THREE-DIMENSIONAL SIMULATION OF SEISMIC WAVE PROPAGATION IN THE METROPOLITAN AREA OF İZMİR, TURKEY

7/30/2019 THREE-DIMENSIONAL SIMULATION OF SEISMIC WAVE PROPAGATION IN THE METROPOLITAN AREA OF ZMR, TURKEY

1/99

THREE-DIMENSIONAL SIMULATION OF

SEISMIC WAVE PROPAGATION IN THE

METROPOLITAN AREA OF ZMR, TURKEY

by

Gkhan GKTRKLER

December, 2002

zmir


2/99

THREE-DIMENSIONAL SIMULATION OFSEISMIC WAVE PROPAGATION IN THE

METROPOLITAN AREA OF ZMR, TURKEY

A Thesis Submitted to the

Graduate School of Natural and Applied Sciences of

Dokuz Eyll University

In Partial Fulfillment of the Requirements for

the Degree of Doctor of Philosophy in Geophysical Engineering, GeophysicalEngineering Program

by

Gkhan GKTRKLER

December, 2002

zmir


3/99

To the memory of my father,

Vedat GKTRKLER


4/99

ACKNOWLEDGMENTS

I would like to thank The Department of Geophysical Engineering of Dokuz Eyll

University for their support during my thesis study. I owe special thanks to The

Scientific and Technical Research Council of Turkey (TUBITAK) Marmara

Research Center (MAM) Earth and Marine Sciences Research Institute for

generously letting me use their computer facilities for simulation studies. Also, I

would like to thank my advisor Prof. Dr. A. Gngr Taktak for his support and

guidance.


5/99

ABSTRACT

Using a finite-difference scheme, 3-D seismic wave propagation in the

metropolitan area of zmir, Turkey was simulated. The scheme is based on the

velocity-stress formulation of the wave equation on a staggered-grid. A 3-D elastic

model was constructed using well data drilled for engineering purposes and limited

seismic experiments in the zmir Bay. The model consists mainly of unconsolidated

sediment cover overlying a basement. Seismic wave propagation was simulated for a

hypothetical earthquake on the western segment of the zmir fault. It was defined as a

point source at the depth of 5 km. Simulations were carried out by using two

different approaches to the source: an explosive pressure source and a rupture having

normal fault features. Lateral propagation of the basin-edge-generated waves in the

bay area and resonating seismic energy in the Bornova basin were the main features

of the wave propagation induced by the pressure source. The basin-edge-generated

waves are considered as the Rayleigh surface waves. Calculation of the normalized

cumulative kinetic energy and peak particle velocity on the surface of the study area

indicates the largest values in the vicinity of the epicenter and the bay area including

the Balova and Karyaka-Bostanl areas. The Bornova basin is characterized by

relatively low values of kinetic energy and peak particle velocity. Broad features of

the wave propagation were observed in the simulation for a hypothetical rupture. The

direct S-wave propagation was the main event of the wave propagation, and P-wavewas quite negligible as the result of the source type used. Basin-edge-generated

waves in the bay area and S-to-P conversion were the other features of the wave

propagation.

Keywords: finite difference method, simulation, velocity-stress formulation, seismic

wave propagation, zmir fault.


6/99

ZET

Bir sonlu farklar algoritmas (staggered-grid finite difference) kullanlarakzmir

metropolitan alannda boyutlu (3B) sismik dalga yaylm simlasyonu

gerekletirilmitir. Yntem, dalga denkleminin hz-gerilme eklinde ifade

edilmesine dayanmaktadr. Mhendislik amal alan sondaj kuyular ve zmir

Krfezindeki kstl sismik almalardan yararlanarak 3B bir hz modeli

oluturulmutur. Model, biri sedimanter dolguyu, dieri temeli temsil eden iki

birimden olumaktadr. zmir Faynn bat segmenti zerinde, yaklak 5 km

derinlikte varsaymsal bir depremden kaynaklanan sismik dalga yaylm, nokta

kaynak yaklam kullanlarak modellenmitir. Simlasyon almalar, sismik

kaynak ilk nce bir basn kayna, daha sonra ise normal fay karakterine sahip bir

deprem kayna kabul edilerek gerekletirilmitir. zmir Krfezi civarnda,

sedimanter dolgu ile ana kaya arasndaki ara yzeyde (zmir Fay) retilen fazlarn

kuzeye doru yaylm ve Bornova Basenindeki rezonans basn kaynann sebep

olduu dalga yaylmnn en belirgin zellikleridir. Ara yzeyde retilen fazlar

Rayleigh yzey dalgas olarak yorumlanmtr. alma alannn yzeyinde

normalize edilmi kinetik enerji ve maksimum parack hz dalmlar

hesaplanmtr. Buna gre, en yksek deerler episantr civarnda ve Balova ile

Karyaka-Bostanl blgelerini iine alan krfez blgesinde grlmektedir. Ayrca

Bornova Baseni greceli olarak dk deerlerle temsil olunmaktadr. Deprem

kayna kullanlarak gerekletirilen simlasyon, alma alannda dalga yaylmnnok genel zelliklerini ortaya koymutur. Direkt S dalgas yaylm, simlasyonun en

belirgin zelliidir. Kullanlan kaynak trnden dolay belirgin bir P dalgas yaylm

gzlenmemitir. Basen kenarlarnda retilen fazlar ve S-P mod dnmleri dalga

yaylmnn dier zellikleridir.

Anahtar Szckler: sonlu farklar yntemi, simlasyon, hz-gerilme denklemi,

sismik dalga yay

l

m

, zmir Fay

.


7/99

CONTENTS

Page

Contents ....................................................................................................................... 7

List of Tables ...............................................................................................................x

List of Figures ............................................................................................................xi

Chapter One

INTRODUCTION

1. Introduction..............................................................................................................1

Chapter Two

GEOLOGY, TECTONICS, and SEISMICITY

2.1. Geology and Tectonics of the Western Anatolia ............................................... 5

2.2. Geology of the Study Area............................................................................... 10

2.2.1. Bornova Plain........................................................................................... 10


8/99

2.2.2. Balova Area ............................................................................................11

2.2.3. zmir Bay.................................................................................................. 12

2.2.4. Karyaka-Bostanl Area .......................................................................... 12

2.3. Major Tectonic Elements in the Study Area .................................................... 12

2.3.1. Bornova Fault........................................................................................... 13

2.3.2. zmir Fault ................................................................................................ 13

2.4. Seismicity of the Study Area............................................................................ 15

2.4.1. Historic Seismicity................................................................................... 16

2.4.2. Present-Day Seismicity ............................................................................ 18

Chapter ThreeMETHOD: STAGGERED-GRID FINITE-DIFFERENCE

3.1. Computational Method .................................................................................... 22

3.2. Velocity-Stress Formulation of the Wave Equation ........................................ 24

3.3. Finite-Difference Implementation.................................................................... 25

3.4. Source Implementation .................................................................................... 29

3.5. Boundary Conditions .......................................................................................32

3.5.1. Absorbing Boundary Conditions ............................................................. 32

3.5.2. Free-Surface Boundary Conditions.......................................................... 34


9/99

Chapter Four

SIMULATION STUDIES

4.1. Three-Dimensional Model for the Study Area................................................. 42

4.2. Seismic Source Used in Simulations ............................................................... 44

4.3. Results of Wave Propagation Simulations....................................................... 45

4.3.1. Simulation for an Explosive Pressure source........................................... 47

4.3.2. Simulation for a Hypothetical Earthquake............................................... 56

Chapter Five

CONCLUSIONS

5. Conclusions............................................................................................................65

References.................................................................................................................. 68

Appendix A ................................................................................................................80

Appendix B ................................................................................................................82

Appendix C ................................................................................................................83

Appendix D ................................................................................................................84


10/99

LIST OF TABLES

Page

Table 4.1. Modeling parameters used in 3D simulation

with a pressure source ............................................................................................48

Table 4.2. Earthquake rupture parameters .................................................................56

Table 4.3. Modeling parameters used in 3D simulation

for an earthquake................................................................................................... 57


11/99

LIST OF FIGURES

Page

Figure 2.1. Majorgeologic units and tectonic elements in the western

Anatolia....................................................................................................................7

Figure 2.2. Map showing major neotectonic structures and neotectonic

provinces in Turkey ................................................................................................. 8

Figure 2.3. Major structural elements in western Anatolia..........................................9

Figure 2.4. Geological map ofzmir and adjacent areas............................................ 11

Figure 2.5. Tectonic elements in the study area.........................................................14

Figure 2.6. Destructive earthquakes in Turkey and adjacent areas between

10 AD 1000 AD ................................................................................................... 19

Figure 2.7. Major earthquakes (M > 5.9) in Turkey and its vicinity during

the 20th century...................................................................................................... 19

Figure 2.8. Epicenterdistribution of historical earthquakes in the western

Anatolia.................................................................................................................20

Figure 2.9. Major earthquakes, which caused damages in zmir and its vicinity

during the 20th century ........................................................................................... 20

Figure 2.10. Earthquake focal mechanism in the Aegean region .............................. 21

Figure 3.1. Staggered grid used in the finite difference calculations.........................26

Figure 3.2. Definition of the faultorientation parameters (strike s, dip ,

rake ) and Cartesian coordinates (x, y, z)...........................................................30


12/99

Figure 3.3. Representation of the body-force distribution in the x-direction (fx)

based on generalized moment-tensor source description.......................................33

Figure 3.4. Wave-field variables in an xz plane......................................................... 36

Figure 3.5. Snapshots of some of the wave-field variables in a homogeneous

medium................................................................................................................... 37

Figure 3.6. Snapshots of horizontal and vertical components at 1.8, 2.5

and 3.1 s ................................................................................................................. 38

Figure 3.7. Comparison of synthetic seismograms calculated by

finite-difference (FD) and frequency-wavenumber (FK) technique...................... 40

Figure 3.8. Synthetic seismogram calculated by finite difference scheme

utilizing the moment-tensor source formulation is compared with that

obtained by frequency-wavenumber integration...................................................41

Figure 4.1. Model of basementdepth distribution in the study area..........................46

Figure 4.2. Pressure-time history (top) and amplitude spectrum (bottom) of thesource-time function used in the simulation ........................................................... 47

Figure 4.3. Snapshots of 3D-simulated wave propagation in the study area

for a pressure source at the depth of 5 km ............................................................. 49

Figure 4.4. Seismic record sections for the radial and vertical velocities along

two profiles running N-S........................................................................................ 52

Figure 4.5. Time histories of radial and vertical velocities at four different

sites (marked by solid triangles) in the study area................................................53

Figure 4.6. Normalized cumulative kinetic energy and peak particle velocity

distributions on the surface of the study area......................................................... 55


13/99

Figure 4.7. Source-time function used in 3-D simulation for a hypothetical

earthquake on the zmir fault ................................................................................. 57

Figure 4.8. Snapshots of 3D-simulated seismic wave propagation in the

study area for a hypothetical earthquake with a focal depth of 5 km ....................59

Figure 4.9. Time histories in the form of seismic record section for the radial,

tangential and vertical components of the particle velocity along the profile

AA across the Balova region, zmir Bay, and Karyaka-Bostanl region ........ 61

Figure 4.10. Seismic record sections of the radial, tangential, and vertical

components of the particle velocity along the profile BB across the

Bornova basin ....................................................................................................... 62

Figure 4.11. Time histories of the particle velocity at four different sites (marked

by filled triangles) in the study area......................................................................64


14/99

1

CHAPTER ONE

INTRODUCTION

1. Introduction

Understanding the characteristics of seismic wave propagation in a region may

help to mitigate earthquake hazards. One way to understand that is numericalmodeling. Developments in computer sciences have made realistic seismic wave-

propagation simulations feasible since 1990s. Realistic simulation means modeling

three-dimensional (3-D) elastic wave propagation in the earth. As known, many

cities in Turkey are located near the rupture zones of large earthquakes, and the city

of zmir is one of them. Therefore, in the framework of this thesis study, 3-D

simulation of seismic waves in the metropolitan area ofzmir is studied. On the other

hand, zmir is one of nine cities in the world selected for the RADIUS (RiskAssessment Tools for Diagnosis of Urban Areas Against Seismic Disasters) project.

Because of geological characteristic of the region in which the city is located, it is

under the serious earthquake risk. Also the city experienced many destructive

earthquakes in the past. Therefore, an Earthquake Disaster Masterplan for the city

has been prepared by collaboration of the Bosphorus University and Istanbul

Technical University. In this masterplan, earthquake hazard analysis has been carried

out and earthquake hazard scenario has been developed for the city. The zmir fault,

which is the main active fault system in the citys metropolitan area, was chosen as

the scenario fault for these studies (Selvitopu & Tuna, 2000). The study area

mainly comprises the zmir Bay and the surrounding area. It includes the zmir Bay

in the west, the Bornova plain in the east, the Karyaka-Bostanl area in the north of

the bay and the Balova area in the south of the bay. It also covers some parts of the

Buca district but the geological structure is taken as the bedrock there. Since the

model did not cover that area completely, taking into account its geology would not

be realistic. The model covers a volume of 15 (N S) x 27 (E W) x 7 (Depth) km.


15/99

2

Using a 3-D staggered-grid finite-difference (FD) scheme, seismic wave

propagation was simulated in the study area. A 3-D model was constructed using

well data drilled for water and geothermal explorations and limited marine seismic

studies in the zmir Bay. It mainly includes a sedimentary basin over the basement.

Simulations are carried out for a hypothetical earthquake on the western segment of

the zmir fault. It is a point source at the depth of 5 km. Seismic wavefields are

calculated by two different approaches to the source: an explosive pressure source

and a rupture with normal fault mechanism.

Using some numerical methods, simulation of seismic wave propagation within

the earth is known as seismic modeling and it aims to obtain the seismogram at a

certain location for a given subsurface structure and source function. Simulating

wave propagation on a numerical mesh, representing the subsurface by finite number

of points, is called as grid method or full-wave equation method because it

propagates the complete wavefield through the model (Carcione et al., 2002). Any

heterogeneity of the medium is easily included into model in the grid method. After

the work of Alterman & Karal (1968), use of finite-difference method became astandard tool in seismic modeling. They solved an elastic wave propagation problem

in a layered half-space induced by a compressional buried point source. Boore (1972)

discussed seismic wave propagation in heterogeneous materials by use of the finite-

difference methods. Alford et al. (1974) studied the effects of the second-order and

forth-order finite-difference operators for space derivatives on the accuracy of

acoustic wave propagation calculations. Kelly et al. (1976) introduced the

homogeneous and heterogeneous finite-difference formulations of elastic wavefieldin two-dimensional media, and they successfully applied the method to different

earth models. Following Madariaga (1976), Virieux (1986, 1984) showed P-SV and

SH-wave propagations on a staggered-grid based on velocity-stress formulation.

Levander (1988) calculated P-SV seismograms using a forth-order finite-difference

scheme based on the Madariaga-Virieux staggered-grid formulation. As a result of

the advancements in computer technologies, 3-D simulations of seismic waves

became possible for geoscientists. Frankel & Vidale (1992) used finite-difference


16/99

3

method to model 3-D wave propagation in the Santa Clara Valley, California for an

aftershock of the Loma Prieta earthquake (1989). Frankel (1993) modeled three-

dimensional ground motions in the San Bernardino Valley, California for

hypothetical earthquakes on the San Andreas fault. Introducing the moment-tensor

source description, he successfully included earthquakes with arbitrary source

mechanism in simulations and modeled seismic wave propagation for a point source

and an extended rupture. Yomogida & Etgen (1993) simulated 3-D seismic waves in

the Los Angeles basin for the Whittier-Narrows earthquake (1988) using a high-order

scheme on a staggered grid. Olsen et al. (1995) simulated 3-D elastic wave

propagation in the Salt Lake basin, Utah. Olsen & Archuleta (1996) carried out

simulations in the metropolitan area of the greater Los Angeles area for the

earthquakes on the Los Angeles Fault system using a 3-D velocity-stress staggered-

grid finite-difference scheme. They modeled propagating ruptures with constant slip

on the fault system. Pitarka et al. (1998) studied the near-fault ground motion for the

1995 Hyogoken Nanbu (Kobe) earthquake, Japan by 3-D simulation. Sato et al.

(1999) modeled 3-D ground motions in the Tokyo metropolitan area for the 1990

Odawara earthquake and the great 1923 Kanto earthquake in Japan. Employing an

algorithm similar to that of Graves (1996), Frankel & Stephenson (2000) carried out3-D ground-motion simulations in the Seattle region by hypothetical earthquakes on

the Seattle fault. Also, Satoh et al. (2001) modeled waveforms of strong motions in

the Sendai basin, Japan, by staggered-grid 3-D finite-difference scheme using

variable grid spacing.

A 3-D staggered-grid finite-difference scheme was employed to simulate seismic

wave propagation in the study area. It follows the algorithm described by Graves(1996). The scheme is based on the velocitystress formulation of the wave equation.

It propagates the complete wavefield in a heterogeneous elastic medium. Arbitrary

velocity and density distributions can be included in the modeling without any

difficulty. The scheme is fourth-order-accurate in space and second-order-accurate in

time and uses the effective media parameters (Randall et al., 1991). The

implementation of the source is achieved by using the generalized moment-tensor

source description. It is based on the work of Frankel (1993). Using this source


17/99

4

description a wide range of seismic sources from explosion to shear dislocation is

easily introduced to simulations. The source implementation is realized as applied to

either the velocity or the stress components of the wavefield (e.g., Graves, 1996;

Olsen & Archuleta, 1996). No anelastic attenuation is taken into account in

simulations. I apply absorbing boundary conditions to all edges of the computational

domain except the free surface. In each simulation, the grid spacing and time step

were 150 m and 0.017 s, respectively. A 17-s simulation was achieved.

Propagation of the basin-edge-generated waves in the bay area and prolonged

duration of seismic energy in the Bornova basin are the main features of the wave

propagation for the pressure source. The ground-motion parameters (cumulative

kinetic energy and peak particle velocity) of this simulation indicate the largest

values near the epicenter and in the bay area comprising the Balova and Karyaka-

Bostanl areas. Relatively low values exist over the Bornova basin. Broad features of

the wave equation are observed in the simulation for a hypothetical rupture on the

western segment of the zmir fault. The direct S-wave propagation is the main event

and P-wave is not strong due to the source type used. The Bornova basin does not

show a strong impact on the wave propagation, but this is the result of the simulationparameters used rather than that of the geological setting in the Bornova basin. Due

to computational power restrictions the simulation were carried out using relatively

large grid spacing and this resulted in reduced resolution. Therefore, I consider the

simulation for a hypothetical earthquake as a modeling study, which reveals gross

features of the wave propagation in the study area.

In the following pages, a brief discussion on the geology, tectonics and seismicityof the western Anatolia is given in Chapter 2. It is followed by discussion on the

geology, major tectonic elements and seismicity of the study area. Chapter 3 includes

the details of simulation method. In this chapter, computational method, finite-

difference implementation of the scheme, implementation of the source and

boundary conditions are discussed. In Chapter 4, 3-D elastic model for the study are

and the results of the wave propagation simulations are discussed, and conclusion are

given in Chapter 5.


18/99

5

CHAPTER TWO

GEOLOGY, TECTONICS, and SEISMICITY

2.1. Geology and Tectonics of the Western Anatolia

There are four major paleotectonic units in the western Anatolia (Figure 2.1)

(engr et al., 1985; engr, 1987; Ylmaz, 1997). These units are generally in thedirection of NE-SW. They had come together at the different times prior to the

middle Miocene as a result of different tectonic processes. They are as the following

from north to south (Erdik et al., 1999):

Sakarya continent, zmir Ankara suture zone, Menderes massive, Lycian nappes

Sakarya continent locates between the zmir-Ankara suture zone in the south and

Inner-Pontid suture zone in the north. It has a basement being composed of

metamorphic and non-metamorphic Paleozoic units. The Mesozoic and Cenozoic

units overlay the basement (Ylmaz, 1997). The zmir-Ankara suture zone is between

the Sakarya continent and the Menderes massive. It consists of ophiolitic melangeand peridotites. It has experienced metamorphism at some places (Ylmaz, 1997). It

is named as the Bornova schist or melange in near zmir (Kaya, 1981; Erdoan &

Gngr, 1992). The Menderes massive, which is the most important metamorphic

unit in the western Anatolia, is located between the zmir-Ankara suture zone and

Lycian nappes. The massive has complex lithology and structure. It is thought that

the main phase of metamorphism had taken place between the Late Cretaceous and

Early Miocene (Ylmaz, 1997). Lycian nappes are between the Menderes massive


19/99

6

and the Bey Dalar autochthon. Obduction of the oceanic crust onto the Anatolid

Torid platform during the subduction along the zmir-Ankara suture zone in the Late

Cretaceous together with accretionary complex of the subduction phase of the

continental collision in the Late PaleoceneEarly Eocene has been considered for the

origin of Lycian nappes for last three decades (Brunn et al, 1971; Graciansky, 1972;

engr & Ylmaz, 1981; engr et al., 1984; Ersoy, 1990; Erdik et al., 1999).

A wide spread magmatic activity is observed in the region. Age of granites, which

consist of granodoirites and monozonites, is about 3520 Ma. According to Ylmaz

(1989, 1990) there exist three different phases in the period of the MiocenePliocene.

The first period produced calcalkaline magma (Late OligoceneEarly Miocene); the

second phase is a transition period (Miocene), and alkaline magma is the product of

the third period (PlioQuaternary). Volcanic rocks also indicate three different

phases (Kaya, 1981). The first period took place between 3015 Ma and included

very different compositions (e.g., basaltic andesite, andesite and dasite), and volcanic

activity was quiet between 1512 Ma (Kaya, 1981). The second phase of the activity

took place between 1210 Ma. Kula basalts are the product of the last period and

they are very young (300.00010.000 a).

Neotectonics of Anatolia is known better than its paleotectonics even though

neotectonics of the region includes many controversial subjects. In the following

lines broad features of Turkeys neotectonics will be discussed in the basis of the

work of Bozkurt (2001). The main driving force of active tectonics in Turkey is the

interactions among the Eurasian, Anatolian and Arabian plates. The northward

movement of the African and Arabian plates relative to the Eurasian plate causesthis. Three major elements resulting from this interaction control the neotectonics of

the country. These are the North Anatolian Fault Zone (NAFZ), East Anatolian Fault

Zone (EAFZ) and the Aegean-Cyprean Arc (Figure 2.2). The NAFZ and EAFZ are

intracontinental strike-slip faults, and the Anatolian block moves toward west from

the collision zone of the Arabian and Eurasian plates (engr & Ylmaz, 1981;

engr et al., 1985). The rate of this escape is ~20 mm year (Barka, 1992; Westaway,

1994; Kahle et al., 1998). This extrusion is accompanied by anticlockwise rotation in


20/99

7

the Aegean region (McKenzie, 1970; Dewey & engr, 1979; Rotstein, 1984;

Jackson and McKenzie, 1988; Seber et al., 1997). Consequently, this tectonic

mechanism has created four different neotectonic proviences in Turkey (Figure 2.2).

These are West Anatolian Extensional Province, North Anatolian Province, Central

Anatolian Ova Province and East Anatolian Contractional Province (engr et al,

1985; Bozkurt, 2001).

Figure 2.1. Majorgeologic units and tectonic elements in the western Anatolia.

(From Seyitolu & Scott, 1996)


21/99

8

As a part of the Aegean Extensional Province, a region of extension including

parts of Greece, Macedonia, Bulgaria and Albania (Bozkurt, 2001), the western

Anatolia is one of the most rapidly being deformed continental regions in the world,

the present widely spread seismicity is an indicator of this deformation (Jackson &

McKenzie, 1988; Ambraseys, 1988; Taymaz et al., 1991). Currently, the region is

experiencing NS extension at a rate of ~3040 mm year (Oral et al., 1995; Le

Pichon et al., 1995). Besides of seismicity, high heat flow, intensive faulting and

volcanism are the other characteristics of the region. The present-day geomorphology

is characterized by a series of approximately EW trending major grabens (e.g.,

Edremit, Bakray, Simav, Gediz, Kk Menderes, Byk Menderes and Gkova

grabens) and NE SW trending secondary (crosscutting) grabens (Westaway, 1990;

Paton, 1992; Seyitolu & Scott, 1992; Seyitolu et al., 1992; Koyiit et al., 1999;

Bozkurt, 2000) (Figure 2.3). Therefore, basinforming normal faults are the

characteristic elements of neotectonic features of western Anatolia. The secondary

features in the region are the basins trending NNE and their intervening horsts (e.g.,

Grdes, Demirci, Selendi basins) (engr, 1987; Ylmaz et al., 2000).

Figure 2.2. Map showing major neotectonic sutructures and neotectonic provinces in

Turkey. (From Bozkurt, 2001)


22/99

9

There are several models for the cause and origin of extensional mechanism in the

region (Bozkurt, 2001). These are tectonic escape (Dewey & engr, 1979; engr

1979, 1980, 1987; engr et al., 1985), back-arc spreading (Le Pichon & Angelier,

1979; Meulenkamp et al., 1988), orogenic collapse (Dewey, 1988; Seyitolu & Scott,

Figure 2.3. Major structural elements in western Anatolia. (From Bozkurt, 2001)

1996; Seyitolu et al., 1992) and episodic (a two-stage graben) models (Koyiit et

al., 1999). The tectonic escape model considers the westward motion of the

Anatolian block since the late Serravalian (12 Ma). The back-arc spreading model


23/99

10

suggests that back-arc extension is the cause for the extensional regime as a result of

the south-southwestward migration of the Aegean Trench system. The origin date of

the subduction rollback process is controversial and they range between 60 Ma and 5

Ma. The spreading and thinning of over-thickened crust is considered as the cause of

the extension following the latest Palaeocene collision by the orogenic collapse

model. Episodic approach takes a orogenic collapse (Mioceneearly Pliocene) as the

first phase and westward motion of the Anatolian block (PlioQuaternary) as the

second phase of NS extensional regime (Bozkurt, 2001). Also, there is no

agreement on the age of the grabens. Suggestions can be classified into three major

groups. These are (1) they commenced to form during the Tortonian (engr &

Ylmaz, 1981; engr et al., 1985; engr, 1987), (2) their formation was started

during the Early Miocene (Seyitolu & Scott, 1992, 1996), (3) they are considered as

Plio-Quaternary structures (Koyiit et al., 1999; Bozkurt, 2000; Ylmaz et al., 2000)

(Bozkurt, 2001).

2.2. Geology of the Study Area

2.2.1. Bornova Plain

The geological map in Figure 2.4 indicates two groups of rocks in the region. The

first group is the Cretaceous and Tertiary consolidated rocks. These outcrop on the

hills surrounding the Bornova plain and they also form the basement of the plain.

Therefore, they are named as the basement rock. The second group includes

Quaternary unconsolidated formations. These are the units filling the basin. The

basement includes three main rock units as sedimentary, Neogene rocks and Tertiary

volcanic rocks. The oldest formation is the Cretaceous flysh. It outcrops on the small

areas in the southern eastern borders of the plain. On the large areas, which are in the

east and southeast also in the north the Cretaceous limestone outcrops. Neogene

limestones are located along the northeastern and southern borders of the plain and

there is discordance between the Cretaceous and Neogene limestones. Miocene

(Tertiary) volcanic rocks are seen along the northwestern and southeastern edges of

the plain and they overlay the sedimentary rocks. The main unit is andesite. The

Bornova plain has very flat surface. The elevation changes from 90 m in the eastern


24/99

11

end to 0.5 m in the zmir bay. The sedimentary fill in the basin comprises clay, sand

and gravel beds (DSI, 1971).

2.2.2. Balova Area

As the area is one of the most important geothermal fields in the western Anatolia,

there are a number of wells drilled for geothermal energy by MTA (The Directorate

Figure 2.4. Geological map of zmir and adjacent areas. The map was compiled

from MTA, 1973; Ate, 1994; Erien et al., 1996. (Modified from Erdik et al., 1999.)

of Mineral Research and Exploration). Thus, our knowledge of the subsurface region

is mainly based on drilling works. Quaternary sediments and Cretaceous flysh are the

main units. Based on the geological observations and deep drillings the Cretaceous


25/99

12

flysh is the oldest unit in the region. The flysh includes meta-sandstone, meta-

claystone, meta-siltstone and limestone, serpentine, diabas mega blocks. It is

alloctone on the Menderes massive metamorphits. Faults related with graben system

play an important role in the development of geothermal system in this region. The

thickness of the sedimantary fill deepens toward the north from 22 m to 182 m

approximately (Ylmazer, 1989; etiner, 1999).

2.2.3. zmir Bay

According to the marine seismic studies in the zmir bay carried out by Institute of

Marine Science and technology of Dokuz Eyll University, there are four different

geological units in the bay area. These are Quaternary sediments, Neogene

sediments, Neogene volcanic facies and Cretaceous flysh. These data were complied

using the refraction studies carried out in the inner and middle bay area. Even though

we have information on the layering and seismic wave velocities in the bay area,

depth information and topography of interfaces are still problematic (Ulu & zdar,

1988; Gnay, 1998).

2.2.4. Karyaka-Bostanl Area

The area is covered by Gediz alluvium. It probably overlies the andesitic rocks.

The thickness of the sediments is problematic. Even though there are wells with the

depths of ~200 m, they do not mostly reach the basement. Therefore, our knowledge

of the thickness is not reliable. The alluvium is mainly composed of sand, silt and

clay. It also includes very thin (in the range of a few centimeters) organic clay levels.

The sediments are mainly water saturated due to low elevation. Thus, they lack of

compactness. Also, swamps are observed in the areas near the coastline (Gnay,

1998).

2.3. Major Tectonic Elements in the Study Area

Neotectonic structures in zmir and adjacent areas indicate three major directions

as E-W, NE-SW and NW-SE. The dominant morphological structures are in the


26/99

13

direction of E-W. These units which show normal fault characteristics are located in

the zmir bay and western end of the Gediz graben system. Faults with the directions

of NE-SW and NW-SE are dominant in the surrounding region. They have different

kinematic features, and this implies that the region has very complex tectonic

features. The main active faults in the study area (Figure 2.5) are the zmir and

Bornova faults (Erdik et al., 1999; Emre & Barka, 2000).

2.3.1. Bornova Fault

This fault is situated in the northeast ofzmir bay and it is in the direction of E-W.

It has normal fault characteristics. It might be considered as the conjugate component

of the zmir fault. Our knowledge on its activity is very limited. This fault formed in

the neotectonic period (Erdik et al., 1999; Emre & Barka, 2000).

2.3.2. zmir Fault

This fault forms the southern border of the zmir Bay. It runs in the direction ofEW. It comprises two major segments. The one is between zmir and Pnarba, and

then other is between Gzelbahe and kuyular. Based on geomorphological

features, it is in the form of normal fault. The eastern segment between zmir and

Pnarba includes two small segments, trending E-W. In the west of Kadifekale the

fault jumps toward south about 5 km. The western segment is between Gzelbahe

and kuyular. The footwall of the fault along this segment created a 1000m

topography. Alluvial fans have been formed in Narldere. Also a delta has developed

on the hanging wall of the fault between Balova nad Narl dere. Moreover, the

Agamemnon thermal springs, known since ancient times, is between Balova and

Narldere. Because of dense settlement in both Balova and Bornova regions

geological observations of zmir fault are very limited (Erdik et al., 1999; Emre &

Barka, 2000). Also our knowledge of its seismic activity is not satisfactory but

available historical data show that the fault had generated hazardous earthquakes in

the past (Ergin et al., 1967; Ambraseys & Finkel, 1995).


27/99

14

Figure 2.5. Tectonic elements in the study area. They are in the form of normal fault. The zmir

border of the zmir Bay, and the Bornova fault is considered as its conjugate component. (Modi


28/99

15

2.4. Seismicity of the Study Area

Turkey is located within the most seismically active region in the world, which is

known as the Mediterranean Earthquake Belt (Bozkurt, 2001), and it is a part of the

Alpine Himalayan Zone. Anatolia has experienced many destructive earthquakes in

the past and recent times. The events of 1458 Erzincan, 1509 and 1556 stanbul,

1688 and 1778 zmir, 1766 Marmara, 1912 Mreftearky, 1939 Erzincan, 17

August 1999 Kocaeli and 12 November 1999 Dzce might be mentioned as

examples (Erdik et al., 1999). Seismicity of a region is governed by its tectonic

regime. The seismic activity in Turkey is the result of the lithospheric collision

between the African and Eurasian plates.

Epicenter distribution of the earthquakes occurred in Turkey and adjacent areas

between 10AD1000AD are shown in Figure 2.6. Relation between epicenter

distributions and tectonic proviences given in Figure 2.2 is in excellent agreement. In

addition, Figure 2.7 shows the epicenters of the major events (M > 5.9) of the 20th

century. It displays almost the same pattern between the earthquake distribution and

tectonic proviences as the historical events. Comparison of these two seismicity

maps reveals that recent seismicity is a mere repetition of the historical pattern of

seismicity. On the other hand, Figures 2.8 and 2.9 show historical and recent major

events in the western Anatolia, respectively. Most of the earthquakes are clearly

related with the horstgraben system. Again current seismicity may be considered as

a repetition of the historical one. The overall seismicity of the region is manifested

by a number of mediummagnitude earthquakes and earthquake swarms (Erdik et al.,

1999). Earthquake focal mechanisms in the Aegean region are given in Figure 2.10.

Since basin-bounding normal faults are the main tectonic features in the western

Anatolia (Bozkurt, 2001), the area is characterized by normal fault solutions.

2.4.1. Historic Seismicity (pre1900)

In historic period of the seismicity of the western Anatolia many hazardous

earthquakes had occurred as shown in Figure 2.8. A list of major historical events


29/99

16

affected the city of zmir is given as follows. Intensity (Io) is in MSK (Medvedev

Sponheur Karnik) scale.

1. 17, Asia Minor (zmir, Efes, Sart, Aydn, Manisa ve Alaehir; Io=X),2. 178, zmir (Io=VIII),3. 688, zmir (Io=IX),4. 1039, zmir (Io=VIII),5. 1056, zmir (Io=VIII),6. 1688 July 10, zmir (Io= X),7.

1723 September, zmir (Io=VIII),

8. 1739 April 4, zmir (Io=IX),9. 1778 July 3-5, zmir (Io=IX) (Ambraseys & Finkel, 1995, Erdik et al., 1999).

The event of 17 AD was catastrophic for the region. It caused severe damage in

12 major Ionian cities (Guidobani et al., 1994). Among the events above the

earthquakes of 1688, 1739 and 1778 were very destructive for the city ofzmir. The

event of 1688 was a smallmagnitude and locallydestructive earthquake. More than5000 people died and many houses and public buildings collapsed. Small - scale

seismic seawaves occurred (Ambraseys & Finkel, 1995). In the following, a broad

definition of the disaster is given

... The shock occurred at 11 h 45 m and lasted 20 to 30 seconds. In zmir much of

the destruction was caused in the lowlying area of the city and most east- facing

walls collapsed, together with three quarters of the houses and public buildings.

Out of seventeen large mosques only three were left standing, shattered and on

the verge of collapse.

... The shock started a fire in the European quarter of the city that spread rapidly

along the Street of France from the coast, spreading eastwards to the quarter of

Apano Mahalas.


30/99

17

... As a result of the earthquake, the fort of Sancak Burnu, situated on a peninsula

at the entrance of the Gulf ofzmir, about three kilometers from the city, was

totally destroyed. The fort and ground around it sunk to the extent that the site

became an islet separated from the mainland by a stretch of sea 30 metres wide.

The fort itself sunk into the ground bodily to the extent that the sea reached the

embrasures and the cannon within. On the mainland in the vicinity of the fort,

about three quarters of the houses were destroyed by the shock.

Elsewhere, the ground in the low lying parts of the city opened up with the first

shock and in places water was ejected from fissures. After the earthquake, it was

found that the seashore in Smyrna had advanced inland as result of a general

sinking of the ground by about 60 centimetres. (Ambraseys & Finkel, 1995; pp.

91-92)

The area near the fort of Sancak Burnu (see Figure 2.5) is considered as the epicenter

of the earthquake (Ergin et al.1967, Ambraseys & Finkel, 1995) and this event is

taken into account an activity of the zmir fault.

The event of 1739 occurred in the Gulf of zmir. It was a damaging earthquake

and caused a widespread destruction in the city. Also it caused damage in Foa. It hit

the Smyrna at very early hours of the day (4 h 15 m) without any foreshocks. About

80 people died. The delta at the mouth of the Gediz River submerged because of the

earthquake (Ambraseys & Finkel, 1995).

On the 3rd of July, 1778 there was a main shock, almost totally damaged the city.

The earthquake, lasted about 15 seconds, occurred at 2 h 30 m. Many houses and

public buildings collapsed. There were aftershocks continued for 24 hours, and they

increased the damaged. A second strong shock hit the city at 13 h 30 m on the 5th of

July. It brought down walls and houses and commenced a fire burning down half of

the city in 36 hours. Aftershocks went on for six weeks. As a result of these

earthquakes more than 200 people lost their lives (Ambraseys & Finkel, 1995).


31/99

18

2.4.2. Present-day Seismicity

During the 20th century the western Anatolia experienced major earthquakes

(Figure2.9), and zmir and adjacent areas have been damaged by these events. A list

of major earthquakes is given the following with intensities (Io) in MSK scale:

1. 1928 March 31, Tepeky-Torbal (38.09N - 27.35E; M=6.5; Io=IX),2. 1939 September 22, Dikili (39.05N - 26.93E; M=6.5; Io=VIII),3. 1949 July 23, Karaburun-eme (38.55N - 26.27E; M=6.6; Io=VIII),4. 1953 March 18, Yenice-Gnen (40.00N - 27.50E; M=7.2; Io=IX),5. 1955 July 16, Ske-Balat (37.70N - 27.20E, M=6.7, Io=VIII),6. 1969 March 25, Demirci (39.20N - 28.40E, M=6.1, Io=VIII),7. 1969 March 28, Alaehir (38.45N - 28.50E, M=6.5, Io=VIII),8. 1974 February 1, zmir (38.50N 27.20E, M=5.5, Io=VII),9. 1977 December 9, zmir (38.56N - 27.47E, M=4.8, Io=VII),10.1977 December 16, zmir (38.41N - 27.19E, M=5.5, Io=VII) (Erdik et al., 1999).

The list includes the earthquakes with the epicenters in zmir and some seriousevents (M > 6) with the epicenters in the surrounding area. A more detailed list of the

earthquakes of the present time is given in Appendix D.

The shock of 1974 caused heavy damage in Alsancak, Konak and Karyaka.

About 47 houses have been affected. Two people died and seven people have been

injured. After three years, the city experienced two successive earthquakes in a

month. These were not strong shocks. They caused some damage in about 40 housesand 20 people have been injured.


32/99

19

Figure 2.6. Destructive earthquakes in Turkey and adjacent areas between

10 AD1000 AD. (From Ambraseys, 1971.)

Figure 2.7. Major earthquakes (M > 5.9) in Turkey and its vicinity during

the 20th century. (From Erdik et al., 1999.)


33/99

20

Figure 2.8. Epicenterdistribution of historical earthquakes in the western

Anatolia. (From Erdik et al., 1999.)

Figure 2.9. Major earthquakes, which caused damages in zmir and its

vicinity during the 20th century. (From Erdik et al., 1999.)


34/99

21

Figure 2.10. Earthquake focal mechanism in the Aegean region. They are mainly the

events of Mw 5.5. The earthquakes of Mw 6.0 are indicated by the larger

symbols. (From Jackson, 1994.)


35/99

22

CHAPTER THREE

METHOD:STAGGERED-GRID FINITE-DIFFERENCE

3.1. Computational Method

Finite-difference techniques are widely used to solve a broad range of seismicwave propagation problems from exploration to earthquake simulation. One

advantage of these techniques is their ability to model wave propagation through

structurally complex media. Of these techniques, one is staggered-grid finite-

difference scheme. It has become a very popular numerical tool in computational

seismology since the works of Madariaga and Virieux. Madariaga (1976) developed

a staggered-grid finite-difference method for modeling expanding circular crack, and

Virieux (1986, 1984) adapted the scheme to model SH and P-SV wave propagation

in a two-dimensional (2-D) medium.

In a staggered-grid scheme, some of wave-field components are defined at

different nodes of the grid as opposed to the conventional finite-difference approach,

in which the components are located at the same nodes, and only displacements are

calculated at these nodes of the grid (e.g., Alterman & Karal, 1968; Kelly et al.,

1976). In a staggered-grid configuration, the grids for particle displacements

(velocities) and stresses are shifted from those for other components by half a grid

length in space (Yomogida & Etgen, 1993). Use of this grid configuration has

important advantages compared with the conventional finite-difference algorithm.

They can be summarized as the following:

Since the velocity components are located at different nodes, the scheme isstable for all range of the Poissons ratio. This means that the stability

condition is not a function of the Poissons ratio. Therefore, the same code


36/99

23

can be used for models including liquid-solid interfaces without any special

treatments for the interfaces,

It has small grid dispersion and grid anisotropy, and they are relativelyinsensitive to Poissons ratio,

The system includes no spatial derivatives of the material properties. Thismeans that treatment of the internal interfaces does not require explicit

boundary conditions and interfaces are represented by changes in material

properties (elastic parameters and density). Therefore, medium

heterogeneity has no influence on the form of differential terms,

The source insertion is very simple and can be easily initiated in terms ofparticle displacement/velocity (via body forces) or stress,

Since velocity and stress components are not calculated at the same nodelocation, infinite amplitudes at the source location and very large values at

the adjacent nodes due to the source singularity are avoided (Alterman &

Karal, 1968; Virieux, 1986),

A stable and accurate representation of a planar free-surface boundarycondition is easily satisfied (Virieux, 1984; 1986; Levander, 1988; Graves,

1996).

Modeling wave propagation over a staggered-grid can be achieved by using oneof displacement-stress (Yomogida & Etgen, 1993; Ohminato & Chouet, 1997;

Moczo et al., 2000), velocity-stress (Olsen & Archuleta, 1996; Graves, 1996) or

displacement-velocity-stress (Moczo et al., in press) formulations. In the framework

of this study, I used a staggered-grid finite-difference algorithm to model seismic

wave propagation expressed as the first-order elastodynamic equations of motion in

terms of velocity and stress. I followed the formulation of Graves (1996), and in the

following pages, implementation of the scheme will be explained in the basis of his


37/99

24

work. Also, some details of this algorithm are given in Appendices A, B and C.

Details of the other types of formulation could be found in the articles mentioned

above.

3.2. Velocity-Stress Formulation of the Wave Equation

Wave propagation in a three-dimensional, linearly elastic and isotropic medium is

described by equations of motion.

Equations of momentum conversation:

ttux = xxx + yxy + zxz + fx,

ttuy = xxy + yyy + zyz + fy, (3.1)

ttuz = xxz + yyz + zzz + fz,

and stress-strain relations:

xx = ( + 2) x ux + (y uy + z uz ),

yy = ( + 2) y uy + (x ux + z uz ),

zz = ( + 2) z uz + (x ux + y uy ), (3.2)

xy = (y ux + x uy),

xz = (z ux + x uz),

yz = (z uy + y uz).

In these equations, (ux, uy, uz) is the displacement vector;

(xx, yy, zz, xy, xz, yz) is the stress tensor; (fx, fy, fz) is the body force vector; is

the density; and are Lam coefficients; x = /x, y = /y, z = /z, and tt =

2/t2.

These equations can be transformed into a set of first-order differential equations

as the following:


38/99

25

tvx = b(xxx + yxy + zxz + fx),

tvy = b(xxy + yyy + zyz + fy), (3.3)

tvz = b(xxz + yyz + zzz + fz),

and

xx = ( + 2) x vx + (y vy + z vz),

yy = ( + 2) y vy + (x vx + z vz),

zz = ( + 2) z vz + (x vx + y vy), (3.4)

xy = (y vx + x vy),

xz = (z vx + x vz),

yz = (z vy + y vz).

Here, (vx, vy, vz) is the particle velocity vector. b(x, y, z) is the lightness or the

buoyancy (inverse of density).

3.3. Finite - Difference Implementation

Solution of the system of equations (3.3) and (3.4) can be easily obtained using a

staggered-grid finite-difference approximation. Details on stability, grid dispersion

and numerical accuracy analyses of the staggered-grid finite-difference

approximation and details on its numerical implementation can be found in related

articles (e.g, Virieux, 1986; Levander, 1988; Randall, 1989; Moczo et al., 2000).

Configuration of the wavefield variables and media parameters on the staggered-

grid mesh are shown in Figure (3.1). The system is staggered in space and it is also

staggered in time. The numerical scheme, which is equivalent to the system of

equations (3.3) and (3.4) is given as the following:


39/99

26

Figure 3.1. Staggered grid used in the finite difference calculations. The wave-field

variables and media parameters are defined at specific nodes of the unit cell, as

shown in the top of the figure. By using a series of unit cell, the model space is filled

up. The indices i, j and k represent the coordinates x, y and z, respectively. h is the

grid spacing. (From Graves, 1996.)


40/99

27

n kjixzxzyxyxxxxn

kjxi

n

kjxi fDDDbtvv ,,2/12/1

,,2/12/1

,,2/1 |)( ++

++ ++++=

n

kjiyyzzyyyxyxy

n

kjyi

n

kjyifDDDbtvv

,2/1,

2/1

,2/1,

2/1

,2/1,|)(

+

+

+

+++++= (3.5)

n

kjizzzzyzyxzxz

n

kjzi

n

kjzi fDDDbtvv 2/1,,2/1

2/1,,2/1

2/1,, |)( +

++

+ ++++=

for the particle velocities, and

2/1,,,,

1,, |)()2(

++ ++++= n kjizzyyxxn

kjxxi

n

kjxxi vDvDvDt

2/1,,,,

1,, |)()2(

++ ++++= n kjizzxxyyn

kjyyi

n

kjyyi vDvDvDt

2/1,,,,

1,, |)()2(

++ ++++= n kjiyyxxzzn

kjzzi

n

kjzzi vDvDvDt (3.6)

[ ] 2/1 ,2/1,2/1,2/1,2/11 ,2/1,2/1 |)( + +++++ ++ ++= n kjiyxxyHxyn kjxyin kjxyi vDvDt

[ ] 2/1 2/1,,2/12/1,,2/11 2/1,,2/1 |)( + +++++ ++ ++= n kjizxxzHxzn kjxzin kjxzi vDvDt

[ ] 2/1 2/1,2/1,2/1,2/1,1 2/1,2/1, |)( + +++++ ++ ++= n kjizyyzHyzn kjyzn kjyz vDvDt

for the stresses.

In these equations, the subscripts and superscripts are used for the spatial indices

and time index, respectively. If the grid spacing is h and the time step is t then the

following expression

2/1,,2/1

++

n

kjxiv (3.7)

shows the x-component of velocity calculated at the point x = [i + (1/2)]h, y = jh, z =

kh, and time t = [n + (1/2)] t. Dx, D

y, D

zrepresent spatial differential operators.


41/99

28

Either secondorder or fourthorder (or higher) operators can be employed. In 3-D

applications use of secondorder operators is not efficient since they require

increased number of grid points causing high computational cost. Thereby, fourth

order operators are preferred in 3-D simulations. Considering this, I used a fourth

order operator for the spatial derivatives and a secondorder operator for the time

stepping, O( 42 , xt ) (see Appendix A). The following equations defines the

effective media parameters, used in equations (3.5) and (3.6):

2,,1,, kjikji

x

bbb

++=

2,1,,, kjikji

y

bbb

++= (3.8)

21,,,, ++= kjikjiz

bbb

for the buoyancy, and

( ) 1,1,1,1,,,1,,4

/1/1/1/1

++++

+++= kjikjikjikjiHxy

( ) 11,,11,,,,1,,4

/1/1/1/1

++++

+++= kjikjikjikjiHxz

(3.9)

( ) 11,1,1,,,1,,,4

/1/1/1/1

++++

+++= kjikjikjikjiHyz

for the rigidity. The expressions in equation (3.9) are harmonic averaging of the

shear modulus. The use of effective media parameters in the staggered-grid

formulation (Randall et al., 1991) generates more accurate results and also ensures


42/99

29

numerical stability in case of an interface with large media contrast intersecting the

free surface (Graves, 1996).

3.4. Source Implementation

In velocity-stress staggered-grid finite difference method, implementation of

source can be carried out using either the velocity components (e.g., Yomogida &

Etgen, 1993; Graves, 1996) or the stress components (e.g., Coutent et al., 1995;

Olsen et al., 1995). A general approach is to use a generalized moment-tensor source

description. Using moment-tensor approach a wide range of source types from

explosion (implosion) to earthquakes can be included in simulations. In this study, I

am interested in modeling seismic wave propagation induced by earthquakes. So, I

will try to explain the representation of earthquakes in velocity-stress staggered-grid

finite-difference scheme.

Earthquakes can be described as shear dislocations along a planar fault.

Therefore, an earthquake source can be simulated by a shear fault and seismic

moment (Mo). A shear fault is described by some orientation parameters in Cartesiancoordinates. These are strike s, dip and rake . Figure (3.2) depicts these

parameters. Strike is measured clockwise round from north (0 s < 2); dip is

measured down from horizontal (0 /2) and the angle between strike direction

and slip is rake (- < ). For a reverse or a thrust fault, for example, dip is 0


43/99

30

Figure 3.2. Definition of the faultorientation parameters (strike s, dip , rake )

and Cartesian coordinates (x, y, z). u is the fault slip. This coordinate system is used

in obtaining moment tensor components. (From Aki & Richards, 1980.)

ssxx MM 2

0 sinsin2sin2sincossin += ,

yxssxy MMM =

+= 2sinsin2sin2

1

2coscossin0 ,

zxssxz MMM =+= sinsin2coscoscoscos0 , (3.10)

ssyy MM 2

0 cossin2sin2sincossin = ,

( ) zyssyz MMM == cossin2cossincoscos0 ,

sin2sin0MMzz = .

Following the algorithm presented by Frankel (1993), Graves (1996) introduced a

generalized moment-tensor source description using a distribution of body forces as


44/99

31

added to the individual velocity components. In his approach, an equivalent

distribution of body-force couples centered at the grid location x = ih, y = jh, z = kh

(h is grid spacing) can be defined by moment-tensor components.

Mxx(t), Mxy(t) and Mxz(t) are the moment-tensor components contributing to the x

component of the body-forces, fx. The component Mxx(t), for example, represents a

force couple with a moment arm of length h aligned in the x direction. Mxx(t)/h is the

strength of each force. Since the body force is the force per unit volume, we have

Mxx(t)/h4 by normalizing the term with the volume of the grid cell, h3. Then, we get

the equivalent body-force distribution for this component of the body force as:

fxi+1/2, j, k=( )

4h

tMxx ,

(3.11)

fxi-1/2, j, k=( )

4h

tMxx .

In a similar manner, the contributions of Mxy

(t) and Mxz

(t) to the body-force

distribution are

fxi-1/2, j+1, k =( )44h

tMxy,

fxi+1/2, j+1, k=( )44h

tMxy,

fxi-1/2, j-1, k=

( )44h

tMxy

,

fxi+1/2, j-1, k =( )

44h

tMxy,

(3.12)

fxi-1/2, j, k+1 =( )44h

tMxz ,

fxi+1/2, j, k+1 =( )4

4h

tMxz ,


45/99

32

fxi-1/2, j, k-1 =( )

44h

tMxz ,

fxi+1/2, j, k-1 =( )

44h

tMxz .

The illustrations of these force distributions are shown in Figure (3.3). The

corresponding expressions for the y and z components of body forces, fy and fz are

given in Appendix B.

As I mentioned previously, source implementation is also possible via stress

components of the wave-field in staggered-grid finite-difference scheme. Using thegeneralized moment-tensor approach the implementation of the source is quite

straightforward. It is achieved by adding the term

( )3h

tMt ij&

(3.13)

to the stress tensorij(t). Here ijM&

is the ijth component of the moment-rate tensor of

the earthquake; h is the grid spacing and h3 is the volume of the grid cell. ij(t) is the

ijth component of the stress tensor at time t (Gottschmmer & Olsen, 2001). Explicit

forms of the term above are given in Appendix C.

3.5. Boundary Conditions

3.5.1. Absorbing Boundary Conditions

In the numerical simulation of wave propagation, one of the serious problems is

artificial reflection generated by the edges of the computational domain. To obtain

reliable solutions these artificial phases should be reduced. This may be achieved by

using absorbing boundary conditions. Type of such boundary conditions might be


46/99

33

Figure 3.3. Representation of the body-force distribution in the x-direction (fx) based

on generalized moment-tensor source description. As shown in the figure, it is

applied to the vx component of the wave field. The vectors in each diagram indicate

the force direction, and the expression to the right of each diagram defines thestrength of the body force. Representations for fy and fz are made in similar fashion.

(From Graves, 1996.)

classified as two general catagories: transmitting (Lysmer & Kuhlmeyer, 1969;

Clayton & Engquist, 1977; Reynolds, 1978; Randall, 1988; Higdon, 1991) and

attenuating (Cerjan et al., 1985; Dablain, 1986) boundary conditions. The first

category is a derivation from various approximations of the wave equation at the


47/99

34

boundary, which makes the edges of the mesh transparent to outward-moving waves.

In the second category, an attenuating region is added as a strip of nodes along the

edges of the computational domain. Waves travelling through that region are damped

by gradual reduction of the amplitudes (Cao & Greenhalgh, 1998). In the framework

of this thesis study a combination of these two boundary conditions is employed for

artificial reflection reduction. Along the borders of the domain of computation A1

absorbing boundary condition of Clayton & Engquist (1977) is used as applied to the

velocity components. The A1 boundary condition is a paraxial approximation of the

wave equation. By modeling only outward-moving energy artificial edge reflections

can be reduced. They are computationally cheap and easy to implement. They are

able to absorb energy over a wide range of incident angles. The difference equations

corresponding to A1 boundary conditions and details of their implementation are

given in Ohminato & Chouet (1997). To reduce the edge reflections further each side

of the computational domain was extended by a strip of 20 nodes, having attenuative

feature except the free surface (Cerjan et al., 1985). Within a strip both velocity and

stress components of wavefield are attenuated by means of multiplying by

exponentially decreasing terms (Hestholm & Ruud, 1994).

3.5.2. Free-surface Boundary Conditions

To model wave propagation in a semi-infinite space, we need to satisfy the free-

surface boundary conditions. When surface topography is negligible compare to

wavelength of the phases propagating areas with slowly changing topography we can

explicitly formulate the free-surface conditions using a planar free-surface

assumption (Levander, 1988; Graves, 1996; Gottschmmer & Olsen, 2001). Usuallythis is the case in 3-D earthquake simulations. Therefore, they are considered as

long-period wave propagation modeling. Numerically stable and accurate

implementation of the planar free surface can easily be achieved by explicitly

satisfying zero-stress condition at the surface (e.g., Levander, 1988; Graves, 1996).

In this section Graves (1996) zero-stress formulation will be described. Choosing

the z axis as positive downward and letting the plane z = 0 be the free surface (Figure

3. 4), the zero-stress condition is met by setting


48/99

35

zz = xz = yz = 0| z = 0 . (3.14)

Since we set the free surface at vertical index k, and zz is located at the surface, then

0=kzz . (3.15)

As a result of model discretizing, we need particular values of the velocity and stress

components at and above the free-surface boundary. The following expressions are

obtained by imaging yzxzzz ,, components of the stress tensor as odd functions

around the free surface:

11 + = kzzk

zz ,

2

1

2

1+

=k

xz

k

xz , 23

2

3+

=k

xz

k

xz , (3.16)

2

1

2

1+

=k

yz

k

yz , and 23

2

3+

=k

yz

k

yz .

xx, yy, xy are not needed above the free-surface. The following difference equations

are derived by using the above relations with equations (3.2) for the velocity

components at the free-surface boundary:

[ ]kyykxxkzz vDvDvD ++

=

2,

[ ] [ ] 21

2

1+ +=+ kzxxz

k

zxxz vDvDvDvD , (3.17)

[ ] [ ] 21

2

1+ +=+ kzyyz

k

zyyz vDvDvDvD .

Here D is second-order difference operator (Appendix A). Above difference

equations can be solved to obtain the velocity components along the grid row just


49/99

36

above the free surface given the interior values of vx, vy, and vz at and below the free

surface.

Gottschmmer & Olsen (2001) showed that centering the staggered wavefield

at the free surface by averaging it across the free surface produced more accurate

solutions. Therefore, seismograms for the vertical velocity component at the free

surface boundary are obtained by averaging the components above and below the

surface.

Figure 3.4. Wavefield variables in an xz plane. The zero-stress free-surface

boundary is coincident with the normal stress nodes (open circles). (From Graves,

1996.)

Figure 3.5 shows snapshots in the xz-plane of some of the wave-field components

(xx, zz, xz, vx, vz) in an infinite homogeneous medium (vp = 4000 m/s, vs = 2300

m/s, = 1.8 g/cm3

). I have used the same values of velocities and density as Graves


50/99

37

(1996). The medium is excited by a pressure source. For this reason, only P-wave is

propagating in the medium.

Figure 3.5. Snapshots of some of the wave-field variables in a homogeneous

medium. Since a pressure source has been used, only P-waves are propagating in the

medium.

To test the accuracy of implementation of the planar free surface, I solved a wave

propagation problem in a 3-D half-space (vp = 4000 m/s, vs = 2300 m/s, = 1.8

g/cm3), and it is similar to Lambs problem. I used a point explosive pressure source


51/99

38

located just below the free surface. It emits a 25-Hz Ricker wavelet. What is

expected by the solution of this problem is Rayleigh surface wave excitation and

generation of PS phase by P to S conversion at the free surface. Figure 3.6 shows the

snapshots of the vertical (vz) and horizontal (vx) particle velocities at times of 1.8, 2.5

and 3.1 s. In the snapshots at 2.5 and 3.1 s, Rayleigh wave propagating along the

free surface and propagation of the PS phase through the medium are clearly seen in

each component.

Figure 3.6. Snapshots of horizontal and vertical components at 1.8, 2.5 and 3.1 s.

Rayleigh wave excitation and generation of converted phase PS by using a pressure

source located just below the surface are very clear.

A more quantitative comparison of the free surface condition implementation is

given in the figure below (Figure 3.7). Synthetic seismograms obtained by staggered-


52/99

39

grid finite-difference scheme are compared with those obtained by analytical

solution. Again a half- space model (vp = 4000 m/s, vs = 2300 m/s, = 1.8 g/cm3)

was used. The seismograms were calculated in an observation point on the surface at

a horizontal range of 20 km. An explosion source was placed at the depth of 0.5 km

from the surface. The source time function was a triangle, which is 1 sec wide.

Numerical solutions have carried out using a grid spacing of 0.25 km and a time step

of 0.025 s. Analytical solution of the problem have been obtained by a frequency-

wavenumber (FK) integration technique (e. g., Wang & Herrmann, 1980; Saikia,

1994). The seismograms have been filtered by a low-pass filter at 1 Hz. Figure 7

shows comparison of seismograms of vertical and radial components from each

method by the end of a 16-s modeling. There is a very good agreement in both

waveforms and amplitudes. The direct P-wave arrives about 5 s and a very strong

Rayleigh wave arrives about 9 s after the origin time. The misfit in the tail of the

Rayleigh wave is caused by artificial edge reflections, which cannot be suppressed

completely by the absorbing boundaries.

Using the same problem discussed above, I tested the accuracy of the generalized

moment-tensor source description scheme. I used an earthquake source located atdepth of 2.5 km. It was simulated using a dip-slip (DS) fault having the orientation

parameters (, , ) as (90, 90, 90) and a seismic moment (Mo) of 11016 N - m.

The seismograms were calculated in an observation point on the surface at a

horizontal range of 10 km. The source time function was again a 1-sec triangle.

Comparison between analytical solutions obtained by FK technique and FD scheme

is shown in Figure 3.8. Observation azimuth of each component is indicated on the

figure. There is an excellent agreement between seismogram calculated by eachmethod considering amplitudes and waveforms.


53/99

40

Figure 3.7. Comparison of synthetic seismograms calculated by finite difference

(FD) and frequency-wavenumber (FK) technique. They were calculated using a half-

space model and a pressure source at the depth of 0.5 km. Comparison indicates

good agreement between the seismograms.


54/99

41

Figure 3.8. Synthetic seismogram calculated by finite difference scheme utilizing the

moment-tensor source formulation is compared with that obtained by frequency-

wavenumber integration. The agreement between them is very good, and this

indicates the accuracy of earthquake source implementation algorithm.


55/99

42

CHAPTER FOUR

SIMULATION STUDIES

4.1. Three-Dimensional Model for the Study Area

Earthquake simulations like the one studied within the framework of this thesis

have some requirements. Mainly, these are a three-dimensional (3-D) model of themedium in which wave propagation will be simulated, and type of source. The

question of 3-D model requires physical and geometrical parameters of the medium.

Geometrical parameters are the number of layers, thickness of the layers, topography

of interfaces, etc. Physical parameters, on the other hand, include density and seismic

velocity distributions in the model. Type of the source is to define what kind of

faulting mechanism generates earthquake.

To construct a 3-D model, I subdivided the study area into four regions. These are

the Bornova basin (it also includes the downtown area of the city), Balova area,

zmir Bay, and KaryakaBostanl area (Figure 4.1). Each area was studied

separately and then the results were combined to obtain a global model for the study

area. Since I carried out a lowfrequency wave propagation simulation and I am

mainly interested some broad features in the study area which are observable in the

frequency range up to 1 Hz, I assumed a simplified twolayer model: a sedimentary

layer with low velocity underlaid by a high velocity basement. On the other hand,

our limited knowledge of both the subsurface structure and velocity distribution does

not allow building a more complex model. Use of a simplified model is also a

common approach in such modeling studies (e.g., Frankel & Vidale, 1992;

Yomogida & Etgen, 1993; Frankel, 1993; Olsen et al., 1996). Data used for

constructing a reliable 3-D model are based on the wells drilled for water and

geothermal explorations by DSI (The State Hydrology Department), MTA (The


56/99

43

Directorate of Mineral Research and Exploration) and private companies and some

limited seismic experiments in the zmir Bay carried out by Institute of Marine

Sciences and Technology of Dokuz Eyll University.

In the Bornova basin the main source of the data comes from the wells drilled for

water exploration by DSI and some private companies. They are in the depth range

of 100-350 m. Especially, a study known as The zmir Water Project carried out in

1971 by DSI yielded valuable data for subsurface structure in the Bornova basin, and

I mainly used this data set. In the Balova area, there area number of wells drilled for

geothermal energy by MTA as the region is one of the most important geothermal

fields in the western Anatolia. They have depths ranging from 100-700 m. Thus our

knowledge of the subsurface in the area is based on these drilling works. These wells

are divided into three groups as shallow production wells, gradient wells for

temperature measurements and deep production wells. Considering the vertical

extent of the model, I preferred to use the gradient and deep production wells.

Although we have information on broad layering and seismic velocities in the bay of

zmir based on seismic studies, our knowledge of depth and topography of interfaces

is not satisfactory. Seismic experiments reveals four different geologic units in thebay area (Ulu & zdar, 1988; Gnay, 1998); these are together with corresponding

average P-wave velocities:

Quaternary sediments (1700 m/s), Neogene sediments (2000 m/s), Neogene volcanic facies (2600 m/s), Cretaceous flysh (3200 m/s).

In the KaryakaBostanl area, I mainly used the data from wells drilled by privatecompanies for engineering purposes. The well coverage in the area is not satisfactory

and most of them do not penetrate the basement. Actually this was a common

disadvantage of developing a model based on information from wells.

Figure 4.1 shows the map of basement depth in the study area. The model covers

an area of 15 (N S) x 27 (E W) x 7 (Depth) km. Due to the computational

restrictions, I limited the vertical extent of the model to 7 km. As seen from the map,


57/99

44

the model mainly comprises the metropolitan area of the city. The topography of

surrounding hills is not included. The maximum basement depth is in the bay area

with a value of > 400 m. The part of the basin in the Bornova plain (i.e., the eastern

end of the basin) is characterized by values of depth to bedrock ranging from 100 m

to 300 m. It is deeper in the south than that in the north. This reveals halfgraben

feature of the basin. This is a common characteristic of the grabens in western

Anatolia (Ylmaz et al., 2000). This also implies that the southern border of the basin

is more active compared to the northern border. As mentioned previously, the

southern border is formed by the zmir fault.

Considering the seismic refraction experiments carried out in the zmir bay, I

assigned a P-wave velocity of 2000 m/s, and density of 2.0 g/cm3 for the sedimentary

layer of the model. The refraction experiments indicate a P-wave velocity ranging

from 1700 m/s to 2000 m/s in sedimentary units. These studies also give an average

P-wave velocity of 3200 m/s for the Cretaceous flysh, which is considered as the

basement rock. Therefore I assumed the basement to have a slightly higher velocity

of 3500 m/s, and a density of 2.6 g/cm3. The value (2000 m/s) assigned for the

sedimentary unit is relatively higher. The reason for choosing this value is to reducethe number of grid points used in simulation. Use of lower velocities requires smaller

grid spacing, and this causes an increase in grid dimensions. Because of our limited

computational power relatively high velocity was preferred. The velocities are

uniform within each layer. That is, no velocity gradient is taken into account in the

model. I adopted density values for the units from literature. S-wave velocities are set

to be 3 times lower than the P-wave velocities. A constant grid spacing of 150 m is

employed for both the horizontal and vertical directions. This yielded 141 x 221 x 65(= 2,025,465) grid points.

4.2. Seismic Source Used in Simulations

Even though we have no enough seismological observations for the activity of the

fault, historical records of the seismicity of the city indicate some major events likely

related with the zmir fault. The event of 10 July 1688 caused a general sinking of


58/99

45

the ground by about 60 cm and the seashore advanced inland. The shock almost

ruined the city. Based on the damage in the fort of Sancak Burnu (Yenikale), the

epicenter of the event is assumed to be near Sancak Burnu peninsula (Ergin et al.,

1967; Ambraseys & Finkel, 1995). This peninsula is situated on the delta developed

on the hanging wall of the zmir fault between Balova and Narldere (see Figure

2.5). Also the earthquake occurred on 4 April 1739 is taken as an event having the

epicenter in the Gulf of zmir (Ambraseys & Finkel, 1995). As a result of the

earthquake, the delta at the mouth of the Gediz River submerged, and some other

morphological changes occurred. Again the city experienced widespread damage.

Another destructive shock of the citys history took place in the July of 1778. The

city was damaged almost totally and some morphological changes were again

reported (Ambraseys & Finkel, 1995, p. 156). Both heavy damage in the city and

morphological changes stress the possibility of these earthquakes being related with

the fault systems in the citys metropolitan area. As mentioned above, the zmir fault

is more active, and it is most likely responsible for destructive seismic activity in the

citys past. Therefore, a hypothetical earthquake on the zmir fault was assumed as

the source in simulation of the wave propagation in the study area. The focal depth of

this event was set to be at 5 km, and it was considered as a point source having anormal fault mechanism. Its epicenter is shown in Figure 4.1 by a star.

4.3. Results of Wave Propagation Simulation

In the framework of this thesis study, 3-D simulation of seismic wave propagation

in the study area is studied by two different approaches to seismic source. In the first

approach, seismic wave propagation is induced by an explosive pressure sourcewhile it is achieved by hypothetical earthquake (a dislocation source) in the second

approach. Each source has the same hypothetical coordinate and depth. The reasons

for use of a pressure source are its simplicity as a source compared with an

earthquake (considering the radiation patterns for different wave types) and to

analyze the broad features of the basins response to wave propagation by means of a

simple source. Analysis of wave propagation using such simplifications is common


59/99

7/30/2019 THREE-DIMENSIONAL SIMULATION OF SEISMIC WAVE PROPAGATION IN THE METROPOLI

Documents

THREE-DIMENSIONAL SIMULATION OF SEISMIC WAVE PROPAGATION IN THE METROPOLITAN AREA OF İZMİR, TURKEY