**Meet the editor**

Prof. Abbas Moustafa is associate professor, Department of Civil Engineering, Minia University, Egypt. He is also a consultant engineer and head of structural group, Hamza Associates, Giza, Egypt. Prof. Moustafa was a senior research associate at Vanderbilt University and a JSPS fellow at Kyoto and Nagasaki Universities. During his career Prof. Moustafa was the chairman of

Department of Civil Engineering, Giza Institute of Engineering, Giza, Egypt. He has about 50 research papers published in international journals and conferences. He is the editor of two books on earthquake-resistant structures and advances on geotechnical earthquake engineering. He co-authored a book on improving the earthquake-resilience of buildings. Prof. Moustafa is editorial board member and reviewer for several regional and international journals. His research interest includes earthquake engineering, seismic and blast design of structures, nonlinear dynamics, random vibration, structural reliability, structural health monitoring and uncertainty modeling.

## Contents

#### **Preface XI**


## Preface

Chapter 8 **Stability and Run-out Analysis of Earthquake-induced**

Chapter 9 **Simplified Multi-Block Constitutive Model Predicting the**

Chapter 10 **Detection of Accelerating Transient of Aseismic Rock Strain**

Chapter 11 **Seismic Reliability-Based Design Optimization of Reinforced Concrete Structures Including Soil-Structure**

Chapter 12 **Initial Shapes of Cable-Stayed Bridges during Construction by**

**Underground Pipes Due to Blast Loads Using Finite**

Chapter 14 **Effect Evaluation of Radiative Heat Transfer and Horizontal**

Chapter 15 **Acute Psychiatric Trauma Intervention — The January 2010**

Chapter 13 **A Study on the Dynamic Dimensionless Behaviours of**

**using Precursory Decline in Groundwater Radon 253**

Mohsen Khatibinia, Sadjad Gharehbaghi and Abbas Moustafa

**Cantilever Methods – Numerical Simulation and Validation of**

**Seismic Displacement of Saturated Sands along Slip Surfaces**

**Landslides 203** Yingbin Zhang

**VI** Contents

Ming-Ching T. Kuo

**Interaction Effects 267**

**the Kao Ping Hsi Bridge 305** Ming-Yi Liu and Pao-Hsii Wang

**Wind on Fire Whirlwind 357**

**Element Method 331** Akinola Johnson Olarewaju

**Haiti Earthquake 379** Kent Ravenscroft

Seigo Sakai

**with Strain Softening 235** Constantine A. Stamatopoulos

> Earthquakes remain the most challenging natural hazard to the engineering community, due to the inherent uncertainty involved in their occurrence, in terms of time, location, size and the catastrophes they cause. Earthquake consequences include tsunami, landslides, fires, explosions, damage to roads, railways, harbors, airports, nuclear power plants, oil and gas pipelines, high-voltage lines, water and communication networks and collapse of stor‐ age tanks, bridges, hospitals, schools, residential buildings and office buildings. Massive de‐ structions and large life losses have occurred during recent earthquakes, such as January 2010 Haiti earthquake, March 2011 Japan earthquake and the more recent 2015 Nepal earth‐ quake. This book deals with characteristics and hazard assessments of earthquake ground motion and associated effects on slopes, land-slides, the built environment and humans.

> This book contains fifteen chapters covering several interesting research topics written by researchers and experts in the fields of earthquake and structural engineering. The book provides the state-of-the-art on recent progress in the field of seimology, earthquake engi‐ neering and structural engineering. The book should be useful to graduate students, re‐ searchers and practicing structural engineers. The book deals with seismicity, seismic hazard assessment and system oriented emergency response for abrupt earthquake disaster, the nature and the components of strong ground motions and several other interesting top‐ ics, such as dam-induced earthquakes, seismic stability of slopes and landslides. The book also tackles the dynamic response of underground pipes to blast loads, the optimal seismic design of RC multi-story buildings, the finite-element analysis of cable-stayed bridges under strong ground motions and the acute psychiatric trauma intervention due to earthquakes.

> Chapters 1-5 involve an updated seismogenic model for Egypt, the seismcity features of Mexico City, assessment of seismic hazard of a territory, the de-trended fluctuation analysis and the windowing Higuchi's method applied to the South California seismicity and a simu‐ lation and evaluation system oriented to the emergency response effectiveness of the abrupt earthquake disaster. The rotational components of the seismic fields are studied in Chapter 6. Chapters 7-10 deal with dams-induced earthquakes, stability of earthquake-induced land‐ slides and predicting triggering, seismic displacement of slopes and detecting accelerating of aseismic rock strain. The optimal seismic design of RC multi-story structures and the fi‐ nite-element analysis of cable-stayed bridges under earthquake loads are investigated in Chapters 11 and 12, respectively. Chapters 13 and 14 deal with behavior of underground pipes due to blasts and effects of radiative heat transfer and horizontal wind on fire whirl‐ wind. Chapter 15 deals with the acute psychiatric trauma intervention with a special focus on the 11th March 2011 Haiti earthquake.

The research reported in this book should be of crucial interest to seismologists, structural and geo-technical engineers, graduate students and researchers of the structural and earth‐ quake engineering fields. I'd like to thank the contributors of this book for their cooperation during the review process of the book chapters. Special thanks to Ms. Iva Simcic for her ef‐ fort in managing and producing the book.

> **Prof. Abbas Moustafa** Department of Civil Engineering Faculty of Engineering Minia University, Minia, Egypt

## **An Updated Seismic Source Model for Egypt**

R. Sawires, J.A. Peláez, R.E. Fat-Helbary, H.A. Ibrahim and M.T. García Hernández

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/58971

**1. Introduction**

The research reported in this book should be of crucial interest to seismologists, structural and geo-technical engineers, graduate students and researchers of the structural and earth‐ quake engineering fields. I'd like to thank the contributors of this book for their cooperation during the review process of the book chapters. Special thanks to Ms. Iva Simcic for her ef‐

**Prof. Abbas Moustafa**

Faculty of Engineering

Department of Civil Engineering

Minia University, Minia, Egypt

fort in managing and producing the book.

VIII Preface

Since the pioneering work of Cornell [1], it is clear that seismic hazard assessment depends on several models, among them perhaps one of the most significant, and usually poorly under‐ stood, is the delineation and characterization of the seismic source model for a particular region. Identification and characterization of the potential seismic sources in any region is one of the most important and critical inputs for doing seismic hazard analysis.

In fact, the characterization of seismic source zones depends on the interpretation of the available geological, geophysical and seismological data obtained by many tools such as tectonic studies, seismicity, surface geological investigations and subsurface geophysical techniques [2]. In addition, the characterization depends on the definition of different surface and sub-surface active faults.

Modern investigations on Probabilistic Seismic Hazard Assessment (PSHA) for any region at any scale, requires that the study region should be subdivided into different seismic sources. The issue of seismic source delineation and characterization is often a controversial one in the practice of seismic hazard analyses, both deterministic and probabilistic, as the information available relating to geology and seismotectonics can vary from region to another region.

It has been common practice since the development of PSHA by Cornell [1] and McGuire [3], to utilize areal source zones of seismic homogeneity [4 and 5]. In the classic form, earthquake sources range from clearly understood and well defined faults to less well understood and less well-defined geologic structures to hypothetical seismotectonic provinces extending over many thousands of square kilometers whose specific relationship to the earthquake generating process is not well known [2].

Recent PSHA at a local or a regional scale is usually based on approaches and computer codes (e.g., FRISK: [6]; SEISRISK III: [7]; CRISIS 2014: [8], etc.) that require the study area to be

© 2015 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.

subdivided into seismic source zones which can be generated by delineating a number of polygons over active seismic areas. These polygons, sometimes have a complex shape, which reflects the complexity of the different faults and tectonic trends (e.g., [9]). The delineation will serve for two purposes: i) adequately represents the geological and tectonic setting together with the recorded seismicity, and ii) it allows for expected variations in future seismicity.

## **2. Seismicity and seismotectonic setting of Egypt**

Egypt is situated in the northeastern corner of the African Plate, along the southeastern edge of the Eastern Mediterranean region. It is interacting with the Arabian and Eurasian Plates through divergent and convergent plate boundaries, respectively. Egypt is surrounded by three active tectonic plate boundaries: the African-Eurasian plate boundary, the Gulf of Suez-Red Sea plate boundary, and the Gulf of Aqaba-Dead Sea Transform Fault (Figure 1). The seismic activity of Egypt is due to the interaction and the relative motion between the plates of Eurasia, Africa and Arabia. Within the last decade, some areas in Egypt have been struck by significant earthquakes causing considerable damage. Such events were interpreted as the result of this interaction.

Based on the geophysical studies in the territory of Egypt, Youssef [10] classified the main structural elements of Egypt (Figure 2) into the following fault categories: a) Gulf of Suez-Red Sea, b) Gulf of Aqaba, c) east-west, d) north-south, and e) N45°W trends. However, Meshref [11], from the magnetic tectonic trend analysis, showed the tectonic trends which influenced Egypt throughout its geologic history as: a) NW (Rea Sea-Gulf of Suez), b) NNE (Aqaba), c) east–west (Tethyan or Mediterreanean Sea), d) north–south (Nubian or East African), e) WNW (Drag), f) ENE (Syrian Arc), and g) NE (Aualitic or Tibesti) trends.

The seismicity of Egypt has been studied by many authors [e.g., 12-22]. Although Egypt is an area of relatively low to moderate seismicity, it has experienced some damaging local shocks throughout its history, as well as the effects of larger earthquakes in the Hellenic Arc and the Eastern Mediterranean area. In addition, it has also been affected by earthquakes in Southern Palestine and the Northern Red Sea [18].

In Egypt, mostly population settlements are concentrated along the Nile Valley and Nile Delta, so, the seismic risk is generally related to the occurrence of moderate size earthquakes at short distances (e.g., MS 5.9, 1992 Cairo earthquake), rather than bigger earthquakes that are known to occur at far distances along the Northern Red Sea, Gulf of Suez, and Gulf of Aqaba (e.g., MS 6.9, 1969 Shedwan, and MW 7.2, 1995 Gulf of Aqaba earthquakes), as well as the Mediter‐ ranean offshore (e.g., MS 6.8, 1955 Alexandria earthquake) [23].

Egypt is suffering from both interplate and intraplate earthquakes; intraplate earthquakes are less frequent but still represent an important component of risk in Egypt. Shallow-depth seismicity (Figure 3) is concentrated mainly in the surrounding plate boundaries and on some active seismic zones like Aswan, Abu Dabbab, and Cairo-Suez regions, while the deeper activity is concentrated mainly along the Cyprian and Hellenic Arcs due to the subduction process between Africa and Europe.

**Figure 1.** Global tectonic sketch for Egypt and its vicinity (redrawn after Ziegler [24] and Pollastro [25]).

subdivided into seismic source zones which can be generated by delineating a number of polygons over active seismic areas. These polygons, sometimes have a complex shape, which reflects the complexity of the different faults and tectonic trends (e.g., [9]). The delineation will serve for two purposes: i) adequately represents the geological and tectonic setting together with the recorded seismicity, and ii) it allows for expected variations in future seismicity.

2 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Egypt is situated in the northeastern corner of the African Plate, along the southeastern edge of the Eastern Mediterranean region. It is interacting with the Arabian and Eurasian Plates through divergent and convergent plate boundaries, respectively. Egypt is surrounded by three active tectonic plate boundaries: the African-Eurasian plate boundary, the Gulf of Suez-Red Sea plate boundary, and the Gulf of Aqaba-Dead Sea Transform Fault (Figure 1). The seismic activity of Egypt is due to the interaction and the relative motion between the plates of Eurasia, Africa and Arabia. Within the last decade, some areas in Egypt have been struck by significant earthquakes causing considerable damage. Such events were interpreted as the

Based on the geophysical studies in the territory of Egypt, Youssef [10] classified the main structural elements of Egypt (Figure 2) into the following fault categories: a) Gulf of Suez-Red Sea, b) Gulf of Aqaba, c) east-west, d) north-south, and e) N45°W trends. However, Meshref [11], from the magnetic tectonic trend analysis, showed the tectonic trends which influenced Egypt throughout its geologic history as: a) NW (Rea Sea-Gulf of Suez), b) NNE (Aqaba), c) east–west (Tethyan or Mediterreanean Sea), d) north–south (Nubian or East African), e) WNW

The seismicity of Egypt has been studied by many authors [e.g., 12-22]. Although Egypt is an area of relatively low to moderate seismicity, it has experienced some damaging local shocks throughout its history, as well as the effects of larger earthquakes in the Hellenic Arc and the Eastern Mediterranean area. In addition, it has also been affected by earthquakes in Southern

In Egypt, mostly population settlements are concentrated along the Nile Valley and Nile Delta, so, the seismic risk is generally related to the occurrence of moderate size earthquakes at short distances (e.g., MS 5.9, 1992 Cairo earthquake), rather than bigger earthquakes that are known to occur at far distances along the Northern Red Sea, Gulf of Suez, and Gulf of Aqaba (e.g., MS 6.9, 1969 Shedwan, and MW 7.2, 1995 Gulf of Aqaba earthquakes), as well as the Mediter‐

Egypt is suffering from both interplate and intraplate earthquakes; intraplate earthquakes are less frequent but still represent an important component of risk in Egypt. Shallow-depth seismicity (Figure 3) is concentrated mainly in the surrounding plate boundaries and on some active seismic zones like Aswan, Abu Dabbab, and Cairo-Suez regions, while the deeper activity is concentrated mainly along the Cyprian and Hellenic Arcs due to the subduction

**2. Seismicity and seismotectonic setting of Egypt**

(Drag), f) ENE (Syrian Arc), and g) NE (Aualitic or Tibesti) trends.

ranean offshore (e.g., MS 6.8, 1955 Alexandria earthquake) [23].

result of this interaction.

Palestine and the Northern Red Sea [18].

process between Africa and Europe.

**Figure 2.** Distribution of major surface and subsurface faults. Compiled and redrawn from EGSMA [26] geologic map, from Riad [27], and from Issawi [28].

## **3. Review of seismic zoning studies in Egypt**

Seismic hazard assessments for Egypt, based on the zoning approach, has been carried out by many authors in the last decades, based upon the main tectonic features prevailed, the dominant tectonic stresses, the history of seismicity in the region, and the distribution of the recorded earthquakes. These authors were used different criteria to obtain seismic source zonation maps.

Among those studies, those carried out by the following authors: Sieberg [12 and 13], Gergawi and El-Khashab [15], Maamoun and Ibrahim [29], Maamoun *et al.* [16], Albert [30 and 31], Kebeasy *et al.* [32], Kebeasy [17 and 33], Marzouk [34], Fat-Helbary [35-37], Reborto *et al.* [38], Mohammed [39], El-Hadidy [40], Fat-Helbary and Ohta [41], El-Sayed and Wahlstörm [42], Abou Elenean [19 and 43], Badawy [44], Deif [45], Riad *et al.* [46], Abou Elenean and Deif [47], El-Sayed *et al.* [48], Fat-Helbary and Tealeb [49], El-Amin [50 and 51], El-Hefnawy *et al.* [52], Abdel-Rahman *et al.* [53], El-Hadidy [54 and 55], Deif *et al.* [56 and 57], Fat-Helbary *et al.* [58] and Mohamed *et al.* [59].

Egypt was divided into different seismic zones by many researchers, using the distribution of historical and instrumental earthquakes. Maamoun and Ibrahim [29] and Kebeasy [33] divided Egypt into four main seismic trends: i) Northern Red Sea-Gulf of Suez-Cairo-Alexandria, ii) Eastern Mediterranean-Cairo-Fayoum, iii) Mediterranean Coastal Dislocation, and iv) Aqaba-Dead Sea Transform. More recently, Maamoun *et al.* [16] added another two trends to the previous four: i) Hellenic and Cyprian Arcs, and ii) Southern Egyptian trend.

In reviewing the seismicity of Egypt, Kebeasy [17] suggested three main seismic zones: i) Aqaba-Dead Sea Transform, ii) Northern Red Sea-Gulf of Suez-Cairo-Alexandria, iii) Eastern Mediterranean-Cairo-Fayoum zones. In addition, he defined other local seismic zones (e.g., El-Gilf El-Kebeir, Aswan and Qena zones).

Fat-Helbary [36] assessed the seismic hazard for Aswan region. He used both of line sources and area source models. Five active faults in the Aswan region (Kalabsha, Seiyal, Gebel El-Barqa, Kurkur, and Khur El-Ramla Faults) were modeled as seismic lines. On the other hand, six area source zones (Old Stream, North Kalabsha, Khur El-Ramla, East Gebel Marawa, Abu Dirwa, and Kalabsha zones) were considered in the assessment. This study was followed by successive assessments by different authors to include other neighbor regions in Upper Egypt (e.g., [37, 41, 49, 50, 51, 57 and 58]).

Using the relation between the paleo-stresses, the present-day stresses and the distribution of earthquake epicenters, El-Hadidy [40] deduced five major trends in Egypt. They are: i) Pelusium megashear, ii) Eastern Mediterranean-Cairo-Fayoum-El-Gilf El-Kebeir, iii) Nubian-Mozambique, iv) Qena-Aqaba-Dead Sea, and v) Northern Red Sea-Gulf of Suez-Cairo-Alexandria seismotectonic trends. Furthermore, he identified some local zones on the Red Sea, Gulf of Suez, Gulf of Aqaba, Nile Delta, and Cairo-Suez regions.

According to the earthquake distribution, focal mechanisms and the structural and tectonic information, Abou Elenean [19] suggested five seismotectonic sources. They are: i) Gulf of Suez-Northern Eastern Desert, ii) Southwest Cairo (Dahshour), iii) Northern Red Sea, iv) Gulf of Aqaba, and v) Aswan zones. Deif [45], for a seismic hazard assessment study, delineated four additional seismic sources for the southern part of Egypt. They are: i) Abu Dabbab, ii) El-Gilf El-Kebeir, iii) Wadi Halfa, and iv) Northern Nasser's Lake zones.

Riad *et al.* [46] constructed a more detailed seismic zoning map for Egypt and its surroundings. Their regional delineation consists of five main trends: i) the Greek trend, based on the seismic zone regionalization of Papazachos [61], ii) the Dead Sea trend, which mainly based on the earthquake catalogue of Israel and its vicinity [62], iii) Pelusium and Qattara trend, iv) Eastern Mediterranean trend, and v) Aswan area, in Southern Egypt.

El-Hefnawy *et al.* [52], based on the tectonic regime, seismicity, faults location, and focal mechanism solutions, divided the regional seismicity in and around Sinai Peninsula into 25 source zones. His study was succeeded by a certain number of studies that considered a more detailed zonation for the same area (e.g., [53, 54 and 56]).

Recently, Abou Elenean [43] established a detailed zonation map for whole Egypt and its surroundings, considering the recent seismicity distribution and focal mechanism data. He delineated 41 seismic source zones of shallow-depth earthquakes (h < 60 km) in and around Egypt. In addition, he considered 7 seismic sources for intermediate-depth events within the Hellenic Arc (after [63]). More recently, El-Hadidy [55] and Mohamed *et al.* [59] established a new and modified seismic zoning map for Egypt and its surroundings which is based on the compilation of previous studies [53, 57 and 64].

## **4. Data sources**

**3. Review of seismic zoning studies in Egypt**

zonation maps.

and Mohamed *et al.* [59].

El-Gilf El-Kebeir, Aswan and Qena zones).

(e.g., [37, 41, 49, 50, 51, 57 and 58]).

Seismic hazard assessments for Egypt, based on the zoning approach, has been carried out by many authors in the last decades, based upon the main tectonic features prevailed, the dominant tectonic stresses, the history of seismicity in the region, and the distribution of the recorded earthquakes. These authors were used different criteria to obtain seismic source

4 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Among those studies, those carried out by the following authors: Sieberg [12 and 13], Gergawi and El-Khashab [15], Maamoun and Ibrahim [29], Maamoun *et al.* [16], Albert [30 and 31], Kebeasy *et al.* [32], Kebeasy [17 and 33], Marzouk [34], Fat-Helbary [35-37], Reborto *et al.* [38], Mohammed [39], El-Hadidy [40], Fat-Helbary and Ohta [41], El-Sayed and Wahlstörm [42], Abou Elenean [19 and 43], Badawy [44], Deif [45], Riad *et al.* [46], Abou Elenean and Deif [47], El-Sayed *et al.* [48], Fat-Helbary and Tealeb [49], El-Amin [50 and 51], El-Hefnawy *et al.* [52], Abdel-Rahman *et al.* [53], El-Hadidy [54 and 55], Deif *et al.* [56 and 57], Fat-Helbary *et al.* [58]

Egypt was divided into different seismic zones by many researchers, using the distribution of historical and instrumental earthquakes. Maamoun and Ibrahim [29] and Kebeasy [33] divided Egypt into four main seismic trends: i) Northern Red Sea-Gulf of Suez-Cairo-Alexandria, ii) Eastern Mediterranean-Cairo-Fayoum, iii) Mediterranean Coastal Dislocation, and iv) Aqaba-Dead Sea Transform. More recently, Maamoun *et al.* [16] added another two trends to the

In reviewing the seismicity of Egypt, Kebeasy [17] suggested three main seismic zones: i) Aqaba-Dead Sea Transform, ii) Northern Red Sea-Gulf of Suez-Cairo-Alexandria, iii) Eastern Mediterranean-Cairo-Fayoum zones. In addition, he defined other local seismic zones (e.g.,

Fat-Helbary [36] assessed the seismic hazard for Aswan region. He used both of line sources and area source models. Five active faults in the Aswan region (Kalabsha, Seiyal, Gebel El-Barqa, Kurkur, and Khur El-Ramla Faults) were modeled as seismic lines. On the other hand, six area source zones (Old Stream, North Kalabsha, Khur El-Ramla, East Gebel Marawa, Abu Dirwa, and Kalabsha zones) were considered in the assessment. This study was followed by successive assessments by different authors to include other neighbor regions in Upper Egypt

Using the relation between the paleo-stresses, the present-day stresses and the distribution of earthquake epicenters, El-Hadidy [40] deduced five major trends in Egypt. They are: i) Pelusium megashear, ii) Eastern Mediterranean-Cairo-Fayoum-El-Gilf El-Kebeir, iii) Nubian-Mozambique, iv) Qena-Aqaba-Dead Sea, and v) Northern Red Sea-Gulf of Suez-Cairo-Alexandria seismotectonic trends. Furthermore, he identified some local zones on the Red Sea,

According to the earthquake distribution, focal mechanisms and the structural and tectonic information, Abou Elenean [19] suggested five seismotectonic sources. They are: i) Gulf of

Gulf of Suez, Gulf of Aqaba, Nile Delta, and Cairo-Suez regions.

previous four: i) Hellenic and Cyprian Arcs, and ii) Southern Egyptian trend.

For the construction of any database of seismic sources, there are two basic steps: first, all of the active faults that affect a specific region need to be recognized, and secondly, each seismogenic structure should be seismotectonically parameterized. In order to recognize the active faults, it is necessary to analyze the seismicity. It is common practice to start analyzing the historical and instrumental seismicity that affects the specific region. Like many other places all over the world, the seismicity in Egypt is not homogeneously distributed, neither in frequency nor in density. Historical information is similarly not uniform all over the region.

#### **4.1. An updated earthquake catalogue**

A complete and consistent earthquake catalogue in a region is essential in order to study the distribution of earthquakes in space, time, and magnitude. In the current work, the identifi‐ cation and characterization of regional seismic source zones is based on a unified compiled earthquake catalogue, after Sawires *et al.* [60], for Egypt and its surroundings which covers the area from 21° to 38° N and 22° to 38° E, and extends from 2200 B.C. until 2013 in the time period.

Different earthquake magnitude scaling relations, correlating different scale magnitudes, were used to develop a unified earthquake catalogue for the study region in the moment magnitude (MW) scale. The dependent events were removed from the catalogue to ensure a time-inde‐ pendent (Poissonian) distribution of earthquakes (Figure 3).

**Figure 3.** Distribution of the seismicity (2200 B.C. - 2013) and focal mechanism solutions (1940 – 2013) in and around Egypt (after Sawires *et al.* [60]). Symbols and focal sphere sizes are in proportion the moment magnitude. Focal sphere colours refer to different fault types (blue: strike-slip; green: normal; red: reverse).

#### **4.2. Focal mechanism data**

Different local and international sources were examined and focal mechanism data were compiled into a single database. The solutions of the Global Catalogue of CMT Harvard [65], the International Seismological Centre (ISC) [66], the National Earthquake Information Centre (NEIC) [67], the Regional CMT catalogues (RCMT) in the Mediterranean region [68], as well as ZUR-RMT catalogue of the Institute of Technology (ETH) of Zurich were also included in the catalogue. More than 600 focal mechanism solutions were collected covering different active seismic zones (Figure 3) in Egypt and surroundings, spanning the spatial area from 21˚ to 38˚N, and from 22˚ to 38˚E. Most of them have a magnitude greater than or equal to MW 3.0, occurring in the time period 1940 to 2013.

### **4.3. Geological, tectonic and geophysical data**

Several geological, geophysical and tectonic maps were inspected for the purpose of getting more information about the present active faults (e.g., Aswan region) and also for the identi‐ fication of the prevailed tectonic and structural trends in the study region. Among these studies are those of Said [69-71], Youssef [10], Shata [72], Neev [73], Neev *et al.* [74 and 75], El-Shazly [76], Riad [27], Maamoun [77], Issawi [78], EGSMA [26], Riad *et al.* [47 and 79], Maamoun *et al.* [16], Sestini [80], Schlumberger [81], Woodward-Clyde Consultants [82], Kebeasy [17], Meshref [11], Barazangi *et al.* [83], Guiraud and Bosworth [84], Abdel Aal *et al.* [85], Philobbos *et al.* [86], and Hussein and Abdallah [87].

#### **4.4. Crustal structure data**

(MW) scale. The dependent events were removed from the catalogue to ensure a time-inde‐

6 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Figure 3.** Distribution of the seismicity (2200 B.C. - 2013) and focal mechanism solutions (1940 – 2013) in and around Egypt (after Sawires *et al.* [60]). Symbols and focal sphere sizes are in proportion the moment magnitude. Focal sphere

Different local and international sources were examined and focal mechanism data were compiled into a single database. The solutions of the Global Catalogue of CMT Harvard [65], the International Seismological Centre (ISC) [66], the National Earthquake Information Centre (NEIC) [67], the Regional CMT catalogues (RCMT) in the Mediterranean region [68], as well as ZUR-RMT catalogue of the Institute of Technology (ETH) of Zurich were also included in the catalogue. More than 600 focal mechanism solutions were collected covering different active seismic zones (Figure 3) in Egypt and surroundings, spanning the spatial area from 21˚

colours refer to different fault types (blue: strike-slip; green: normal; red: reverse).

**4.2. Focal mechanism data**

pendent (Poissonian) distribution of earthquakes (Figure 3).

The crustal structure plays an important role in Seismology. It can be used, as in the current study, for the discrimination between the crustal (shallow-depth) seismicity, the intermediatedepth, and the deeper one.

Several studies have been carried out to evaluate the crustal structure and thickness in Egypt by using different types of datasets coming from seismic reflection surveys, deep seismic sounding, shallow refractions, and gravity (e.g., [34, 40 and 88-108]). In the delimitation of the different seismic zones, the most recent study [108] was taken into our consideration (Figure 4). Their results show that the Moho discontinuity is getting shallow toward the northern and eastern coast of Egypt, and deeper toward Western Desert and Northeastern Sinai. This discontinuity is located at depth of 31-33 km in Greater Cairo and Dahshour, 32-35 km in Sinai, 33–35 km along the Nile River, 30 km near the Red Sea coast, and 39 km towards the Western Desert.

## **5. Detailed description of the new proposed shallow-depth seismic source model**

Seismic sources define areas that share common seismological, tectonic, and geologic attrib‐ utes, and that can be described by a unique magnitude-frequency relation. In terms of PSHA, a seismic source represents a region of the earth's crust in which future seismicity is assumed to follow specified probability distributions for occurrences in time, earthquake sizes, and locations in space [109].

Araya and Der Kiureghian [109] discriminate between seismogenic and seismicity sources. Seismogenic zones lack the development of a clear history relating the contemporary seismic activity to a geologic structure. For such zones, critical gaps in the Quaternary geologic history preclude direct evidence of active faulting. Seismogenic zones are, by far, the most common type of source zone employed in PSHA. Commonly, seismogenic zones are area sources, but the zone type applies also to inferred associations of seismicity with individual faults. On the other hand, seismicity zones are source zones that are defined with no consideration of their relation to geologic structures. They are defined solely based on the spatial distributions of the seismic history, and their use and reasonableness can only be judged relative to the intended use of the final hazard estimate. This will be the terminology used in this work.

**Figure 4.** Depth of Moho discontinuity in Egypt (after Abdelwahed *et al.* [108]).

As mentioned previously, the separation of the study area into smaller, seismotectonically homogeneous zones is based on criteria mainly related with the present-day tectonic regime, epicenter distribution, focal mechanism data and the location of known faults. In the present work, we decided to employ simple geometric shapes for the definition of the seismic source model. The regional seismicity of concern to Egypt was divided into 28 seismic sources (Figure 5). These zones was related to the tectonic activity of the previously defined local active belts. Thus, the majority of the proposed sources zones can be considered seismogenic zones, except some sources which can be considered seismicity sources. The delineation of the seismicity sources was based upon the earthquake distribution, this is because there is no enough geologic and tectonic data covering these sources. Both seismogenic and seismicity sources are descri‐ bed below in more details. For each of these source zones, the seismicity parameters (b-value and activity rates) were computed by applying the Gutenberg-Richter [110] relationship and using the least square method considering the entire earthquake events within each zone. Moreover, maximum observed magnitude Mmax was defined using the earthquake subcatalogue for each source. Those estimated values will serve as initial inputs for a seismic hazard assessment for Egypt in the near future.

The details of the selection of these seismic sources, together with the estimation of its seismicity parameters and maximum observed magnitude, are given below for each source category, which grouped depending on the similarities of the prevailed tectonic environment.

#### **5.1. Seismic sources along the Gulf of Aqaba–Dead Sea Transform Fault**

the zone type applies also to inferred associations of seismicity with individual faults. On the other hand, seismicity zones are source zones that are defined with no consideration of their relation to geologic structures. They are defined solely based on the spatial distributions of the seismic history, and their use and reasonableness can only be judged relative to the intended

use of the final hazard estimate. This will be the terminology used in this work.

8 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Figure 4.** Depth of Moho discontinuity in Egypt (after Abdelwahed *et al.* [108]).

The Aqaba-Dead Sea Transform Fault (DST) is a 1100 km long left-lateral strike-slip fault (Figure 6) that accommodates the relative motion between Africa and Arabia [111, 112]. It is a seismically active transform boundary, connecting the Red Sea spreading center in the south to the Northern Mediterranean Triple Junction to the north. Its main left-lateral sense of motion is recognized by minor pull-aparts in young sediments [113], cut and offset of drainage lines and man-made structures (e.g., [114-121]).

The Gulf of Aqaba-Dead Sea Transform Fault (Figure 6) is subdivided into three parts; southern, central and northern [122]. The first part, which starts from the Gulf of Aqaba and passing through the Dead Sea and the Jordan Valley, is characterized by the occurrence of N12°E to N20°E left-lateral strike-slip faults. The second part of the DST is characterized by the occurrence of about 200 km long NNE–SSW restraining bend, where the DST branches into different faults. The major one, called the Yammouneh Fault, which connects the first and third parts of the DST, while the other faults connect the DST with the Palmyride Fold Belt (PFB) [122-124]. The last and the northern part of the DST is characterized by the occurrence of two different N–S striking faults surrounding the Ghab Valley and intersecting through a complex braided fault system with the East Anatolian Fault and the Cyprian Arc [125-127]. This intersection corresponds to the Hatay "fault–fault–trench" triple junction that forms the plate boundaries between Arabia, Africa and Anatolia [128].

**Figure 5.** Proposed seismic source zones in Egypt and its surroundings.

#### *5.1.1. Gulf of Aqaba seismogenic sources (EG-01 till EG-04)*

The Gulf of Aqaba experienced the largest Egyptian earthquake (MW 7.2, November 1995) which struck the area and its effects were extending till Cairo. Over than 1000 aftershocks are recorded. The aftershocks area reached a length of about 110 km, striking N 30° E, which in turn parallel to the Gulf of Aqaba trend [129]. Potential damage was observed at Nuweiba city at the western part of the gulf.

The Gulf of Aqaba has been considered to be the most active seismic area over the last few decades, characterized by swarm activity [130-132]. There is no information about the seis‐ micity of the Gulf of Aqaba until the year 1983. However, from January till April 1983, over than 500 events were reported, reaching a maximum recorded magnitude of 4.8. These earthquake events were felt at different places along the gulf area, as well as along the Arava Valley founding a general consideration [133]. From August 1993 up to February 1994, a large earthquake swarm was associated with relatively high magnitudes, reaching a 5.8 value. This swarm included about 1200 events occurred south to the 1983 swarm. Another earthquake swarm has been recorded and located at the central part of the Gulf of Aqaba on November 2002. Over than 10 events with magnitude above 4.0 were recognized, and many other events with magnitudes below this value. Some of these earthquakes were felt, but without damage for buildings at the epicentral area.

**Figure 6.** The main structural elements along the DST (redrawn after Heidbach and Ben-Avraham [134]).

**Figure 5.** Proposed seismic source zones in Egypt and its surroundings.

*5.1.1. Gulf of Aqaba seismogenic sources (EG-01 till EG-04)*

at the western part of the gulf.

for buildings at the epicentral area.

The Gulf of Aqaba experienced the largest Egyptian earthquake (MW 7.2, November 1995) which struck the area and its effects were extending till Cairo. Over than 1000 aftershocks are recorded. The aftershocks area reached a length of about 110 km, striking N 30° E, which in turn parallel to the Gulf of Aqaba trend [129]. Potential damage was observed at Nuweiba city

10 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

The Gulf of Aqaba has been considered to be the most active seismic area over the last few decades, characterized by swarm activity [130-132]. There is no information about the seis‐ micity of the Gulf of Aqaba until the year 1983. However, from January till April 1983, over than 500 events were reported, reaching a maximum recorded magnitude of 4.8. These earthquake events were felt at different places along the gulf area, as well as along the Arava Valley founding a general consideration [133]. From August 1993 up to February 1994, a large earthquake swarm was associated with relatively high magnitudes, reaching a 5.8 value. This swarm included about 1200 events occurred south to the 1983 swarm. Another earthquake swarm has been recorded and located at the central part of the Gulf of Aqaba on November 2002. Over than 10 events with magnitude above 4.0 were recognized, and many other events with magnitudes below this value. Some of these earthquakes were felt, but without damage

The interior of the Gulf of Aqaba is occupied by three elongated en-echelon basins transected by longitudinal faults [131]. This en-echelon system produces several tectonic basins, which are forming rhombic-shaped grabens. Thus, three basins in the Gulf of Aqaba are present. They are, from south to north, Tiran "Arnona"-Dakar, Aragonese and Elat "Aqaba" Basins.

The heterogeneity of the focal mechanism solutions for the earthquake events taken place in the gulf area, indicates its geologic structure complexity. Some fault plane solutions exhibit normal faulting, which are related to the faults that form the boundaries of the major basins in the gulf. Others indicate left-lateral motion of the transform [112]. The focal mechanism of the MW 7.2, 1995 Aqaba earthquake as well as some aftershocks, show a strike-slip movement with predominant normal components, with the exception of only one solution located on the eastern coast of the Gulf of Aqaba, and exhibits strike-slip movement with a little reverse component in the NNW-SSE and ENE-WNW nodal planes [19].

According to the seismic activity, the epicentral distribution and the local tectonics, different seismogenic sources were delineated in the gulf area (Figure 7).


Previous focal mechanism solution studies for moderate to large earthquakes located in the Gulf of Aqaba region (e.g., [135-138]) assert the dominance of ENE-WSW extension (N60°- 80°E). Furthermore, field studies [139, 140] observed two conjugate faults along the Gulf of Aqaba: NNE left-lateral strike-slip faults parallel to the gulf that release the majority of stress, and a nearly ESE-WNW normal faults along the margins of pull-apart basins. On the other hand, body waveform inversion of the MW 6.1, August 3, 1993, and the MW 7.2 November 22, 1995 events, support the occurrence of normal faulting take place along the transverse NNW-SSE and ESE-WNW faults, while left-lateral strike-slip movement occurs along NNE major Aqaba trend [135].

#### *5.1.2. Arava Valley (EG-05) seismogenic source*

The Arava Valley is located to the north of the Gulf of Aqaba. It is an inter-basin zone trending NE-SW. Its faults extend over 160 km from the Gulf of Aqaba to the Dead Sea and provide morphological evidence of essentially strike-slip motion [120]. It is characterized by a low seismicity level compared with the surrounding area, despite clear indications of recent faulting [141]. Klinger *et al.* [120] emphasized the limited earthquake activity in the Arava Valley in the instrumental period. Shapira and Jarradat [133] stated that, from preliminary paleoseismicity studies, the border-faults of Arava Valley generate earthquakes bigger than magnitude 6.0 with an average return period of 1000-3000 years.

There is no historical earthquakes included in this seismogenic source zone. The biggest recorded event is the mb 5.2, December 18, 1956 earthquake. Two focal mechanism solutions are known in the northern part of this source, both of them exhibiting strike-slip faulting with normal component.

**Figure 7.** Shallow-depth seismicity (h ≤ 35 km) and delineated seismic sources along the Gulf of Aqaba-Dead Sea Transform Fault.

#### *5.1.3. Eastern Central Sinai (EG-06) seismogenic source*

**a.** The EG-01 (Tiran – Dakar Basin) seismogenic source lies at the southern part of the Gulf of Aqaba. It includes the MS 4.4, February 2, 2006 earthquake. There is no historical earthquakes included in this source zone. The majority of the available focal mechanism

**b.** The EG-02 (Aragonese Basin) seismogenic source lies to the north of the previous EG-01 zone, and is considered the focal area of the MW 7.2, November 22, 1995 earthquake, which

**c.** The EG-03 (Elat Basin) seismogenic source located to the north of the EG-02 seismic zone and considered as the extension area of the MW 7.2, 1995 Aqaba earthquake rupture. It is characterized by a low seismicity level, if compared with the other two zones of the Gulf of Aqaba. Two historical events have been included in this area source, the Imax VIII, March

**d.** In addition to the previous seismogenic sources, a delineation of a separate and fourth zone is taken place. This source lies to the east of the gulf and characterized by dispersed moderate seismicity. This zone is the EG-04 (Eastern Gulf of Aqaba) seismogenic source. The major earthquake included in this area source is the mb 4.5 December 26, 1995

Previous focal mechanism solution studies for moderate to large earthquakes located in the Gulf of Aqaba region (e.g., [135-138]) assert the dominance of ENE-WSW extension (N60°- 80°E). Furthermore, field studies [139, 140] observed two conjugate faults along the Gulf of Aqaba: NNE left-lateral strike-slip faults parallel to the gulf that release the majority of stress, and a nearly ESE-WNW normal faults along the margins of pull-apart basins. On the other hand, body waveform inversion of the MW 6.1, August 3, 1993, and the MW 7.2 November 22, 1995 events, support the occurrence of normal faulting take place along the transverse NNW-SSE and ESE-WNW faults, while left-lateral strike-slip movement occurs along NNE major

The Arava Valley is located to the north of the Gulf of Aqaba. It is an inter-basin zone trending NE-SW. Its faults extend over 160 km from the Gulf of Aqaba to the Dead Sea and provide morphological evidence of essentially strike-slip motion [120]. It is characterized by a low seismicity level compared with the surrounding area, despite clear indications of recent faulting [141]. Klinger *et al.* [120] emphasized the limited earthquake activity in the Arava Valley in the instrumental period. Shapira and Jarradat [133] stated that, from preliminary paleoseismicity studies, the border-faults of Arava Valley generate earthquakes bigger than

There is no historical earthquakes included in this seismogenic source zone. The biggest recorded event is the mb 5.2, December 18, 1956 earthquake. Two focal mechanism solutions are known in the northern part of this source, both of them exhibiting strike-slip faulting with

solutions inside this area source reflects normal faulting mechanism.

12 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

is considered the largest event to occur along the DST in the last century.

18, 1068, and the Imax VIII-IX, May 2, 1212 earthquakes.

earthquake.

Aqaba trend [135].

normal component.

*5.1.2. Arava Valley (EG-05) seismogenic source*

magnitude 6.0 with an average return period of 1000-3000 years.

An E-W trending dextral strike-slip faults with up to 2.5 km of displacement has been recognized in central Sinai by Steintz *et al.* [142]. It is called the Themed Fault. The Tih Plateau (in central Sinai) is traversed by the Themed Fault, which extends for about 200 km from the vicinity of eastern margin of the Suez Rift to the DST [71]. The Themed Fault has been reactivated along a pre-existing fault, identifying the southern border of the Early Mesozoic passive continental margin of the Eastern Mediterranean Basin in central Sinai [143].

To the north of the previous fault, the central Sinai-Negav shear zone is located, which is proposed by Shata [72] and Bartov [144]. It is a narrow E to ENE trending fault belt discrimi‐ nating and separating the North Sinai Fold Belt (tectonically unstable area) from the Tih Plateau (tectonically stable area) in middle and Southern Sinai [145].

The EG-06 seismogenic source lies to the west of the previous EG-05 source and to the east of the Sinai sub-Plate. This seismogenic source includes the low seismic activity related to the Themed Fault, central Sinai-Negav shear zone, Paran Fault and Baraq/Paran Fault junction. This source has a great tectonic effect on Sinai Peninsula and its surrounding areas. There is no historical earthquakes included in this source, and the biggest earthquake located in this zone is the mb 4.8, September 24, 1927 event.

#### *5.1.4. Dead Sea Basin (EG-07) seismogenic source*

The Dead Sea Basin is characterized by a double fault system that is bounded by the Arava Fault from the east, and by the Jordan (Jericho) Fault from the west, hence it occupies a rhombshaped graben between two left-lateral slip faults. The average slip rate on the Dead Sea portion of the transform fault is estimated to be 0.7 cm/yr. [114], which is consistent with the average slip of the overall plate boundary of 0.7-1.0 cm/yr.

Earthquake swarms and a mainshock-aftershock type of activity characterize this seismogenic source. Trenching studies across the Jordan Fault indicate that two large earthquake swarms occurred since about 2000 years ago. One of them is between 200 B.C.- 200 A.D., while the other one is between 700 A.D.- 900 A.D. [114]. El-Isa *et al.* [146] attributes these swarms to subsurface magmatic activity and/or to the isostatic adjustments along the Gulf of Aqaba.

Several historical earthquakes are included inside this source zone. They are the 745 B.C., 33 A.D., 1048, 1212, 1293, and 1458 earthquakes. Their intensities range between VII to VIII. Ben-Menahem *et al.* [147] obtained focal mechanism solutions for some recent events (e.g., the MS 4.9, October 8, 1970 earthquake) which took place in the Dead Sea area. All solutions indicate a left-lateral strike-slip movement on a sub-vertical fault striking with an average trend of N8°-10°E. However, Salamon *et al.* [112] obtained normal focal mechanism solutions for some relatively recent events. These solutions may be describe the earthquake activity of the N-S striking normal faults bordering the Dead Sea Basin. Field observations confirmed this type of activity [113, 148].

#### *5.1.5. Jordan Valley (EG-08) seismogenic source*

The Jordan Valley trends in the N-S direction, linking between the Hula Basin to the north and the Dead Sea Basin to the south. The details about its end in the Sea of Galilee are not clear from the surface features [147]. Garfunkel *et al.* [113] noticed a small amount of compression along the valley and near the Jordan Fault trace. Recent earthquake activity along the Jordan Valley is low compared to the Southern Dead Sea Basin. Ten historical events (before 1900) are included in this area source. They are the 1020 B.C., 578 A.D., 580, 746, 854, 1034, 1105, 1160, 1260, and 1287 events. Their intensities range between IV to XI. The most important earthquake included in this source zone is the Imax XI, 746 event.

#### *5.1.6. Kineret-Hula Basin (EG-09) seismogenic source*

To the north of the previous Jordan Valley source are located the Hula (Shamir-Almagor Fault) and Kineret (Kineret-Sheikh Ali Fault) Basins [149]. Seismic activity in the two mentioned basins was located till the Yammuneh Fault (NE-bend of the Dead Sea Transform). This area source, which surrounded by the Roum Fault from the western side and the Jordan Fault from the eastern side, was considered by Shamir *et al.* [150] as a seismogenic step zone. Three historical events are included in this zone. They are the 19 A.D., 419, and 756 earthquakes. The biggest earthquake is the Imax X, 19 A.D. event.

#### *5.1.7. Northwestern Saudi Arabia (EG-10) seismicity source*

To the east of the EG-01 and EG-02 seismogenic sources, the Northwestern Saudi Arabia EG-10 source has been considered. This source zone covers disperse, low seismicity in the north‐ western part of Saudi Arabia. Two historical events are reported to occur inside this area source. They are the March 18, 1068, and January 4, 1588 earthquakes, both of them with intensity VIII.

#### *5.1.8. Lebanon (EG-11) seismicity source*

The EG-06 seismogenic source lies to the west of the previous EG-05 source and to the east of the Sinai sub-Plate. This seismogenic source includes the low seismic activity related to the Themed Fault, central Sinai-Negav shear zone, Paran Fault and Baraq/Paran Fault junction. This source has a great tectonic effect on Sinai Peninsula and its surrounding areas. There is no historical earthquakes included in this source, and the biggest earthquake located in this

14 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

The Dead Sea Basin is characterized by a double fault system that is bounded by the Arava Fault from the east, and by the Jordan (Jericho) Fault from the west, hence it occupies a rhombshaped graben between two left-lateral slip faults. The average slip rate on the Dead Sea portion of the transform fault is estimated to be 0.7 cm/yr. [114], which is consistent with the

Earthquake swarms and a mainshock-aftershock type of activity characterize this seismogenic source. Trenching studies across the Jordan Fault indicate that two large earthquake swarms occurred since about 2000 years ago. One of them is between 200 B.C.- 200 A.D., while the other one is between 700 A.D.- 900 A.D. [114]. El-Isa *et al.* [146] attributes these swarms to subsurface

Several historical earthquakes are included inside this source zone. They are the 745 B.C., 33 A.D., 1048, 1212, 1293, and 1458 earthquakes. Their intensities range between VII to VIII. Ben-Menahem *et al.* [147] obtained focal mechanism solutions for some recent events (e.g., the MS 4.9, October 8, 1970 earthquake) which took place in the Dead Sea area. All solutions indicate a left-lateral strike-slip movement on a sub-vertical fault striking with an average trend of N8°-10°E. However, Salamon *et al.* [112] obtained normal focal mechanism solutions for some relatively recent events. These solutions may be describe the earthquake activity of the N-S striking normal faults bordering the Dead Sea Basin. Field observations confirmed this type

The Jordan Valley trends in the N-S direction, linking between the Hula Basin to the north and the Dead Sea Basin to the south. The details about its end in the Sea of Galilee are not clear from the surface features [147]. Garfunkel *et al.* [113] noticed a small amount of compression along the valley and near the Jordan Fault trace. Recent earthquake activity along the Jordan Valley is low compared to the Southern Dead Sea Basin. Ten historical events (before 1900) are included in this area source. They are the 1020 B.C., 578 A.D., 580, 746, 854, 1034, 1105, 1160, 1260, and 1287 events. Their intensities range between IV to XI. The most important earthquake

To the north of the previous Jordan Valley source are located the Hula (Shamir-Almagor Fault) and Kineret (Kineret-Sheikh Ali Fault) Basins [149]. Seismic activity in the two mentioned

magmatic activity and/or to the isostatic adjustments along the Gulf of Aqaba.

zone is the mb 4.8, September 24, 1927 event.

*5.1.4. Dead Sea Basin (EG-07) seismogenic source*

of activity [113, 148].

*5.1.5. Jordan Valley (EG-08) seismogenic source*

included in this source zone is the Imax XI, 746 event.

*5.1.6. Kineret-Hula Basin (EG-09) seismogenic source*

average slip of the overall plate boundary of 0.7-1.0 cm/yr.

To the north of the previous seismic source and along the eastern boundaries of the EG-04, EG-05, EG-07, EG-08, and EG-09 sources, the Lebanon EG-11 seismicity source has been considered. This area source covers a dense disperse low-magnitude seismicity in Lebanon and Southern Syria. Nine historical earthquakes are located inside this area source. The most important among them are the 972, 1159, and 1182 events. Their felt intensities are Imax IX, IX-X, and IX, respectively.

The computed b-value, the annual rate of earthquakes, and the observed recorded maximum magnitude for the delineated seismic sources along the Gulf of Aqaba-Dead Sea Transform Fault are displayed in Table 1.


**Table 1.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones along the Gulf of Aqaba-Dead Sea Transform Fault.

#### **5.2. Seismic sources along the Red Sea Rift**

The Arabian Plate is continuing to rotate away from the African Plate along the Red Sea Rift spreading center. The Red Sea occupies a long and slightly sinuous NW-trending escarpmentbound basin, 250-450 km wide and 1900 km long, between the uplifted shoulders of the African and Arabian shields. It is part of a rift system extending from the Gulf of Aden to the northern end of the Gulf of Suez. The overall trend of the rift is N30˚W, although a few kinks occur at around 15˚N, 18˚N, and 22˚N.

Depending on the structural setting and morphology of the Red Sea, it can be subdivided into four different zones (Figure 8). Each zone are representing distinct stage in the development of the continental margin and the generation of the mid-ocean ridge spreading system [151, 152]. These zones are:


Based on the morphological and structural features of the Red Sea, the Egyptian part (northern latitude 22°N) can be divided into three distinct seismogenic source zones (EG-12, EG-13, and EG-14) (Figure 9). Each zone represents different stage of development [159]. The delineation is made, based upon the occurrence of the transverse structures, change of the fault trend along the axial rift and the variety of the seismic activity along the rift axis.

#### *5.2.1. Southern Red Sea (EG-12) seismogenic source*

The EG-12 Southern Egyptian Red Sea seismogenic source represents the northern part of the transition zone. It is characterized by NW-SE trending faults. The boundary proposed by Bonati [160], north latitude 25ºN, is found herein to coincide with the NE-trending transform faults and the associated seismicity. Only one historical event is included in this seismic source, the Imax VI-VII, 1121 earthquake.

**Figure 8.** Tectonic framework of the Red Sea region (redrawn after Ghebreab [158]).

#### *5.2.2. Central Red Sea (EG-13) seismogenic source*

**5.2. Seismic sources along the Red Sea Rift**

on both sides of other zones [151, 152].

around 15˚N, 18˚N, and 22˚N.

152]. These zones are:

[156].

occurred [152].

the Imax VI-VII, 1121 earthquake.

The Arabian Plate is continuing to rotate away from the African Plate along the Red Sea Rift spreading center. The Red Sea occupies a long and slightly sinuous NW-trending escarpmentbound basin, 250-450 km wide and 1900 km long, between the uplifted shoulders of the African and Arabian shields. It is part of a rift system extending from the Gulf of Aden to the northern end of the Gulf of Suez. The overall trend of the rift is N30˚W, although a few kinks occur at

16 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Depending on the structural setting and morphology of the Red Sea, it can be subdivided into four different zones (Figure 8). Each zone are representing distinct stage in the development of the continental margin and the generation of the mid-ocean ridge spreading system [151,

**i.** *Active sea-floor spreading (Southern Red Sea):* It is located between 15°N and 20°N and

**ii.** *Transition zone (central Red Sea):* It is located between 20°N to about 23°20´N, where

**iii.** *Late stage continental rifting (Northern Red Sea):* This zone composed of a wide trough

**iv.** *Active rifting:* This zone representing the expected line along which the Southern Red

Based on the morphological and structural features of the Red Sea, the Egyptian part (northern latitude 22°N) can be divided into three distinct seismogenic source zones (EG-12, EG-13, and EG-14) (Figure 9). Each zone represents different stage of development [159]. The delineation is made, based upon the occurrence of the transverse structures, change of the fault trend along

The EG-12 Southern Egyptian Red Sea seismogenic source represents the northern part of the transition zone. It is characterized by NW-SE trending faults. The boundary proposed by Bonati [160], north latitude 25ºN, is found herein to coincide with the NE-trending transform faults and the associated seismicity. Only one historical event is included in this seismic source,

considered separately or it can be added to the first mentioned zone.

the axial rift and the variety of the seismic activity along the rift axis.

*5.2.1. Southern Red Sea (EG-12) seismogenic source*

characterized by a well-developed axial trough which has developed through normal sea-floor spreading during the last 5 Ma [153-155] or even older, at about 9–12 Ma

the axial trough becomes discontinuous, in which the central Red Sea consists of a series of 'deeps' alternating with shallow 'inter-trough zones' [157]. An identical zone may flanks the deep axial trough between the side walls of the shallow main trough

without a distinct spreading center, in spite of a number of small isolated "deeps" is

Sea may be propagate through the Danakil Depression Afar. This zone may be

The EG-13 Central Egyptian Red Sea seismogenic source is located to the northwest of the previous zone. It corresponds to the region north of latitude 24º30´N, which consists of a broad main trough without a recognizable spreading center [152]. Recent recorded seismicity could indicate the expected location of the axial rift. In this zone, the degree of seismicity is relatively low and scattered, compared to the previous zone. Like the previous zone, there is only one historical event included here. It is the Imax V, 1899 earthquake. The maximum observed magnitude along this source corresponds to the mb 4.7 (MS 5.1), July 30, 2006 earthquake.

#### *5.2.3. Northern Red Sea (EG-14) seismogenic source*

The EG-14 Northern Egyptian Red Sea seismogenic source is characterized by higher seismic activity than the previous two sources. This activity may be due to the juncture between the two gulfs. Daggett *et al.* [161] studies of the low-magnitude seismicity shows that, the high seismic activity of the northern Red Sea is different from the activity at the southern part of the Gulf of Suez. There is no earthquakes related to this area source before the year 1900. In addition, the mb 5.0 (MS 5.0) March 22, 1952 event represents the biggest recorded earthquake till now.

**Figure 9.** Shallow-depth seismicity (h ≤ 35 km) and delineated seismic sources along the Red Sea-Gulf of Suez and the Nile River.

Seismicity parameters for the delineated seismic sources along the Red Sea Rift are displayed

in Table 2.


**Table 2.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones along the Red Sea Rift.

#### **5.3. Seismic sources along the Gulf of Suez**

The Gulf of Suez is considered to be the plate boundary between the African Plate and Sinai sub-Plate [162]. It extends along a NW trend from latitude 27°30′ N to 30°N. The Gulf of Suez constitutes the northern part of the Red Sea Rift System. It was developed, together with the Red Sea and the Gulf of Aqaba, as one of the three arms of the Sinai Triple Junction [69, 81 and 163-166].

The Gulf of Suez has been interpreted as being a complex half-graben system [139], or an asymmetric graben [167]. It is composed of three successive half-grabens, as mentioned by Moustafa [168], with opposite tilt directions: northern, central, and southern. These distinct half-grabens include several rift blocks of a uniform dip direction. The dip direction, along the Gulf of Suez Rift, changes from the north to the south as: SW to NE and again to SW defining the three half-grabens, respectively.

Two-accommodation zones [169] coexist among these half-grabens which extend transversely across the rift (Figure 10). These are the Galala-Zenima [168] or Gharandal [167] accommoda‐ tion zone, of broad extension (about 60 km wide) in the north, and the Morgan [168] or Sufr El Dara [170] accommodation zone (20 km wide) in the south. Both zones exhibit a broad range of deformation, including distinct normal, oblique, or strike-slip faults [171], or wide complex zones of normal faulting, trans-tension [172-174] or broad warping [175].

The Gulf of Suez is considered to be an aseismic area during the first half of the last century and this consideration let some researchers (e.g., [176, 177]) to conclude that all the present motion taking place in the Red Sea Rift is transferred into shearing along the DST. Ben-Menahem [178] and Salamon *et al.* [111] studied the seismic activity of the Suez Rift. Fault plane solutions of the mb 6.1, March 31, 1969 earthquake and other low-magnitude events show that the Gulf of Suez Rift is active which agree with Ben-Menahem and Aboodi [179] results. Considering the tectonic setting, seismicity and earthquake faulting mechanisms, the Gulf of Suez can be divided into three seismogenic sources (Figure 9) as follow.

#### *5.3.1. Southern Gulf of Suez (EG-15) seismogenic source*

Seismicity parameters for the delineated seismic sources along the Red Sea Rift are displayed

**Figure 9.** Shallow-depth seismicity (h ≤ 35 km) and delineated seismic sources along the Red Sea-Gulf of Suez and the

18 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Yearly Number of Earthquakes**

**Above MW 4.0 Above MW 5.0** EG-12 1.00 0.4359 0.0434 Imax VI-VII on 1121/--/-- EG-13 0.91 0.3029 0.0376 mb 4.7 on 2006/07/30 EG-14 1.13 0.6425 0.0472 mb 5.0 on 1952/03/22

**Table 2.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source

**Observed Mmax**

in Table 2.

Nile River.

**Source Zone b-value**

zones along the Red Sea Rift.

The EG-15 Southern Gulf of Suez seismogenic source is distinguished by intensive structural deformation. It is characterized by its relatively high seismic activity. The higher seismicity rate at the southern part of the Gulf of Suez is related to the crustal movements among the three surrounding plates: Arabian Plate, African Plate, and Sinai sub-Plate. Six historical events are included in this zone. Those are 28 B.C., 955, 1091, 1195, 1778, and 1839 events. Their intensities range from VI-VII to VIII. The most important event occurred inside this area source is the MW 6.8, March 31, 1969 Shedwan earthquake [16, 181]. Three foreshocks and 17 after‐ shocks (mb 4.5-5.2) located in the Shedwan Island district are related to this big event. However, Maamoun and El-Khashab [182] mentioned that 35 foreshocks, taken place during the last half of March 1969, were preceding the main earthquake. The focal mechanism solutions of the largest two earthquakes (MW 6.8, March 31, 1969 and MW 5.5, June 28, 1972 earthquakes) show a normal faulting mechanisms with negligible shear component along the NW-trending fault plane that it is in agreement with the main axis of the Gulf of Suez [183]. This is also consistent

**Figure 10.** Tectonic setting of the Gulf of Suez. Red lines refer to normal faults (redrawn after Meshref [11]; and Younes and McClay [180]).

with the results obtained using the waveform inversion techniques proposed by Huang and Solomon [184].

#### *5.3.2. Central Gulf of Suez (EG-16) seismogenic source*

The seismic activity in the EG-16 Central Gulf of Suez seismogenic source is relatively low when compared with the previous source. Five historical events are included in this source zone: the 1220 B.C., 1425, 1710, 1814, and 1879 earthquakes. Its intensities range from IV to VII. The most important earthquake inside this area was the MS 6.2 March 6, 1900 event.

Abou Elenean [20] computed some focal mechanism solutions for earthquakes which taken place in the central part of the gulf, showing generally normal faulting, following the main gulf trend. A few of these events show slight strike-slip component, especially for those events closer to the transfer zones of the three gulf dip provinces [11]. This change, from a purely normal faulting in the southern part to a mixed (strike-slip and normal) movement, supports the separation between the southern and middle seismogenic zones in the Gulf of Suez.

## *5.3.3. Northern Gulf of Suez (EG-17) seismogenic source*

Finally, the EG-17 Northern Gulf of Suez seismogenic source is characterized by its low seismic activity. Two large earthquakes occurred before the year 1900. They are the Imax VI, 742, and Imax V, 1754 earthquakes. Focal mechanism analyses for this seismogenic zone indicate normal faulting mechanism. Fault plane solutions by Abou Elenean [20] showed that the events located at the gulf apex show normal faults, generally trending NW-SE to WNW-ESE, and reflect a good agreement with the surface faults crossing the Eastern Desert from the gulf apex towards Cairo.

Abou Elenean [20] concluded that the focal mechanisms of small to moderate size earthquakes based on the P-wave polarities by Badway and Horváth [185-187], Badawy [188] and Salamon *et al.* [112], show the existence of few thrust faulting mechanisms along the Gulf of Suez trend. The author argues that these unexpected mechanisms could be due to the lack of local stations with clear polarities at that time. On the other hand, borehole breakouts analyses performed by Badawy [188] show a different stress direction, inconsistent with the NE-SW tension direction estimated from earthquake focal mechanisms.

Seismicity parameters for the delineated seismic sources along the Gulf of Suez are displayed in Table 3.


**Table 3.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones along the Gulf of Suez.

#### **5.4. Seismic sources of the Egyptian Eastern Desert**

with the results obtained using the waveform inversion techniques proposed by Huang and

**Figure 10.** Tectonic setting of the Gulf of Suez. Red lines refer to normal faults (redrawn after Meshref [11]; and Younes

20 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

The seismic activity in the EG-16 Central Gulf of Suez seismogenic source is relatively low when compared with the previous source. Five historical events are included in this source zone: the 1220 B.C., 1425, 1710, 1814, and 1879 earthquakes. Its intensities range from IV to VII.

Abou Elenean [20] computed some focal mechanism solutions for earthquakes which taken place in the central part of the gulf, showing generally normal faulting, following the main

The most important earthquake inside this area was the MS 6.2 March 6, 1900 event.

Solomon [184].

and McClay [180]).

*5.3.2. Central Gulf of Suez (EG-16) seismogenic source*

The Eastern Desert of Egypt, structurally, is a part of the Arabian-Nubian Shield. It lies within the fold and thrust belt of the Pan-African continental margin [189]. It is underlain mainly by the Pre-Cambrian basement of igneous and metamorphic rocks, which constitutes the Nubian Shield that had been formed before the Red Sea opening. It is believed that Nubian Shield basement was stabilized during the Pan-African Orogeny (about 570 Ma ago) [190].

Stern and Hedge [191] divided the Eastern Desert belt into three structural domains (Figure 2): northern, central and southern. These domains are separated by two major faults: i) the first is the Safaga-Qena zone, extending from Safaga to Qena, and ii) the second one is the Marsa Alam-Aswan fault zone. The Eastern Desert is characterized by E-W trending faults in the southern part, which changes to ENE-WSW in the middle one, near to Hurghada city. Further to the north, towards the Cairo-Suez District, the main fault trend becomes in the E-W direction.

However, Youssef [10] classified the main tectonic structures developed in the Eastern Desert into three main groups: i) NW-SE trending normal faults parallel to the Gulf of Suez-Red Sea Rift, ii) NE-SW trending faults parallel to the Gulf of Aqaba, and iii) a set of fault system trending nearly in the E-W direction. In addition, there are many simple and open folds with a NW-SE trend and low plunges.

Deif *et al.* [57] quote that the relationship between the earthquake activity in the Eastern Desert and the causal structures is not fully understood, due to the lack of geological and geophysical studies in this region. Furthermore, no historical earthquakes have been reported in the current seismogenic sources [17, 21]. The following seismogenic sources are identified (Figure 9).

#### *5.4.1. Western Red Sea Coast (EG-18) seismicity source*

In addition to the Red Sea seismogenic sources mentioned above, there are some earthquakes located in the region which extends to the west, from the EG-12 Southern Egyptian Red Sea source till the western coast of the Red Sea. This activity may be related to the block adjustment in this region or to some ocean floor spreading. This source is characterized by a low seismic activity. The biggest observed earthquake is the ML 4.5, May 23, 1990 earthquake.

#### *5.4.2. Southern Eastern Desert (EG-19) seismicity source*

This seismicity source exhibit a low seismic activity rate in comparison to the adjacent Red Sea seismic sources. There are no focal mechanism solutions for earthquake events inside this area source. The ML 4.4, July 15, 1991 earthquake is the biggest recorded event in this zone.

#### *5.4.3. Southern Abu Dabbab (EG-20) seismicity source*

Depending on both the changes in the seismicity rate and distribution, another seismicity source (EG-20) has been considered to the north of the previous zone. The same as the previous, there is no focal mechanism solutions in this source. The biggest recorded event is the ML 4.7, January 21, 1982 earthquake.

#### *5.4.4. Abu Dabbab (EG-21) seismicity source*

The Abu Dabbab region is located in the central part of the Eastern Desert of Egypt. The moderate level of seismic activity and extremely tight clustering of low-magnitude earth‐ quakes at Abu Dabbab suggests that the seismicity in this area is not directly related to regional tectonics. One possible explanation is that the activity is related to magmatic intrusions into the Pre-Cambrian crust, but there is no direct evidence to support this hypothesis [161].

The most important event included inside this area source is the MS 5.3, November 12, 1955 earthquake. This event is felt in the Upper Egypt in Aswan and Qena cities, and as far as Cairo, but no damage was reported. Its focal mechanism solution has normal and strike-slip faulting components produced by a NNW minimum compressive stress and a NE maximum com‐ pressive stress. Fault planes strike roughly E-W or N-S to NE-SW. Another important event related to this area is the MW 5.1, July 2, 1984 earthquake, which is felt strongly in Aswan, Qena and Quseir cities. A large number of foreshocks and a huge sequence of aftershocks are recorded. The focal depth of the whole sequence was less than 12 km.

Seismicity parameters for the delineated seismic sources of the Eastern Desert of Egypt are displayed in Table 4.


**Table 4.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones of the Eastern Desert.

#### **5.5. Seismic sources along Nasser's Lake, Nile Valley and Cairo-Suez region**

#### *5.5.1. Southern Aswan (EG-22) seismogenic source*

is the Safaga-Qena zone, extending from Safaga to Qena, and ii) the second one is the Marsa Alam-Aswan fault zone. The Eastern Desert is characterized by E-W trending faults in the southern part, which changes to ENE-WSW in the middle one, near to Hurghada city. Further to the north, towards the Cairo-Suez District, the main fault trend becomes in the E-W direction. However, Youssef [10] classified the main tectonic structures developed in the Eastern Desert into three main groups: i) NW-SE trending normal faults parallel to the Gulf of Suez-Red Sea Rift, ii) NE-SW trending faults parallel to the Gulf of Aqaba, and iii) a set of fault system trending nearly in the E-W direction. In addition, there are many simple and open folds with

22 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Deif *et al.* [57] quote that the relationship between the earthquake activity in the Eastern Desert and the causal structures is not fully understood, due to the lack of geological and geophysical studies in this region. Furthermore, no historical earthquakes have been reported in the current seismogenic sources [17, 21]. The following seismogenic sources are identified (Figure 9).

In addition to the Red Sea seismogenic sources mentioned above, there are some earthquakes located in the region which extends to the west, from the EG-12 Southern Egyptian Red Sea source till the western coast of the Red Sea. This activity may be related to the block adjustment in this region or to some ocean floor spreading. This source is characterized by a low seismic

This seismicity source exhibit a low seismic activity rate in comparison to the adjacent Red Sea seismic sources. There are no focal mechanism solutions for earthquake events inside this area source. The ML 4.4, July 15, 1991 earthquake is the biggest recorded event in this zone.

Depending on both the changes in the seismicity rate and distribution, another seismicity source (EG-20) has been considered to the north of the previous zone. The same as the previous, there is no focal mechanism solutions in this source. The biggest recorded event is the ML 4.7,

The Abu Dabbab region is located in the central part of the Eastern Desert of Egypt. The moderate level of seismic activity and extremely tight clustering of low-magnitude earth‐ quakes at Abu Dabbab suggests that the seismicity in this area is not directly related to regional tectonics. One possible explanation is that the activity is related to magmatic intrusions into the Pre-Cambrian crust, but there is no direct evidence to support this hypothesis [161].

The most important event included inside this area source is the MS 5.3, November 12, 1955 earthquake. This event is felt in the Upper Egypt in Aswan and Qena cities, and as far as Cairo,

activity. The biggest observed earthquake is the ML 4.5, May 23, 1990 earthquake.

a NW-SE trend and low plunges.

*5.4.1. Western Red Sea Coast (EG-18) seismicity source*

*5.4.2. Southern Eastern Desert (EG-19) seismicity source*

*5.4.3. Southern Abu Dabbab (EG-20) seismicity source*

January 21, 1982 earthquake.

*5.4.4. Abu Dabbab (EG-21) seismicity source*

The geological structural pattern of the Nasser's Lake and Aswan region is characterized by a regional basement rock uplift and regional faulting [192-197]. Faults around the Aswan region, according to their behavior, are grouped into three categories [82]:


cracks observed along the fault trace. Likely this fault is inactive [192]. The fault planes of this system are nearly vertical (80-85°).

**iii.** The third one is a fault system trending NNE-SSW (Figure 11) and lies to the east of Nasser's Lake. The Dabud Fault, which represents the main fault of this group, is about 36 km length. Geological evidences indicate reverse-slip, opposed to the tectonic setting of the area.

In addition to the previous fault systems, Deif [57] has mentioned three faults located at the High Dam area. They are the Powerhouse, the Spillway and the Channel Faults. Deif [57] provided that the evidence of the occurrence of these faults is hidden below the Aswan High Dam and Nasser's Lake. These three faults show no evidence of being active in the Quaternary, and are considered as inactive with no significant hazard to the Aswan region [82].

No historical earthquakes were reported by Ambraseys *et al.* [18] inside this area source. However, two historical events (epicentral intensity VII) were reported by Maamoun *et al.* [16] to be located at the same place of the MW 5.8, November 14, 1981 earthquake. These two events occurred in 1210 B.C. and in 1854.

**Figure 11.** Geological and tectonic features around Nasser's Lake (redrawn after Woodward-Clyde Consultants [82]).

Woodward-Clyde Consultants [82] evaluated the fault system in the Kalabsha area and reported that the Western Desert Fault System consists of a set of E-W faults that exhibit dextral-slip displacement, and a set of N-S faults that exhibit sinistral-slip displacement. The E-W faults are longer, and have greater degree of activity in the Quaternary, having larger total slip rates (about 0.03 mm/yr.) than the N-S faults (0.01–0.02 mm/yr.).

Many seismic hazard studies have been carried out in the Aswan area and its surroundings due to its importance and neighborhood to the High Dam (e.g., [51, 57 and 58]). Three alternative seismotectonic models for Aswan area have been considered in these studies. The first model consider the Aswan Area as one seismotectonic model, while in the second one is subdivided into six seismotectonic provinces. The third model is mainly depending on the fault seismic sources. The latter one is based mainly on the well-known defined active faults and its associated seismic activities.

However, this work, the Aswan region and its surroundings is considered as one source zone (Figure 9). The main earthquake that took place inside this area was the MW 5.8, November 14, 1981 event. This earthquake occurred in the Nubian Desert of Aswan. It is of great significance because of its possible association with Nasser's Lake. Its effects were strongly felt up to Assiut city (440 km to the north from Kalabsha Fault), as well as to Khartoum city (870 km to the south). Several cracks on the western bank of the Nasser's Lake, and several rock-falls and minor cracks on the eastern bank, are reported. The largest of these cracks is about one meter in width and 20 km in length. This earthquake was preceded by three foreshocks and followed by a large number of aftershocks. The focal depth of this earthquake is estimated to be 25 km. The composite fault plane solution of this event indicates a nearly pure strike-slip faulting with a normal-fault component [49, 195].

#### *5.5.2. Luxor- Southern Beni Suef (EG-23) seismogenic source*

cracks observed along the fault trace. Likely this fault is inactive [192]. The fault planes

Nasser's Lake. The Dabud Fault, which represents the main fault of this group, is about 36 km length. Geological evidences indicate reverse-slip, opposed to the

**iii.** The third one is a fault system trending NNE-SSW (Figure 11) and lies to the east of

24 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

In addition to the previous fault systems, Deif [57] has mentioned three faults located at the High Dam area. They are the Powerhouse, the Spillway and the Channel Faults. Deif [57] provided that the evidence of the occurrence of these faults is hidden below the Aswan High Dam and Nasser's Lake. These three faults show no evidence of being active in the Quaternary,

No historical earthquakes were reported by Ambraseys *et al.* [18] inside this area source. However, two historical events (epicentral intensity VII) were reported by Maamoun *et al.* [16] to be located at the same place of the MW 5.8, November 14, 1981 earthquake. These two events

**Figure 11.** Geological and tectonic features around Nasser's Lake (redrawn after Woodward-Clyde Consultants [82]).

Woodward-Clyde Consultants [82] evaluated the fault system in the Kalabsha area and reported that the Western Desert Fault System consists of a set of E-W faults that exhibit

and are considered as inactive with no significant hazard to the Aswan region [82].

of this system are nearly vertical (80-85°).

tectonic setting of the area.

occurred in 1210 B.C. and in 1854.

Several geophysical studies have been carried out by many authors using different approaches in individual localities lying along the Nile Valley. The most interesting geological studies in the Nile Valley are those carried out by Said [69-71], Issawi [78], Philobbos *et al.* [86], and El-Younsy *et al.* [196]. All these works were conducted independently and aimed to obtain information about the drainage system, the stratigraphy and structural geology in this part of Egypt.

The Nile Valley is a large elongated Oligo-Miocene rift, trending N-S as an echo of the Red Sea rifting. There is no agreement among scientists, till now, about the origin of the Nile Valley. Some authors [197, 198] supported the opinion of the erosional origin of the Nile Valley, while many others (e.g., [11, 12, 13, 17, 70 and 199]) consider the tectonic origin. This is supported by the fault scarps bordering the cliffs of the Nile Valley, the numerous faults recognized on its sides [70, 71 and 199] and the most recent focal mechanism solutions. Furthermore, geological studies of the Nile Valley show that, it occupies the marginal area between two main tectonic blocks (the Eastern Desert and the Neogene-Quaternary platform), which in turn behaves as a barrier that prevents the further extension of the East African Orogenic Belt activity to the west [71].

From the structural point of view, the faults and joints are the most deformational features observed at the cliffs bordering the Nile stream [69 and 70]. These faults have different directions (Figure 2). The most abundant present the NW-SE and NNW-SSE trends, while others (less abundant) exhibit the WNW-ESE, ENE-WSW and NE-SW directions. Most of the major valleys, at the east of the Nile River, are generated and controlled in a more or less degree by these faults.

To the north of Aswan area, in the region between Luxor and Southern Beni Suef, along the Nile River, there is a low seismicity level, which coincides with the main trend of the Nile River. This active area has been considered as a separate seismogenic source. Several historical earthquakes are reported to occur along the Nile River in this area source that may be due to the high population density along the Nile River in the ancient times. These earthquakes are the 600 B.C., 27 B.C., 857, 967, 997, 1264, 1299, 1694, 1778, and 1850 events. Their intensities range from V to VIII. Focal mechanism solutions exhibit reverse faulting mechanism to the west of the Nile River, in the area between Luxor and Assiut. However, normal faulting mechanism with strike-slip component appears to the north of Assiut till Beni Suef city.

#### *5.5.3. Beni Suef – Cairo – Suez District (EG-24) seismogenic source*

To the north of the previous zone and to the west of the Gulf of Suez, there is a moderate seismic activity between Beni Suef and Cairo, on the River Nile, till Suez, on the apex of the Gulf of Suez (Figure 9). Three fault trends are affecting the Cairo-Suez district: the first one is trending E-W, which aligned by latitude 30°N, and it is very dominant, while the other two (ENE and NW) are spatially more abundant [200]. The faults are predominantly normal, and have produced a series of fault blocks with a large strike-slip component [200].

Field observations, satellite images, aerial photographs and seismic profiles confirm that the region between Cairo and Suez is active from a tectonic point of view. Seismic activity are noticed along this belt at Wadi Hagul and Abu Hammad. However, the earthquake distribu‐ tion in this area is very scattered, and cannot be attributed to a specific known fault. This disperse seismicity yields a difficulty in delineating seismic zones. It is assumed that the seismic potential is uniform throughout the zone, although this is not entirely clear.

Sixty one historical earthquakes are related to this area source. The most important among them are the 935, 1111, 1259, 1262, 1303, and 1588 events. Moreover, the most important instrumental earthquake taken place in this source is the MW 5.8, October 12, 1992 event. Its epicenter was located about 40 km south of Cairo, in Dahshour. It caused a disproportional damage (estimated at more than L.E. 500 million) and the loss of many lives. The shock was strongly felt, and caused sporadic damage and life loss in the Nile Delta, around Zagazig. Damage was extended to reach Fayoum, Beni Suef and Minia cities. The mostly affected area was Cairo, especially its old sections, Bulaq and the southern region, along the western bank of the Nile to Gerza (Jirza) and El-Rouda. In all, 350 buildings collapsed completely and 9000 were irreparably damaged, killing 545 persons and injuring 6512. Most causalities in Cairo were victims of the horrible stampedes of students rushing out from schools. Approximately, 350 schools and 216 mosques were destroyed and there was about 50000 homeless.

Abdel Tawab *et al.* [201] studied the surface tectonic features of the area around Dahshour and Kom El-Hawa, and found a major N55°E trending normal fault at Kom El-Hawa (800 m length of surface trace with a vertical displacement of 40 cm) and a major E-W trending open fracture at Dahshour area (1200 m in length). Maamoun *et al.* [202] concluded that, most of the surface lineaments recorded after the occurrence of the main shocks are trending E-W to NW-SE. Abou Elenean [19] studied the focal mechanism solutions for some earthquakes in Dahshour area, and found normal faulting with a large strike-slip component. The first nodal plane is trending nearly E-W, showing coincidence with the surface lineaments that appeared directly after the occurrence of the MS 5.9, 1992 earthquake.

directions (Figure 2). The most abundant present the NW-SE and NNW-SSE trends, while others (less abundant) exhibit the WNW-ESE, ENE-WSW and NE-SW directions. Most of the major valleys, at the east of the Nile River, are generated and controlled in a more or less degree

26 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

To the north of Aswan area, in the region between Luxor and Southern Beni Suef, along the Nile River, there is a low seismicity level, which coincides with the main trend of the Nile River. This active area has been considered as a separate seismogenic source. Several historical earthquakes are reported to occur along the Nile River in this area source that may be due to the high population density along the Nile River in the ancient times. These earthquakes are the 600 B.C., 27 B.C., 857, 967, 997, 1264, 1299, 1694, 1778, and 1850 events. Their intensities range from V to VIII. Focal mechanism solutions exhibit reverse faulting mechanism to the west of the Nile River, in the area between Luxor and Assiut. However, normal faulting mechanism with strike-slip component appears to the north of Assiut till Beni Suef city.

To the north of the previous zone and to the west of the Gulf of Suez, there is a moderate seismic activity between Beni Suef and Cairo, on the River Nile, till Suez, on the apex of the Gulf of Suez (Figure 9). Three fault trends are affecting the Cairo-Suez district: the first one is trending E-W, which aligned by latitude 30°N, and it is very dominant, while the other two (ENE and NW) are spatially more abundant [200]. The faults are predominantly normal, and

Field observations, satellite images, aerial photographs and seismic profiles confirm that the region between Cairo and Suez is active from a tectonic point of view. Seismic activity are noticed along this belt at Wadi Hagul and Abu Hammad. However, the earthquake distribu‐ tion in this area is very scattered, and cannot be attributed to a specific known fault. This disperse seismicity yields a difficulty in delineating seismic zones. It is assumed that the

Sixty one historical earthquakes are related to this area source. The most important among them are the 935, 1111, 1259, 1262, 1303, and 1588 events. Moreover, the most important instrumental earthquake taken place in this source is the MW 5.8, October 12, 1992 event. Its epicenter was located about 40 km south of Cairo, in Dahshour. It caused a disproportional damage (estimated at more than L.E. 500 million) and the loss of many lives. The shock was strongly felt, and caused sporadic damage and life loss in the Nile Delta, around Zagazig. Damage was extended to reach Fayoum, Beni Suef and Minia cities. The mostly affected area was Cairo, especially its old sections, Bulaq and the southern region, along the western bank of the Nile to Gerza (Jirza) and El-Rouda. In all, 350 buildings collapsed completely and 9000 were irreparably damaged, killing 545 persons and injuring 6512. Most causalities in Cairo were victims of the horrible stampedes of students rushing out from schools. Approximately,

have produced a series of fault blocks with a large strike-slip component [200].

seismic potential is uniform throughout the zone, although this is not entirely clear.

350 schools and 216 mosques were destroyed and there was about 50000 homeless.

Abdel Tawab *et al.* [201] studied the surface tectonic features of the area around Dahshour and Kom El-Hawa, and found a major N55°E trending normal fault at Kom El-Hawa (800 m length

*5.5.3. Beni Suef – Cairo – Suez District (EG-24) seismogenic source*

by these faults.

In addition to the previous earthquake, there were three important earthquakes located inside this source zone. One of them located to the southwest of Suez, is the mb 4.9 (MS 4.8), March 29, 1984 Wadi Hagul earthquake. It was strongly felt in Suez, Ismailia and Cairo. A large number of aftershocks were recorded by nearby temporary stations. The second earthquake was located Northeast Cairo; it is the mb 4.8, April 29, 1974 Abu Hammad earthquake. It was strongly felt in Lower Egypt (Nile Delta) and Southwest Israel. The last earthquake was the mb 5.0, January 2, 1987 Ismailia event.

Mousa [203] and Hassib [204] computed two nodal planes trending ENE-WSW and NNW-SSE, with left-lateral strike-slip motion along the second plane, for the Abu Hammad event. They computed the same strike-slip with reverse component for the Wadi-Hagul earthquake. In addition, the mechanism of the Ismailia earthquake shows also strike-slip movement with two nodal planes trending N68° E and S24°E, with steep dip angles (each of them is 80°) [205].


The seismicity parameters for the delineated seismic sources along the Nile River are displayed in Table 5.

**Table 5.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones along the Nile River.

#### **5.6. Seismic sources along the Mediterranean Coastal Line**

The Mediterranean Coastal area is characterized by small to moderate seismicity. This area is located at the southeastern part of the Mediterranean Sea. It separates between the high seismic activities along the Gulf of Aqaba-Dead Sea Transform Fault and the seismicity of the Medi‐ terranean Sea (Hellenic and Cyprian Arcs). Moreover, it separates the Southern Cyprus seismic activity from the Northern Egypt activity. Hence, this area has been divided into three seismic sources (Figure 12), based mainly on the available focal mechanism data and the seismic activity.

**Figure 12.** Shallow-depth seismicity (h ≤ 35 km) and seismic source zones delineated for the Mediterranean coastal line.

#### *5.6.1. Eastern Mediterranean Coast (EG-25) seismicity source*

This area source is parallel to the eastern coastal line of the Mediterranean Sea. It is located to the west of the previous quoted sources EG-07, EG-08, and EG-09, and to the southeast of Cyprus. It includes all the seismicity located to the west of the DST, and those earthquakes are not related with the Cyprian Arc. 29 historical events are included inside this area source. The most important among them are the 590 B.C., 525 B.C., 12 B.C., 306, 332, 551, 1269, and 1546 earthquakes.

#### *5.6.2. Northern Delta (EG-26) seismicity source*

This source is located to the northwest of the Nile Delta region. It extends from Alexandria towards the Mediterranean Sea in NE direction. 23 historical events are included inside this large area source, among them the 796, 951, 955, 956, 1303, 1341, and 1375 earthquakes. Moreover, the mb 6.5 (MS 6.8), September 12, 1955 Alexandria earthquake, represents the most important recorded event inside this source. This earthquake was felt in the entire Eastern Mediterranean Basin. In Egypt, it was strongly felt, and led to the loss of 22 lives and damage in the Nile Delta, between Alexandria and Cairo [17]. The destruction of more than 300 buildings of old brick construction was reported in Rosetta, Idku, Damanhour, Mohmoudya and Abu-Hommos. A maximum intensity of VII was assigned to a limited area in Behira province, where 5 people killed and 41 were injured.

Mostly of the focal mechanism data inside this area source reflects reverse faulting mechanism with, sometimes, strike-slip component, except one event, showing a strike-slip motion with a notable normal component (the MW 4.5, April 9, 1987 event).

#### *5.6.3. Western Mediterranean Coast (EG-27) seismicity source*

The Western Egyptian Mediterranean Coastal zone is located to the north of the Egyptian-Libyan boundary. Only two historical events are reported inside this source: the Imax VIII, 262, and Imax VI, 1537 earthquakes. However, the most important recorded earthquake is the MW 5.5, May 28, 1998 Ras El-Hekma event. This earthquake is widely felt in Northern Egypt. Intensity of VII is assigned at Ras El- Hekma village (~300 km west of Alexandria), and an intensity of V–VI at Alexandria city [206]. Ground fissures trending NW–SE were observed along the beach. Some cracks were also observed in concrete buildings. Furthermore, some people left their houses. The windows rattled and hanging objects swung, but the direction of the ground motion was poorly identified [206].

Recent studies concerning the crustal structure and focal mechanism of the MW 5.5, May 28, 1998 Ras El-Hekma earthquake suggested that this source is an extension of the compressional stress from the Hellenic Arc. This compressional stress reactivated the old Triassic normal faults as reverse faults, or reverse faults with strike-slip component. This activity coincides with the hinge zone geometry proposed by Kebeasy [17]. Mostly of the focal mechanism analyses data indicate reverse faulting with some strike-slip component.

Seismicity parameters for the delineated seismic sources along the Mediterranean coastal line are displayed in Table 6.


**Table 6.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones along the Mediterranean coastal line.

#### **5.7. Seismic sources of the Western Desert**

**Figure 12.** Shallow-depth seismicity (h ≤ 35 km) and seismic source zones delineated for the Mediterranean coastal

28 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

This area source is parallel to the eastern coastal line of the Mediterranean Sea. It is located to the west of the previous quoted sources EG-07, EG-08, and EG-09, and to the southeast of Cyprus. It includes all the seismicity located to the west of the DST, and those earthquakes are not related with the Cyprian Arc. 29 historical events are included inside this area source. The most important among them are the 590 B.C., 525 B.C., 12 B.C., 306, 332, 551, 1269, and 1546

This source is located to the northwest of the Nile Delta region. It extends from Alexandria towards the Mediterranean Sea in NE direction. 23 historical events are included inside this large area source, among them the 796, 951, 955, 956, 1303, 1341, and 1375 earthquakes. Moreover, the mb 6.5 (MS 6.8), September 12, 1955 Alexandria earthquake, represents the most important recorded event inside this source. This earthquake was felt in the entire Eastern Mediterranean Basin. In Egypt, it was strongly felt, and led to the loss of 22 lives and damage in the Nile Delta, between Alexandria and Cairo [17]. The destruction of more than 300 buildings of old brick construction was reported in Rosetta, Idku, Damanhour, Mohmoudya and Abu-Hommos. A maximum intensity of VII was assigned to a limited area in Behira

Mostly of the focal mechanism data inside this area source reflects reverse faulting mechanism with, sometimes, strike-slip component, except one event, showing a strike-slip motion with

*5.6.1. Eastern Mediterranean Coast (EG-25) seismicity source*

*5.6.2. Northern Delta (EG-26) seismicity source*

province, where 5 people killed and 41 were injured.

a notable normal component (the MW 4.5, April 9, 1987 event).

line.

earthquakes.

#### *5.7.1. El-Gilf El-Kebeir (EG-28) Seismogenic Source*

Issawi [28] studied the geology of El-Gilf El-Kebeir region, and concluded that the area is affected by three main faults (Figure 2). The first one is the Gilf Fault, which strikes N-S for a distance of 150 km inside Egypt. Its extension in Sudan is unknown. Its northward extension is not traced. He interpreted this fault as a normal, gravity, strike and hinge type of structure. The second one is Kemal Fault, which limits the northwestern side of the Gilf Plateau. It is normal, strike fault which trends NW-SE. The Kemal Fault intersects the Gilf Fault at its northern end. The third one is the Tarfawi Fault, which has the same trend similar to the Gilf Fault. Its length, in Egypt, is 220 km but it extends in Sudan. He interpreted this fault as a normal, gravity and hinge fault.

The only recorded earthquake in this area source is the mb 5.3 (ML 5.7), December 9, 1978 El-Gilf El-Kebeir earthquake. It had a reverse faulting mechanism. Riad and Hosney [207] studied its focal mechanism and concluded that, a shear direction did exist in the basement rocks of the southern part of the Western Desert and has been explained as due to compressional stress resulting from the spreading of the Red Sea. Their fault planes solution shows that the P-axis is almost perpendicular to the Red Sea spreading axis. They concluded that the Gilf Plateau is probably divided into two parts by a fault striking nearly E-W. Some authors [e.g., 208 and 209] pointed out that this activity is linked to the pre-existing weak zones, while, Abou Elenean [19] linked such an intraplate activity to the intersection of more than one local fault.

In the current work, the Gilf El-Kebeir (EG-28) seismogenic source covers the seismic activity in this area, as well as the above mentioned faults.

## **6. Eastern Mediterranean region seismic sources**

The Mediterranean region is characterized by a very complex tectonics that can be generally described in the frame of the collision between the Eurasian and African Plates [183, 210-219]. It can be divided into western, central, and eastern basins.

The Eastern Mediterranean region, which defines the region lying between the Caspian Sea and the Adriatic Sea through Caucasus, Anatolia, Aegean Sea and Greece, is one of the world's most seismically active regions. Recent tectonics of the Eastern Mediterranean region has been studied intensely in the last four decades. The Eastern Mediterranean region is known to be seismically active over a period of more than 2000 years based on historical and instrumental records. The tectonic and seismotectonic studies reflect a highly complicated tectonic setting.

It is characterized by two main seismic regions: the Hellenic and Cyprian Arcs (Figure 13). The Cyprian Arc has a similar geometry to the Hellenic Arc and the two are often compared (e.g., [220]). However, the observed seismic activity and the well-known plate movement in the Eastern Mediterranean area, suggest that the previously mentioned arcs are affected by a very distinct tectonic activity. The convergence across the first one (Hellenic Arc) is 20–40 mm/yr. (two to three times faster across the Cyprian Arc). Thus, this biggest displacement level yields in higher seismicity rate at much deeper levels (up to 300 km) [220].

The Cyprian Arc represents a tectonic plate margin separating the Anatolian sub-Plate (to the north) from the Nubian and Sinai sub-Plates (to the south) (Figure 13). It is connected from the west by the Hellenic Arc, and from the east by the Dead Sea and the East Anatolian Faults. In addition, it extends from the Gulf of Antalia, to the west to the Gulf of Iskenderun, to the east. On the other hand, the Hellenic Arc is considered to be the most active seismic region in Europe. It is represents the convergent plate boundary between the African Plate and the Eurasian Plate (Aegean sub-Plate) in the Mediterranean area (Figure 13).

**Figure 13.** Tectonic map of the Eastern Mediterranean region (after Ziegler [221]; Meulenkamp *et al.* [222]; and Dewey *et al.* [223]).

#### **6.1. SHARE shallow-depth seismic sources (h ≤ 20 km)**

The only recorded earthquake in this area source is the mb 5.3 (ML 5.7), December 9, 1978 El-Gilf El-Kebeir earthquake. It had a reverse faulting mechanism. Riad and Hosney [207] studied its focal mechanism and concluded that, a shear direction did exist in the basement rocks of the southern part of the Western Desert and has been explained as due to compressional stress resulting from the spreading of the Red Sea. Their fault planes solution shows that the P-axis is almost perpendicular to the Red Sea spreading axis. They concluded that the Gilf Plateau is probably divided into two parts by a fault striking nearly E-W. Some authors [e.g., 208 and 209] pointed out that this activity is linked to the pre-existing weak zones, while, Abou Elenean

30 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

[19] linked such an intraplate activity to the intersection of more than one local fault.

in this area, as well as the above mentioned faults.

**6. Eastern Mediterranean region seismic sources**

It can be divided into western, central, and eastern basins.

in higher seismicity rate at much deeper levels (up to 300 km) [220].

Plate (Aegean sub-Plate) in the Mediterranean area (Figure 13).

In the current work, the Gilf El-Kebeir (EG-28) seismogenic source covers the seismic activity

The Mediterranean region is characterized by a very complex tectonics that can be generally described in the frame of the collision between the Eurasian and African Plates [183, 210-219].

The Eastern Mediterranean region, which defines the region lying between the Caspian Sea and the Adriatic Sea through Caucasus, Anatolia, Aegean Sea and Greece, is one of the world's most seismically active regions. Recent tectonics of the Eastern Mediterranean region has been studied intensely in the last four decades. The Eastern Mediterranean region is known to be seismically active over a period of more than 2000 years based on historical and instrumental records. The tectonic and seismotectonic studies reflect a highly complicated tectonic setting.

It is characterized by two main seismic regions: the Hellenic and Cyprian Arcs (Figure 13). The Cyprian Arc has a similar geometry to the Hellenic Arc and the two are often compared (e.g., [220]). However, the observed seismic activity and the well-known plate movement in the Eastern Mediterranean area, suggest that the previously mentioned arcs are affected by a very distinct tectonic activity. The convergence across the first one (Hellenic Arc) is 20–40 mm/yr. (two to three times faster across the Cyprian Arc). Thus, this biggest displacement level yields

The Cyprian Arc represents a tectonic plate margin separating the Anatolian sub-Plate (to the north) from the Nubian and Sinai sub-Plates (to the south) (Figure 13). It is connected from the west by the Hellenic Arc, and from the east by the Dead Sea and the East Anatolian Faults. In addition, it extends from the Gulf of Antalia, to the west to the Gulf of Iskenderun, to the east. On the other hand, the Hellenic Arc is considered to be the most active seismic region in Europe. It is represents the convergent plate boundary between the African Plate and the Eurasian

The Seismic Hazard Harmonization in Europe (SHARE) project [224], since the year 2009 till 2013, worked in establishing an appropriate seismic hazard model for Europe and Turkey. This project delivered a seismic hazard reference model for the current use of the European building design and seismic regulations, Eurocode 8 (EC8), that came into force in 2010.

The EU-FP7 European Commission Project (SHARE), aiming at providing an updated stateof-the art time-independent seismic hazard model, envisioned to serve as a reference model for the revision of the EC8 building code. SHARE, in addition, contributes its results to the Global Earthquake Model (GEM, www.globalquakemodel.org), a public/private partnership initiated and approved by the Global Science Forum of the OECD- GSF, aiming to provide a uniform hazard and risk model around the globe.

The Euro-Mediterranean area is complex from a seismotectonic point of view. The plate boundary between Africa and Europe runs roughly west to east from the Mid-Atlantic Ridge to Eastern Turkey with different mechanisms including continental collision, subduction, and transcurrent movement. Moving away from the plate boundary, the stable continental region is also locally rather active.

SHARE inherits knowledge from national, regional and site-specific PSHAs, assessed new data, assembled the data in a homogeneous fashion, and built comprehensive hazard relevant databases. In the frame of this project, the establishment of a seismic source model for Europe and the surrounding areas was considered. This model is built upon the available local and regional models as well as newly defined source zones. It has been developed during eight separate workshops by the SHARE consortium. Almost 80 experts from 28 countries from the informed European-Mediterranean seismological community have participated in building the zonation model.

The principle for seismic source zones is that they represent enclosed areas within which, a uniform seismicity distribution and maximum magnitude is expected. Background sources have been avoided in the sense that all areas have been covered by seismic sources, i.e., even very low seismicity areas are covered with areal source zones. The principles along which seismic source zones in the current model have been constructed are based on information from geological structures on different scales, tectonics and seismicity.

Seismicity also follows these structures well, e.g., as can be seen along the North Anatolian Fault, the Gulf of Corinth and the Hellenic Arc. The use of fault source information has also been done in the delineation of the source zones, especially in the case of the foundation of the sources for Balkans, Greece and Turkey, Italy and Portugal. b-value, annual activity rates, and maximum expected magnitude were computed using different approaches and methods and included in the SHARE project database (www.share-eu.org) [225].

In the current work, 53 shallow-depth seismic sources (h ≤ 20 km) from the SHARE source model (Figure 5), were considered to the north of Egypt, till latitude 38° N, and covering the Greece and Turkey regions. Some of the events located at this region were felt and caused few damages in the northern part of Egypt (e.g., the Imax VIII, August 8, 1303 offshore Mediterranean earthquake, the Imax VI, February 13, 1756 and the MS 7.4, June 26, 1926 Hellenic Arc earth‐ quakes, the MW 6.8, October 9, 1996 Cyprus earthquake, and the MS 6.4, October 12, 2013 Crete earthquake). Thus, these source zones have a certain contribution to the seismic hazard in Northern Egypt.

The model in the Greek and Cyprian area build to a large extent upon the previous works of Papiouannou and Papazachos [64] and Papiouannou [226]. The Turkish model [227, 228] is provided as a cooperation between the EMME project and SHARE. The Turkish model is further a hybrid model, in the sense that the area sources have been delineated with respect to the integrated fault line sources from the main faults, like the North and East Anatolian Faults.

#### **6.2. Intermediate-depth seismic sources (20 ≤ h ≤ 100 km)**

Intermediate focal depth earthquakes occur in the Eastern Mediterranean region (Southern Greece and Turkey) define a Benioff zone of stair shape which dips from the convex side of the Cyprian and the Hellenic Arcs to its concave side (from the Eastern Mediterranean to the Greek and Turkish lands) [229-231]. Some of these earthquakes are moderate to large earth‐ quakes, and constitute a seismic threat for the whole Mediterranean area, including Northern Egypt. Since, because of their magnitudes and focal depths, these earthquakes produce seismic waves of large amplitude and period which travel large distances with low attenuation [232]. Therefore, these earthquakes can contribute to the seismic hazard of Northern Egypt.

In this work, intermediate-depth sources for earthquakes having focal depths ranging from 20 km to 100 km have been delineated. Below this depth (100 km) and considering the large distance from Egypt, deep events have no contribution to the seismic hazard. Thus, 7 inter‐ mediate-depth source zones have been considered in the Hellenic and Cyprian subduction zones to cover the intermediate-depth seismicity (20 ≤ h ≤ 100 km) (Figure 14). The zoning was based on the seismicity distribution and the tectonic setting of the region. Seismicity parame‐ ters for these intermediate-depth seismic sources are displayed in Table 7.

**Figure 14.** Intermediate-depth seismicity (20 ≤ h ≤ 100 km) and delineated intermediate-depth seismogenic source zones for the Eastern Mediterranean region.


**Table 7.** b-value, annual rate of earthquakes, and maximum observed magnitude for the delineated seismic source zones of the Eastern Mediterranean region.

## **7. Conclusion**

The principle for seismic source zones is that they represent enclosed areas within which, a uniform seismicity distribution and maximum magnitude is expected. Background sources have been avoided in the sense that all areas have been covered by seismic sources, i.e., even very low seismicity areas are covered with areal source zones. The principles along which seismic source zones in the current model have been constructed are based on information

32 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Seismicity also follows these structures well, e.g., as can be seen along the North Anatolian Fault, the Gulf of Corinth and the Hellenic Arc. The use of fault source information has also been done in the delineation of the source zones, especially in the case of the foundation of the sources for Balkans, Greece and Turkey, Italy and Portugal. b-value, annual activity rates, and maximum expected magnitude were computed using different approaches and methods and

In the current work, 53 shallow-depth seismic sources (h ≤ 20 km) from the SHARE source model (Figure 5), were considered to the north of Egypt, till latitude 38° N, and covering the Greece and Turkey regions. Some of the events located at this region were felt and caused few damages in the northern part of Egypt (e.g., the Imax VIII, August 8, 1303 offshore Mediterranean earthquake, the Imax VI, February 13, 1756 and the MS 7.4, June 26, 1926 Hellenic Arc earth‐ quakes, the MW 6.8, October 9, 1996 Cyprus earthquake, and the MS 6.4, October 12, 2013 Crete earthquake). Thus, these source zones have a certain contribution to the seismic hazard in

The model in the Greek and Cyprian area build to a large extent upon the previous works of Papiouannou and Papazachos [64] and Papiouannou [226]. The Turkish model [227, 228] is provided as a cooperation between the EMME project and SHARE. The Turkish model is further a hybrid model, in the sense that the area sources have been delineated with respect to the integrated fault line sources from the main faults, like the North and East Anatolian

Intermediate focal depth earthquakes occur in the Eastern Mediterranean region (Southern Greece and Turkey) define a Benioff zone of stair shape which dips from the convex side of the Cyprian and the Hellenic Arcs to its concave side (from the Eastern Mediterranean to the Greek and Turkish lands) [229-231]. Some of these earthquakes are moderate to large earth‐ quakes, and constitute a seismic threat for the whole Mediterranean area, including Northern Egypt. Since, because of their magnitudes and focal depths, these earthquakes produce seismic waves of large amplitude and period which travel large distances with low attenuation [232].

Therefore, these earthquakes can contribute to the seismic hazard of Northern Egypt.

In this work, intermediate-depth sources for earthquakes having focal depths ranging from 20 km to 100 km have been delineated. Below this depth (100 km) and considering the large distance from Egypt, deep events have no contribution to the seismic hazard. Thus, 7 inter‐ mediate-depth source zones have been considered in the Hellenic and Cyprian subduction zones to cover the intermediate-depth seismicity (20 ≤ h ≤ 100 km) (Figure 14). The zoning was

from geological structures on different scales, tectonics and seismicity.

included in the SHARE project database (www.share-eu.org) [225].

**6.2. Intermediate-depth seismic sources (20 ≤ h ≤ 100 km)**

Northern Egypt.

Faults.

To reach a more realistic seismic hazard quantification in Egypt, it is necessary to recognize the seismic source zones, including the seismic activity that can affect different regions all over the country. In the current work, a new seismic source model for Egypt and its surroundings is proposed, using all available geological, geophysical, tectonic and earthquake data, aimed at carrying out seismic hazard studies.

This work presents a detailed review on major tectonic features and the correlation of seis‐ micity with them, to demarcate seismic sources in Egypt and neighborhood. The Gulf of Aqaba-Dead Sea Transform, the Red Sea-Gulf of Suez Rift, and the Cyprian and Hellenic Arcs are the three most active seismotectonic belts in the region, which have produced several large earthquakes in the recent past. On the basis of a comprehensive and critical analysis of the seismotectonic characteristics, different seismic sources are defined to model the seismicity for the assessment of seismic hazard in Egypt.

Focal mechanism solutions data, active faults data, as well as an updated earthquake catalogue for the period 2200 B.C.–2013 are taken into account. Potential seismic sources are modeled as area sources, in which configuration of each seismic source is controlled, mainly, by the fault extension and seismicity distribution.

The proposed seismic source model consists of 28 shallow-depth seismic zones (h ≤ 35 km) for the Egyptian territory and its surroundings, specified on the basis of mainly seismotectonic and seismicity criteria. In addition, the authors have considered 53 shallow-depth seismic sources (h ≤ 20 km) for the Eastern Mediterranean region after SHARE (2013). Furthermore, the current model involves 7 delineated intermediate-depth seismic sources (20 ≤ h ≤100 km) covering the intermediate-depth seismicity in the Eastern Mediterranean region.

Seismicity parameters (b-value and activity rates) of the Gutenberg–Richter magnitude– frequency relationship have been estimated for each one of the seismic sources. In addition, the maximum observed magnitude for each seismic source zone was reported from the sources sub-catalogues. The coordinates of these seismic source zones and the estimated seismicity parameters can be directly inserted into PSHA after the estimation of the maximum expected magnitude for each source. The computation of seismic hazard for Egypt using these data will form the subject matter of a future paper.

## **Acknowledgements**

The first author wants to thank the Egyptian Government for funding him in the Joint-Supervision Mission program at the University of Jaén, Spain. This research was supported by the Aswan Regional Earthquake Research Centre and the Spanish Seismic Hazard and Active Tectonics research group.

## **Author details**

R. Sawires1,4, J.A. Peláez2 , R.E. Fat-Helbary3 , H.A. Ibrahim1 and M.T. García Hernández2

1 Department of Geology, Faculty of Science, Assiut University, Assiut, Egypt


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is proposed, using all available geological, geophysical, tectonic and earthquake data, aimed

34 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

This work presents a detailed review on major tectonic features and the correlation of seis‐ micity with them, to demarcate seismic sources in Egypt and neighborhood. The Gulf of Aqaba-Dead Sea Transform, the Red Sea-Gulf of Suez Rift, and the Cyprian and Hellenic Arcs are the three most active seismotectonic belts in the region, which have produced several large earthquakes in the recent past. On the basis of a comprehensive and critical analysis of the seismotectonic characteristics, different seismic sources are defined to model the seismicity for

Focal mechanism solutions data, active faults data, as well as an updated earthquake catalogue for the period 2200 B.C.–2013 are taken into account. Potential seismic sources are modeled as area sources, in which configuration of each seismic source is controlled, mainly, by the fault

The proposed seismic source model consists of 28 shallow-depth seismic zones (h ≤ 35 km) for the Egyptian territory and its surroundings, specified on the basis of mainly seismotectonic and seismicity criteria. In addition, the authors have considered 53 shallow-depth seismic sources (h ≤ 20 km) for the Eastern Mediterranean region after SHARE (2013). Furthermore, the current model involves 7 delineated intermediate-depth seismic sources (20 ≤ h ≤100 km)

Seismicity parameters (b-value and activity rates) of the Gutenberg–Richter magnitude– frequency relationship have been estimated for each one of the seismic sources. In addition, the maximum observed magnitude for each seismic source zone was reported from the sources sub-catalogues. The coordinates of these seismic source zones and the estimated seismicity parameters can be directly inserted into PSHA after the estimation of the maximum expected magnitude for each source. The computation of seismic hazard for Egypt using these data will

The first author wants to thank the Egyptian Government for funding him in the Joint-Supervision Mission program at the University of Jaén, Spain. This research was supported by the Aswan Regional Earthquake Research Centre and the Spanish Seismic Hazard and

, H.A. Ibrahim1

and M.T. García Hernández2

, R.E. Fat-Helbary3

1 Department of Geology, Faculty of Science, Assiut University, Assiut, Egypt

covering the intermediate-depth seismicity in the Eastern Mediterranean region.

at carrying out seismic hazard studies.

the assessment of seismic hazard in Egypt.

extension and seismicity distribution.

form the subject matter of a future paper.

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R. Sawires1,4, J.A. Peláez2

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## **Dynamical Features of the Seismicity in Mexico by Means of the Visual Recurrence Analysis**

Alejandro Ramírez-Rojas, Lucía R. Moreno-Torres, Ricardo T. Páez-Hernández and Israel Reyes-Ramírez

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/59440

## **1. Introduction**

The recurrence, based in the recurrence Poincare theorem, is a fundamental property of dynamical systems that has been exploited to characterize the behavior of dynamical systems in the phase space. Recurrence is defined when an orbit visits a region of phase space that was previously visited [1]. In this context, the so-called recurrence plot (RP), introduced by Eckmann et al in [2], is a powerful tool for the visualization and analysis of the underlying dynamics of the systems in the phase space like determinism, divergence, periodicity, stationarity among others, for instance the lengths of the diagonal line structures in the RP are related to the positive Lyapunov exponent [3]. Methods based in RP have been successfully applied to wide class of data obtained in physiology, geology, physics, finances and others. RP are especially suitable for the investigation of rather short and non-stationary data [4], and complex systems [5]. For deterministic systems the analysis in the phase space is relatively direct because their solutions are represented as time series, nevertheless, for real natural systems like clime, atmosphere, dimetilsulphure production [6], some of their dynamical variables are gathered as punctual processes. Particularly, the representation of a seismic sequence as a time series is one of the most debated questions in Geophysics, nevertheless natural time analysis, introduced by in [7] by Varotsos et al considers sequences of events and, with this methodology has been possible to identify signals with noises [8] and characterize seismic processes from an order parameter properly defined [9]. Taking in consideration that faults and tectonic plates can be considered as dynamical systems which permit to apply techniques derived from the dynamical systems theory and nonlinear analysis like recurrence plots, clustering, entropy, fractality, correlation, memory among other. In this work we studied

© 2015 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.

properties of the seismicity occurred in Mexico in the period 2006-2014, reported by Servicio Sismológico Nacional, (www.ssn.unam.mx), by considering the occurrence of events as sequences of magnitudes (time series) and determining the recurrence plots. Based on the Visual Recurrence Analysis (VRA), it is possible to get dynamical features of the seismicity. The most important seismic region in Mexico is located along the Mexican Pacific coast. In [10] was proposed a division of 19 regions of the seismo tectonic zone. They took into account seismic characteristics of the existing catalogs for the seismicity occurring in Mexico from 1899 to 2007, for details see [9] and references therein. In order to characterize the Mexican seismicity as a dynamical system driven by the tectonic movements in the Pacific edge, we proposed to investigate the qualitative dynamical features for the dispersion zone, Baja California, and for the subduction zone formed by La Ribera and Cocos plates subducting beneath the Northa‐ merica plate. Taking into account the Geophysical structure, the seismic activity and the bvalues in the Gutemberg-Richter law, in this work, six selected regions have been considered. These six regions are named: Baja California (Z1), Jalisco-Colima (Z2), Michoacán (Z3), Guerrero (Z4) and Oaxaca (Z5) and Chiapas (Z6), the first one corresponds with a dispersion zone and the other ones are subduction regions, [11]. The analyzed data set in this work correspond with the Mexican catalogue which is complete for magnitudes greater than 3, within the mentioned period. Since a geophysical point of view, the seismic activity should be individually characterized in each region because the underlying dynamics shows particular features, as is described in the next section. First, seismic data are represented as a temporal sequence of magnitudes, then, the phase space is reconstructed, by estimating the time delay and the embedding dimension. In order to distinguish some features of the underlying dynamics of each Mexican region seismic, the aim of this work is to study the recurrence plot behavior based on the visual recurrence analysis, taking into account the sequence of events (magnitudes) in time and, on the other hand, analyzing the inter-events time series. Our analysis shows important differences in the recurrence maps of each region. Our finding suggest that the patterns obtained could be associated with the local geophysical structures of each subduction and dispersion zones driven by their characteristic nonlinear dynamical features of each region.

#### **2. Methodology**

#### **2.1. Phase space reconstruction**

To reconstruct the dynamics of the system is necessary to convert the time series in state vectors, being the principal step the phase space reconstruction. Takens [12] showed that it is possible to recreate a topologically equivalent picture of the original multidimensional system behavior by using the time series of a single observable variable. The idea is to estimate a time delay *τ*, and an embedding dimension *m*. The parameters, *m* and *τ*, must be properly chosen, although there exist some algorithms to do that, appropriated and tested methods are the Mutual Information function to obtain the time delay and, to get the embedding dimension, the False Nearest Neighbors. Once the time delay and the embedding dimension have been approached, the phase space can be reconstructed. For a time series of a scalar variable

Dynamical Features of the Seismicity in Mexico by Means of the Visual Recurrence Analysis http://dx.doi.org/10.5772/59440 55

$$\text{tr}(t\_i), \text{ i = 1, 2, 3, \dots, N} \tag{1}$$

the next vector is construct in phase space

properties of the seismicity occurred in Mexico in the period 2006-2014, reported by Servicio Sismológico Nacional, (www.ssn.unam.mx), by considering the occurrence of events as sequences of magnitudes (time series) and determining the recurrence plots. Based on the Visual Recurrence Analysis (VRA), it is possible to get dynamical features of the seismicity. The most important seismic region in Mexico is located along the Mexican Pacific coast. In [10] was proposed a division of 19 regions of the seismo tectonic zone. They took into account seismic characteristics of the existing catalogs for the seismicity occurring in Mexico from 1899 to 2007, for details see [9] and references therein. In order to characterize the Mexican seismicity as a dynamical system driven by the tectonic movements in the Pacific edge, we proposed to investigate the qualitative dynamical features for the dispersion zone, Baja California, and for the subduction zone formed by La Ribera and Cocos plates subducting beneath the Northa‐ merica plate. Taking into account the Geophysical structure, the seismic activity and the bvalues in the Gutemberg-Richter law, in this work, six selected regions have been considered. These six regions are named: Baja California (Z1), Jalisco-Colima (Z2), Michoacán (Z3), Guerrero (Z4) and Oaxaca (Z5) and Chiapas (Z6), the first one corresponds with a dispersion zone and the other ones are subduction regions, [11]. The analyzed data set in this work correspond with the Mexican catalogue which is complete for magnitudes greater than 3, within the mentioned period. Since a geophysical point of view, the seismic activity should be individually characterized in each region because the underlying dynamics shows particular features, as is described in the next section. First, seismic data are represented as a temporal sequence of magnitudes, then, the phase space is reconstructed, by estimating the time delay and the embedding dimension. In order to distinguish some features of the underlying dynamics of each Mexican region seismic, the aim of this work is to study the recurrence plot behavior based on the visual recurrence analysis, taking into account the sequence of events (magnitudes) in time and, on the other hand, analyzing the inter-events time series. Our analysis shows important differences in the recurrence maps of each region. Our finding suggest that the patterns obtained could be associated with the local geophysical structures of each subduction and dispersion zones driven by their characteristic nonlinear dynamical

54 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

To reconstruct the dynamics of the system is necessary to convert the time series in state vectors, being the principal step the phase space reconstruction. Takens [12] showed that it is possible to recreate a topologically equivalent picture of the original multidimensional system behavior by using the time series of a single observable variable. The idea is to estimate a time delay *τ*, and an embedding dimension *m*. The parameters, *m* and *τ*, must be properly chosen, although there exist some algorithms to do that, appropriated and tested methods are the Mutual Information function to obtain the time delay and, to get the embedding dimension, the False Nearest Neighbors. Once the time delay and the embedding dimension have been approached, the phase space can be reconstructed. For a time series of a scalar variable

features of each region.

**2. Methodology**

**2.1. Phase space reconstruction**

$$\mathbf{Y}(t\_i) = \begin{bmatrix} \mathbf{x}(t\_i), \ \mathbf{x}(t\_i + \tau), \ \mathbf{x}(t\_i + 2\tau), \ \cdots, \ \mathbf{x}(t\_i + (m-1)\tau) \end{bmatrix} \tag{2}$$

where i = 1 to N – (*m* – 1)τ, τ is time delay, *m* is the embedding dimension and N – (m – 1)τ is number of states in the phase space. According with the embedding theorem [12] dynamics reconstructed using this formula is equivalent to the dynamics in the phase space in the sense that characteristic invariants of the system are conserved.

#### **2.2. Mutual information function**

Formally, the Mutual Information is defined, for two stochastic variables X and Y, as I(X;Y) = H(Y,X) – H(X|Y) – H(Y|X) where H(Y,X) is the joint entropy, H(X|Y) and H(Y|X) are the conditional entropies. If X represents the sequence x(t<sup>i</sup> ) and Y the respective sequence x(t<sup>i</sup> + τ) the Mutual Information Function (MIF) is able to calculate the global correlation in a time series taking into account the linear and non linear contributions, being MIF the most frequently used to calculate the time delay and described as follows:

$$\begin{aligned} & \left( \mathbf{x} \{ t\_i \} \right) \\ & \mathbf{x} \{ t\_i + \tau \} \\ & P(\text{O}) \\ & P \\ & \frac{P \left( \mathbf{x} \{ t\_i \}, \mathbf{x} \{ t\_i + \tau \} \right)}{P \left( \mathbf{x} \{ t\_i \}, \mathbf{x} \{ t\_i + \tau \} \right) \log\_2 } \\ & I(\tau) = \sum\_{i=1}^{N} \end{aligned} \tag{3}$$

The mutual information I(τ) is a measure of the relative entropy between the joint distribution and the product of distributions P(x(t<sup>i</sup> )) and P(x(t<sup>i</sup> + τ)), where P(x(t<sup>i</sup> ), x(ti + τ)) is the joint probability of the signal measured between the times t<sup>i</sup> and t<sup>i</sup> + τ. The expressions P(x(t<sup>i</sup> )) and P(x(t<sup>i</sup> + τ)) indicates the and marginal probabilities. MIF is a nonlinear generalization of the linear autocorrelation function. According to [13] the suitable value of τ is attained with the first local minimum of I(τ). When the time series is uncorrelated or random, like white noise, the next equality holds

$$\mathbf{x}(t\_i)$$
 
$$\mathbf{x}(t\_i + \tau)$$
 
$$P$$

and I(τ) = 0 [14]. Typical cases are white noise, periodic and periodic + noise and Rossler time series. In Figure 1 the MIF behavior for this typical cases are depicted.

**Figure 1.** MIF behavior for white noise, periodic + noise are uncorrelated signals with a time delay τ = 1. For periodic and Rossler τ = 3 and 13 respectively.

#### **2.3. False nearest neighbors**

False Nearest Neighbors method (FNN) is an iterative algorithm which estimates the minimal embedding dimension of the system proposed by [15]. The idea is based in the uniqueness theorem of a trajectory in the phase space. A nearest neighbor P of a point Q in a phase space of d-dimensional embedding is labeled false if these points are close only due to the projection from a higher-dimensional (d+1)-dimensional phase space. Thus, the FNNs will separate if the data is embedded in (d+1)-dimensional space, while the true neighbors will remain close. When all the FNNs have been detected, then the minimal sufficient embedding dimension can be identified as the minima dimension needed to achieve zero fractions of the FNNs being the embedding dimension required. For each vector Y(i), its nearest neighbor Y(j) is looked in a m-dimensional space. In order to do a comparison, the distance d((Yi).Y(j)) is calculated. By iteration of points, the condition:

$$\mathcal{M}\_{i} = \frac{\left\| \begin{array}{c} \begin{array}{c} \begin{array}{c} \begin{array}{c} \begin{array}{c} (i \end{array} \end{array} \end{array} \right\| \begin{array}{c} \begin{array}{c} \begin{array}{c} (i \end{array} \end{array} \end{array} \end{array} \right\|}{\left\| \begin{array}{c} \begin{array}{c} (i \end{array} \end{array} \right\|} \begin{array}{c} \begin{array}{c} (i \end{array} \end{array} \right\|} \end{} \tag{5}$$

Running Title <sup>5</sup>

If *Mi* exceeds a threshold *Mth*, this vector is marked as a nearest neighbor. When the fraction *Mi* of vectors that satisfy the condition *Mi* >*Mth*, tends to zero the embedding dimension is attained in this case. The FNN is exemplifying with a simple case in Figure 2. 19 ���� � ‖�������������‖ ‖���������‖ <sup>20</sup>, (5) 21 If *Mi* 22 exceeds a threshold *Mth*, this vector is marked as a nearest neighbor. When the fraction *Mi* of vectors that satisfy the condition *Mi* 23 >*Mth*, tends to zero the embedding Dynamical Features of the Seismicity in México by Means of the Visual Recurrence Analysis 5

1 Figure 1. MIF behavior for white noise, periodic + noise are uncorrelated signals with a

8 False Nearest Neighbors method (FNN) is an iterative algorithm which estimates the 9 minimal embedding dimension of the system proposed by [15]. The idea is based in the 10 uniqueness theorem of a trajectory in the phase space. A nearest neighbor P of a point Q in a 11 phase space of d-dimensional embedding is labeled false if these points are close only due to 12 the projection from a higher-dimensional (d+1)-dimensional phase space. Thus, the FNNs 13 will separate if the data is embedded in (d+1)-dimensional space, while the true neighbors 14 will remain close. When all the FNNs have been detected, then the minimal sufficient

24 dimension is attained in this case. The FNN is exemplifying with a simple case in Figure 2.

2 time delay = 1. For periodic and Rossler = 3 and 13 respectively.

18 distance d((Yi).Y(j)) is calculated. By iteration of points, the condition:

6 False Nearest Neighbors

3 4 5

7

**2.4. Recurrence Plot (RP)**

and I(τ) = 0 [14]. Typical cases are white noise, periodic and periodic + noise and Rossler time

56 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Figure 1.** MIF behavior for white noise, periodic + noise are uncorrelated signals with a time delay τ = 1. For periodic

False Nearest Neighbors method (FNN) is an iterative algorithm which estimates the minimal embedding dimension of the system proposed by [15]. The idea is based in the uniqueness theorem of a trajectory in the phase space. A nearest neighbor P of a point Q in a phase space of d-dimensional embedding is labeled false if these points are close only due to the projection from a higher-dimensional (d+1)-dimensional phase space. Thus, the FNNs will separate if the data is embedded in (d+1)-dimensional space, while the true neighbors will remain close. When all the FNNs have been detected, then the minimal sufficient embedding dimension can be identified as the minima dimension needed to achieve zero fractions of the FNNs being the embedding dimension required. For each vector Y(i), its nearest neighbor Y(j) is looked in a m-dimensional space. In order to do a comparison, the distance d((Yi).Y(j)) is calculated. By

*Mi* <sup>=</sup> *<sup>Y</sup>* (*<sup>i</sup>* <sup>+</sup> 1) - *<sup>Y</sup>* ( *<sup>j</sup>* <sup>+</sup> 1)

*<sup>Y</sup>* (*i*) - *<sup>Y</sup>* ( *<sup>j</sup>*) , (5)

and Rossler τ = 3 and 13 respectively.

**2.3. False nearest neighbors**

iteration of points, the condition:

series. In Figure 1 the MIF behavior for this typical cases are depicted.

38 false nearest neighbor. 39 **Figure 2.** In 1D, B and B' seem to be nearest neighbors of A, nevertheless in 2D, B' is a false nearest neighbor. **Figure 2.** In 1D, B and B' seem to be nearest neighbors of A, nevertheless in 2D, B' is a false nearest neighbor.

37 Figure 2. In 1D, B and B' seem to be nearest neighbors of A, nevertheless in 2D, B' is a

40 For the mentioned examples, the false nearest neighbor fraction is calculated as an

41 embedding function and is depicted in the Figure 3. To get the embedding dimension, first 42 was estimated the time delay for each time series by evaluating the respective MIF. For 43 white noise and periodic with noise time series, the embedding dimension is high and for For the mentioned examples, the false nearest neighbor fraction is calculated as an embedding function and is depicted in the Figure 3. To get the embedding dimension, first was estimated the time delay for each time series by evaluating the respective MIF. For white noise and periodic with noise time series, the embedding dimension is high and for periodic and Rossler signals, the dimension is short. For the mentioned examples, the false nearest neighbor fraction is calculated as an embedding function and is depicted in the Figure 3. To get the embedding dimension, first was estimated the time delay for each time series by evaluating the respective MIF. For white noise and periodic with noise time series, the embedding dimension is high and for periodic and Rossler signals, the dimension is short.

**Figure 3.** The fraction of false nearest neighbors, as a function of the embedding dimension, is depicted, for white noise (black), periodic (green), periodic with noise (blue) and Rossler (red) time series. **Figure 3.** The fraction of false nearest neighbors, as a function of the embedding dimension, is depicted, for white noise (black), periodic (green), periodic with noise (blue) and Rossler (red) time series.

In [2] Eckmann et al. introduced the so-called Visual Recurrence Analysis (VRA) based on a graphical method designed to locate hidden recurrent patterns, nonstationarity and structural

#### **2.4. Recurrence Plot (RP)**

In [2] Eckmann et al introduced the so-called Visual Recurrence Analysis (VRA) based on a graphical method designed to locate hidden recurrent patterns, nonstationarity and structural changes observed in the phase space of a dynamical system. The aim of the Recurrence Plot (RP) method is to visualize the recurrences of dynamical systems as a function of time. A brief description is as follows: assuming an orbit of the system in the phase space {*x* → <sup>1</sup>, *x* <sup>→</sup> 2, *x* → <sup>3</sup>, ⋯, *x* → *<sup>N</sup>* }. Each vector of this trajectory corresponds with a state of the system where their components can represent physical quantities, for example, position and velocity for mechanic systems like a pendulum or, pressure, volume and temperature for thermodynam‐ ical states. Then, in order to get the RP, the recurrence matrix must be constructed which is defined as [5]:

$$R\_{i,j} = \begin{cases} 1if \parallel \stackrel{\star}{\boldsymbol{\omega}}\_i \cdot \stackrel{\star}{\boldsymbol{\omega}}\_j \parallel \leq \varepsilon \\ 0if \parallel \stackrel{\star}{\boldsymbol{\omega}}\_i \cdot \stackrel{\star}{\boldsymbol{\omega}}\_j \rVert \geq \varepsilon \end{cases} i, \ j = 1, \ \cdots, N \tag{6}$$

were *ε* >0 is an error. Roughly speaking, the matrix elements represent the distance between two vectors in the times *i* and *j*. Once the RP has been obtained from the recurrence matrix, a quantification of the features can be done, for example from periodic patterns to chaotic behavior [5, 16]. As it is well known, in an experiment only a sequence of scalar values can be measured and it is assumed that the information is available on an univariate time series, which is part of a larger n-dimensional (maybe deterministic) model.

Figure 4 shows examples of RP of the four cases described above: white noise, periodic, periodic with noise and chaotic systems.

#### **3. Seismic regions and data set**

We analyzed the whole seismic catalog of the Mexican SSN, (www.ssn.unam.mx) from 2006 to 2014 Due to geophysics features of the Mexican subduction zone, it has been described in [9 and references [20,21,24] therein], sugesting that it can be studied in segments where the six regions are: Baja California (Z1), Jalisco–Colima (Z2), Michoacán (Z3), Guerrero (Z4), Oaxaca (Z5) and Chiapas (Z6), in Figure 5 the six regions are showed.

The following panel of Figure 6 displays the seismicity within 2006-2014 periods for each region. It can be observed the seismicity monitored in Region Z1, Peninsula of Baja California where the Pacific–North America plate boundary in southern California and the north side of Baja California peninsula. The seismicity in Region Z2, Jalisco-Colima is a subduction zone located to the west, where the Rivera plate subducts at a steep angle. In the Region Z3 Michoacán, the dip angle of the Cocos plate decreases gradually toward the southeast. For the region Z4, Guerrero is bounded approximately by the onshore projection of the Orozco and O'Gorman fracture zones, the subducted slab is almost horizontal and moves under upper continental plate. The regions Z5, Oaxaca and Z6, Chiapas are located in the southeastern of

Dynamical Features of the Seismicity in Mexico by Means of the Visual Recurrence Analysis http://dx.doi.org/10.5772/59440 59

**2.4. Recurrence Plot (RP)**

{*x* <sup>→</sup> 1, *x* → <sup>2</sup>, *x* → <sup>3</sup>, ⋯, *x* →

defined as [5]:

In [2] Eckmann et al introduced the so-called Visual Recurrence Analysis (VRA) based on a graphical method designed to locate hidden recurrent patterns, nonstationarity and structural changes observed in the phase space of a dynamical system. The aim of the Recurrence Plot (RP) method is to visualize the recurrences of dynamical systems as a function of time. A brief description is as follows: assuming an orbit of the system in the phase space

58 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

their components can represent physical quantities, for example, position and velocity for mechanic systems like a pendulum or, pressure, volume and temperature for thermodynam‐ ical states. Then, in order to get the RP, the recurrence matrix must be constructed which is

were *ε* >0 is an error. Roughly speaking, the matrix elements represent the distance between two vectors in the times *i* and *j*. Once the RP has been obtained from the recurrence matrix, a quantification of the features can be done, for example from periodic patterns to chaotic behavior [5, 16]. As it is well known, in an experiment only a sequence of scalar values can be measured and it is assumed that the information is available on an univariate time series, which

Figure 4 shows examples of RP of the four cases described above: white noise, periodic,

We analyzed the whole seismic catalog of the Mexican SSN, (www.ssn.unam.mx) from 2006 to 2014 Due to geophysics features of the Mexican subduction zone, it has been described in [9 and references [20,21,24] therein], sugesting that it can be studied in segments where the six regions are: Baja California (Z1), Jalisco–Colima (Z2), Michoacán (Z3), Guerrero (Z4), Oaxaca

The following panel of Figure 6 displays the seismicity within 2006-2014 periods for each region. It can be observed the seismicity monitored in Region Z1, Peninsula of Baja California where the Pacific–North America plate boundary in southern California and the north side of Baja California peninsula. The seismicity in Region Z2, Jalisco-Colima is a subduction zone located to the west, where the Rivera plate subducts at a steep angle. In the Region Z3 Michoacán, the dip angle of the Cocos plate decreases gradually toward the southeast. For the region Z4, Guerrero is bounded approximately by the onshore projection of the Orozco and O'Gorman fracture zones, the subducted slab is almost horizontal and moves under upper continental plate. The regions Z5, Oaxaca and Z6, Chiapas are located in the southeastern of

*Ri*, *<sup>j</sup>* ={

is part of a larger n-dimensional (maybe deterministic) model.

(Z5) and Chiapas (Z6), in Figure 5 the six regions are showed.

periodic with noise and chaotic systems.

**3. Seismic regions and data set**

1*if x* → *<sup>i</sup>* - *x* → *<sup>j</sup>* ≤*ε*

0*if x* → *<sup>i</sup>* - *x* → *<sup>j</sup>* >*ε*

*<sup>N</sup>* }. Each vector of this trajectory corresponds with a state of the system where

*i*, *j* =1, ⋯, *N* (6)

**Figure 4.** In this panel the RP of the cases described above: a) White noise, b) periodic, c) periodic with noise and d) Rossler. Can be observed the different structures of the four examples described above.

Mexico, the dip of the subduction zone gradually increases to a steeper subduction in Central America.

As is showed in Figure 6, the number of earthquakes reported by the SSN in each region is different. Firstly, the seismicity in the region Z1, peninsula of Baja California, shows two periods of time, the fist one from 2006 to 2010 and the second one from 2011 to 2014, in the first period little seismic activity compared to the second is observed, however, a sudden change in the seismic activity is observed, this behavior in the seismic activity before and after 2010 can be observed in the regions Z2 and Z3 corresponding with Jalisco-Colima and Michoacán respectively This situation may be due to system upgrades monitoring stations. As mentioned above, the Z1 region evolve with a process in which the peninsula of Baja California is separated from the continental plate, while in the other regions, the dynamics is driven by subduction between continental plate and plates Rivera and Cocos. Specifically, Jalisco-Colima region (Z2) the subduction is given between La Rivera and The north-America plates where the stress and strain fields determine the direction of movement in which La Rivera subducts being different from the case of the Cocos plate. According with the catalogue, Guerrero (Z4),

**Figure 5.** The six regions are showed in this map. The region Z1 is a dispersion and the regions from Z2 to Z6 the seismicity is driven by subduction regions.

Oaxaca (Z5) and Chiapas (Z6), are the regions with a high seismic activity. It can be observed that in all regions have occurred earthquakes with magnitudes M ≈ 7. By considering this division of six regions and the seismic activity showing seismic clustering, the b-values in the G-R law were recalculated in each case by using the Aki model [17]:

$$\mathbf{b} = \frac{\log(e)}{M \cdot M\_{c'}} \tag{7}$$

where *<M>* is the average magnitude and *Mc* is the completeness magnitude of the seismic sequence that represents the minimum magnitude over which the frequency-magnitude distribution behaves as the power-law, *N~10-bM* [18]. The b-values calculated for each region are depicted in Figure 7 and resumed in Table 1.


**Table 1.** The b-values calculated for each region.

**Figure 6.** Seismicity monitored in the six regions: Z1 Peninsula of Baja California. Z2 Jalisco-Colima. Z3 Michoacán. Z4 Guerrero. Z5, Oaxaca. Z6 Chiapas.

Oaxaca (Z5) and Chiapas (Z6), are the regions with a high seismic activity. It can be observed that in all regions have occurred earthquakes with magnitudes M ≈ 7. By considering this division of six regions and the seismic activity showing seismic clustering, the b-values in the

**Figure 5.** The six regions are showed in this map. The region Z1 is a dispersion and the regions from Z2 to Z6 the

where *<M>* is the average magnitude and *Mc* is the completeness magnitude of the seismic sequence that represents the minimum magnitude over which the frequency-magnitude distribution behaves as the power-law, *N~10-bM* [18]. The b-values calculated for each region

, (7)

G-R law were recalculated in each case by using the Aki model [17]:

are depicted in Figure 7 and resumed in Table 1.

seismicity is driven by subduction regions.

**Table 1.** The b-values calculated for each region.

*<sup>b</sup>* <sup>=</sup> *log*(*e*) *M* - *Mc*

60 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**REGION <M"/> b-Value** Baja California (Z1) 3.93 1.32 Jalisco- Colima (Z2) 4.20 1.45 Michoacán (Z3) 3.98 2.41 Guerrero (Z4) 3.91 2.07 Oaxaca (Z5) 3.92 1.97 Chiapas (Z6) 4.07 1.61

**Figure 7.** b-value calculation from the Gutenberg-Richter law for the six regions. In Table 1, the values are resumed.

Because geophysics shaping the seismic zone as well as the various mechanisms and processes that take place in each of the regions, the statistical properties associated with the seismicity of each of these are reflected as different values to the parameters of the laws scaling as in the case of the Gutenberg-Richter law. This situation indicates that the local stress fields and stress must drive the interactions between different parts of a complex system, such as the Earth's crust. So, through a study in the context of dynamic systems, where the seismic activity is considered as a response to the underlying dynamics is possible to observe different charac‐ teristics of the system and not observed directly from a statistical point of view. Although seismicity is considered, as a sequence of events whose measurable variable is the magnitude, cannot be put aside the temporal component, that is, the distribution of interevent defined as the time between two earthquakes within a region while. It is noteworthy that there are time series studies interevent by multifractal analysis for seismicity in Italy [19].

The Figure 8 shows the interevent time series of the seismicity studied. For this time series the behavior of the MIF and FNN fraction is calculated.

**Figure 8.** Interevent time series associated with the seismic activity observed in 2006-2014 period

## **4. Results**

Because geophysics shaping the seismic zone as well as the various mechanisms and processes that take place in each of the regions, the statistical properties associated with the seismicity of each of these are reflected as different values to the parameters of the laws scaling as in the case of the Gutenberg-Richter law. This situation indicates that the local stress fields and stress must drive the interactions between different parts of a complex system, such as the Earth's crust. So, through a study in the context of dynamic systems, where the seismic activity is considered as a response to the underlying dynamics is possible to observe different charac‐ teristics of the system and not observed directly from a statistical point of view. Although seismicity is considered, as a sequence of events whose measurable variable is the magnitude, cannot be put aside the temporal component, that is, the distribution of interevent defined as the time between two earthquakes within a region while. It is noteworthy that there are time

62 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

The Figure 8 shows the interevent time series of the seismicity studied. For this time series the

series studies interevent by multifractal analysis for seismicity in Italy [19].

**Figure 8.** Interevent time series associated with the seismic activity observed in 2006-2014 period

behavior of the MIF and FNN fraction is calculated.

In this work six seismic sequences and their respective interevent time series were analyzed by means of the RP method. Firstly the phase space is reconstructed for each sequence. The MIF and FNN fraction for the magnitudes sequences are depicted in Figures 9 and 10. In order to reconstruct the phase space, the time delay *τ*, and the embedding dimension *m*, were estimated by taking the first minima of the mutual information function and the False Nearest Neighbors algorithms respectively. Then the recurrence matrix is obtained whose matrix elements, *Ri j*, are the distances *Dij*, between states *Y(ti )* and *Y(tj )* in the reconstructed phase space, to calculate *Dij*, the Euclidean norm was chosen. The *τ–*values and *m-*values are contained in the Table 2. Once the recurrence matrix is obtained the distribution of distances between states computed, in Figure 12 the probability distribution function (pdf) for distances is showed. The *rmax*-value of the pfd for Z2, Z4, Z5 and Z6 are located around *rmax* ≈1.2 and *rmax* < 1 for Z1 and Z3. As has been mentioned, Z1 is a region where the peninsula is separating from the continental plate and Z3 is located where the border between La Rivera and Cocos plates are in contact and subducted into the continental plate. Regarding the shape of PDF in all cases an exponential tail is observed.


**Table 2.** The *τ–*values and *m-*values for each region for the case of seismicity sequence.

From the behavior of MIF is possible to identify the correlation in seismic sequences. According to this behavior, the region with the lowest correlation is Z2 (Jalisco-Colima) and the highest correlation is Z5 (Oaxaca), as is showed in Figure 9. However, the behavior of the FNN fraction as function of the embedding dimension of the seismic sequences indicates that all of them are in phase spaces of high dimension being the shorter Z3 with *m* = 7.

To calculate the recurrence matrix, the distances between pairs of vectors were computed in phase space. By definition this matrix is symmetric because *Dij* = *Dji*, and the principal diagonal *Dii = 0*. The Recurrence Plot is the graphical representation of the recurrence matrix. The examples of RP depicted in Figure 4, were drawn in black and white because the recurrence matrix was built according to definition given in Eq. (1). In order to take into account all distances computed and perhaps their distribution (Figure 12), a color code allows character‐ izing qualitatively some features of the dynamics as are displayed, in the panel of Figure 11, the RP of the six seismic sequences. According [5, 20, 21], RP of some cases of different topologies can be distinguished, for instance: Stationary systems display homogeneous RP like white noise, for periodic or cuasi-periodic systems appears recurrent structures as diagonal lines and checkerboard forms, for non-stationary systems drifts are present, abrupt changes in the systems indicates extreme events, vertical (horizontal) lines represent time intervals where a state remains constant or changes very slowly. In general, the RP of the seismicity occurred from 2006 to 2014 are displayed in Figure 11 where, in a first glance, typical patterns, like periodicity or cuasi periodicity and white noise are not observed. Nevertheless, clusters bordered for vertical and horizontal lines are present suggesting slow changes in the system. The color distribution and the clusters in RP of BC(Z1), JC(Z2), and Ch(Z6) suggest drifts indicating non stationary dynamics associated possibly with their geophysical features because in BC, the Pacific–North America plate boundary in southern California and the north of Baja California peninsula where many faults are connected in a complex geometrical pattern, continuing into a divergent tectonic plate in the Gulf of California. In Jalisco–Colima region, the Rivera plate subducts at a steep angle plate in Central America and for Ch, the Cocos plate subducts beneath the coast but two perpendicular faults, Clipperton and Tehuantepec, contribute wlth their local dinamical evolution. More similar RP structures are dysplayed in M, G and O, which seems to show more stability because the respectives RP are more uniform which could be indicating that the dynamics is driven by the interacion between the Cocos plate which subducts in the same direction beneath the North America plate and the dip angle of the Cocos plate decreases gradually. Our findings are consistent with the results reported in [11] where an analysis of non extensive model of the similar regions were studied indicating that JC region is the most unstable seismic zone in Mexico.

**Figure 9.** MIF behavior for the magnitude seismic sequences of the six regions.

in the systems indicates extreme events, vertical (horizontal) lines represent time intervals where a state remains constant or changes very slowly. In general, the RP of the seismicity occurred from 2006 to 2014 are displayed in Figure 11 where, in a first glance, typical patterns, like periodicity or cuasi periodicity and white noise are not observed. Nevertheless, clusters bordered for vertical and horizontal lines are present suggesting slow changes in the system. The color distribution and the clusters in RP of BC(Z1), JC(Z2), and Ch(Z6) suggest drifts indicating non stationary dynamics associated possibly with their geophysical features because in BC, the Pacific–North America plate boundary in southern California and the north of Baja California peninsula where many faults are connected in a complex geometrical pattern, continuing into a divergent tectonic plate in the Gulf of California. In Jalisco–Colima region, the Rivera plate subducts at a steep angle plate in Central America and for Ch, the Cocos plate subducts beneath the coast but two perpendicular faults, Clipperton and Tehuantepec, contribute wlth their local dinamical evolution. More similar RP structures are dysplayed in M, G and O, which seems to show more stability because the respectives RP are more uniform which could be indicating that the dynamics is driven by the interacion between the Cocos plate which subducts in the same direction beneath the North America plate and the dip angle of the Cocos plate decreases gradually. Our findings are consistent with the results reported in [11] where an analysis of non extensive model of the similar regions were studied indicating

64 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

that JC region is the most unstable seismic zone in Mexico.

**Figure 9.** MIF behavior for the magnitude seismic sequences of the six regions.

**Figure 10.** The fraction of false nearest neighbors, as a function of the embedding dimension, is depicted for all regions.

The distribution function associated with the distances between states in phase space allows us to observe the most likely value, and suggest a other possible criterion for determining characteristics distances among all states in the phase space and to determine the ε-value in the definition of the matrix recurrence (Ec. 7). The Figure 12 shows the pdf of the distances for the six sequences of seismic magnitudes. It is observed that the maximum values of the pdf are located in different possitions and possibly this behavior could be associated with the geophysics features of the regions: Z2, Z4, Z5 and Z6 are subduction zones where Z3 is determined by the relative motion between the Rivera plate and the Continental plate, while the other three are determined by the interaction of the Cocos plate subducting under the continental plate. For Z1 the seismic activity is produced by the movement of separation between the peninsula and the continental shelf of North America and the Z3, the seismic activity is determined by the interaction of the plates Rivera in contact with the plate subduct‐ ing Cocos and both the continental plate.

On the other hand, the results of the interevent time series are showed in Figure 13 for MIF behavior and Figure 14 for FNN fraction. In Table 3 the *τ* –values and the embeeding dimension *m*-values are presented. In contrast with the seismic sequences of magnitudes, the interevent time series the correlations are similar, nevertheless the FNN fraction decrese almost monot‐ onically indicanting high embedding dimension. This behavior is similar with the example of periodic with noise time series suggesting that the inerevent time series could be described with a possible detrministic model plus a stochastic process.

Figure 11. Recurrence Plot of Baja California and Jalisco-Colima (upper). Michoacan and Guerrero (middle), Oaxaca and Chiapas (below) **Figure 11.** Recurrence Plot of Baja California and Jalisco-Colima (upper). Michoacan and Guerrero (middle), Oaxaca and Chiapas (below)

Figure 12. Probability distribution function of the distance between states in the phase space for the six regions

Dynamical Features of the Seismicity in Mexico by Means of the Visual Recurrence Analysis http://dx.doi.org/10.5772/59440 

**Figure 12.** Probability distribution function of the distance between states in the phase space for the six regions

**Figure 13.** MIF for sequences of interevents.

onically indicanting high embedding dimension. This behavior is similar with the example of periodic with noise time series suggesting that the inerevent time series could be described

Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

 **0.5 1.5 2.5 3.5 4.5** 

 **0.5 1.5 2.5 3.5** 

*Region Z2*

**200 300 400 500 600**

*Region Z4*

**<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>2000</sup>**

*Region Z6*

**<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>2000</sup> <sup>2500</sup> <sup>3000</sup> <sup>3500</sup>**

 **0.5 1.5 2.5 3.5 4.5** 

> **0.5 1.5 2.5 3.5 4.5**

Figure 11. Recurrence Plot of Baja California and Jalisco-Colima (upper). Michoacan and Guerrero (middle), Oaxaca and Chiapas (below)

**Figure 11.** Recurrence Plot of Baja California and Jalisco-Colima (upper). Michoacan and Guerrero (middle), Oaxaca

Figure 12. Probability distribution function of the distance between states in the phase space for the six regions

with a possible detrministic model plus a stochastic process.

*Region Z1* 

**<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup> <sup>1000</sup>**

*Region Z3*

**<sup>0</sup> <sup>200</sup> <sup>400</sup> <sup>600</sup> <sup>800</sup>**

*Region Z5*

**<sup>0</sup> <sup>500</sup> <sup>1000</sup> <sup>1500</sup> <sup>2000</sup> <sup>2500</sup> <sup>3000</sup>**

and Chiapas (below)


**Table 3.** The *τ–*values and *m-*values for each region, in this case for interevent sequence.

**Figure 14.** The fraction of false nearest neighbors, as a function of the embedding dimension, is depicted for all regions,

now for the interevent sequence.

#### **5. Concluding remarks**

It is well known that the Mexican Pacific is an important seismic region where large earth‐ quakes have occurred with devastating consequences producing significant economic downturns and especially many human losses. Due to interactions between subduction zones and the slow separation of the Baja California Peninsula, this region is considered a complex system that evolves as consequence of many processes that occur in the interior of the Earth as well as in the areas of contact between the surfaces involved. In this context, [10] proposed a division of 19 regions of the seismo tectonic zone taking into account seismic characteristics of the existing catalogs for the seismicity occurring in Mexico from 1899 to 2007 and a seismic historic compilation from previous publications and of some catalogs. In order to distinguish some features of the underlying dynamics of each Mexican region seismic, the aim of this work is to study the recurrence plot behavior based on the visual recurrence analysis, taking into account the sequence of events (magnitudes) in time and, on the other hand, analyzing the inter-events time series. Our analysis shows important differences in the recurrence maps of each region. In a similar way by considering the seismicity monitored by SSN within the period 2006-2014, and identifying clusters of earthquakes that can be associated with the geophysical features of the Mexican Pacific, six regions were considered to study (Figure 5). In this paper we studied dynamical features of the six seismic regions located along Mexican Pacific coast. The analyzed data set corresponds with the Mexican seismic catalogue reported by the SSN. First, sequences of magnitude of earthquakes and the interevent time series were studied. Their analysis was performed by means of the phase state reconstruction and the RP of each region. Our findings indicate a possible correlation between the RP calculated and the geophysical features characteristics in each zone (panel of Figure 11). RP displayed of BC, JC and Ch show non periodicities, correlation (not white noise structure), non stationariety. For M, G and O, RP are more similar and stability is observed. The results for the interevents time series, short correlation and large embedding dimension, suggest the possibility to establish a combination between a detremiistic model plus a stochastic noise. Our finding suggest that the patterns obtained could be associated with the local geophysical structures of each subduction and dispersion zones driven by their characteristic nonlinear dynamical features of each region.

## **Acknowledgements**

**REGION Interev interev**

68 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Baja California (Z1) 4 20 Jalisco- Colima (Z2) 5 20 Michoacán (Z3) 4 13 Guerrero (Z4) 5 20 Oaxaca (Z5) 4 20 Chiapas (Z6) 4 20

**Table 3.** The *τ–*values and *m-*values for each region, in this case for interevent sequence.

**Figure 14.** The fraction of false nearest neighbors, as a function of the embedding dimension, is depicted for all regions,

It is well known that the Mexican Pacific is an important seismic region where large earth‐ quakes have occurred with devastating consequences producing significant economic downturns and especially many human losses. Due to interactions between subduction zones and the slow separation of the Baja California Peninsula, this region is considered a complex system that evolves as consequence of many processes that occur in the interior of the Earth

now for the interevent sequence.

**5. Concluding remarks**

*τ m*

This work was supported by the Irreversible Processes Physics Research Area of Universidad Autónoma Metropolitana, México. ARR, LRMT and RTPH thanks to Basic Sciences Depart‐ ment of UAM. IRR thanks UPIITA-IPN México. ARR thanks the bilateral Project CNR (Italy) and CONACyT (México).

## **Author details**

Alejandro Ramírez-Rojas1\*, Lucía R. Moreno-Torres1 , Ricardo T. Páez-Hernández1 and Israel Reyes-Ramírez2

\*Address all correspondence to: alexramro@gmail.com

1 Departamento de Ciencias Básicas, Col. Reynosa, Azcapotzalco, México D. F., México

2 Unidad Profesional Intedisciplinaria en Ingeniería y Tecnologías Avanzadas, México D.F., Mexico

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70 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

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of the Mexican Pacific coast, Physica A 392 (2013) 2507–2512


## **Assessment of Seismic Hazard of a Territory**

V.B. Zaalishvili

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/59367

## **1. Introduction**

The aim of this work is to analyze the modern concepts of the seismic hazard of the territory, its evaluation and development of an algorithm for such assessments. One of the main problems is the adequacy of such assessments. In order to analyze the physical mechanisms of different approaches the evolution of methods and techniques on one side, and their comparison with the other side should be presented. It is also necessary to show the physical validity of choice of approach and its accessibility and simplicity, which increases the reliability of the final results. The next task is to analyze the integral estimates of seismic hazard of a territory. It is necessary to consider the calculation of the expected seismic effects on the final stage of the algorithm.

Seismic hazard assessment is the basis of modern seismic design and engineering. Seismic hazard maps of different contents and scales are result of such investigations. It makes possible to take into account all the features of the territory forming mentioned hazard. In particular, expected on the territory typical seismic impacts and calculated on the basis of world ach‐ ievements not only of the West but also of the East are taking into account features of possible seismic sources (active seismic faults, their seismic potential, etc.).

The new integrated method for seismic hazard assessment is presented. Probabilistic maps of seismic hazard are created in the result of this assessment. The following databases were formed to analyze seismic hazard and seismicity of the territory: macroseismic, seismologic and database of possible seismic source zones (or potential seismic sources-PSS). With usage of modern methods (over-regional method of IPE RAS-Russia) and computer program (SEISRisk-3 – USA) in GIS probabilistic seismic hazard maps for the Republic North Ossetia-Alania in intensity units (MSK-64) at a scale of 1:200 000 with exceedance probability of 1%, 2%, 5%, 10% for a period of 50 years that corresponds to recurrence period of 5000, 2500, 1000, 500 years were created. Furthermore, for the first time the probabilistic seismic hazard maps

© 2015 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.

were made in acceleration units for territory of Russia. For the large scale building is likely to be used 5% probability map, i.e. for the major type of constructions, whereas for high respon‐ sibility construction should be used 2% probability map. The approach based on the physical mechanisms of the source is supposed to use to produce the synthesized accelerograms generated using real seismic records interpretation.

For each of zoning objects the probabilistic map of the seismic microzonation with location of different calculated intensity zones (7,8,9,9\*) is developed (the zones, composed by clay soils of fluid consistency at quite strong loadings can be characterized by liquefaction are marked by the index 9\*). Similar results are observed for maps in acceleration units.

The integrated approach is based on the latest achievements in engineering seismology. It can reduce measure of inaccuracy in earthquake engineering and construction and also signifi‐ cantly increase the adequacy or foundation for assessments.

Carrying out of investigations on mapping of seismic hazards such as detailed seismic zoning (DSZ), which is based on the most advanced field research methods and analysis of every subject of the sufficiently large region (for example Caucasus) in a scale of 1: 100 000 or 1: 200 000 allows to create a physically reasonable general DSZ map of any wide territory. Such maps are generated organically through summation or the imposition of the calculated seismic fields that are a reflection of seismic potential of the corresponding seismic sources.

## **2. Assessment of seismic hazard: General and detailed seismic zoning**

Expected seismic hazard assessment is reduced to seismic potential estimation of a particular seismic source or a combination of sources. Wherein the mentioned potential is formed by a number of factors, such as geodynamic (tectonic movements), geological and geophysical features of the territory, the catalog of strong earthquakes, local soil conditions (geotechnical, hydrogeological and geomorphological conditions), resonance properties, attenuation rates, and others. At the same time physical validity problem of hazard level is one of the important problems of engineering seismology. The involved assessment of seismic hazard, presented as seismic zoning maps, in fact is a long-ranged forecast of the earthquake strength and location unlike short-range and middle-range earthquake forecast.

There can be marked out three types of analysis, three consecutive stages of seismic zoning:


In the result of seismic zoning the appropriate maps of GSZ, DSZ and SMZ were created. The difference between DSZ and GSZ lies in investigation scale. During DSZ can be and has to be studied all potential sources of possible earthquakes that may be not taken in account because of their relatively small seismic potential during GSZ analyzing. It is necessary to note that in actual conditions of consequences of seismic hazard generation with that types of sources can have, if not great, but evident negative effect. At once both types of zoning are quite similar, not to mention minuteness.

were made in acceleration units for territory of Russia. For the large scale building is likely to be used 5% probability map, i.e. for the major type of constructions, whereas for high respon‐ sibility construction should be used 2% probability map. The approach based on the physical mechanisms of the source is supposed to use to produce the synthesized accelerograms

74 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

For each of zoning objects the probabilistic map of the seismic microzonation with location of different calculated intensity zones (7,8,9,9\*) is developed (the zones, composed by clay soils of fluid consistency at quite strong loadings can be characterized by liquefaction are marked

The integrated approach is based on the latest achievements in engineering seismology. It can reduce measure of inaccuracy in earthquake engineering and construction and also signifi‐

Carrying out of investigations on mapping of seismic hazards such as detailed seismic zoning (DSZ), which is based on the most advanced field research methods and analysis of every subject of the sufficiently large region (for example Caucasus) in a scale of 1: 100 000 or 1: 200 000 allows to create a physically reasonable general DSZ map of any wide territory. Such maps are generated organically through summation or the imposition of the calculated seismic fields

by the index 9\*). Similar results are observed for maps in acceleration units.

that are a reflection of seismic potential of the corresponding seismic sources.

**2. Assessment of seismic hazard: General and detailed seismic zoning**

Expected seismic hazard assessment is reduced to seismic potential estimation of a particular seismic source or a combination of sources. Wherein the mentioned potential is formed by a number of factors, such as geodynamic (tectonic movements), geological and geophysical features of the territory, the catalog of strong earthquakes, local soil conditions (geotechnical, hydrogeological and geomorphological conditions), resonance properties, attenuation rates, and others. At the same time physical validity problem of hazard level is one of the important problems of engineering seismology. The involved assessment of seismic hazard, presented as seismic zoning maps, in fact is a long-ranged forecast of the earthquake strength and location

There can be marked out three types of analysis, three consecutive stages of seismic zoning: **1.** general seismic zoning – GSZ or SZ, which is realized in 1:5 000 000 or 1:2 500 000 scale;

**2.** detailed seismic zoning DSZ, which was originally carried out in 1:50 000 - 500 000 scale;

In the result of seismic zoning the appropriate maps of GSZ, DSZ and SMZ were created. The difference between DSZ and GSZ lies in investigation scale. During DSZ can be and has to be studied all potential sources of possible earthquakes that may be not taken in account because of their relatively small seismic potential during GSZ analyzing. It is necessary to note that in

generated using real seismic records interpretation.

cantly increase the adequacy or foundation for assessments.

unlike short-range and middle-range earthquake forecast.

**3.** seismic microzonation – SMZ, in 1: 5 000 - 10 000 scale.

Despite similar name with GSZ and DSZ the third stage or stage of seismic hazard assessment in SMZ type has absolutely other physical meaning. The usage of SMZ allows taking into account the seismic properties of site soils, including physicomechanical and dynamical properties of soil.

Seismic hazard assessment of any given territory on the initial stage was performed using mainly deterministic methods. In the deterministic methods, all parameters of a close partic‐ ular source (magnitude), medium (particular site), the distance from the source to the site, the wave attenuation when propagating through a particular medium (the propagation paths of seismic energy in the form of waves) are mostly known or thoroughly investigated and finally form the medium (soils) reaction of a site in the form of maximum seismic effect. Medium is considered in a simplified form - combined horizontal layers. A number of such deterministic computer programs is known.

At present in developed countries the hazard assessment is increasingly performed using probabilistic methods. Probabilistic seismic hazard assessment techniques include various alternative models of earthquake sources (focuses), return periods of events, accounting of attenuation models of seismic energy and accordingly the seismic effect. Herein the probabil‐ istic method takes into account uncertainty bounds of certain parameters that are mainly random and the most important - the probabilistic nature of the actual implementation of the seismic event that is formed by a number of random factors. The last circumstance significantly reduced the intensity of emotions that was in the 60-70 years of the last century about devel‐ opment of a reliable method for prognosis of strong earthquakes. Multifactorial nature of the earthquake, on the other hand made it even more complicated to obtain reliable prognoses. Although increasing depth of investigation made such a prognosis more reliable.

Almost all major seismic zoning maps in former USSR were deterministic. They include the first map of 1937 and map of 1978.

In 1947 S.V. Medvedev proposed to differentiate the seismic hazard zones depending on the return period of strong earthquakes and durability of various buildings and structures [9]. Thus, in 1947, an offer to take into account seismicity or seismic activity of the territory when creating maps was made. Later, the famous scientist of former USSR Yu.V.Riznichenko for the first time introduced the concept of seismic "shakeability" and developed the first algorithm and program for its calculation [16]. Unfortunately, these and other progressive ideas and developments have not been used in the process of creating new maps for a variety of reasons. With that, this approach was developed in the West [5]. Just then K.A. Cornell suggested differentiating between seismic hazard and risk. The risk began to be understood not as risk of seismic event occurrence, but only as economic and social losses. The probabilistic seismic zoning maps with the probability of seismic hazard exceeding (or not exceeding) in certain time periods were first created in the West.

It is well known that nature is essentially non-linear. There are always uncertainties in nature laws that completely eliminate the use of deterministic seismic zoning maps. In other words, physically-based maps of seismic hazard differentiation or seismic zoning maps must be probabilistic. Herein the risk that always exists should be assessed and has to be the minimum.

This has led to a situation where the deterministic approach is expelled or banished from consideration. At the same time, it should be noted that the deterministic seismic hazard maps sometimes give estimates that are close to reality. In this context for calculation of seismic hazard in the beginning were used both map types.

The map that was developed later than the map of 1978 to some extent was taking into account the probabilistic nature of the formation of zones of seismic hazard, although essentially still not very different from deterministic.

The probabilistic approach was implemented for the first time in the new, more advanced seismic zoning maps of Russian Federation. These maps are called general seismic zoning maps or GSZ-97.

General map GSZ -97 is presented on Fig. 1. The map generalization is enough for state overall planning, but is not enough for reliable estimation of real objects seismic conditions.

The DSZ process is a complex of very complicated and expensive geology-tectonical, geo‐ physical and seismical investigations for quantitative estimation of seismic effect in any site of perspective region [1]. This investigation type estimated quantitatively the source seismic effects only on concerned site GSZ (more precisely for mean soil conditions). [28]

**Figure 1.** Map of General seismic zoning GSZ-97 of Russia

The modern DSZ has clear and argumented content. There are some methods that may be used in GSZ and DSZ for seismic generic structures (SGS) identifications. It is identification of hazardous earthquake occurrence zones. [12]

### **2.1. Seismogeological method**

It is well known that nature is essentially non-linear. There are always uncertainties in nature laws that completely eliminate the use of deterministic seismic zoning maps. In other words, physically-based maps of seismic hazard differentiation or seismic zoning maps must be probabilistic. Herein the risk that always exists should be assessed and has to be the minimum. This has led to a situation where the deterministic approach is expelled or banished from consideration. At the same time, it should be noted that the deterministic seismic hazard maps sometimes give estimates that are close to reality. In this context for calculation of seismic

76 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

The map that was developed later than the map of 1978 to some extent was taking into account the probabilistic nature of the formation of zones of seismic hazard, although essentially still

The probabilistic approach was implemented for the first time in the new, more advanced seismic zoning maps of Russian Federation. These maps are called general seismic zoning

General map GSZ -97 is presented on Fig. 1. The map generalization is enough for state overall

The DSZ process is a complex of very complicated and expensive geology-tectonical, geo‐ physical and seismical investigations for quantitative estimation of seismic effect in any site of perspective region [1]. This investigation type estimated quantitatively the source seismic

The modern DSZ has clear and argumented content. There are some methods that may be used in GSZ and DSZ for seismic generic structures (SGS) identifications. It is identification of

planning, but is not enough for reliable estimation of real objects seismic conditions.

effects only on concerned site GSZ (more precisely for mean soil conditions). [28]

hazard in the beginning were used both map types.

not very different from deterministic.

**Figure 1.** Map of General seismic zoning GSZ-97 of Russia

hazardous earthquake occurrence zones. [12]

maps or GSZ-97.

At the turn of XIX and XX centuries G.Abiсh, A.E.Lagorio and the other scientists found out as a result of earthquakes epicentral zones investigations that earthquakes are connected with tectonic structures. So, when describing the strongest Vern earthquake consequences (1887) Mushketov I.V. (1889) straightly connected earthquakes with fractures and faults. He believed that earthquakes have maximum effect on the lines of large and new faulting (Mushketov, 1891). He also discovered that some groups of earthquakes are connected with transverse structures. Later on the basis of the Kebi earthquake investigation results Bogdanovich K.I. introduced the concept of seismotectonic elements and showed migration of seismic shocks within seismically active zone.

Thus, seismogeological method determined the connection between strong earthquakes and tectonic structures. Such connections were named geologic criteria of seismicity. [12, 28].

#### **2.2. Seismotectonical methods**

By the results of Garm region between Pamir and Tien Shan in the late 40-es of the XX century Gubin I.E. for the first time introduced the term seismotectonical method. Herewith he connected strong seismic events with ruptured occurrence with the width up to several tens of kilometers. He supposed that within such a zone "seismogenity" remains and "seismogenity level" corresponds to other similar zones which are characterized by development processes of equal intensity. Gubin's law of seismotectonic says that in active structures of similar type and size maximum earthquakes originated as the result of rock displacement along active faults are characterized by equal values of focuses and magnitudes. The method at that connects geologic criterion of seismicity with a velocity of new fault displacements.

#### **2.3. Seismostructural method**

This method was offered in the middle of 50-es by Belousov V.V., Goryachev A.V., Kirillova I.V., Petrushevskiy B.A., Rezanov I.A., Sorskiy A.A. But the main development the method gained in the works of Petrushevskiy B.A. Such method connects seismic events with large structural complexes – blocks. Mentioned blocks were separated with the help of historical and structural analysis [12].

The analysis of blocks scale allowed connecting a considerable range of earthquake focuses depths with them and with deep faults. The deepest faults are located on the boundary of the Pacific Ocean and Eurasian and American continents. The concept about strong earthquake focuses connection with three-dimensional structures of Earth crust was later developed by Gorshkov G.P. (1984) [28]. Although the direction is considered as promising it needs to be fleshed out.

#### **2.4. Tectonophysical method**

The method was developed in the end of 50-es by Gzovsky M.V. [12]. The feature of the method is the connection of strong seismic event with the areas of maximum shearing stress. Such areas are characterized by faults and maximum gradients of average velocities of tectonic move‐ ments. Although Gzovsky M.V. made earthquake energy dependent on a number of factors it is practically impossible to make exact calculations. It was defined exceptionally by qualitative but not quantitative terms of mechanical properties of Earth crust and its viscosity in the region of maximum shearing stresses.

#### **2.5. Method of quasi-homogeneous zones allocating**

This method was first offered in the end of 50-es of the XX century as well as the previous method. The concept of the method consisted in detection of quasi-homogeneous areas where earthquake could be caused by the presence of geological and geophysical criteria. In this case it was supposed that some of them are connected with tectonic movements [12]. Since the number of characteristics is endless the number of situations with maximum magnitudes can also be endless. It stipulated an extension of characteristics and usage of all geological, seismological and geophysical data for allocation of zones with different seismic potential of tectonic nature. Data correlation allows giving prognosis of maximum magnitude Mmax.

Today the techniques developed by Reisner and Ioganson are frequently used. At that the whole number of characteristics such as relief, crustal thickness, heat flow density, isostatic anomalies of gravity force, stratum depth of consolidated basement etc. is used for analysis. Realization of the techniques supposes usage of reference sites from all active regions of the world. In this connection such approach is named overregional [28].

#### **2.6. Method of seismically active nodes**

This method was also offered in the end of 50-es of the XX century. Data analysis of central Asia earthquakes allowed Reiman V.M. connecting disjunctive nodes to which strong earth‐ quakes or seismogenetic nodes are confined. The method was significantly developed by Rantsman E.Ya. (1979). She used the approach to the number of world regions and connected focuses of strong earthquakes with these nodes. Herewith the author noticed that "focuses can exceed nodes in size and amount up to thousands kilometers". Structure differentiation on their seismicity is realized with the help of formalized criteria (relief type, maximum height, distance from node edges, volume of soft sediments etc.). It was determined that transverse uplands form structures which generate nodes [12].

#### **2.7. Paleoseismological method**

The method (Solonenko V.P., Khromovskikh V.S., Nikonov et al.) allows allocating PSS zones and assessing their seismic potential (maximum magnitude and seismic intensity) on the basis of study of paleosiesmodislocations spatial orientation. As a rule, seismotectonic dislocations are used for the assessment of these parameters. The number of formulas which connect statistic correlations between seismodislocation characteristics (length, shift amplitude) and seismologic parameters (magnitude, focus depth, seismic impacts intensity) of earthquake is known. Return period of earthquake is determined by paleoseismodislocations age. Herewith all existing approaches are compared: geologic-geomorphological, archeological, historical data and the results of radiocarbon dating, dendrochronology, connections of tree growth and earthquakes and lichenometry (lichen dating).

## **3. Detailed seismic zoning**

are characterized by faults and maximum gradients of average velocities of tectonic move‐ ments. Although Gzovsky M.V. made earthquake energy dependent on a number of factors it is practically impossible to make exact calculations. It was defined exceptionally by qualitative but not quantitative terms of mechanical properties of Earth crust and its viscosity in the region

78 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

This method was first offered in the end of 50-es of the XX century as well as the previous method. The concept of the method consisted in detection of quasi-homogeneous areas where earthquake could be caused by the presence of geological and geophysical criteria. In this case it was supposed that some of them are connected with tectonic movements [12]. Since the number of characteristics is endless the number of situations with maximum magnitudes can also be endless. It stipulated an extension of characteristics and usage of all geological, seismological and geophysical data for allocation of zones with different seismic potential of tectonic nature. Data correlation allows giving prognosis of maximum magnitude Mmax.

Today the techniques developed by Reisner and Ioganson are frequently used. At that the whole number of characteristics such as relief, crustal thickness, heat flow density, isostatic anomalies of gravity force, stratum depth of consolidated basement etc. is used for analysis. Realization of the techniques supposes usage of reference sites from all active regions of the

This method was also offered in the end of 50-es of the XX century. Data analysis of central Asia earthquakes allowed Reiman V.M. connecting disjunctive nodes to which strong earth‐ quakes or seismogenetic nodes are confined. The method was significantly developed by Rantsman E.Ya. (1979). She used the approach to the number of world regions and connected focuses of strong earthquakes with these nodes. Herewith the author noticed that "focuses can exceed nodes in size and amount up to thousands kilometers". Structure differentiation on their seismicity is realized with the help of formalized criteria (relief type, maximum height, distance from node edges, volume of soft sediments etc.). It was determined that transverse

The method (Solonenko V.P., Khromovskikh V.S., Nikonov et al.) allows allocating PSS zones and assessing their seismic potential (maximum magnitude and seismic intensity) on the basis of study of paleosiesmodislocations spatial orientation. As a rule, seismotectonic dislocations are used for the assessment of these parameters. The number of formulas which connect statistic correlations between seismodislocation characteristics (length, shift amplitude) and seismologic parameters (magnitude, focus depth, seismic impacts intensity) of earthquake is known. Return period of earthquake is determined by paleoseismodislocations age. Herewith all existing approaches are compared: geologic-geomorphological, archeological, historical

world. In this connection such approach is named overregional [28].

**2.6. Method of seismically active nodes**

uplands form structures which generate nodes [12].

**2.7. Paleoseismological method**

of maximum shearing stresses.

**2.5. Method of quasi-homogeneous zones allocating**

Analysis of the considered approaches shows that each method characterizes one or another aspect of the problem. Herewith some of them are developed straight on the assumption of practice demands. Other methods suppose a number of complimentary stages for achievement of final problem investigation. Overregional method is referred to the first group and we'll try to use it.

For avoidance of any doubt let us consider typical way of seismic hazard level determination and all other attributes necessary for goal achievement. So let's begin to realize the problem of assessment on the level of detailed seismic zoning (DSZ) by the example of the territory of the Republic North Ossetia-Alania (Zaalishvili, Rogozhin, 2011).

As was mentioned above we chose overregional seismotectonic method for allocation of PSS zones; such method permits to identify seismic or seismogenic source quite completely. Although there are some disadvantages on practice the method gives quantitative indices and it is characterized by the certain decision-making algorithm. The method was successfully used in works of prof. Rogozhin E.A. in many countries of the world (Russia, Israel, China, Kirghizia etc.). We were able to realize the method in North Ossetia exactly due to his active support. At the same time, this does not preclude obtaining reliable results and other known methods. The methodology used in most probabilistic seismic hazard analysis was first defined by Cornell and as usually accepted it consists of four steps [5, 15, 28]: 1. Definition of earthquake source zones (SSZ), 2. Definition of recurrence characteristics for each source, 3. Estimation of earthquake effect and 4. Determination of hazard at the site. The probabilistic hazard maps were created on the basis of investigation of corresponding territory main characteristic. 1-4 stages of such work realization are given further by the example of the territory of North Ossetia.

#### **3.1. Definition of earthquake sources**

As it was mentioned previously probabilistic assessment gain the largest extension at seismic hazard assessment of territory in the world in recent years. Various investigations had shown that such assessment gives physically more proved results. Indeed, at such assessment it is possible to forecast more sequentially a location of expected seismic events, their intensity etc. [14, 17]. The main difference from other methods consists in the fact that special processing of the existing data allows accounting uncertainties caused by our half knowledge of cause-andeffect relations and random factors at formation of our understanding about spatiotemporal realization of one or another seismic event. It is necessary to mention the computer program EQRISK of McGuire [8]. This program noticeably simplified assessments of seismic hazard what caused its wide extension. It came to a point where seismic hazard assessment with the help of probabilistic approach sometimes is called Cornell - McGuire's method.

The investigations on determination and parameterization of the seismic source zones in recent decades has been realized by V.P.Solonenko, V.S.Khromovskikh, E.A.Rogozhin, V.I.Ulomov, V.G.Trifonov, I.P.Gamkrelidze and others [6, 12, 17, 20, 21]. On the basis of investigation results of the active faults located southward of the Great Caucasian ridge, parameters of seismic source zones were chosen according to data of I.P.Gamkrelidze work [6]. We used the investigation results of Ulomov V.I., Rogozhin E.A., Trifonov V.G. for accounting the indices of Northern Caucasus in our work. On the first stage of seismic hazard map making there was carried out an approximate or expert calculation of seismic potential (Мmax) of different determined active faults in the form of zones of possible seismic sources (PSS zones) for the territory of the Republic North Ossetia-Alania. Further the map of allocation (zoning) of such PSS-zones was made.

**Figure 2.** Map of PSS zones of the territory of the Republic North Ossetia-Alania. Red triangles – basic seismic stations in the region. Blue and black lines are the state borders of North Ossetia.

Maximum magnitude of expected earthquakes (seismic potential, Мmax) was assessed on the results of usage of the over-regional seismotectonic method of seismic hazard assessment, offered by G.I.Reisner..


**Table 1.** PSS zones for North Ossetia characteristics (numbers in the rings on Fig.2)

The investigations on determination and parameterization of the seismic source zones in recent decades has been realized by V.P.Solonenko, V.S.Khromovskikh, E.A.Rogozhin, V.I.Ulomov, V.G.Trifonov, I.P.Gamkrelidze and others [6, 12, 17, 20, 21]. On the basis of investigation results of the active faults located southward of the Great Caucasian ridge, parameters of seismic source zones were chosen according to data of I.P.Gamkrelidze work [6]. We used the investigation results of Ulomov V.I., Rogozhin E.A., Trifonov V.G. for accounting the indices of Northern Caucasus in our work. On the first stage of seismic hazard map making there was carried out an approximate or expert calculation of seismic potential (Мmax) of different determined active faults in the form of zones of possible seismic sources (PSS zones) for the territory of the Republic North Ossetia-Alania. Further the map of allocation (zoning) of such

80 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Figure 2.** Map of PSS zones of the territory of the Republic North Ossetia-Alania. Red triangles – basic seismic stations

Maximum magnitude of expected earthquakes (seismic potential, Мmax) was assessed on the results of usage of the over-regional seismotectonic method of seismic hazard assessment,

in the region. Blue and black lines are the state borders of North Ossetia.

offered by G.I.Reisner..

PSS-zones was made.

Usage of this method showed that the Northern Caucasus is the region of very high seismic hazard. In 2007 it was determined on data of field investigations that for the urbanized territories of North Ossetia (Fig.2), (table 1), [14, 17, 28]It is necessary to notice that on the next stage each possible seismic source was subjected to more exact assessment of its seismic potential. This stage is named a parameterization of seismic sources. The Mmax was determined by the data of the above mentioned authors.

On the next stage of investigations it was necessary to determine a range of strong earthquake focuses depths. There are no such deep hypocenters as in other regions. The range varies a little and the depth amounts 20-25 km. Herewith it is necessary to notice that hypocenters depths obviously increase monotonically to Grozny city and Caspian Sea. With a lack of data about earthquake distribution the average value of depth was assumed equal to 10 km (see Table 1).

#### **3.2. Seismicity of North Ossetia-Alania and its connection with PSS zones**

The catalogue of strong earthquakes was defined further. It supposes to check the existing data by correlating it with catalogues of certain authors and results of international investigations. Seismicity data for each zone were defined by the following catalogues: New Catalogue... 1982, Corrected Catalogue of Caucasus, Institute of Geophysics Ac. Sci. Georgia (in data base of IG), the Special Catalogue of Earthquakes for GSHAP test area Caucasus (SCETAC), compiled in the frame of the Global Seismic Hazard Assessment Program (GSHAP), for the period 2000 BC - 1993, N.V. Kondorskaya (editor), (Ms>3.5) Earthquake catalogues of Northern Eurasia (for 1992-2000), Catalogue of NSSP Armenia, Special Catalogue for the Racha earthquake 1991 epicentral area (Inst. Geophysics, Georgia) and also the Catalogue of North Ossetia 2004–2006.

Corrected Catalogue of Caucasus contains data for more than 61000 of earthquakes, including 300 historical events [26, 28]. The issue is seismic events which are referred to historical period meaning last 20 centuries or a new era. So the catalogue was defined. In certain cases when needed a depth of event focuses was recalculated.

Values *a* and *b* of law of frequency and the largest magnitude were determined only for large zones. This fact was caused by absence of such data. Well known formula of Gutenberg-Richter was applied in calculations:

$$\log(N/T) = a - bM \tag{1}$$

where: N-number of events for a time period T, а and b are parameters of inclination and level of recurrence graph at М=0, respectively.

Analysis of recurrence graph dependence on distance allowed determining representativity and weighted contribution of each seismic zone. Herewith the opportunity of taking into account curve deviation of density distribution became available.

#### **3.3. Estimation of earthquake effect**

Thus seismic effect was estimated in intensity units and peak ground acceleration (PGA). Observation data and instrumental data on 43 significant earthquakes that occurred in Caucasus were revised to obtain the necessary information [19].

Data on 37 earthquakes was selected and in some cases the maps in the 1:500 000 scale were created. It was determined at the formation of the maps that within three isoseists for events with magnitude Ms>6 coefficient values are quite high (ν~4.5-5.0). For small and moderate earthquakes such values are less (ν~3.4). Data analysis allowed obtaining two different formulas for strong and weak earthquakes:

$$I = 1.5M\_{\odot} - 3.4\lg(\Delta^2 + h^2)^{1/2} + 3.0 \text{ for small events} \tag{2}$$

$$I = 1.5M\_{\odot} - 4.7\lg(\Lambda^2 + h^2)^{1/2} + 4.0 \text{ for large events} \tag{3}$$

where: MS – the surface-wave magnitude, Δ – epicentral distance, h – focal depth

We used the second formula at the assessment of seismic hazard. Maximum intensity in the focus at that was 9 points (for magnitudes 6.5-7.0) and for 8 points the magnitudes were 5.5-6.0.

Due to the fact that on Caucasus in the period between June 1990 and September 1998 about 500 accelerograms were obtained for 300 relatively strong earthquakes [19] they became the basis for the formulas of macroseismic fields. The data of temporary and constant instrumental systems on Southern Caucasus and nearby areas were used during the data analysis. They included 84 corrected accelerograms from 26 earthquakes with magnitudes between 4.0 and 7.1. Correlations were obtained with the help of two step regression model (Joyner and Boore). The resulting equation for larger horizontal values of peak horizontal acceleration is:

$$\begin{aligned} \log \text{PHA} &= 0.72 + 0.44M - \log R - 0.00231 + 0.28p\_{\prime} \\ \text{R} &= \left( D^2 + 4.52 \right)^{1/2} \end{aligned} \tag{4}$$

where:

the Special Catalogue of Earthquakes for GSHAP test area Caucasus (SCETAC), compiled in the frame of the Global Seismic Hazard Assessment Program (GSHAP), for the period 2000 BC - 1993, N.V. Kondorskaya (editor), (Ms>3.5) Earthquake catalogues of Northern Eurasia (for 1992-2000), Catalogue of NSSP Armenia, Special Catalogue for the Racha earthquake 1991 epicentral area (Inst. Geophysics, Georgia) and also the Catalogue of North Ossetia 2004–2006. Corrected Catalogue of Caucasus contains data for more than 61000 of earthquakes, including 300 historical events [26, 28]. The issue is seismic events which are referred to historical period meaning last 20 centuries or a new era. So the catalogue was defined. In certain cases when

82 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Values *a* and *b* of law of frequency and the largest magnitude were determined only for large zones. This fact was caused by absence of such data. Well known formula of Gutenberg-Richter

where: N-number of events for a time period T, а and b are parameters of inclination and level

Analysis of recurrence graph dependence on distance allowed determining representativity and weighted contribution of each seismic zone. Herewith the opportunity of taking into

Thus seismic effect was estimated in intensity units and peak ground acceleration (PGA). Observation data and instrumental data on 43 significant earthquakes that occurred in

Data on 37 earthquakes was selected and in some cases the maps in the 1:500 000 scale were created. It was determined at the formation of the maps that within three isoseists for events with magnitude Ms>6 coefficient values are quite high (ν~4.5-5.0). For small and moderate earthquakes such values are less (ν~3.4). Data analysis allowed obtaining two different

where: MS – the surface-wave magnitude, Δ – epicentral distance, h – focal depth

2 2 1/2 1.5 3.4lg( ) 3. for small events 0 *<sup>S</sup> IM h* = - D+ + (2)

2 2 1/2 1.5 4.7 lg( ) 4. for large events 0 *<sup>S</sup> IM h* = - D+ + (3)

lg( / ) *N T a bM* = - (1)

needed a depth of event focuses was recalculated.

was applied in calculations:

of recurrence graph at М=0, respectively.

**3.3. Estimation of earthquake effect**

formulas for strong and weak earthquakes:

account curve deviation of density distribution became available.

Caucasus were revised to obtain the necessary information [19].

PHA – peak horizontal acceleration in cm/sec2 ,

M – surface-wave magnitude,

D – hypocentral-distance in km;

p is 0 for 50-percentile values and 1 for 84-percentile.

It is necessary to mention that coefficients of attenuation for horizontal accelerations are similar to the coefficients for Western part of North-America. Herewith analogous indices in Europe are less than on Caucasus and adjacent areas.

#### **3.4. Determination of hazard**

The probabilistic seismic hazard maps in intensity units (MSK-64) and in acceleration units for the territory of North Ossetia were worked out in a scale 1:200000 with exceedance probability for a period of 50 years (standard time of building or construction durability!) with 1%, 2%, 5%, 10%. All works were carried out in GIS technologies. At that return periods are equal to 5000, 2500, 1000 and 500 years correspond to the given probabilities (Fig. 3, 4).

The essence of the approach consists in the fact that the longer a considered time period the higher an intensity of design earthquake is. The recurrence is changing depending on the level of design intensity. So, expected intensity equal to 10 points corresponds to a period of 5000 years, 9 points – 2500 years, 8 – 1000 years, and finally, intensity level equal to 7 points corresponds to return period of 500 years [18, 26-28].

For calculation of design seismic effect we used computer program SEISRisk- 3 [5, 8]. When choosing an intensity map it is necessary to correlate obtained maps with real intensity effect of expected earthquake on considered territory. At that we must choose the map which will correspond most of all to a real situation particularly to territory features [10].

**Figure 3.** Probabilistic maps of seismic hazard (DSZ) in the intensity units (MSK-64) with the exceedance probability 5% (a) and 2% (b) for North Ossetia territory and adjacent areas [27].

**Figure 4.** Probabilistic map of seismic hazard (DSZ) in acceleration units (PGA) with exceedance probability 5% (а) and 2% (b) for North Ossetia territory [27, 28].

Thus, for the first time in Russia we realized seismic hazard assessment quite detailed. In this connection it is necessary to remind that seismic hazard map that is included in building code of Russia has the scale M 1:2 000 000 and our map has the scale M 1:200 000! Besides it must be noted that some part of the map of General seismic zoning of Russia has the scale М 1:8 000 000! It, undoubtedly, can characterize the maps in a scale М 1:200 000 as the maps of detailed seismic zoning. It should be noted that we simultaneously worked out seismic hazard maps both in traditional for Russia intensity units and in acceleration units.

Further analysis of the data which characterize the territory allowed concluding quite reason‐ ably that 5 % map with exceedance probability of 50 years is the most appropriate for the Republic territory. It corresponds to earthquake recurrence of 1000 years. Exactly such recurrence was revealed for seismic events with 8 points intensity with the help of special field investigations of the previous earthquakes on the territory of North Ossetia. Thus, we recommended this map for mass construction. At calculation of responsible buildings and constructions to seismic impacts where risk of expected economic and social losses reaches higher values we recommend 2 % map for seismic hazard level with exceedance probability of 50 years (Fig.3). The zone of increased 9 intensity is clearly seen on intensity map. Such intensity is caused by presence of powerful Vladikavkaz fault (Fig.2). Correlation of seismic hazard maps in intensity and acceleration units shows that for acceleration map we have smoother change of hazard level (Fig.3, 4). Indeed, offset distance with any level of hazard can't show such abrupt intensity changes only in cases of appearance of additional hazards or changing of some other conditions, for example, soil conditions, which we don't take into account. That is why seismic hazard maps in acceleration units are more preferable for engineers. The history of forming of seismic processes observation networks stipulated quite full absence of acceleration records on the territory of Russia. On the other hand acceleration maps usage allows reaching any monotonous transition between different zones boundaries with change of consideration stage. It is very important under the conditions of increased seismic hazard. New approach where nonintegral values instead of whole-number values (for example, 8.1 or 7.5) are considered as intensity level of seismic hazard was worked out in recent years in Russia. It is hard characterizing and even understanding an assessment of seismic effect equal to 0.1 or 0.7 intensity. In spite of its conditional and uncertain characteristic this approach was used on practice widely at Olympic objects constructing in Sochi. It is obvious that authors used the so-called "expert" assessments here.

(a) (b)

84 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Figure 3.** Probabilistic maps of seismic hazard (DSZ) in the intensity units (MSK-64) with the exceedance probability

(a) (b)

**Figure 4.** Probabilistic map of seismic hazard (DSZ) in acceleration units (PGA) with exceedance probability 5% (а) and

Thus, for the first time in Russia we realized seismic hazard assessment quite detailed. In this connection it is necessary to remind that seismic hazard map that is included in building code

5% (a) and 2% (b) for North Ossetia territory and adjacent areas [27].

2% (b) for North Ossetia territory [27, 28].

The way out is independent creation of seismic hazard maps in units of peak ground acceler‐ ations (PGA). We have worked out such maps for exposition of 50 years with exceedance probability. They have the scale M 1:200 000 and probability 1%, 2%, 5%, 10% (Fig. 4). Rapid change of acceleration levels on those maps can be excluded within reasonable rates. Exactly these maps (which were the first on the territory of Russia and CIS) while being probabilistic maps of detailed seismic zoning will be the basis for creation of probabilistic maps of seismic microzonation. Maps of seismic microzonation as a rule are made in scales 1:2000, 1: 5000 or 1: 10 000 [28]. It is possible to made maps in larger scale but it doesn't have practical sense. Indeed, soil conditions do not generally change faster and at construction of certain building or structure we always know soils on more detailed level. In this connection it is necessary to remember that we create maps of microzonation in the form of schemes for typical soils of investigated territory.

At the same time hydroelectric stations or atomic power stations may need higher level of protection. That's why considerably larger return periods can be considered for such objects. According to the accepted approaches for investigated territory the period will be 5000 years with the intensity 10 points. At the same time this period easily can be 2500 years with intensity 9 points for majority of other responsible objects (high-rise building etc.). Herewith very interesting consequence appears. It consists in the fact that level of territory security under otherwise equal conditions depends on a level of economic potential of this or that country. Developed country within common sense can presume any economically accessible level of design intensity. And we can see that earthquake consequences of the same level are always more drastic and catastrophic for poor hindward country. On the other hand in authoritarian state it all depends on a good will of bodies of government, which know that fact. Exactly due to that at strong consequences of natural and anthropogenic processes they can be concealed truckle to bodies of government. For example, the fact that death toll after strong Ashkhabad earthquake in 1948 amounted to 80 000 people was brought to light only many years on. In all fairness it must be noted that such and more egregious facts also took place later in other countries.

## **4. Seismic microzonation of territory**

The sites with reference soil conditions corresponding to specified seismic hazard level are specified in the process of seismic microzonation. In Russia as reference soil conditions for a given territory are traditionally considered the soils with mean seismic properties (usually soils with shear wave velocity of 250–700 m/s). For example in Georgia depending on specific engineering-geological situation for a given territory the reference soils in their seismic properties can be worst or mean. In USA firm rocks are referred to reference soils. Seismic microzonation concludes the computation of intensity increments caused by soil condition differences. Seismic microzonation is carried out with the help of instrumental and calcula‐ tional methods [28].

#### **4.1. Instrumental method of seismic microzonation**

The main method of seismic microzonation is an instrumental method. Exactly this method urges to solve a forecast problem of forming earthquake intensity. However the calculational method which allows modeling any definite conditions of area and impact features is often characterized as more reliable. It is very important for high power soil stratum. Usage of both methods together significantly increases the results validity.

#### *4.1.1. Seismic microzonation on the basis of strong earthquakes instrumental records*

A number of corresponding international projects were worked out for receiving a data about different soils behavior at strong earthquakes. It is necessary to mention that the data of permanent systems of instrumental observations on the island Taiwan (the groups SMART-1 and SMART-2.) [25, 26, 28] in our opinion were characterized by the most reliable background. It is also necessary to notice that obtaining of even strong earthquake record cannot guarantee its adequate proper usage. Therefore working out of approaches which can increase physical validity of the data is very topical problem. In particular one can create design impacts with taking into account seismic sources features (for example, accelerograms) for the level of DSZ [25, 26, 28]. Further accounting a distortion of wave field caused by soil condition change we can receive new implementation of each site. Herewith usage of even single record of strong earthquake will give very important results for testing of strong earthquake design records.

### *4.1.2. Seismic microzonation with the help of weak earthquakes records*

At the same time hydroelectric stations or atomic power stations may need higher level of protection. That's why considerably larger return periods can be considered for such objects. According to the accepted approaches for investigated territory the period will be 5000 years with the intensity 10 points. At the same time this period easily can be 2500 years with intensity 9 points for majority of other responsible objects (high-rise building etc.). Herewith very interesting consequence appears. It consists in the fact that level of territory security under otherwise equal conditions depends on a level of economic potential of this or that country. Developed country within common sense can presume any economically accessible level of design intensity. And we can see that earthquake consequences of the same level are always more drastic and catastrophic for poor hindward country. On the other hand in authoritarian state it all depends on a good will of bodies of government, which know that fact. Exactly due to that at strong consequences of natural and anthropogenic processes they can be concealed truckle to bodies of government. For example, the fact that death toll after strong Ashkhabad earthquake in 1948 amounted to 80 000 people was brought to light only many years on. In all fairness it must be noted that such and more egregious facts also took place later in other

86 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

The sites with reference soil conditions corresponding to specified seismic hazard level are specified in the process of seismic microzonation. In Russia as reference soil conditions for a given territory are traditionally considered the soils with mean seismic properties (usually soils with shear wave velocity of 250–700 m/s). For example in Georgia depending on specific engineering-geological situation for a given territory the reference soils in their seismic properties can be worst or mean. In USA firm rocks are referred to reference soils. Seismic microzonation concludes the computation of intensity increments caused by soil condition differences. Seismic microzonation is carried out with the help of instrumental and calcula‐

The main method of seismic microzonation is an instrumental method. Exactly this method urges to solve a forecast problem of forming earthquake intensity. However the calculational method which allows modeling any definite conditions of area and impact features is often characterized as more reliable. It is very important for high power soil stratum. Usage of both

A number of corresponding international projects were worked out for receiving a data about different soils behavior at strong earthquakes. It is necessary to mention that the data of permanent systems of instrumental observations on the island Taiwan (the groups SMART-1 and SMART-2.) [25, 26, 28] in our opinion were characterized by the most reliable background.

countries.

tional methods [28].

**4. Seismic microzonation of territory**

**4.1. Instrumental method of seismic microzonation**

methods together significantly increases the results validity.

*4.1.1. Seismic microzonation on the basis of strong earthquakes instrumental records*

It is obvious that the number of earthquakes is limited except the fact that you live in Japan. That's why registration of soil vibrations caused by weak earthquakes in absence of strong earthquakes became quite important factor. Formation of weak earthquake database became a reliable basis for data testing. Herewith that single virtual record of strong earthquake which at first glance was neglected will take an important place again. It is clearly seen that linear deformations during weak earthquakes must be transformed into nonlinear-elastic and even into nonelastic links "deformations – tensions". Amplitude-frequency characteristics of areas and recording form significantly vary when changing soils (Fig. 5) [25, 28].

Increase of the soil stratum depth (alluvium) considerably changes the character of earthquake records in the process of approaching the city.

**Figure 5.** Scheme of California earthquake in Koaling city

Calculation of intensity increment with the help of weak earthquakes is realized by the formula [25]:

$$
\Delta I = \text{3.3lg}A\_{\text{i}} / A\_{0\text{\textdegree}} \tag{5}
$$

where: *Ai* , *A*0 are the vibration amplitudes of investigated and reference soils, respectively. The usage of tool in the form of registration of strong and weak earthquakes needs the organization of instrumental observations in a waiting mode.

#### *4.1.3. Seismic microzonation with the help of weak earthquakes records*

Strong earthquake extremely seldom occur on territories with small and moderate seismic activity. At that hazard level not only decreases but it can even increase due to impossibility of timely unloading of high tensions. In this connection when calculating intensity increment of weak earthquake records the dependence "deformation – tension" is linear. It causes inaccuracies in soil behavior assessments at expected strong earthquakes when dependence is nonlinear.

Calculation of intensity increment with the help of weak earthquakes is realized by the formula [25]:

$$\Delta I = \text{3.3lg}A\_i / A\_{0^\prime} \tag{6}$$

where: *Ai* , *A*0 are the vibration amplitudes of investigated and reference soils, respectively.

The usage of tool in the form of registration of strong and weak earthquakes needs the organization of instrumental observations in a waiting mode.

#### *4.1.4. Seismic microzonation using microseisms*

The results of microseisms observations [25] are used as subsidiary instrumental tool of SMZ. Strictly speaking, the reference of microseism on their origin to the purely natural phenomena is not quite correct. Numerous artificial sources, influence degree of which can't be controlled, undoubtedly, take part in their forming along with the natural sources (Fig. 6)

Intensity increment for strong earthquakes on microseism is calculated by the formula [25]:

$$\Delta I = \mathfrak{Z} \lg A\_{\flat} / A\_{\flat \prime} \tag{7}$$

where: *Ai* , *A*0 are the maximum amplitudes of microvibrations for investigated and reference soils, respectively.

Impossibility of the compliance of necessary standard conditions of microseism registration and large spread in values of maximum amplitudes limit the usage of microseism for calcu‐ lation of soil intensity increment.

The above mentioned causes the application of microseism tool only in complex with other instrumental tools. Spectral features for different sites are estimated by means of H/Vrations [11, 25].


**Figure 6.** Microseisms records (10.07.1996, Voronezh Region, Russia)

#### *4.1.5. Seismic microzonation using explosive impact*

The usage of tool in the form of registration of strong and weak earthquakes needs the

88 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Strong earthquake extremely seldom occur on territories with small and moderate seismic activity. At that hazard level not only decreases but it can even increase due to impossibility of timely unloading of high tensions. In this connection when calculating intensity increment of weak earthquake records the dependence "deformation – tension" is linear. It causes inaccuracies in soil behavior assessments at expected strong earthquakes when dependence is

Calculation of intensity increment with the help of weak earthquakes is realized by the

, *A*0 are the vibration amplitudes of investigated and reference soils, respectively.

The usage of tool in the form of registration of strong and weak earthquakes needs the

The results of microseisms observations [25] are used as subsidiary instrumental tool of SMZ. Strictly speaking, the reference of microseism on their origin to the purely natural phenomena is not quite correct. Numerous artificial sources, influence degree of which can't be controlled,

Intensity increment for strong earthquakes on microseism is calculated by the formula [25]:

Impossibility of the compliance of necessary standard conditions of microseism registration and large spread in values of maximum amplitudes limit the usage of microseism for calcu‐

The above mentioned causes the application of microseism tool only in complex with other instrumental tools. Spectral features for different sites are estimated by means of H/V-

, *A*0 are the maximum amplitudes of microvibrations for investigated and reference

undoubtedly, take part in their forming along with the natural sources (Fig. 6)

<sup>0</sup> 3.3lg / , *<sup>i</sup>* D*I= A A* (6)

<sup>0</sup> 2lg / , *<sup>i</sup>* D*I= A A* (7)

organization of instrumental observations in a waiting mode.

organization of instrumental observations in a waiting mode.

*4.1.4. Seismic microzonation using microseisms*

nonlinear.

formula [25]:

where: *Ai*

where: *Ai*

soils, respectively.

rations [11, 25].

lation of soil intensity increment.

*4.1.3. Seismic microzonation with the help of weak earthquakes records*

The intensity increment ΔI of the soils of the zoned territory is calculated by the formula [25] at usage of weaker explosions:

$$\Delta I = \text{3.3lg}A\_i / A\_{0^\prime} \tag{8}$$

where: Ai , A0 are vibrational amplitudes of the investigated and reference soils, respectively.

Execution of powerful explosions on the territory of cities, settlements or near the responsible buildings is connected with large and often insurmountable obstacles (technical and ecological problems, safety problems, labouriousness and economical expediency) and practically isn't used nowadays. This leads to the wide spreading of nonexplosive vibration sources [28].

#### *4.1.6. Seismic microzonation using nonexplosive impulse impact*

The features of SMZ methods development led to the situation when the tool of elastic wave excitation with the help of low-powered sources (for example, hammer impact with m = 8–10 kilograms) has become the most wide spread in the CIS countries, in order to determine S- and P-wave propagation velocities in soils of the typical areas of territory. Velocity values are used in order to calculate the intensity increment using the tool of seismic rigidities by S.V.Medve‐ dev [25]:

$$
\Delta\text{I} = 1.67 \text{ kg} \,\text{p}\_{\text{i}} \text{V}\_{\text{i}} / \text{p}\_{0} \text{V}\_{0} \tag{9}
$$

where: *ρ0V0* and *ρ<sup>i</sup> Vi* is the product of the soil consistency and P-wave (S-wave) velocity – seismic rigidities of the reference and the investigated soil, respectively.

The intensity increment, caused by soil watering, is calculated by the formula

$$
\Delta I = K \,\mathrm{e}^{-0.04k\_{\mathrm{rx}}^2} \tag{10}
$$

where K = 1 for clay and sandy soils; К = 0.5 for large-fragmental soils (with sandy-argillaceous filler not less than 30%) and strongly weathered rocks; К = 0 for large-fragmental firm soils consisting of magmatic rocks (with sandy-argillaceous filler up to 30%) and weakly weathered rocks; hGL is the groundwater level.

The given approach of S.V.Medvedev gained unexpectedly wide extension in 70-es of the XX century due to its simplicity and efficiency (CIS countries and countries of Eastern Europe, USA, Chile, Italy, India). This approach could be realized on practice in a very short time etc. thanks to its territory seismic regime independence. To a certain extent this blocked the development of other alternative approaches. At the same time negative sides of such approach soon were revealed. In the case of watered soils absence formation of intensity increment exceptionally due to type of correlated soils didn't hold up against criticism and gave incon‐ formity with displayed differences of correlated soils at strong earthquakes. Thereafter it brought to the approach disregarding almost in all countries besides CIS countries [25, 28]. On the other hand it is necessary to notice that in case of such work performance all opportunities must be used.

By means of the special investigations it was determined that the reliability of calculated intensity increments considerably increases at usage of modern powerful impulsive energy sources (Fig. 7).

**Figure 7.** Surficial gas-dynamical pulse source (SI-32)

The lowering of final results quality is to a certain extent caused by the fact that in the tool of "intensities" the seismic effect dependence in soils on frequency or "frequency discrimination" of soils [22] and also the origin of typical "nonlinear effects" at strong movements isn't taken into account. A.B.Maksimov tried to remedy this deficiency by developing the tool, where frequency peculiarities of soils were taken into account [25]:

$$
\Delta I = 0.8 \,\mathrm{kg} \,\mathrm{p}\_0 V\_0 f\_0^2 \, / \,\mathrm{p}\_i V\_i f\_i^2 \tag{11}
$$

where: f0, fi are predominant frequencies of reference and investigated soils, respectively.

A.B.Maksimovs' tool didn't find wide distribution, as frequency differences of soil vibrations with sharply different strength properties (at usage of traditional for the seismic exploration of small depths low-powered sources) were insignificant and the calculation results on the formulas (9) and (11) were practically similar [22].

Intensity increment was determined by the following formula [25]:

$$
\Delta I = 0.8 \,\mathrm{kg} \,\mathrm{p}\_0 V\_0 f\_{\mathrm{wa}0}^2 / \,\mathrm{p}\_i V\_i f\_{\mathrm{wa}l}^2 \tag{12}
$$

where: fwa0, fwai are weighted-average vibration frequencies of reference and investigated soils, respectively.

Weighted-average vibration frequency of soils was calculated at that on the formula [22, 28]:

$$f\_{\text{wa}} = \sum A\_i f\_i / \sum A\_i \tag{13}$$

where: Ai and fi are the amplitude and the corresponding frequency of vibration spectrum, respectively.

#### *4.1.7. Seismic microzonation using vibration impact*

ii 00 D rr I =1.67 lg V / V (9)

GL 0.04 e *<sup>h</sup> I=K* - D (10)

is the product of the soil consistency and P-wave (S-wave) velocity –

where: *ρ0V0* and *ρ<sup>i</sup>*

must be used.

sources (Fig. 7).

*Vi*

rocks; hGL is the groundwater level.

**Figure 7.** Surficial gas-dynamical pulse source (SI-32)

seismic rigidities of the reference and the investigated soil, respectively.

The intensity increment, caused by soil watering, is calculated by the formula

90 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

2

where K = 1 for clay and sandy soils; К = 0.5 for large-fragmental soils (with sandy-argillaceous filler not less than 30%) and strongly weathered rocks; К = 0 for large-fragmental firm soils consisting of magmatic rocks (with sandy-argillaceous filler up to 30%) and weakly weathered

The given approach of S.V.Medvedev gained unexpectedly wide extension in 70-es of the XX century due to its simplicity and efficiency (CIS countries and countries of Eastern Europe, USA, Chile, Italy, India). This approach could be realized on practice in a very short time etc. thanks to its territory seismic regime independence. To a certain extent this blocked the development of other alternative approaches. At the same time negative sides of such approach soon were revealed. In the case of watered soils absence formation of intensity increment exceptionally due to type of correlated soils didn't hold up against criticism and gave incon‐ formity with displayed differences of correlated soils at strong earthquakes. Thereafter it brought to the approach disregarding almost in all countries besides CIS countries [25, 28]. On the other hand it is necessary to notice that in case of such work performance all opportunities

By means of the special investigations it was determined that the reliability of calculated intensity increments considerably increases at usage of modern powerful impulsive energy

> At usage of a vibration source (Fig. 8) the calculation of intensity increment is realized with the help of the formula [25]:

$$
\Delta I = 2 \lg S\_{\perp} / S\_{0^{\prime}} \tag{14}
$$

where: Si and S0 are the squares of vibration spectra of investigated and reference soils, respectively.

The developed tool was used at SMZ of the territories of cities Tbilisi, Kutaisi, Tkibuli, single areas of the Large Sochi city. The tools' feature consists in the fact that it allows to assess soil seismic hazard without any preliminary investigations: at realization of direct measurements

**Figure 8.** Vibration source (SV-10/100)

of soil thickness response on standard (vibration or impulse) impact. Later the formula was successfully used at SMZ of the sites of Novovoronezh atomic power-plant (APP) with the help of an impulsive source.

#### *4.1.8. Seismic microzonation on the basis of taking into account soil nonlinear properties*

The comparison of the absorption and nonlinearity indices with the corresponding spectra of soil vibrations shows that at higher absorption the spectrum square prevails in LF field and at high nonlinearity it prevails in HF field of the spectrum. In other words, the presence of absorption is displayed in additional spreading of LF spectrum region, and the presence of nonlinearity – in spreading of HF range.

All the mentioned allowed to obtain the formula for calculation of intensity increment on the basis of taking into account nonlinear – elastic soil behavior or elastic nonlinearity (at usage of vibration source) [25, 28]:

$$
\Delta I = \Im \lg A\_i f\_{\text{unl}} / A\_0 f\_{\text{nu0}} \tag{15}
$$

where: Ai fwai, A0fwa0 are the products of spectrum amplitude on weighted-average vibration frequency of investigated and reference soils, respectively.

The formula (14) characterizes soil nonlinear–elastic behavior at the absence of absorption.

If the impulsive source is used at SMZ then the formula will have the form [25]:

$$
\Delta I = 2 \lg A\_i f\_{\text{nu}} / A\_0 f\_{\text{nu}0'} \tag{16}
$$

#### *4.1.9. Seismic microzonation based on accounting of soil inelastic properties*

of soil thickness response on standard (vibration or impulse) impact. Later the formula was successfully used at SMZ of the sites of Novovoronezh atomic power-plant (APP) with the

The comparison of the absorption and nonlinearity indices with the corresponding spectra of soil vibrations shows that at higher absorption the spectrum square prevails in LF field and at high nonlinearity it prevails in HF field of the spectrum. In other words, the presence of absorption is displayed in additional spreading of LF spectrum region, and the presence of

All the mentioned allowed to obtain the formula for calculation of intensity increment on the basis of taking into account nonlinear – elastic soil behavior or elastic nonlinearity (at usage of

The formula (14) characterizes soil nonlinear–elastic behavior at the absence of absorption.

If the impulsive source is used at SMZ then the formula will have the form [25]:

fwai, A0fwa0 are the products of spectrum amplitude on weighted-average vibration

0 0 3lg / , *i wai wa* D =*I Af Af* (15)

0 0 2lg / , *i wai wa* D =*I Af Af* (16)

*4.1.8. Seismic microzonation on the basis of taking into account soil nonlinear properties*

92 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

help of an impulsive source.

**Figure 8.** Vibration source (SV-10/100)

vibration source) [25, 28]:

where: Ai

nonlinearity – in spreading of HF range.

frequency of investigated and reference soils, respectively.

The estimation of potential soil nonelasticity adequately and physically proved at intensive seismic loadings is the most important problem of SMZ as soil liquefaction and differential settlement of the constructions are observed at strong earthquakes (Niigata, 1966; Kobe, 1995).

For direct assessment of soil nonelasticity the specific scheme of the realization of experimental investigations (fig. 9, a) with gas-dynamic impulsive source GSK-6M (with two radiators) was used. Chosen longitudinal profile location allowed making impact sequentially by two emitters from near and somewhat far radiation zones. The HF component that quickly attenuates with distance (Fig. 9, b) prevails in the spectrum of soil vibrations, caused by near emitter. In a case of distant emitter impact the LF component predominates in the spectrum of vibrations (Fig. 9, c). In other words, at nonlinear-elastic deformations the main energy is concentrated in the HF range of spectrum and at nonelastic – in the LF range. The signal spectrum has the symmetrical form in the far and practically linear-elastic zone.

Elastic linear and nonlinear vibrations are characterized for the given source by the constancy of the real spectrum square, which is the index of definite source energy value, absorbed by soil (which is deformed by the source). The analysis of strong and destructive earthquake records and also the analysis of specially carried out experimental impacts showed that at nonelastic phenomena spectra square of corresponding soil vibrations is not the constant value. It can decrease and the more it decreases, the less the soil solidity and the greater the impact value is [28].

At usage of vibratory energy source, the whole number of new formulas [25] was obtained in order to assess soil seismic hazard with taking into account the amount of their nonelasticity:

$$
\Delta I = 2.4 \left[ \lg \left( \text{S}\_{\text{rl}} \right)\_{\text{n}} \left( \text{S}\_{\text{r}0} \right)\_{\text{d}} / \left( \text{S}\_{\text{rl}} \right)\_{\text{d}} \left( \text{S}\_{\text{r}0} \right)\_{\text{n}} \right] \tag{17}
$$

where: (Sri)n,d (Sr0)n,d are the squares of real spectra of soils under investigation and reference soils in near and distant zones of the source, respectively.

$$
\Delta I = \text{3.31g}[(A\_i f\_{ani})\_n (A\_0 f\_{aw0})\_d / (A\_i f\_{ani})\_d (A\_0 f\_{aw0})\_n] \,\text{J} \tag{18}
$$

where: (Ai fawi)n,d and (A0 faw0)n,d are the amplitudes and weighted-average frequencies of soils under investigation and reference soils in near and distant zones of the source, respectively.

If a powerful impulsive source is used the offered formulas will be as following:

$$\Delta I = 1.2 \text{[Ig(S}\_{r)}\_{n}\text{(S}\_{r0})\_{d} / (\text{S}\_{r0})\_{d}\text{(S}\_{r0})\_{n}\text{]}.\tag{19}$$

where: (Sawi)nd and (Saw0)nd are the squares of real spectra of soils under investigation and reference soils in near and distant zones of the source, respectively;

$$\Delta I = \mathcal{Z} \lg[(A\_i f\_{ani})\_u (A\_0 f\_{un0})\_d / \langle A\_i f\_{ani} \rangle\_d (A\_0 f\_{un0})\_u] \,\tag{20}$$

where: (Ai fawi)n,d and (A0 faw0)n,d are the amplitudes and weighted-average frequencies of soils under investigation and reference soils in near and distant zones of the source, respectively.

**Figure 9.** Investigation of site spectral features by means of GSK-6M seismic source: a) experiment scheme; b) records of first source impact; c) records of second source impact

The formulas (17) and (18) are adequate only for loose dispersal soils. The formulas (17) and (18) were used at SMZ of Kutaisi city territory. Besides, using the formulas (19) and (20) nonelastic deformation properties of soils in full-scale conditions on Novovoronezh APP-2 site were defined more accurately [25, 28]. The formulas were obtained based on physical principle that underlies the scheme used at the soil looseness assessment.

#### **4.2. Calculational method of seismic microzonation**

In order to analyze the features of soil behavior with introduction of definite engineering– geological structure characteristics of investigated site as initial data the calculational method of SMZ is used: values of shear wave velocities, modulus of elasticity, index of extinction, power of soil layers, their consistency etc. Calculational method includes the following techniques: thin-layer medium, multiple-reflected waves, finite-difference method, finiteelements analysis (FEA) and others.

Nonlinear soil properties can be taken into account in the problems of earthquake engineering with the usage of instrumental and calculation methods. The main method of seismic micro‐ zonation is the instrumental method. However, it is often necessary to use calculational method for solving such problems. Calculational method allows modeling virtually any conditions that are observed in the nature. The requirements of practice however reduced to the necessity of calculation of soil vibrations for nonlinear-elastic and nonelastic deformation conditions. Solving such a problem it is assumed that elastic half-space behaves as linear-elastic medium and at intensive seismic or dynamic impacts the covering soil stratum displays strong nonlinear properties.

0 0 0 0 2lg[( ) ( ) / ( ) ( ) ], *i awi n aw d i awi d aw n* D =*I Af Af Af Af* (20)

fawi)n,d and (A0 faw0)n,d are the amplitudes and weighted-average frequencies of soils

under investigation and reference soils in near and distant zones of the source, respectively.

94 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**Figure 9.** Investigation of site spectral features by means of GSK-6M seismic source: a) experiment scheme; b) records

The formulas (17) and (18) are adequate only for loose dispersal soils. The formulas (17) and (18) were used at SMZ of Kutaisi city territory. Besides, using the formulas (19) and (20) nonelastic deformation properties of soils in full-scale conditions on Novovoronezh APP-2 site were defined more accurately [25, 28]. The formulas were obtained based on physical principle

In order to analyze the features of soil behavior with introduction of definite engineering– geological structure characteristics of investigated site as initial data the calculational method of SMZ is used: values of shear wave velocities, modulus of elasticity, index of extinction, power of soil layers, their consistency etc. Calculational method includes the following techniques: thin-layer medium, multiple-reflected waves, finite-difference method, finite-

Nonlinear soil properties can be taken into account in the problems of earthquake engineering with the usage of instrumental and calculation methods. The main method of seismic micro‐ zonation is the instrumental method. However, it is often necessary to use calculational

of first source impact; c) records of second source impact

that underlies the scheme used at the soil looseness assessment.

**4.2. Calculational method of seismic microzonation**

elements analysis (FEA) and others.

where: (Ai

Received instrumental stress-strain dependences can be applied, for example, for plastic clay soil shown in Fig. 10. Offered by A.V.Nikolaev [13] conception of the so-called soil bimodu‐ larity is taken into account in that dependence [25]. Considerable differences in "weak" soils behavior at compression and extension underlie in the phenomenon. Such soil is characterized at extension by very small modulus of shearing.

Solving of the given nonlinear problem for soils in the analytic form is usually based on considerable assumptions due to the complication of adequate accounting of behavior features of such complicated system as the soil. Thus, the numerical solving of nonlinear problems on the present-day stage of knowledge is the most proved under the condition that the data of field or laboratory investigations are considered in these or those connections [23, 24, 28].

**Figure 10.** Instrumental stress-strain curve, showing property of soil bimodularity

So, the basis for solution of calculation nonlinear problems is the correlation determined using experimental investigations. Otherwise stated, programs for solving of calculation nonlinear problems are in essence analytical-empirical. Such programs like SHAKE, NERA etc. are the most adequate.

#### *4.2.1. Equivalent linear model – SHAKE and EERA programs*

One of the first models which take into account nonlinear soil behavior is equivalent linear model. Equivalent linear approximation involves Kelvin–Voight model's modification (for taking some types of nonlinearity into account) and, for example, is realized in the programs SHAKE [2] and EERA [27]. Equivalent linear model is based on the hypothesis that shear modulus G and attenuation coefficient ξ are the functions of shearing strain γ. At calculations in both programs the parameters of soil multilayered structure were accounted in "natural occurrence" through the introduction of values of shear modulus G and attenuation coefficient ξ for each layer in thickness structure. With the help of layer combination it allowed receiving a necessary deformation level which fully corresponds to real thickness deformation at hard loads.

#### *4.2.2. NERA program*

It is necessary to notice that approach used in the EERA work out became later the basis of new computer program of NERA (Nonlinear Site Response Analysis) [2]. This program allows calculating nonlinear reaction of soil thickness on seismic impact. It is based on the medium model that was offered by Iwan (1967) and Mroz (1967). For short this model is often called the IM model. It is demonstrated that this model supposes strain-deformation simulating of nonlinear curves, using a number of n mechanical elements, which have different sliding resistance Rj and stiffness kj, where R1 < R2 <... < Rn. Initially the residual stresses in all elements are equal to zero. At monotonically increasing load the element j deforms until the transverse strain τ reaches R<sup>j</sup> . After that the element j keeps positive residual stress, which is equal to Rj . The equation, describes dynamics of soil medium, is solved by the method of central differ‐ ences.

#### *4.2.3. Calculation of nonlinear absorptive ground medium vibrations using multiple reflected waves' tool of seismic microzonation*

Let's suppose that we have the seismic wave, which falls on the soil thickness surface. Let's assume that soil thickness is nonlinear absorptive unbounded medium with the density ρ and S-wave propagation velocity vS. At small deformations the value of shear modulus G will be maximum for the given soils:

$$\mathbf{G} = \mathbf{G}\_{\text{max}} = \rho \boldsymbol{\upsilon}\_{\text{S}}^{2} \tag{21}$$

At the deformation increase the value G remains constant at first but at reaching some value (which is definite for each material or soil) the value G considerably changes, i.e. the soil begins to display its nonlinear properties. At the continued deformation increase the growth of stresses decelerates and then can remain unchanged until material destruction or hardening, i.e. until structural condition change.

As the main soil index, which characterizes its type and behavior at intensive loads, the value of plasticity PI was chosen. The parameters, which are necessary for calculations, are deter‐ mined on basis of empirical ratios [7, 25]:

$$k\left(\gamma, PI\right) = 0.5 \left\{ 1 + \tanh\left[ \ln \frac{0.000102 + n\left(PI\right)}{\gamma} \right]^{0.892} \right\} \tag{22}$$

where

ξ for each layer in thickness structure. With the help of layer combination it allowed receiving a necessary deformation level which fully corresponds to real thickness deformation at hard

96 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

It is necessary to notice that approach used in the EERA work out became later the basis of new computer program of NERA (Nonlinear Site Response Analysis) [2]. This program allows calculating nonlinear reaction of soil thickness on seismic impact. It is based on the medium model that was offered by Iwan (1967) and Mroz (1967). For short this model is often called the IM model. It is demonstrated that this model supposes strain-deformation simulating of nonlinear curves, using a number of n mechanical elements, which have different sliding

are equal to zero. At monotonically increasing load the element j deforms until the transverse

The equation, describes dynamics of soil medium, is solved by the method of central differ‐

*4.2.3. Calculation of nonlinear absorptive ground medium vibrations using multiple reflected waves'*

Let's suppose that we have the seismic wave, which falls on the soil thickness surface. Let's assume that soil thickness is nonlinear absorptive unbounded medium with the density ρ and S-wave propagation velocity vS. At small deformations the value of shear modulus G will be

At the deformation increase the value G remains constant at first but at reaching some value (which is definite for each material or soil) the value G considerably changes, i.e. the soil begins to display its nonlinear properties. At the continued deformation increase the growth of stresses decelerates and then can remain unchanged until material destruction or hardening,

As the main soil index, which characterizes its type and behavior at intensive loads, the value of plasticity PI was chosen. The parameters, which are necessary for calculations, are deter‐

0.000102

ì ü ï ï é ù +

<sup>g</sup> ï ï ë û î þ

*n PI*

( ) ( ) 0.492

g= + í ý ê ú

, 0.5 1 tanh ln

and stiffness kj, where R1 < R2 <... < Rn. Initially the residual stresses in all elements

. After that the element j keeps positive residual stress, which is equal to Rj

<sup>2</sup> *GG v* max *<sup>S</sup>* = = r (21)

.

(22)

loads.

*4.2.2. NERA program*

resistance Rj

ences.

strain τ reaches R<sup>j</sup>

*tool of seismic microzonation*

maximum for the given soils:

i.e. until structural condition change.

mined on basis of empirical ratios [7, 25]:

*k PI*

$$\begin{aligned} \ln(P\_l) &= \begin{cases} 0.0 & \text{for} & \text{PI} = 0, \\ 3.37 \cdot 10^{-6} PI^{1.404} & \text{for} & 0 < PI \le 15, \\ 7.0 \cdot 10^{-7} PI^{1.976} & \text{for} & 15 < PI \le 70, \\ 2.7 \cdot 10^{-5} PI^{1.115} & \text{for} & PI > 70 \end{cases} \\ d &= 0.272 \left\{ 1 - \tanh \left[ \ln \left( \frac{0.000556}{\gamma} \right)^{0.4} \right] \right\} \text{e}^{-0.0145Pi^{1.3}} \end{aligned}$$

Then the change of shear modulus is determined on basis of the ratio

$$\frac{G}{G\_{\text{max}}} = k(\gamma, PI)(\sigma)^d,\tag{23}$$

where G is the current shear modulus, σ is normal stress.

Seismic energy absorption is calculated by the formula

$$\xi = 0.333 \frac{1 + \exp\left(-0.0145 PI^{1.3}\right)}{2} \left[ 0.586 \left(\frac{G}{G\_{\text{max}}}\right)^2 - 1.547 \frac{G}{G\_{\text{max}}} + 1 \right] \tag{24}$$

On the basis of the given ratios and introduced by us ratios for determination of necessary indices (normal stress, deformation etc), nonlinear version of the program ZOND was worked out [25]. From the database of strong motions AGESAS, which was formed by us [26, 28], the accelerogram, which was recorded on rocks in Japan, with the characteristics (magnitude, epicentral distance, spectral features etc.) similar to the territory of Tbilisi city, was chosen as the accelerogram, given into the bedrock.

The analysis of the results of linear and nonlinear calculations models of definite areas of Tbilisi city territory confirms the adequacy of calculations to the physical phenomena, which were obtained in soils at intensive loads (Fig. 11). With the increase of seismic impact intensity the nonlinearity display increases. Absorption grows simultaneously. Hence the resulting motion at quite high impacts levels can be lower than the initial level. It corresponds to the fact, which is known on the results of analysis of strong earthquake consequences, which happened in recent yares (for example, Northridge earthquake, 1994).

**Figure 11.** Results of calculations using multiple reflected waves' tool in linear (a) and nonlinear (b) cases.

#### *4.2.4. Calculation of nonlinear soil response using FEM tool of seismic microzonation*

The problem of the determination of soil massif response on dynamic impact with taking soil nonlinear properties into account can be solved by usage of finite element method (FEM) in the following way [25].

Soil medium is represented in the form of two-dimensional massif, which is approximate by triangular finite elements. The net, which consists of triangular elements, allows to describe quite accurately any relief form and form of the layer structure of soil massif with its physicsmechanical parameters. Within finite element the soil is homogeneous with inherent to its characteristics, which vary in time depending on impact intensity. Earthquake accelerogram of horizontal or vertical direction, which is applied, as a rule, to the foundation of soil massif, is used as the impact. Soil is in the conditions of plane deformation and it is considered as an orthotropic medium. Axes of the orthotropy coincide with the directions of main strains [28]. The problem of nonlinear dynamics of soil massif is solved by means of the consecutive determination of mode of deflection of the system on the previous step. The system is linearelastic on each step.

#### **4.3. Instrumental-calculational method of seismic microzonation**

In recent years a new «instrumental-calculational» method of SMZ (per se simultaneously having the features of both instrumental and calculational method) which includes tool of «instrumental-calculation analogies» has been developed in Russia in recent years [25]. Its usage is based on direct usage of modern databases of strong movements.

As a basis at realization of tool instrumental database of strong movements, registered in definite soil conditions, is used. As a result of given database with the help of numerical calculations it is possible more or less safely to forecast behavior of these or those soils (or their combination) for strong (weak) earthquakes with typical characteristics for the investigated territory (magnitude, epicentral distance, focus depth etc.).

#### **4.4. Relief influence on the earthquake intensity in SMZ problems**

The correlation analysis of the dependence of seismic intensity increment on true altitude, slope steepness and relief roughness showed that the main factors, which change the value of seismic intensity, are the first two indices [25]. It conforms well to the investigation results of V.B.Zaalishvili, who introduced the new parameter of the relief coefficient (Fig. 12):

**Figure 12.** Relief coefficient R

(a) (b)

The problem of the determination of soil massif response on dynamic impact with taking soil nonlinear properties into account can be solved by usage of finite element method (FEM) in

Soil medium is represented in the form of two-dimensional massif, which is approximate by triangular finite elements. The net, which consists of triangular elements, allows to describe quite accurately any relief form and form of the layer structure of soil massif with its physicsmechanical parameters. Within finite element the soil is homogeneous with inherent to its characteristics, which vary in time depending on impact intensity. Earthquake accelerogram of horizontal or vertical direction, which is applied, as a rule, to the foundation of soil massif, is used as the impact. Soil is in the conditions of plane deformation and it is considered as an orthotropic medium. Axes of the orthotropy coincide with the directions of main strains [28]. The problem of nonlinear dynamics of soil massif is solved by means of the consecutive determination of mode of deflection of the system on the previous step. The system is linear-

In recent years a new «instrumental-calculational» method of SMZ (per se simultaneously having the features of both instrumental and calculational method) which includes tool of «instrumental-calculation analogies» has been developed in Russia in recent years [25]. Its

As a basis at realization of tool instrumental database of strong movements, registered in definite soil conditions, is used. As a result of given database with the help of numerical calculations it is possible more or less safely to forecast behavior of these or those soils (or their combination) for strong (weak) earthquakes with typical characteristics for the investigated

**Figure 11.** Results of calculations using multiple reflected waves' tool in linear (a) and nonlinear (b) cases.

98 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

*4.2.4. Calculation of nonlinear soil response using FEM tool of seismic microzonation*

**4.3. Instrumental-calculational method of seismic microzonation**

territory (magnitude, epicentral distance, focus depth etc.).

usage is based on direct usage of modern databases of strong movements.

the following way [25].

elastic on each step.

Later the data analysis allowed to offer the empirical formula for the possible amplification calculation K and intensity increment ∆I, which are caused by the relief [25]:

$$K = -0.1 + 0.681 \text{g} \, R \tag{25}$$

where R= α × H is the relief coefficient; α is the relief slope angle, degree; H is height, m.

The analysis of the experimental data shows that intensity increment can vary at that inde‐ pendently of the type of rocks, from 0 to 1.5 degree.

Finally, let's try to assess the amplification of vibrational amplitude, which is caused by relief, with the help of the calculational method of FEM (Fig.13).

**Figure 13.** Final elements analysis (FEA) application example: a) Variation of amplitudes of displacement, velocity and acceleration along surface; b) calculational model; c) seismograms, calculated in points A, B, C, D.

Itwasdeterminedthatthevibrational amplitude considerablychanceswiththe relief.Thegiven dependence at that is various for the displacements, velocities and accelerations. The largest value of the amplification is observed for displacements and the maximum ratio of vibration‐ al amplitudes,for example,inthepointCto thepointA,is 2.1 andforthepointD– 3.2.It satisfies well the results of experimental observations where the ratio in the point C for the S-wave is equal to 2.3 and in the spectral region the maximum values are 1.8 (at T = 0.4 s) and 3.2 (at T = 0.7 s) for P- and S-waves accordingly. Spectral analysis also shows the resonance increase of vibrational amplitudes in the top part of the slope on the frequency 1.6 Hz (i.e. T=0.6 s).

Considerably fewer investigations are dedicated to the influence of the underground relief on the intensity. At the vee couch of the rocks, which are covered by sedimentary thickness, the ratio between wave length and the sizes of vee stripping have influence on seismic intensity change. Seismic intensity increment in the given case is formed by the wave interference and can be 1.5–2.0 degree.

Thus, at the execution of SMZ works in the mountain regions or under the conditions of billowy relief, it is necessary to pay special attention to the influence of surface or underground relief on the intensity forming. It is necessary to continue the investigations in order to obtain statistically proved ratio for the calculation of intensity increment, caused by relief.

#### **4.5. Seismic microzonation of Vladikavkaz city**

If we consider 5% DSZ map as basis for seismic microzonation so seismic intensity of 8 points corresponds to reference grounds for whole territory. Then, maps of seismic microzonation of cities must be created. According to the above mentioned maps of detailed zoning the maps of seismic microzonation with probability 1%, 2%, 5% or 10 %, correspondingly, were made up (Fig. 14).

**Figure 14.** The maps of seismic intensity microzonation for probabilities of 5% (a) and 2% (b) for the central part of Vladikavkaz city territory [26, 28].

Though, that definitions of the word «zoning» are similar, actually they are quite different in essence. Unlike the maps of detailed seismic zoning, which give seismic potential (Mmax) and source features, the maps of seismic microzonation give assessments of soil condition influence (sands, rocks, pebbles, clays etc., their combination; watering; relief (as underground as surface); spectral distribution of incoming wave; predominant vibration frequencies on city square etc.) on forming of future earthquake intensity. It should be noted that as a basis the maps of different probability of exceedance will be used and as the initial intensity, the value of which corresponds directly to the intensity of the sites, composed by average soils or characterized by average soil conditions and, therefore, the maps will be referred to the 7, 8 or 9 points (and similarly for acceleration). The zones, composed by clay soils of fluid consistency, which can be characterized by liquefaction at quite strong impacts, are marked by the index 9\*. Intensity calculation here supposes the usage of special approaches in the form of direct taking soil nonlinearity into account [25]. The maps in accelerations units show the similar results. As a rule, the scale of such maps is 1:10 000, in order to have the opportunity of taking them into account at building.

Itwasdeterminedthatthevibrational amplitude considerablychanceswiththe relief.Thegiven dependence at that is various for the displacements, velocities and accelerations. The largest value of the amplification is observed for displacements and the maximum ratio of vibration‐ al amplitudes,for example,inthepointCto thepointA,is 2.1 andforthepointD– 3.2.It satisfies well the results of experimental observations where the ratio in the point C for the S-wave is equal to 2.3 and in the spectral region the maximum values are 1.8 (at T = 0.4 s) and 3.2 (at T = 0.7 s) for P- and S-waves accordingly. Spectral analysis also shows the resonance increase of vibrational amplitudes in the top part of the slope on the frequency 1.6 Hz (i.e. T=0.6 s).

100 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

Considerably fewer investigations are dedicated to the influence of the underground relief on the intensity. At the vee couch of the rocks, which are covered by sedimentary thickness, the ratio between wave length and the sizes of vee stripping have influence on seismic intensity change. Seismic intensity increment in the given case is formed by the wave interference and

Thus, at the execution of SMZ works in the mountain regions or under the conditions of billowy relief, it is necessary to pay special attention to the influence of surface or underground relief on the intensity forming. It is necessary to continue the investigations in order to obtain

If we consider 5% DSZ map as basis for seismic microzonation so seismic intensity of 8 points corresponds to reference grounds for whole territory. Then, maps of seismic microzonation of cities must be created. According to the above mentioned maps of detailed zoning the maps of seismic microzonation with probability 1%, 2%, 5% or 10 %, correspondingly, were made

(a) (b)

**Figure 14.** The maps of seismic intensity microzonation for probabilities of 5% (a) and 2% (b) for the central part of

statistically proved ratio for the calculation of intensity increment, caused by relief.

can be 1.5–2.0 degree.

up (Fig. 14).

Vladikavkaz city territory [26, 28].

**4.5. Seismic microzonation of Vladikavkaz city**

Engineering-geological zoning of territory is the basis of seismic microzonation. It assumes detailed investigations of features of the territory. Such works are quite expensive and laborconsuming. In the same time they are characterized by locality. During design of seismic microzonation maps it is important to adjust and refine data of engineering-geological conditions of investigated territory which are always exists in one or another form and can be used as approximate basis. And finally general view of these conditions must be given. Proven typification of main factors (thickness of quarternary deposits, velocity profile, groundwater level, surface and underlying soils slope angle, etc.). Actual examples of such investigations will be given– (Fig. 15):

**Figure 15.** Verification of engineering-geological conditions by means of H/V technique (a) and final map of seismic microzonaton of Vladikavkaz city (b).

Seismic microzonation maps, as the direct basis of earthquake design and practical construc‐ tion, are maps of seismic hazard. Maps of seismic microzonation not just show where earth‐ quake-resistant buildings are necessary. They show for what intensity buildings and constructions must be designed: 6, 7 or 8 or 9 points. This supposes the attachment of various financing for the implementation of the anti-seismic measures. It should be noted that the seismic zonation maps and microzonation can and should be constructed as well in units of acceleration. This will help to implement a more smooth transition from the borders of one seismic zone to another, thereby increasing the reliability of their allocation.

All types of maps and in particular maps of general and detailed seismic zonation as well as microzonation are nowadays formed in GIS technologies. The use of GIS technologies allows to lay a variety of information on a particular area or the whole territory, for example the city in the form of layers and to investigate their integral effect on the characteristics of seismic hazard occurrence.

### **5. Specified seismic fault and design seismic motion**

Analysis and consequent account of initial accelerograms transformation will become the basis for site effect analysis at strong seismic loadings (Fig. 16) [25, 28].

Methods of such modelling are based on accordance of spectral properties of modelled and real earthquake. In a whole modelling accuracy depending on the purposes of total motion usage and what characteristics defining structural system behaviour must be reproduced.

Earthquake source that is a region of rupture can be considered as point source only for much larger distances than fault size. At close distances effects of finite fault size become more significant. Those phenomena are mainly connected with finite rupture velocity, which causes energy radiation of different fault parts in different times and seismic waves are interference and causes directivity effects [3, 4].

**Figure 16.** Synthetical accelerograms for different source locations: a – western part of fault; b – middle part of fault; c – eastern part of fault; d – scheme of sources of scenarios earthquakes

Let's compare amplitude spectra of obtained design accelerograms with spectrum of real earthquake from considered fault. Data analysis (Fig. 17 and Fig. 18) shows that spectra of calculated and real earthquakes in a whole are similar in their main parameters. It must be noted that spectrum of vertical component of real earthquake is closer to design spectra. The last fact is quite obvious and is explained by proximity to earthquake source. Indeed, close earthquakes in general are characterized by predomination of vertical component. Record of TEA station (located in theatre) was selected due to its location on dense gravel and has a minimal distortions caused by soil conditions.

Seismic microzonation maps, as the direct basis of earthquake design and practical construc‐ tion, are maps of seismic hazard. Maps of seismic microzonation not just show where earth‐ quake-resistant buildings are necessary. They show for what intensity buildings and constructions must be designed: 6, 7 or 8 or 9 points. This supposes the attachment of various financing for the implementation of the anti-seismic measures. It should be noted that the seismic zonation maps and microzonation can and should be constructed as well in units of acceleration. This will help to implement a more smooth transition from the borders of one

All types of maps and in particular maps of general and detailed seismic zonation as well as microzonation are nowadays formed in GIS technologies. The use of GIS technologies allows to lay a variety of information on a particular area or the whole territory, for example the city in the form of layers and to investigate their integral effect on the characteristics of seismic

Analysis and consequent account of initial accelerograms transformation will become the basis

Methods of such modelling are based on accordance of spectral properties of modelled and real earthquake. In a whole modelling accuracy depending on the purposes of total motion usage and what characteristics defining structural system behaviour must be reproduced.

Earthquake source that is a region of rupture can be considered as point source only for much larger distances than fault size. At close distances effects of finite fault size become more significant. Those phenomena are mainly connected with finite rupture velocity, which causes energy radiation of different fault parts in different times and seismic waves are interference

(a) (b)

VLADIKAVKAZ

<sup>1</sup> <sup>2</sup> <sup>3</sup>

(c) (d)

**10 km**

**Figure 16.** Synthetical accelerograms for different source locations: a – western part of fault; b – middle part of fault; c –

seismic zone to another, thereby increasing the reliability of their allocation.

102 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

**5. Specified seismic fault and design seismic motion**

for site effect analysis at strong seismic loadings (Fig. 16) [25, 28].

hazard occurrence.

and causes directivity effects [3, 4].

eastern part of fault; d – scheme of sources of scenarios earthquakes

Analysis of spectrum of weak earthquake shows that peaks are observed on 1.3 and 5.6 Hz (Fig. 17). In spectra of synthesize accelerograms mentioned amplitudes are also observed. At the same time medium response on strong earthquake, undoubtedly, differ from weak earthquake response (Fig. 18).

Usage of maps of detailed seismic zoning in units of accelerations at seismic microzonation level is possible only for calculation method giving results in units of accelerations. Today traditional instrumental method of seismic microzonation does not allow obtaining intensity increments in accelerations due to traditional orientation on macroseismic intensity indexes. The exclusion is the case of investigation of strong earthquakes accelerations when instru‐ mental records are obtained. At the same time investigations are conducted and the problem is supposed to be solved.

**Figure 17.** Spectra of design accelerograms at different source locations of earthquake М=7.1: 1 – western part of fault; 2 – middle part of fault; 3 – eastern part of fault

On the other hand in recent years a new instrumental-calculation method was developed [25]. New method is based on selection from database (including about 5000 earthquake records) soil conditions which are the most appropriate to real soil conditions of the investigated site. Then the selection of seismic records with certain parameters or their intervals follows

**Figure 18.** Spectra of accelerograms of weak earthquake with epicentre in the zone of Vladikavkaz fault. (25.08.2005 10:25 GMT, H = 8 km M= 2.5).

(magnitude, epicentral distance, and source depth). Then maximal amplitudes are recalculated for given epicentral distances. Absorption coefficient can be calculated by attenuation model for given region.

Thus, a new complex method of seismic hazard assessment providing probability maps of seismic microzonation, which are the basis of earthquake engineering, is introduced. Un‐ doubtedly such approach significantly increases physical validity of final results.

Today, we have conditions for detailed seismic zoning maps development like the above mentioned but for all the territory of the Northern Caucasus on the basis of the modern achievements of engineering seismology. Thus algorithm of seismic hazard assessment of the territory that is taking into account multiple factors forming seismic intensity was considered. Forms of typical seismic loadings for firm soils are given, which will be changed from site to site in dependence of differences in ground conditions (engineering-geological, geomorpho‐ logical and hydrogeological conditions).

#### **6. Conclusions**

**1.** The goal of the work was to analyze the modern concepts of the seismic hazard of the territory, its evaluation and development of an algorithm for such assessments. One of the main problems is to account a level of possible result errors, or adequacy of such assessments. The evolution of methods and techniques for seismic hazard assessments is presented. The algorithm of direct account of certain characteristics of the territory is given. The integrity of seismic hazard assessments is specified. Calculation of the expected seismic effects is considered.


## **Nomenclature**

(magnitude, epicentral distance, and source depth). Then maximal amplitudes are recalculated for given epicentral distances. Absorption coefficient can be calculated by attenuation model

**Figure 18.** Spectra of accelerograms of weak earthquake with epicentre in the zone of Vladikavkaz fault. (25.08.2005

Thus, a new complex method of seismic hazard assessment providing probability maps of seismic microzonation, which are the basis of earthquake engineering, is introduced. Un‐

Today, we have conditions for detailed seismic zoning maps development like the above mentioned but for all the territory of the Northern Caucasus on the basis of the modern achievements of engineering seismology. Thus algorithm of seismic hazard assessment of the territory that is taking into account multiple factors forming seismic intensity was considered. Forms of typical seismic loadings for firm soils are given, which will be changed from site to site in dependence of differences in ground conditions (engineering-geological, geomorpho‐

**1.** The goal of the work was to analyze the modern concepts of the seismic hazard of the territory, its evaluation and development of an algorithm for such assessments. One of the main problems is to account a level of possible result errors, or adequacy of such assessments. The evolution of methods and techniques for seismic hazard assessments is presented. The algorithm of direct account of certain characteristics of the territory is given. The integrity of seismic hazard assessments is specified. Calculation of the expected

doubtedly such approach significantly increases physical validity of final results.

104 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

for given region.

10:25 GMT, H = 8 km M= 2.5).

**6. Conclusions**

logical and hydrogeological conditions).

seismic effects is considered.

ACCELEROGRAM - record of ground acceleration changes in time, obtained by accelero‐ graphs.

BEDROCK - a relatively hard, solid rock that commonly underlies soil or other softer uncon‐ solidated sedimentary materials.

DEFORMATION - a change in the original shape and/or volume of a material due to stress and strain.

DENSITY - either (1) the quantity of something per unit measure such as unit length, area, volume, or frequency (see, for example, power spectral density), or (2) the mass per unit volume of a substance under specified conditions of pressure and temperature.

DETAILED SEISMIC ZONING (DSZ) – type of seismic hazard assessment. The main tasks of DSZ – define seismic generating zones, assess focal parameters and their effects.

EARTHQUAKE - a shaking of the Earth that is either tectonic or volcanic in origin or caused by collapse of cavities in the Earth. A tectonic earthquake is caused by fault slip.

EARTHQUAKE ENGINEERING - the field of earthquake engineering is defined as encom‐ passing man's efforts to cope with the harmful effects of earthquakes.

ENGINEERING SEISMOLOGY - that part of seismology which aims primarily at providing seismological data for earthquake engineering, earthquake hazard and earthquake risk applications.

EPICENTER - it is the point on the surface of the Earth, vertically above the place of origin (Hypocenter or Focus) of an earthquake. This point is expressed by its geographical coordi‐ nates in terms of latitude and longitude

EPICENTRAL DISTANCE - distance from a site (usually a recording seismograph station) to the epicenter of an earthquake. It is commonly given in kilometers for local earthquakes, and in degrees (1 degree is about 111 km) for teleseismic events.

FOCAL DEPTH - the conceptual "depth" of an earthquake focus.

GENERAL SEISMIC ZONING (GSZ) - type of seismic hazard assessment of a vast territories through the allocation of large seismic generating zones that determine area seismicity. In the result of GSZ are constructed maps in a scale 1:250 000 – 1:8 000 000, allowing rational planning of the development of different areas, to assess the total cost required for the anti-seismic measures on a national scale.

PEAK HORIZONTAL ACCELERATION - the maximum acceleration amplitude measured (or expected) in a strong-motion accelerogram of an earthquake, abbreviated PHA.

SEISMIC MICROZONATION (SMZ) – type of seismic hazard assessment. Initial seismicity or region intensity is set by maps of general and detailed seismic zoning (GSZ and DSZ). SMZ takes into account soil conditions that increase or decrease initial intensity of seismic vibra‐ tions.

VELOCIGRAM - record of ground velocity vibrations in time, obtained by velocigraphs.

## **Author details**

### V.B. Zaalishvili

BEDROCK - a relatively hard, solid rock that commonly underlies soil or other softer uncon‐

DEFORMATION - a change in the original shape and/or volume of a material due to stress

DENSITY - either (1) the quantity of something per unit measure such as unit length, area, volume, or frequency (see, for example, power spectral density), or (2) the mass per unit

DETAILED SEISMIC ZONING (DSZ) – type of seismic hazard assessment. The main tasks of

EARTHQUAKE - a shaking of the Earth that is either tectonic or volcanic in origin or caused

EARTHQUAKE ENGINEERING - the field of earthquake engineering is defined as encom‐

ENGINEERING SEISMOLOGY - that part of seismology which aims primarily at providing seismological data for earthquake engineering, earthquake hazard and earthquake risk

EPICENTER - it is the point on the surface of the Earth, vertically above the place of origin (Hypocenter or Focus) of an earthquake. This point is expressed by its geographical coordi‐

EPICENTRAL DISTANCE - distance from a site (usually a recording seismograph station) to the epicenter of an earthquake. It is commonly given in kilometers for local earthquakes, and

GENERAL SEISMIC ZONING (GSZ) - type of seismic hazard assessment of a vast territories through the allocation of large seismic generating zones that determine area seismicity. In the result of GSZ are constructed maps in a scale 1:250 000 – 1:8 000 000, allowing rational planning of the development of different areas, to assess the total cost required for the anti-seismic

PEAK HORIZONTAL ACCELERATION - the maximum acceleration amplitude measured (or

SEISMIC MICROZONATION (SMZ) – type of seismic hazard assessment. Initial seismicity or region intensity is set by maps of general and detailed seismic zoning (GSZ and DSZ). SMZ takes into account soil conditions that increase or decrease initial intensity of seismic vibra‐

VELOCIGRAM - record of ground velocity vibrations in time, obtained by velocigraphs.

expected) in a strong-motion accelerogram of an earthquake, abbreviated PHA.

volume of a substance under specified conditions of pressure and temperature.

106 Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

DSZ – define seismic generating zones, assess focal parameters and their effects.

by collapse of cavities in the Earth. A tectonic earthquake is caused by fault slip.

passing man's efforts to cope with the harmful effects of earthquakes.

in degrees (1 degree is about 111 km) for teleseismic events.

FOCAL DEPTH - the conceptual "depth" of an earthquake focus.

solidated sedimentary materials.

and strain.

applications.

nates in terms of latitude and longitude

measures on a national scale.

tions.

Address all correspondence to: vzaal@mail.ru

Geophysics and Engineering Seismology Department of Geophysical Institute of Vladikavkaz Scientific Centre of RAS,, Russian Federation

## **References**


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[19] Smit P., V. Arkanian, Z. Javakhishvili, S. Arefiev, D. Mayer-Rosa, S. Balassanian, T. Chelidze (2000). The Digital Accelerograph Network in the Caucasus. In: "Earth‐ quake Hazard and Seismic Risk Reduction". Kluwer Academic Publishers, pp.

[20] Trifonov, V. G. (1999) Neotectonics of Eurasia. Moscow: Nauchniy Mir, 1999, 252 p.

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[22] Zaalishvili, V.B. (2000) Physical basics of seismic microzonation. Moscow: UIPE RAS,

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