical resistivity imaging are useful tools not only for monitoring changes in the physical properties of this kind of soils but also for associating the different types of soils and rocks with its electrical properties. We have seen the association of these results with the borehole at the site. The strong negative percentage variation in calculated resistivity values presented in the surveyed area shows the important seasonal changes occurring in the tropics, where these negative values are related to the superficial infiltration produced by the rainfall during the transitional season (dry → rainy). The positive percentage changes in model resistivity can be associated with artifacts, linked to inversion method used or due to the removal of the electrodes after each test.

## **Acknowledgements**

of calculated electrical resistivity and thickness. After solving the inverse problem for each dataset, the errors obtained were not greater than 2.1%. **Figure 7(b)** shows a three-layer model

In both cases, the resolution of the inverse problem suggests the existence of a first layer of 14.5–19.7 Ω.m and a variation of thickness from 0.6 m to 1.6; this effect is linked to the change from dry to rainy season. Water-table elevation obtained from a piezometer has shown variation between 1.57 and 0.61 m for each date, followed by a second layer of 8.9 and 9.6 Ω.m and 5.4 and 6.4 m thick for each season, respectively. Finally, there is a last layer with 16.2 and 16.5 Ω.m; the results of this last layer do not show significant changes in their electrical properties and thicknesses. In accordance with the borehole at the site, the two first layers are linked to weathered and fractured sedimentary rock, while the last layer reported for both analyses is

**Figure 8(a)** and **(b)** show the results of inverse problem solution; in these electrical tomographies, it is possible to identify a first horizon related to weathered rocks and clay (13–27 Ω.m) with tones in brown, red, and yellow. The changes in calculated resistivity values are related to the beginning of rainy season; saturation of surface horizons can produce a decrease in calculated resistivity value. At depth, it is possible to identify a low resistivity (6–13 Ω.m) horizon from the result of **Figure 8(a)**. However, these low values are also revealed at shallow depth; see **Figure 8(b)**. About **Figure 8(c)**, high negative percentage changes are linked to increase of water content in subsoil produced by rains which occurred on May 31, 2012. At depth, the percentage changes are close to 0. Positive percentage changes in model resistivity are related to inversion artifacts. It is possible that these unrealistic changes can be linked to

the removal electrode after the first test or inversion scheme used in this analysis.

The results of this study show the value of petrophysical relationship of soil samples in understanding the potential function between the electrical properties of rocks and its volumetric water content. These functions can help to understand the evolution of vadose zone moisture in response to seasonal changes in the tropics. Electrical sounding and electrical resistivity imaging are useful tools not only for monitoring changes in the physical properties of this kind of soils but also for associating the different types of soils and rocks with its electrical properties. We have seen the association of these results with the borehole at the site. The strong negative percentage variation in calculated resistivity values presented in the surveyed area shows the important seasonal changes occurring in the tropics, where these negative values are related to the superficial infiltration produced by the rainfall during the transitional season (dry → rainy). The positive percentage changes in model resistivity can be associated with artifacts, linked to inversion method used or due to the removal of the electrodes after

for each test.

144 Geophysics

linked to hard sedimentary rock.

**5. Conclusions**

each test.

**4.3. Electrical resistivity imaging and time-lapse results**

I am grateful to the Technological University of Panama and National Research System of SENACYT for all their support. I would like to thank the reviewers for their constructive observations.

## **Conflict of interest**

Author discloses no potential conflicts of interest.

## **Author details**

Alexis Mojica1,2\*

\*Address all correspondence to: alexis.mojica@utp.ac.pa

1 Research Laboratory in Engineering and Applied Sciences, CEI, Technological University of Panama, Panama

2 Tocumen Extension and National Research System, SENACYT, Panama

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## *Edited by Anthony Okiwelu*

This book is focused on different aspects of geophysical research, particularly on modern approach in subsurface imaging, tectonics, geohazard, seismicity, and Earth planetary system. Syntheses of results from regional and local studies combined with new techniques of geophysical data acquisition and interpretation from diverse geological provinces are presented. Some of the chapter explained clearly the geophysical technic that can image local sources in urban and rural settings in Israel. An example of studies on basement tectonics and fault reactivation in North America using integrated geophysical methods is also presented. Two modes of seismicity, one involving rotational seismology and another based on seismic response in Mexico using Hilbert-Huang transform (HHT) as an alternative technique for extracting data that will be useful for the assessment of potential earthquake, are discussed in other sets of chapters. The integration of geoelectric methods in another chapter demonstrated delimitation of the resistivity anomalies caused by different types of hydrocarbon contaminants and rocks in rural, industrial, and urban sites. The results of electrical resistivity method to define 1D and 2D electrical models from two datasets acquired in dry and rainy seasons in Panama (Central America) were used to show the relationship between electrical resistivity and volumetric water content. Petrophysical analyses show good fits between resistivity and volumetric water content and known parameters for rocks and soils. The study on Earth planetary system noted that at all stages of the Earth's formation, convective heat and mass transfer are the most important factors in the dynamics of the planet. The chapter on magnetics shows how remanent magnetization and self-demagnetization complicate the inversion and interpretation of magnetic anomaly with examples from iron deposit in South Australia.

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Geophysics

Geophysics