Understanding Time-Variant Stress-Strain in Turkey: A Numerical Modeling Approach

Transcription

1 Understanding Tie-Variant Stress-Strain in Turkey: A Nuerical Modeling Approach Stephanie Beth Nowak Dissertation subitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillent of the requireents for the degree of Doctor of Philosophy In Geosciences Cahit Coruh, Chair Martin Chapan Ronald Kriz Sauel Peavy Jaes Spotila Noveber 23, 24 Blacksburg, VA Keywords: Finite Eleent Modeling, Stress Transfer, North Anatolian Fault Zone, Turkey, Rupture Probability Analysis

2 Understanding Tie-Variant Stress-Strain in Turkey: A Nuerical Modeling Approach Stephanie Beth Nowak (ABSTRACT) Over the past century, a series of large (> 6.5) agnitude earthquakes have struck along the North Anatolian Fault Zone (NAFZ) in Turkey in a roughly East to West progression. The progression of this earthquake sequence began in 1939 with the Ms 8. earthquake near the town of Erzincan and continued westward, with two of the ost recent ruptures occurring near the Sea of Marara in. The sequential nature of ruptures along this fault zone iplies that there is a connection between the location of the previous rupture and that of the future rupture zones. This study focuses on understanding how previous rupture events and tectonic influences affect the stress regie of the NAFZ and how these stress changes affect the probability of future rupture along any unbroken segents of the fault zone using a two diensional finite eleent odeling progra. In this study, stress changes due to an earthquake are estiated using the slip history of the event, estiations of rock and fault properties along the fault zone (elastic paraeters), and the far-field tectonic influence due to plate otions. Stress changes are not easured directly. The stress regie is then used to calculate the probability of rupture along another segent of the fault zone. This study found that when iproper estiates of rock properties are utilized, the stress changes ay be under- or over- estiated by as uch as 35% or ore. Because these calculated stress changes are used in probability calculations, the estiates of probability can be off by as uch as 2%. A two diensional odel was built to reflect the interpreted geophysical and geological variations in elastic paraeters and the 1939 through rupture sequence was odeled. The far-field tectonic influence due to plate otions contributed between 1 and 4 bars of stress to the unbroken segents of the fault zone while earthquake events transferred up to 5 bars of stress to the adjacent portions of the fault zone. The rupture events near Izit and Düzce have increased the probability of rupture during the next ten years along faults in the Marara Sea to 38% while decreasing the probability of rupture along the faults near the city of Bursa by ~6%. Large aounts of strain

3 accuulation are interpreted along faults in the Marara Sea, further copounding the case for a large rupture event occurring in that area in the future. iii

4 Acknowledgeents Thank you, Cahit Coruh, for taking a chance on a set of newlyweds fro Pennsylvania. Without you, both Ethan and I would not have had the opportunity to learn so uch and gain confidence in ourselves as scientists. Thank you for your guidance, discussion, and funding. As your last student, I hope I have ade you proud. Enjoy your retireent and try not to work too hard! To y friends that have coe and gone and to those who have stayed: thanks for the support and the beers. You ade surviving graduate school a lot of fun. For y husband, Ethan: you are y sounding board. Thank you for going into school with e at 2 a.. to hash out ideas for this dissertation and for all those ties I needed you to just listen to e rant about FEM codes, satellite data, and wanting to have a baby. Most of all, thank you for Aelia Irene, our little one. She s the best thing this dissertation produced! For y other, Deborah Oakley. Thanks for waiting for e to find y own way. I think you knew in your heart that I wouldn t let you down. You ve been one of y best friends throughout this entire process and your support was essential to y success. Thank you, Grandpa, for stressing education so uch and for your support throughout y high school and college years. I don t think I would have ade it this far if it wasn t for you. This dissertation is for you. Granda thank you for always asking: Are you done yet? Guess what: I done! iv

5 Table of Contents Chapter 1: Introduction... 1 Section 1.1: Tectonic Setting... 1 Section 1.2: Historical Rupture Sequence... 4 Chapter 2 Approach... 6 Section 2.1 Finite Eleent Modeling with TEKTON Section 2.2 Coparison of COULOMB 1.3 and TEKTON 2.3 Models... 1 Section 2.3 Boundary Conditions and Model Paraeters Utilized in this Study Section Displaceent Models... 2 Chapter 3 Material and Far-Field Tectonic Influence on Stress and Strain Fields of The North Anatolian Fault Section 3.1 The Role of Elastic Moduli in Stress and Strain Transfer Magnitude Section 3.2 Magnitude of Regional Tectonic Influence Chapter 4: Stress Changes in Locked vs. Unlocked Fault Systes Section The 1939 Earthquake (Ms 7.9) Section The Earthquake (Ms6.9) Section The Earthquake (Ms 7.7) Section The Earthquake (Ms7.5) Section The Earthquake (Ms 7.1)...76 Section The Earthquake (Ms 6.8)...81 Section The Earthquake (Ms 6.8) Section The Earthquake (Ms 7.)...92 Section The Earthquake (Ms 6.5)...97 Section The Izit Earthquake (Ms 7.2) Section 4.11 The Düzce Rupture (Ms 7.2) Chapter 5: Earthquake Probability Section Earthquake Probability Analysis Stress Transfer Method Section Earthquake Probability The Strain Accuulation Method Section Areas of Increased Risk v

6 Section Suggestions For Future Reseach References...16 vi

7 List of Figures Figure 1.1: Tectonic setting of Anatolia Figure 1.2: G.P.S. derived strain vectors along the North Anatolian Fault Zone... 4 Figure 1.3: Location of ruptures odeled within this study....5 Figure 2.1: Figure 2.2: Figure 2.3: Coulob stress change associated with a right-lateral strike slip faulting event calculated with boundary eleent and finite eleent ethods(4, eleent odel) Coulob stress change associated with a right-lateral strike slip faulting event calculated with boundary eleent and finite eleent ethods(4 eleent odel) Coponents of the coulob stress change calculation for the Izit rupture event...24 Figure 2.4: Coparison between the calculated shear stress change and coulob stress change for the Izit rupture event Figure 2.5: Coparison between the coulob stress change calculated by boundary eleent and finite eleent ethods for the Izit rupture event. 26 Figure 2.6: Map of the finite eleent odel in relation to the regional tectonic setting...27 Figure 2.7: Slip distribution utilized in odeling the earthquake rupture sequence.. 28 Figure 2.8: Plate otions relative to a stable Eurasia Figure 2.9: Material types utilized in the inhoogeneous odel Figure 2.1: Bouger gravity ap of Turkey Figure 3.1: Shear stress changes along the 1939 rupture zone due to 1939 rupture event for the strongest and weakest aterial types of the inhoogeneous odel vii

8 Figure 3.2: Shear stress changes along the rupture zone due to 1939 rupture event for the strongest and weakest aterial types of the inhoogeneous odel Figure 3.3: Total displaceent along the 1939 and rupture zones for each aterial type odel Figure 3.4: Shear stress changes along the Izit rupture zone due to Izit rupture event for the strongest and weakest aterial types of the inhoogeneous odel Figure 3.5: Shear stress changes along the Düzce rupture zone due to Izit rupture event for the strongest and weakest aterial types of the inhoogeneous odel Figure 3.6: Shear stress changes along the 1939 rupture zone due to 1939 rupture event and the elastic oduli along the fault zone Figure 3.7: Shear stress changes along the rupture zone due to 1939 rupture event and the elastic odule along the fault zone Figure 3.8: Location of rupture events along the North Anatolian Fault Zone over the past century Figure 3.9: Shear stress changes along the 1939 rupture zone due to 1939 rupture event. Local and Regional tectonic influences are copared Figure 3.1: Shear stress changes along the rupture zone due to 1939 rupture event. Local and Regional tectonic influences are copared Figure 3.11: Shear stress changes along the rupture zone due to rupture event. Local and Regional tectonic influences are copared Figure 3.12: Shear stress changes along the rupture zone due to rupture event. Local and Regional tectonic influences are copared Figure 3.13: Shear stress changes along the Izit rupture zone due to Izit rupture event. Local and Regional tectonic influences are copared Figure 3.14: Shear stress changes along the Düzce rupture zone due to Izit rupture event. Local and Regional tectonic influences are copared 54 Figure 4.1: Shear stress changes due to 1939 rupture event for the locked and unlocked cases of the inhoogeneous odel viii

9 Figure 4.2: Displaceent changes due to 1939 rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.3: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.4: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.5: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.6: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.7: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.8: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.9: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.1: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.11: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.12: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.13: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.14: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.15: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel ix

10 Figure 4.16: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.17: Shear stress changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.18: Displaceent changes due to rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.19: Shear stress changes due to Izit rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.2: Displaceent changes due to Izit rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.21: Shear stress changes due to Izit and Düzce rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.22: Displaceent changes due to Izit and Düzce rupture event for the locked and unlocked cases of the inhoogeneous odel Figure 4.23: Modeled stress change at the tie of rupture copared to the stress changes along the fault zone due to the previous rupture event Figure 4.24: Displaceent at the tie of rupture copared to the total strain accuulation along the fault zone due to the previous rupture event Figure 5.1: Relative probability of an earthquake in the 1 years following the 1939 rupture event along the faults of the North Anatolian Fault Zone Figure 5.2: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.3: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.4: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.5: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone x

11 Figure 5.6: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.7: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.8: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.9: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone Figure 5.1: Relative probability of an earthquake in the 1 years following the Izit rupture event along the faults of the North Anatolian Fault Zone Figure 5.11: Relative probability of an earthquake in the 1 years following the Düzce rupture event along the faults of the North Anatolian Fault Zone Figure 5.12: Model derived tectonic strain rate along the NAFZ utilized to calculate the probability of rupture Figure 5.13: Relative probability of an earthquake in the 1 years following the Düzce rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.14: Relative probability of an earthquake in the 1 years following the 1939 rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.15: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.16: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.17: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) xi

12 Figure 5.18: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.19: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.2: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.21: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.22: Relative probability of an earthquake in the 1 years following the rupture event along the faults of the North Anatolian Fault Zone (strain accuulation ethod) Figure 5.23: Relative probability of an earthquake in the 1 years following the Izit and Düzce rupture events along the faults of the North Anatolian Fault Zone (strain accuulation ethod) xii

13 List of Tables Table 2.1: Material classification and associated elastic oduli assued in this study...2 Table 4.1: Shear stress changes along the rupture zones of the NAFZ before and after a rupture event (locked case) Table 4.2: Shear stress change along the rupture zones of the NAFZ before and after a rupture event (unlocked case) Table 5.1: Table 5.2: Probability of future rupture calculated using shear stress transfer ethod...13 Probability of future rupture calculated using strain accuulation ethod xiii

14 Chapter 1: Introduction The North Anatolian Fault Zone (NAFZ) located in Northern Turkey has, over the past century, experienced a ost extraordinary sequence of earthquake events, which have resulted in the rupture of over 1, k of its length (Barka, 1996, Stein et. al, 1997). Most of the ruptures associated with these earthquakes have followed an East to West igration pattern beginning with the Ms= Erzincan earthquake and continuing through, when two devastating Ms>7. earthquakes struck along fault zones located near the cities of Izit and Düzce, Turkey in the onths of August and Noveber, respectively. These two earthquakes, which are situated along the western portion of the NAFZ along a ajor industrial corridor, resulted in tens of billions of dollars of aterial daage, with loss of life initially estiated between 18, to 3, persons (RMS Event Report, 2; Reilinger et. al, 2). At final estiate, 17, 127 persons lost their lives in the August earthquake and alost three ties as any were injured ( The sequential nature of ruptures along this fault zone has provided an opportunity to study how stress and strain transfer along a fault zone contributes to the probability of rupture along the adjacent segents of the fault zone. This study is focused on utilizing Finite eleent odeling to expand our understanding the stress/strain relationship along the North Anatolian Fault Zone in Turkey (e.g. Roth, 1984; Provost et. al, 23; Mantovani et. al, 2 ). Surface deforation data collected fro both field observations and satellite data can then be used in conjunction with estiates of lithology to build finite eleent odels representing the stress and strain changes along the fault zone due to the rupture events. The stress and strain inforation produced by these odels of the rupture sequence and odels including regional tectonic influence are then utilized to understand how the probability of a future rupture along the NAFZ responds to the different boundary conditions. Section 1.1: Tectonic Setting The Anatolian plate is situated between three plates: the Arabian, Eurasian, and African plates (Figure 1.1). Closure of the Bitlis oceanic basin after the collision and aalgaation of continental fragents along the southern argin of the Pontides in North Anatolia during the Eocene and iddle Miocene resulted in the collision between the Arabian and Eurasian plates 1

15 (Bellier et. al, 1997). The collision of the Arabian plate with Eurasia has resulted in the thickening of the continental crust in eastern Turkey and Caucasus Mountains along the Bitlis Fold and Thrust Belt (Bellier et. al, 1997). This thickening of the crust continues today as Arabia continues is northward journey at a rate of 18 /yr +/- 2 /yr (McClusky et. al, 2) into the Eurasian plate. Eurasian Black Sea Plate North Anatolian Fault Zone 3 +/-1 /yr Anatolia EAFZ BTFZ Hellenic Arc Aegean Sea DSFZ 18 +/-2 /yr Arabian Plate Mediterranean Sea 6 +/- 2 /yr African Plate k 25 k 5 k Figure 1.1:Regional tectonic setting of the study area. GPS derived strain rates are shown for each of the ajor plates. Plate boundaries are shown in royal blue, while the NAFZ, which serves as the boundary between the Anatolian and Eurasian plates, is shown in red. Modified after McClusky et. al, 2. Another consequence of the collision between Arabia and Eurasia has been the extrusion of the Anatolian plate (Bellier et. al, 1997). This extrusion is taken up along two ain fault systes: the North Anatolian Fault Zone and the East Anatolian Fault zone. The NAF exhibits a 2

16 dextral behavior while the East Anatolian Fault zone exhibits a sinstral behavior (Westaway et. al, 1994). To the south and west, the African plate is oving northward at a rate of approxiately 5-6 /yr (+/- 2/yr), according to GPS estiates provided by McClusky et. al (2). The subduction of the northern edge of this plate along the Hellenic Arc is occurring at a faster rate than the northward otion of the African plate (Bellier et. al, 1997). Because of this, the Hellenic Arc is oving southward relative to Eurasia (McClusky et. al, 2). This induced otion results in an extensional regie within the Aegean and western Turkey. GPS derived strain rates within the central and southern Aegean are estiated to be 3 /yr +/- 1 /yr to the southwest with relatively coherent otion (McClusky et. al, 2). GPS stations in the southeastern Aegean show increasing velocities of up to 1 /yr southward relative to the southern Aegean near the subduction zone of the Hellenic Arc (McClusky et. al, 2). The widespread extensional regie that exists in western Turkey and the Aegean and the relatively fast GPS easured strain rate is attributed to roll-back of the subducted African plate beneath the Aegean (LePichon et. al, 1979, Meijer et. al, 1996, Bellier et. al, 1997, McClusky et. al, 2). This echanis of slab pull reduces the horizontal stresses in the overriding plate, thus causing the extension seen in western Turkey and the relatively coherent otion of the central and southern Aegean (Bellier et. al, 1997). The collision of the Arabian plate to the east in addition to the extension within the Aegean and its underlying causes provide the ain drivers of the observed otion of Anatolia with respect to Arabia. The North Anatolian fault syste serves as the northern boundary of the Anatolian Plate where it eets with the Eurasian plate. This fault syste is the ain focus of this study. The syste of faults that akes up the North Anatolian Fault Zone is believed to be a consequence of the collision between the Eurasian and Arabian plates (Bellier et. al, 1997) which has been estiated to be active since the late Miocene (Dewey et. al, 1976) or early Pliocene (Westaway, 1994). The North Anatolian Fault Zone extends fro the Karliova Triple Junction (KTJ) in the east to the Sea of Marara in the west, where it splits into three distinct branches: the northern, central, and southern branches. Within the Marara region, the NAFZ transitions between dextral strike slip echaniss and the extensional regie of the Aegean (Gurbuz et. al, 2). 3

17 The branching of the NAF within this region is explained by the increasing influence of Aegean extension. The northern branch within this region is the ost seisically active segent and exhibits a linear distribution of seisicity along the fault zone while the southern and central branches exhibit a ore diffuse pattern of seisicity (Gurbuz et. al, 2). Figure 1.2 shows the location of the Faults of the entire NAFZ and the GPS derived strain rates along the zone. Chapter 3 focuses on the influence that regional tectonics has on the stress and strain patterns along the North Anatolian Fault Zone. Black Sea Marara Sea SMAS DERB AGUZ ISME KKIR ULDA BALI k 2 k 4 k North Anatolian Fault Zone SINC KMAH EAFZ KTJ KRKT Figure 1.2: GPS derived strain vectors for selected stations along the NAFZ. Vectors were digitized fro McClusky et al (2). Station abbreviation shown to the right of corresponding vector. Section 1.2: Historical Rupture Sequence As was stated before, the North Anatolian Fault Zone has exhibited the behavior of rupturing fro roughly east to west in a series of 11 ajor >Ms 6. earthquakes (Figure 1.3). These ruptures initiated in 1939, during the Ms 7.9 Erzincan earthquake. This rupture broke approxiately 36 k of the NAFZ (Barka, 1996) and was the largest rupture event of the series. Modeling of the shear stress and strain patterns produced by this sequence of earthquakes that has ruptured alost 1, k of the NAFZ is included in Chapter 4. This data is utilized to estiate how these ruptures affected the probability of future ruptures along the entire North Anatolian Fault. This analysis is included in Chapter 5. Previous studies involving finite eleent odeling in Turkey have focused on re-creating the GPS derived strain rates of the region (e.g. Kasapoglu et. al, 1983, Lundgren et. al, 1998, Mantovani et. al, 2, Provost et. al, 23). Several of these papers have involved the use of 4

18 variations in the echanical strength of the rocks, based on geologic and geophysical inforation, to odel the GPS velocity field (naely Provost et. al, 23 and Mantovani et. al, 2). Roth (1988) utilized elastic dislocations to odel the stress field of the western part of the North Anatolian Fault Zone. Elastic dislocations have also been used ore recently to odel the rupture sequence and to estiate probability of future ruptures (Stein et. al, 1997). These elastic dislocation odels eploy only one set of elastic paraeters within the odel, which does not necessarily represent geologic conditions. Black Sea Marara Sea Izit Duzce North Anatolian Fault Zone 1939 k 2 k 4 k EAFZ KTJ Figure 1.3: Map showing the location of the ruptures odeled within this study according to the year of rupture. Modified fro Barka (1996). EAFZ = East Anatolian Fault Zone, KTZ = Karliova Triple Junction This study focuses on how variations in the elastic paraeters of the finite eleent odels effect the stress and strain patterns along the NAFZ due to the rupture sequence and regional tectonic influence. Chapter 3 utilizes three rupture exaples in the odeled earthquake sequence to show how shear stress agnitudes change with various elastic paraeters. Chapter 4 eploys the finite eleent odeling algorith TEKTON 2.3 (Melosh et. al, 198) with odels derived fro geologic and geophysical data to show how shear stress patterns and agnitudes change when elastic paraeters are variable within the finite eleent odel. The boundary condition of locked versus unlocked fault zones are tested within Chapter 4 as well and provide insight as to the physicality of these assuptions. The final chapter (Chapter 5) focuses on the integration of probability analysis and odel boundary conditions for earthquake probability analysis. Areas of increased rupture probability are discussed in ters of the odel boundary conditions and observed seisic activity. 5

19 Chapter 2 Approach Introduction In this study, earthquake probability along a fault zone is calculated using the ethod proposed in the paper by Stein et. al (1997). This ethod requires the knowledge of several factors, but the ost iportant of these factors is the knowledge of the stress resolved along that fault zone due to soe stressing event (Ds), such as an earthquake, and the tectonic stressing rate along that fault zone (s). These two factors control the recurrence tie ( ) of a rupturing event, and thus the earthquake probability (see Chapter 5 for details). These factors are related by Equation 2.1. Equation 2.1 σ ' = σ where is the initial recurrence tie. The initial recurrence tie () is the estiated tie between designated agnitude earthquakes along a fault zone. Traditionally, elastic dislocation odeling such as that eployed by the progra COULOMB 1.3 ade available by the USGS (Crouch et. al, 1983; King et. al, 1994; Okada, ; and Toda et. al, 1998) has been used for odeling the shear stress transferred fro a ruptured fault to adjacent fault zones (e.g. Stein et. al, ; Parsons et. al, 2; Toda et. al, 21; King et. al, 1994). This ethod can also be used to estiate the tectonic stressing rate along a fault zone by assuing sall elastic dislocations at the displaceent rate applied at depth. Parsons (22) has used a finite eleent ethod to calculate both Coulob stress change due to a rupture event as well as the effect of tectonic influence on the stresses resolved along a fault zone using both the elastic dislocation (herein referred to as Coulob ) ethod and the finite eleent ethod. His findings indicate that the Coulob ethod of calculating the tectonic stressing rate places very high stress rates along fault zones and very low rates in the areas in between these fault zones. The high stressing rates along the fault zone have the effect of shortening the recurrence tie and as a result, possibly over-estiating the probability of rupture in a given tie frae. The finite eleent odel proposed by Parsons (22) distributes the tectonic stress evenly along the odel space, thus reducing the stressing rate used for probability 6

20 calculations. This, in turn, lengthens the recurrence tie and results in lower probability values (Parsons, 22). The finite eleent ethod of odeling geologic processes presents an opportunity to ore accurately represent the odeled subsurface because of its flexibility in defining variations in aterial properties and odeled fault behaviors. These odel paraeters can affect the stress patterns along and surrounding a fault zone, and thus our estiation of rupture probability. The reasons behind this are presented in Section 2.1. In order to odel the stress field and the tectonic stressing rate of the Anatolian plate around the North Anatolian Fault zone due to the displaceents induced by regional and local tectonic influences, we eploy a finite eleent odeling algorith, TEKTON 2.3 (Melosh et. al, 198) in two diensions to atch the two diensional assuptions of the Coulob calculation. The original code was created by Melosh to odel geologic phenoena and has been enhanced over the years. The latest version of this code is available to the public at Within Section 2.2, the difference between Coulob and finite eleent odeling with TEKTON 2.3 will be discussed using two different geologic odels. The first odel involves a siple N-S trending right-lateral strike slip fault with a slip distribution odeled after King et. al (1994). The results fro finite eleent odeling with TEKTON2.3 will be copared with King s (1994) published results fro the Coulob 1.3 odeling,. The second odel involves the Izit rupture. The TEKTON2.3 odel will be copared with the results included in Parsons et. al (2), where the sae rupture was odeled using the Coulob elastic dislocation technique. These results will be used to justify the interpretations applied throughout this work. Section 2.3 describes the paraeters applied within the TEKTON 2.3 odeling algorith to odel the stress changes that occur due to both the regional tectonic oveents of the surrounding plates and the large-scale rupture events that have occurred along the North Anatolian fault zone since We forulate the odel such that the proble is defined as a plane-strain proble in two diensions along the x-y plane at the seisogenic level. 7

21 Section 2.1 Finite Eleent Modeling with TEKTON 2.3 One of the ain goals of this study was to understand the roles that aterial type (discussed in Chapter 3) and variations in boundary conditions (discussed in Chapter 4) play in the stress patterns odeled along the NAFZ and their ipact on probability calculations. A finite eleent odeling progra, TEKTON version 2.3, has been chosen to odel the stress changes that have occurred due to regional tectonic displaceents and local rupture events along the North Anatolian Fault Zone (NAFZ) because of its flexibility in defining aterial properties as well as odel behavior (boundary conditions) when copared to the Coulob elastic dislocation progra. In the Coulob algorith, all calculations are perfored in a unifor elastic isotropic halfspace (Coulob 1.3 User Guide, p.1). This eans that only one set of aterial paraeters can be utilized at a tie. In TEKTON 2.3, aterial properties can be defined for each individual eleent within the odel space. This allows the user to odel lateral variations in lithology. The TEKTON algorith uses linear shape functions with brick eleents to calculate the direct solution to a generalized Hooke s Law (Melosh et. al, 198). According to the Coulob 1.3 user anual (p. 1), The Coulob 1.3 algorith calculates stress changes using the two diensional boundary eleent ethod developed by Crouch et. al (1983). In our application of the TEKTON algorith, the proble is forulated in ters of displaceent on the x-y plane where each node is defined by two degrees of freedo that define the displaceent boundary conditions of that node. More inforation in the odel boundary conditions is included in Section 2.3. The odel is allowed to displace and the corresponding stresses are calculated. A generalized linear Hooke's law (Equation 2.2) defines the aount of stress that is produced in each eleent due to the displaceent boundary conditions. (Equation 2.2) s ij = C ijkl l kl where s ij is the calculated stress, C ijkl is the stiffness atrix with is constrained by the Young's odulus and Poisson's ratio, and l kl is the strain. When the plane-strain analysis is used in TEKTON, one of the priary assuptions is that the length diension is large when copared to the cross section of a body. Displaceent 8

22 in the z-direction and its first derivative are assued to be zero. These assuptions siplify the calculations, and the relationships between stress and strain can be defined in ters of the Young s odulus and Poisson s ratio. In addition, each eleent is assued to be hoogeneous individually, but the elastic paraeters y differ fro eleent to eleent. The following are the relationship between the Young s Modulus (E), Poisson s ratio (v) stress (s ij ), and strain (l ij ): When the thickness (in our case, the height or z) diension is sall copared to the x and y diensions of the eleent, plane stress is assued. Therefore, the stress in the z-diension is zero. (Equation 2.3) (Equation 2.4) (Equation 2.5) xx ( )( ) ( υ ) 1+ υ 1 2υ [ l υl ] σ E = 1 + yy ( )( ) ( υ ) 1+ υ 1 2υ xx yy [ l υl ] σ E = 1 + σ xy E = 1+ l ( υ) xy yy xx A finite eleent odel is constructed such that the zone of interest is well within the liits of the odel space. This reoves any nuerical "edge effects" that can appear at the boundaries of the odel. Eleents are also constructed such that sall changes in the stress field can be captured. This involves creating eleents that are sall enough to iage displaceents and stress changes, but large enough to adhere to the plane-strain rule of cross-sectional area. Eleent geoetry can also affect the results of the stress and strain odeling. When odeling faults, nodes should be placed along the orientation of the fault zone. This way, the shearing of the eleents occurs in the sae orientation as the fault zone. Eleent length should be large copared to the displaceent along the fault zone to satisfy the requireent of infinitesial strain (du I / da i << ) for linear assuptions. The Section 2.3 describes the geoetry and properties of our odel space in light of the above discussion where these liitations were taken into careful consideration. 9

23 Section 2.2 Coparison of COULOMB 1.3 and TEKTON 2.3 Models The Coulob 1.3 and TEKTON 2.3 algoriths eploy different techniques to perfor stress calculations, but the equations reain the sae. In this section, we copare the results of coulob failure stress calculations in each of the two odeling algoriths. This coparison will be utilized as a basis for the interpretations ade throughout the reaining chapters. The Coulob Failure Criterion The Coulob failure criterion (s f in Equation 2.6) is defined in ters of the shear stress change along a fault (t s ), the noral stresses along that fault (Ds n ), the pore fluid pressure (p), and the coefficient of internal friction (u). Equation 2.6 σ = τ µ ( σ p) f s n A odified version of Equation 2.6 acknowledges that when the stresses within the rock change ore rapidly than pore fluid pressure can change through fluid flow, the pore fluid pressure can be related to the confining stress in the rock by Skeptons coefficient (B) (King et. al, 1994). This coefficient gives the change in pore fluid pressure caused by a seisically induce stress change (Skepton, 1954) and varies between zero and one, where the effective coefficient of friction is defined as u =u(1-b). Equation 2.6 can be now be written as in Equation 2.7 where s n now represents the confining and noral stresses on the fault plane (King et. al, 1994). Equation 2.7 σ = τ + µ (' σ ) f s n In the two diensional case where the x and y axes and fault displaceents are aligned in the horizontal plane, such as the one presented within this study, the stresses on a plane of orientation theta fro the x-axis due to a rupture event can be given by (King et. al, 1994): 1

24 Equation 2.8 Equation 2.9 Equation 2.1 q σ q σ q τ q = σ q = σ xx xx 1 q = ( σ 2 2 q cos θ + 2σ 2 q sin θ 2σ yy q σ xx xy xy q sinθ cosθ + σ q sinθ cosθ + σ q )sin 2θ + τ q q Equation 2.11 σ = τ 13 + µ (' σ 33) f xy cos 2θ yy yy sin cos 2 2 θ θ The change of Coulob stress along the planes oriented at an angle theta fro the x-axis can be written as in Equation 2.11, where the sign of t q 13 is positive for right-lateral strike slipping echaniss and is negative for left-lateral slipping strike slip echaniss. Equations 2.9 through 2.11 were utilized to estiate the Coulob stress change within the odels presented in this study. For right-lateral faults, positive Coulob stress change values correspond to an increase in Coulob stress while negative values indicate a decrease (release, or stress shadow ). In leftlateral faults, the opposite would be true. The Coulob stress change is calculated by using the stress changes associated with the rupture itself and does not include the agnitude of the regional stress field. The regional stress values only decide the optiu fault orientation (King et. al, 1994). If the noral stress values corresponding to the regional stress are large copared to the stresses resolved on the fault zone, the optial fault orientations are decided by the regional stress regie but the range of optial fault orientation can not vary by ore than 3 because the fault ust ove as a function of the regional stress (King et. al, 1994). Coparison with King et. al (1994) Model The odel presented in King et. al (1994) involves a vertical fault that runs fro north to south in the center of a unifor elastic half space. There are no regional stresses iposed on the odel space. The fault is subjected to an elliptical slip distribution and the Coulob stress changes are calculated on infinitesially sall fault planes parallel to the aster fault. This odel is re-created using a finite eleent odeling schee. The first finite eleent odel presented (Model A) consists of 4,41 node syste (1 eter spacing in the x- and y- directions) that define 4, eleents of identical aterial types. This 11

25 re-creates the unifor aterial properties in King et. al (1994) and the very sall grid spacing approxiates the infinitesial fault planes. Another odel (Model B) uses a less dense grid of eleents (4 Eleents) with 1 eter spacing between nodes. This does not approxiate the infinitesial fault planes, but represents the relative type of spacing utilized in the finite eleent odels eployed in the later chapters of this study. The eleents consist of the sae aterial properties as the ore dense odel. Several nodes within the center of the odel space were subjected to a right-lateral slip distribution siilar to the one presented in King et. al (1994) where slip is tapered to zero at the ends of the faults and is axiu at the center of the fault. The results fro Model A are presented in Figure 2.1 while the results fro Model B are presented in Figure 2.2. The stress patterns in these figures represent the coponents of Equation 2.11 as calculated for faults parallel to the ain fault (theta = 9 ). It can be seen fro these results that two diensional finite eleent odeling with TEKTON 2.3 produces the sae flavor of stress patterns as the Coulob 1.3 ethod of stress calculations, even though differences exist due to odel paraeters. In Figure 2.1, a odel consisting of 4, eleents of 1x1 eter size is subjected to the generalized slip pattern fro King et. al (1994). The shear stress (t 13 ) and noral stress (s 33 ) calculations appear to atch with the stress patterns calculated with the Coulob 1.3 algorith, the results of which are presented in King et. al (1994). The resulting Coulob stress change iaged in Figure 2.1 (c) atches fairly well with the results calculated with the Coulob 1.3 algorith, although there are differences. The reasons for the differences between the Coulob 1.3 calculated odel fro King et. al (1994) and the odel calculated using the finite eleent technique ay be related several factors, including eleent geoetry, slip history and fault length. The finite eleent odel used was constructed with 1x1 rectangles oriented along the priary x- and y-axes. The effect of this can be seen along the boundary of the fault zone in Figure 2.1, where the shear stress changes appear to be oriented with these eleents. This effect appears to be ost focused in areas where the stress change is strongest (i.e. near the fault boundary and at the fault tips) and is not seen in the odel fro King et. al (1994). The effective noral stress iaged in Figure 2.1 (b) differs fro that produced with Coulob 1.3 odeling in that the off-fault lobes appear to be closer together along the fault zone 12

26 and do not extend as far into the odel space. This is an effect of the fault length. Shorter faults will have a ore syetric geoetry of off-fault lobes than longer faults (King et. al, 1994). Data on fault length was unavailable in King for exact atching within the odel space. In addition to the above-entioned differences in the calculated effective noral stress patterns for each ethod, the sall stress changes easured near the tips of the fault zone in the Coulob ethod calculated effective noral stress do not exist in the effective noral stress calculated with the finite eleent ethod (Figure 2.1 (b)). This ay be a function of eleent size, which ay be evidenced by the odel shown in Figure 2.2 (b). These sall fault tip lobes appear when a larger eleent size is eployed in the Finite eleent calculation and disappear when a saller eleent size in eployed. The fault slip applied to the finite eleent odel was slightly different than the slip presented in King et. al (1994). An elliptical slip pattern tapering to zero slip at the fault ends was used to approxiate the slip along the fault zone in King et. al (1994) whereas a linear slip pattern was utilized in the finite eleent odel. The slip still tapered to zero at the ends of the fault, but this difference ay contribute to the shape of the stress shadows iaged in Figures 2.1. Figure 2.2 shows the odel calculated by the finite eleent odel consisting of 4 eleents of 1x1 eter size (Figure 2.2 (b)). The fault zone is subjected to the sae tapered slip distribution. Several interesting features exist in this odel, the first of which is the noticeable edge effects which are evident in the ap of effective noral stress (Figure 2.2 (b)). When the ap of effective noral stress is cobined with the shear stress calculation to produce the Coulob stress change ap (Figure 2.2 (c)), these effects becoe ore proinent. If the odel space were increased in size to include ore eleents and the boundaries were farther away fro the actual slipping nodes, these edge effects would disappear. They are only a function of the eleent size in relation to the odel size. This effect is taken into account with the larger odel that represents the odeled rupture sequence along the North Anatolian Fault (Discussed in Section 2.3). The other effect iaged in this odel is the wide band of positive shear stress that exists within the fault zone. In addition, negative lobes that are iaged in Figure 2.2 (a) do not extend as far into the odel space as the negative lobes iaged in King et. al (1994). These are an effect of the eleent size as well, but in general the shapes of the coulob stress change iaged in Figure 2.2 (c) are consistent and share the sae generalized shape. 13

27 As was stated before, the general shape of the stress patterns calculated with the finite eleent ethod copare well with the Coulob 1.3 ethod shown in King et. al (1994), but differences will exist due to variances in the finite eleent odel paraeters. It appears that the saller the eleent size, the better the resolution of the stress changes apparent in the odel. Larger eleent sizes appear to produce gross effects in the stress pattern by enlarging the offfault lobes and extending the stresses off the fault tips as in Figure 2.2 (a). Coparison with a Given Rupture History The August, Izit Rupture Event The Coulob stress change due to the Izit rupture has been odeled by Parsons et. al (2) and by Stein et. al (1997) using the Coulob 1.3 algorith. In this section, we present the Coulob stress change (Equation 2.11) for that sae event using the calculated stress outputs (s xx, s yy, s xy ) fro the TEKTON 2.3 algorith for optially oriented (striking E-W) vertical right-lateral strike slip faults and copare it to the TEKTON 2.3 output of shear stress changes as well as the coulob stress change pattern presented in Parsons et. al (2). The odel is as described as in the following section and the slip history along the vertical fault is as described in Figure 2.7. The surface fault geoetry is shown as a green dotted line on the aps in Figure 2.3 and Figure 2.4. As in Parsons et. al (2), the odel is configured to represent a hoogeneous aterial. Figure 2.3 shows the coponents of the Coulob stress change equation in graphical for. Figure 2.3 (a) is the shear stress change (t 13 ) calculated using Equation 2.1. Figure 2.3 (b) is the effective noral stress change. This was calculated using the TEKTON 2.3 output stress values and Equation 2.9. An effective coefficient of friction of.2 was used as in Parsons et. al (2) for strike-slip faults with large cuulative slip (Reasenberg et. al, ; Parsons et. al, ). The resulting Coulob stress change is docuented in Figure 2.3 (c). The effective noral stresses in the odel space are quite sall copared to the shear stresses produced by the slip along the fault zone. This is shown in graphical for in Figure 2.3 (d) where each of the coponents of Equation 2.11 are plotted together. The effective noral stresses do not contribute very uch to the total stress change, except at the western end of the fault zone, where the noral stress changes contribute up to 4 bars of stress. The lack of 14

28 influence partly corresponds to the fault s distance fro the rupture zone as well as to the low effective coefficient of friction. Figure 2.4 copares the (a)shear stress change coputed by the TEKTON 2.3 algorith with the (b) calculated Coulob stress change. The sall effective coefficient of friction has resulted in both the calculated shear stress and Coulob stress changes to be quite siilar. Figure 2.4 (c) is a cross section along the Düzce rupture zone. The values for both the shear stress and Coulob stress changes are very siilar along the length of the fault, except near the western end where the optiu fault orientation stress change is about ~4 bars ore than the actual shear stress change along the fault zone. This occurs because of the proxiity of the Düzce fault zone to the Izit rupture zone. Figure 2.3 (b and d) show that a positive effective noral stress of ~4 bars exists at this location. The siilarity between the calculated shear stress value and the calculated Coulob stress changes along optiu fault orientations (+/- 3 ) allow for the interpretation that they are siilar and can be considered coparable for use in probability calculations. Figure 2.5 shows the Coulob stress change calculated with the results of the finite eleent odels along optially oriented vertical faults to the Coulob stress change along a siilar fault orientation calculated in Parsons et. al (2). The stress change patterns appear siilar to each other, but difference exist due to several factors including fault geoetry, slip history, and eleent size. The fault geoetry for the Izit rupture used in Figure 2.5 was digitized fro a ap in Barka (1996), while the geoetry used by Parsons et. al (2) is presuably taken fro Barka () and Saroglu et. al () (Stein et. al, 1997). The slip histories utilized in each of the odels are derived fro the sae sources for the odeled results shown (Parsons et. al, 2 used preliinary results of Wright et. al, 21, while this author used results published in that sae paper), but difference in the digitization of these results as they apply to the odel in cobination with the fault geoetry will result in slightly different stress patterns. The eleent size also plays a role in the differences between stress patterns iaged in the finite eleent odel of Figure 2.5, as the negative lobes that surround the ain fault zone are not as wide as the lobes calculated with the Coulob 1.3 algorith. The offfault lobes appear to be siilar in shape, but not necessarily in extent. The stress patterns produced by the Coulob algorith provide a very soothed version of stress changes surrounding a fault zone due to a given rupture. Fro the results shown in 15

29 Figures , it would appear that the stress patterns produced with the finite eleent ethod of calculation allow for finer resolution of the stress changes that occur with these ruptures in addition to providing ore control on the boundary conditions of the odel. The siilarities between the results produced by these two odeling algoriths allow for the use of finite eleent odeling for understanding the stress patterns along and surrounding the North Anatolian fault zone. The flexibility of this ethod in ters of boundary conditions and eleent properties and the enhanced stress pattern resolution ake it an good choice for studying the role aterial properties and regional tectonic influence play in the transfer of stress fro one fault to surrounding faults and the resultant change in future rupture probability. Section 2.3 Boundary Conditions and Model Paraeters Utilized in this Study A two-diensional plane-strain finite eleent odel was created to odel the stress changes that occur due to both the regional tectonic oveents of the surrounding plates and the largescale rupture events that have occurred along the North Anatolian Fault Zone (NAFZ) since The odel was constructed using 98 Nodes and 9552 rectangular eleents oriented to represent the geoetry of the plate boundaries and fault zones iaged in Figure 2.6. The twodiensional odel was constructed to represent a horizontal slice along the x-y plane at approxiately 1 k depth; a zone approxiating the location of a ajority of the NAFZ earthquake hypocenters. We can focus on odeling this elastic interval in only two diensions instead of three because the Coulob stress change is inherently a two diensional calculation, with the interediate stress being ignored (King et. al, 1994). In order to reove the anticipated edge effects like those iaged in Figure 2.3 (b2) fro the area of interest, the odel space was extended well into the surrounding plates where they would not interfere with the easureents of stress and strain along the NAFZ as well as within the Anatolian Plate and Aegean Sea. Node spacing was set at 15 k intervals in the x-direction and varied in the y-direction fro 1 k spacing in the Arabian, Eurasian, and African plates to 1 k intervals along the NAFZ in Anatolia. This node spacing allows the size of the eleents to vary across the odel space so that 1) the nuber of eleents in areas of interest is increased, such as along and surrounding the NAFZ, and 2) the nuber of eleents in areas that are not of 16