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Spatiotemporal variations of stress field in the San Jacinto Fault Zone and South Central Transverse Ranges

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Spatiotemporal variations of stress field in the San Jacinto Fault Zone and South Central Transverse Ranges

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Content SPATIOTEMPORAL VARIATIONS OF STRESS FIELD IN THE SAN JACINTO FAULT ZONE AND SOUTH CENTRAL TRANSVERSE RANGES by Niloufar Abolfathian A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY GEOLOGICAL SCIENCES August 2020 Copyright 2020 Niloufar Abolfathian ii Acknowledgments First and foremost, I would like to express my deepest gratitude to my PhD advisor, Professor Yehuda Ben-Zion, for his full support and guidance throughout the course of my doctoral research. His exceptional scientific knowledge, vision, ideas, and passion to solve challenging problems have encouraged me to engage deeper in earthquake physics and his great mentorship enhanced my critical thinking and problem- solving abilities, and made me ready for my future scientific career. I also want to thank all my teachers and mentors throughout the years. They were my source of encouragement and I appreciate all the knowledge and experience I gained from them. I would like to pay my special regards to my colleagues and collaborators specially Christopher Johnson and Patricia Martínez-Garzón, without whom none of this would have been possible. Thanks for being always there for me. I also wish to specifically thank the USC staff and the invaluable assistance that you all provided during my study. Last but not least, I would like to sincerely thank my family and friends. I wish to express my deepest gratitude to my parents (Nayereh and Abbas) and my beloved brother (Arash), who supported me with their infinite love and understanding during these years. They followed me around the globe and were always there through all the ups and downs. This accomplishment belongs to them as much as it does to me. Finally, I wish to show my respect to all the people who ever suffered from natural hazards, lost their loved ones, and those who stood strong to make the world a better place to live! I like to remind of the Earth, whose peace made me passionate, whose rage made me thoughtful, and whose release of stress made me that much curious to be here today. iii Table of Contents Acknowledgements..............................................................................................................ii List of Tables.......................................................................................................................v List of Figures.....................................................................................................................vi Abstract..............................................................................................................................xii Introduction..........................................................................................................................1 1. Spatiotemporal variations of stress and strain parameters in the San Jacinto Fault Zone.....................................................................................................................................5 1.1 Introduction...............................................................................................................5 1.2 Study area and data....................................................................................................8 1.3 Methodology...........................................................................................................13 1.3.1 Stress tensor inversion of focal mechanisms................................................13 1.3.2 Coseismic strain parameters from focal mechanisms...................................15 1.3.3 Estimation of magnitude of completeness and b-values...............................17 1.4 Results.....................................................................................................................17 1.4.1 Variations of stress parameters along the SJFZ............................................18 1.4.2 Seismicity parameters and faulting styles in the focused study areas..........22 1.4.3 Variations of stress parameters through the seismogenic thickness.............26 1.4.4 Variations of coseismic strain parameters through the seismogenic zone....33 1.4.5 Spatio-temporal variations of stress parameters...........................................35 1.5 Discussion...............................................................................................................38 1.6 Conclusions.............................................................................................................42 1.7 Acknowledgments...................................................................................................44 2. Variations of stress parameters in the Southern California plate boundary around the South Central Transverse Ranges......................................................................................45 2.1 Introduction.............................................................................................................45 2.2 Data and the study area...........................................................................................47 2.3 Methodology...........................................................................................................51 2.3.1 Stress tensor inversion of focal mechanisms................................................51 2.4 Results.....................................................................................................................53 2.4.1 Regional stress variations in Southern California.........................................53 2.4.2 Stress variations near the South Central Transverse Ranges........................54 2.4.3 Stress variations in the SCTR — aftershocks and depth dependency..........61 2.5 Discussion...............................................................................................................63 2.6 Acknowledgments...................................................................................................68 3. Numerical simulations of stress variations with depth of a strike-slip fault..................69 3.1 Introduction.............................................................................................................69 iv 3.2 Model.......................................................................................................................71 3.3 Results and discussion.............................................................................................74 Discussion..........................................................................................................................76 A1. Chapter 1 supplementary figures and tables...............................................................79 A2. Chapter 2 supplementary figures................................................................................92 References..........................................................................................................................95 v List of Tables 1.1 Average seismic and stress parameters for the SJFZ, CH, HS and TR areas, estimated based on the 2000-2009 declustered seismicity. The angle θ is the angle between S Hmax and main fault strike direction (N55°W) ...........................................................11 2.1 Seismic statistics in SCTR, comparing foreshocks, mainshocks, and aftershock ......50 3.1 Selected frictional model parameters in upper and lower crust ..................................73 vi List of Figures 1.1 (a) Spatial distribution of seismicity in the San Jacinto fault zone (SJFZ) used in the study. Declustered earthquakes from 2000 to 2012 are shown in purple circles. Red rectangles denote three focus study areas, Crafton Hills (CH), Hot Springs (HS) and Trifurcation area (TR). Black lines indicate mapped surface traces of the SJFZ, San Andrea fault (SAF) and Elsinore fault (EF). The upper right inset shows the study area in a larger scale (southern California) view. The red star marks the epicenter of the 2010 M W 7.2 El Mayor-Cucapah Earthquake. (b) Distribution of seismicity with depth along the SJFZ (Profile A-A’). Red rectangles mark depth sections of the three focus areas. ..................................................................................................................12 1.2 Maximum horizontal compressional stress orientations (S Hmax ) along the (a) SJFZ, (b) CH, (c) HS and (d) TR areas. The S Hmax orientations are color-coded with red, green, blue, and brown denote reverse, strike-slip, normal and oblique faulting, respectively. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. Purple dashed lines mark the Voronoi cells used in the analysis of seismicity. .........20 1.3 Seismicity along the (a) SJFZ, (b) CH (c) HS and (d) TR areas, color-coded with values of the stress ratio R. Purple dashed lines mark the used Voronoi cells. In a strike-slip faulting environment, R-values around 0.5, 0 and 1 indicate pure strike- slip, transtension and transpression, respectively. ......................................................21 1.4 Variations of b-values with depth in the (a) CH, (b) HS, and (c) TR areas. Green and blue lines display b-values associated with strike-slip and normal faulting, respectively, while black line shows b-value of all events. ........................................24 vii 1.5 Ternary plots showing faulting type distribution vs. depth for the three focus areas. The P, T and B sides represent normalized plunge angles of the maximum, minimum and intermediate compressional stresses, respectively. Red circles show events with circle size denoting the earthquake magnitude. ..........................................................25 1.6 Ternary plots showing faulting type distribution vs. depth for the three focus areas. The P, T and B sides represent normalized plunge angles of the maximum, minimum and intermediate compressional stresses, respectively. Red circles show events with circle size denoting the earthquake magnitude. ..........................................................29 1.7 Same as Figure 1.6 for the Hot Springs area. .............................................................30 1.8 Same as Figure 1.6 for the Trifurcation area. .............................................................31 1.9 Variations of (a) seismicity rate, (b) S Hmax orientation, (c) plunges of principal stress orientations and (d) stress ratios through depth in the three focus areas for the period 2000-2009. The three rows display the results from the CH, HS and TR areas, respectively. Purple and blue bars in the left panels show seismicity rates from the entire and declustered catalogs, respectively. Black arrows indicate the depth interval with enough data for analysis of the stress field orientation. In (b), S Hmax values show the angle between the S Hmax direction and the main fault strike direction of N55°W. In (c), plunges of principal stresses are color coded with red, green and blue as maximum, intermediate and minimum principal stresses, respectively. The median values of derived parameters from different grid cells within given depth intervals are shown in (b, c, d) with colored dots and error bars mark the 90% confidence interval. ......................................................................................................................................39 1.10 Variation of differences between (a) maximum horizontal compressional stress and viii strain, (b) plunges of principal stress and strain tensors, (c) stress and strain ratio, and (d) minimum rotation (Kagan) angle between the stress and strain tensors through the depth in the CH, HS and TR areas. At all depth sections, median values are marked with circles and the error bars show 90% confidence interval. Differences in the plunges of principal stresses in (b) are color coded as in Figure 1.9. .........................34 1.11 Temporal changes of stress ratios (left) and S Hmax (right) in the TR area between 6 and 9 km depth using focal mechanisms from 2 years before the EMC earthquake (top panels) and 2 years after the event (bottom panels). The symbols and notations are the same as in Figure 1.6. ......................................................................................36 1.12 Variations of stress ratio (left) and S Hmax (right) with depth in the TR area using data 2 years before (top panels) and 2 year after (bottom panels) the EMC earthquake. Color circles and error bars denote the same as in Figure 1.9. ...................................37 2.1 Distribution of declustered seismicity with focal mechanisms in the selected region in Southern California, between 1981 to 2017 used for the stress inversion. Each event is color-coded with its hypocentral depth. The brown rectangle denotes a selected region around the South Central Transverse Ranges (SCTR). The yellow squares show focused regions of study, Cajon Pass (CP), and San Gorgonio Pass (SGP). Faults are marked in black lines. Stars show events larger than magnitude 6 in the region during the selected time period. SCTR and yellow text in the figure shows regions of study, while black text defines geology of the area. (SGM: San Gabriel Mountains; SBM: San Bernardino Mountains; SJM: San Jacinto Mountains; CH: Crafton Hills; HS: Hot Springs). .................................................................................49 2.2 Distribution of declustered seismicity with focal mechanisms in the selected region in ix Southern California, between 1981 to 2017 used for the stress inversion. Each event is color-coded with its hypocentral depth. The brown rectangle denotes a selected region around the South Central Transverse Ranges (SCTR). The yellow squares show focused regions of study, Cajon Pass (CP), and San Gorgonio Pass (SGP). Faults are marked in black lines. Stars show events larger than magnitude 6 in the region during the selected time period. SCTR and yellow text in the figure shows regions of study, while black text defines geology of the area. (SGM: San Gabriel Mountains; SBM: San Bernardino Mountains; SJM: San Jacinto Mountains; CH: Crafton Hills; HS: Hot Springs). .................................................................................50 2.3 Regional distribution of the maximum horizontal compressional stress orientations (S Hmax ) at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. The orientations are color-coded in red, green, blue, and brown denoting reverse, strike-slip, normal and oblique faulting, respectively. Purple dashed lines indicate the used Voronoi cells. WTR: West Transverse Ranges; SGM: San Gabriel Mountains; CP: Cajon Pass; CH: Crafton Hills; SJM: San Jacinto Mountains; SGP: San Gorgonio Pass; SBM: San Bernardino Mountains; ECSZ: Eastern California Shear Zone. .................................................................................................................57 2.4 Regional seismicity distribution color-coded with values of the stress ratio R at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. In a strike- slip faulting environment, R-values around 0.5, 0 and 1 indicate pure strike-slip, transtensional and transpressional stress regimes, respectively. Purple dashed lines indicate the used Voronoi cells. ..................................................................................58 x 2.5 Distribution of the maximum horizontal compressional stress orientations (S Hmax ) in fan symbols and the principal stress orientations (Stereonets) in the selected region around SCTR at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. The maximum, intermediate and minimum principal stresses in the stereonets are indicated with red, green, and blue, respectively. Purple dashed lines indicate the used Voronoi cells. CP and SGP shown in pink rectangles. ...................59 2.6 Distribution of the maximum horizontal compressional stress orientations (S Hmax ) in fan symbols and the principal stress orientations (Stereonets) in the selected region around SCTR at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. The maximum, intermediate and minimum principal stresses in the stereonets are indicated with red, green, and blue, respectively. Purple dashed lines indicate the used Voronoi cells. CP and SGP shown in pink rectangles. ...................60 2.7 Distribution of the maximum horizontal compressional stress orientations (S Hmax ) in fan symbols and the principal stress orientations (Stereonets) in the selected region around SCTR at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. The maximum, intermediate and minimum principal stresses in the stereonets are indicated with red, green, and blue, respectively. Purple dashed lines indicate the used Voronoi cells. CP and SGP shown in pink rectangles. ...................62 3.1 A schematic representation of the block model, initial stress distribution, boundary conditions and far field loading applied on the model. ...............................................72 xi 3.2 A schematic representation of the cross section perpendicular to the fault surface of the models changing in the rheology of the BDT zone. .............................................73 3.3 Shear traction variation on the fault surface at selected depths (a). Snapshots of depth variations of the fault slip (b) and the shear stress (c) in the direction parallel to the fault surface in the points from the middle of the fault. The time interval between lines are 10 years. ........................................................................................................75 xii Abstract Knowledge of the state of stress in the brittle crust is crucial to understand fault mechanics, crustal deformations, and further to assess the potential for large earthquakes. I estimate and examine the spatiotemporal background stress field variations in selected regions in Southern California with higher seismicity rates and geological complexities, including the South Central Transverse Ranges (SCTR) and the San Jacinto Fault Zone (SJFZ). The analysis employs the refined stress inversion methodology and the available seismicity catalog of the region including focal mechanisms for the past ~40 years. The background stress field is compared with the stress field obtained from the aftershock focal mechanisms to provide information on the local dominant stress field. Background stress field analysis is generally consistent with previous studies showing that strike-slip faulting is the main faulting type in the study area. Detailed examinations indicate deviations towards transpressional and transtensional stress regimes and rotations in the principal stress orientations as follows. Along the SJFZ, principal stress plunges and the S Hmax trend rotates significantly with depth. These rotations are maximized below ~9 km along SJFZ, near the depth section with the highest seismicity rate and inferred brittle- ductile transition zone. The Crafton Hills area, located in the northwest of the SJFZ, shows the largest rotation of the S Hmax direction (~23º). Together with the increased transtensional stress regime below ~9 km, and lower estimated apparent friction coefficient, the Crafton Hills area is suggested to be a weak fault associated with a deep creep. Mountain ranges near the Cajon Pass, San Gorgonio Pass, and the Hot Springs area indicate higher transpressional stress components that are likely associated with elevated topography. The temporal background stress field variation near the SCTR does xiii not show any significant changes from the average background stress field of the past 37 years. The 2010 Mw 7.2 El Mayor–Cucapah (EMC) event also does not show any implied large-scale background stress rotation along the SJFZ. The only observed temporal background stress field variation is across the time of the EMC earthquake, showing an increase in the stress ratio towards a higher transpressional stress regime after this event near the Trifurcation area. The increase in the stress ratio has potentially resulted from the nearby M w 5.4 event or aseismic slip. In future studies, to improve the spatiotemporal variations of the stress field and giving an insight to hazard analysis, enhancing the incorporated modeling tools and integrating the seismic and geodetic observation are suggested. 1 Introduction The state of stress in the crust and within fault-systems is a fundamental component of tectonic interactions and earthquake fault processes. Estimation of the stress field is possible based on inverting the focal mechanism measurements from the recorded seismic ground motions, which directly addresses coseismic stress field in the seismogenic crust. Recently, with enhancements in seismic data acquisition, analysis methods, and computational capabilities, it is possible to estimate the high-resolution spatiotemporal variations of the crustal stress field. In this study, the spatiotemporal changes in the background stress field are analyzed in selected areas in Southern California, and its correlations with fault and crustal structures are addressed with the goal of understanding the tectonic components affecting the background stress field in the brittle crust. Knowledge of the state of stress in a region together with the ingredients affecting the stress field will help in forecasting seismic probabilities and potential large events. Southern California is overdue for large earthquakes that pose a significant hazard for urban nearby areas (Lozos, 2016; Rockwell et al., 2015; Onderdonk et al., 2013) and is an ideal location for the detailed stress analysis. This region is exceptionally well instrumented and contains a rich moderate size earthquake catalog (2<Mw<5). Seismic data recorded at Southern California Earthquake Data Center (SCEDC) provides catalogs of relocated earthquakes with available fault-plane solutions for the past ~40 years. This region also contains a range of geological structures including complex faulting systems near the San Jacinto Fault Zone (SJFZ), San Andreas Fault (SAF), the junction of the SJFZ and SAF, South Central Transverse Ranges (SCTR), and elevated mountains such 2 as San Gorgonio Mountains. Finally, the nearby-recorded large event of 2010 Mw 7.2 El Mayor-Cucapah (EMC) makes Southern California a unique region to study. In this study, I focus to examine the background state of stress in the best spatial (up to ~2 km) scale near SJFZ and SCTR and analyze the effects of the EMC event on the background stress field along the SJFZ. Previous studies analyze stress field inverting focal mechanisms to compute for the stress tensor orientation and the stress ratio in Southern California (e.g., Jones, 1988; Hardebeck and Hauksson, 2001; Townend and Zoback, 2001; Yang and Hauksson, 2013). These studies have analyzed the stress field in coarse spatial scales and provide regional stress variations in Southern California. They have employed non-declustered seismicity catalog and as a result, the recovered stress field combines background stress field with local stress transfers from the aftershocks. Detailed information on background stress studies on the study areas are discussed in each chapter separately. Moreover, the changes of the stress field through the seismogenic depth have been studied (e.g., Bokelmann and Beroza, 2000; Hardebeck and Hauksson, 2001). Hardebeck and Hauksson (2001) using larger spatial scales indicated that stress field orientation is generally consistent through the seismogenic depth. Bokelmann and Beroza (2000) studied the changes of focal mechanisms with depth in Northern California and inferred the existence of a weaker lower crustal layer in the bottom of the seismogenic zone. Occurrence of large earthquakes (e.g., M > 6.5) causes spatiotemporal stress perturbations on the scale of the seismogenic zone (e.g., Ben-Zion, 2008; Hauksson, 1994; Hauksson et al., 2011; Meng and Peng, 2014) that may lead to local rotations of the stress field (e.g., Hardebeck and Hauksson, 2001; Wesson and Boyd, 2007). This rotation 3 in the stress field has been observed prior to and after the 1992 Mw 7.2 Landers earthquake near Landers main fault trace (Hardebeck and Hauksson, 2001). In collaborative research, we developed a refined stress inversion methodology (Martínez-Garzón et al., 2016a), which analyzes the stress field in higher spatial resolution up to ~2km (the resolution might change based on the seismicity rate in the specified study area). Implying the new technique and using the focal mechanism catalog including improved earthquake focal mechanisms and a larger number of mechanisms compared to previous studies allow estimating the stress field at a finer resolution. The refinements also include employing declustered seismicity, which separates the stress transfer generated by the background tectonic loading. Chapter 1 discusses the background stress field within SJFZ and specifically in Crafton Hills (CH), Hot Springs (HS) and Trifurcation (TR) area. This chapter is focused on the variations of the stress field within the seismogenic depths. It demonstrates that in the potential region for brittle-ductile transition zone, below ~9 km, the principal stress plunges rotate up to 40º, where, as well, maintains the highest seismicity rates (Abolfathian et al., 2019). The associated b-values and coseismic strain field is estimated and is consistent with the variations in the background stress field. At the end of this chapter, the temporal stress variations before and after the 2010 Mw 7.2 El Mayor- Cucapah (EMC) earthquake near the SJFZ, located more than 200 km distance from the EMC epicenter were examined. The results did not show any significant rotation of the stress orientation in this area, but the stress ratios, move toward the transpressional stress regime after the EMC event. In Chapter 2, the background stress field in SCTR is analyzed. This region includes 4 areas near Cajon Pass (CP) and San Gorgonio Pass (SGP) that comprises regions with elevated topography (Abolfathian et al., in review). The stress field using the aftershock mechanisms in the SCTR is estimated independently and compared with the stress field results obtained from the declustered catalog. This comparison gives a better understanding from the main tectonic loading in the SCTR. This chapter discusses the importance of the geological structures such as mountains implying higher transpressional stress field and fault-system interactions implying rotations in the stress field. To better interpret stress inversion results, quasi-static numerical simulations of strike-slip faulting in several crustal structures are performed. The simulations employ the finite element software for solving the partial differential equations describing the tectonic deformation (Chapter 3). The analysis attempts to describe the extent that the rheology of the crustal layers affects the orientation of the stress tensor with depth (Abolfathian et al., in prep). Following these chapters is a discussion combining all the results together and indicating a summary of the relation between the three-dimensional spatial and temporal stress variations with geological structures and seismicity variations in Southern California. Finally, I will conclude with potential direction for future study within this area of research. 5 1. Spatio-temporal variations of stress and strain parameters in the San Jacinto fault zone (Abolfathian et al., 2019) 1.1 Introduction Crustal deformation has multiple components including elastic strain that accumulates in interseismic periods between large events, inelastic strain increments associated with seismic failures of ongoing seismicity, aseismic slip on some fault sections and viscoelastic failure near and below the brittle-ductile transition depth. Knowledge on the stress and strain distributions in the seismogenic crust is important for understanding the mechanics of faulting (e.g., Scholz, 2002) and related slip patterns (Twiss and Unruh, 1998). Occurrence of large earthquakes (e.g., M > 6.5) causes spatio- temporal stress perturbations on a scale of the seismogenic zone (e.g., Ben-Zion, 2008; Hauksson et al., 2011; Meng and Peng 2014) that may lead to local rotations of the stress field (e.g., Hardebeck and Hauksson, 2001; Wesson and Boyd, 2007). With the ongoing densification of seismic instrumentation, larger seismicity catalogs and improved earthquake focal mechanisms are accessible and allow analyses of stress and strain parameters of fault zone regions in finer resolution. The San Jacinto fault zone (SJFZ) is a major component of the plate-boundary in southern California. It is oriented sub-parallel to the San Andreas fault and is currently the most seismically active fault zone in southern California (e.g., Hauksson et al., 2012; Ross et al., 2017a). The SJFZ accommodates a large proportion of the plate motion with slip rates of up to 21 mm/yr (Fialko, 2006). Paleoseismic and historic records indicate that the SJFZ is capable of large (M W > 7.0) earthquakes (e.g., Petersen and Wesnousky, 1994; Rockwell et al., 2015), and has the potential to rupture the entire length of the fault 6 zone in a single event (e.g., Salisbury et al., 2012; Onderdonk et al., 2013). The last through-going event probably occurred on November 22, 1800 (Salisbury et al., 2012) and the average recurrence time for such events is estimated to be 257±79 years (Rockwell et al., 2015). The SJFZ has complex geometry and high diversity of velocity structures and seismicity patterns (e.g., Allam et al., 2014; Cheng et al., 2018). During the era of highly dense seismic sensors (i.e., after year 2000), the SJFZ has not hosted any earthquake with M >~5.5. However, the 2010 Mw 7.2 El Mayor-Cucapah (EMC) earthquake ruptured the southern continuation of the Elsinore fault in Baja California and increased the seismicity rates across most of southern California including the SJFZ (Hauksson et al., 2011; Meng and Peng, 2014). In this study, we employ >14,500 earthquake double-couple focal mechanisms (Yang et al., 2012) to derive high-resolution distributions of stress and coseismic strain parameters (i.e., orientation of principal axes and stress/strain ratios) around sections of the SJFZ. The stress inversions employ the improved methodology of Martínez-Garzón et al. (2016a) where (1) the initial seismicity catalog is declustered to minimize stress interaction between events, (2) an optimum number of events to be inverted is selected based on the uncertainties of the input data, and (3) the analyzed region is objectively discretized into small sub-domains using an optimized k-means algorithm. The stress inversion is then refined by merging the damped least squares algorithm (Hardebeck and Michael, 2006) with the iterative stress inversion refinement based on the fault instability coefficient (Vavryčuk, 2014). The inversion results provide the principal stress orientations and the stress ratio R=(σ 1 −σ 2 )/(σ 1 −σ 3 ) . The elastic properties of rocks in a given spatio-temporal domain provide links between the stress and strain fields. 7 Information on the inelastic strain tensor can be derived from calculating and stacking potency tensors of different earthquakes occurring within a region (e.g., Amelung and King, 1997; Bailey et al., 2009; 2010). The advantage of seismic potency with respect to seismic moment is that the former does not depend on the shear modulus, which is poorly defined across faults and earthquake source volumes (Ben-Zion, 2003). Previous studies analyzed the stress field orientation in southern California utilizing focal mechanisms (e. g. Jones, 1988; Hardebeck and Hauksson, 2001; Townend and Zoback, 2001; 2004; Yang and Hauksson, 2013). These studies analyzed relatively large regions with a coarse spatial resolution. They also employed non-declustered seismicity catalogs, and thus the recovered stress results represent a mixture of the background stress field and stress transfers generating aftershocks. The stress field orientation was found to be generally consistent with depth (e.g., Zoback, 1992; Hardebeck and Hauksson, 2001). However, rheological conditions may differ at some places resulting in local stress variations with depth. For example, Bokelmann and Beroza, (2000) observed rotations of focal mechanisms at the bottom of the seismogenic zone in northern California, suggesting the existence of a weak lower crust layer. Hardebeck and Hauksson (2001) analyzed stress changes prior to and after the 1992 Mw 7.2 Landers earthquake in southern California, and concluded that the stress field rotated near the main fault trace. Ross and Ben-Zion (2013) observed temporal variations of rotation angles between mechanisms of aftershocks of the 1992 Landers earthquake that may contributed to the inferred rotation of the stress field. Bailey et al. (2009; 2010) analyzed coseismic strain fields around several major faults in southern California including the 8 SJFZ. They concluded that properties of the coseismic strain field are controlled primarily by geometrical properties of the faults and plate motion. In the current work we derive stress and coseismic strain fields around the SJFZ at greater resolution than previous studies. We also estimate the brittle-ductile transition depth at different fault sections from depth variations of the b-values of Gutenberg- Richter statistics (e.g., Amitrano, 2003; Spada et al., 2013) and compare the results with derived parameters of the stress field. In addition, we investigate how the occurrence of the 2010 EMC earthquake in Baja California affected the background stress field in the SJFZ region (~200 km away). Our main goals are (1) to resolve the stress field orientation along and across the fault through the seismogenic thickness, (2) to validate the obtained stress results by investigating the consistency between deviatoric stress and strain tensors, and (3) evaluate the impact of a M ≈ 7 regional earthquake at a large distance (~200 km) on the stress field parameters. The subsequent sections are organized as follows. Section 1.2 describes the utilized data, selected regions of interest and catalog processing. Section 1.3 gives a summary of the employed methodologies to calculate the distribution of deviatoric stress and inelastic strain tensors. Section 1.4 describes the results obtained from the various performed analyses. Sections 1.5 and 1.6 provide a discussion of the results and main conclusions of the study. 1.2 Study area and data We utilize earthquake data recorded in years 2000 to 2012 in the region around the SJFZ in southern California (Figure 1.1). This time interval is selected because it is associated with relatively high density of stations and recorded earthquakes. Event hypocenters are taken from the relocated earthquake catalog of Hauksson et al. (2012), 9 where 90% of horizontal and vertical errors are smaller than 0.75 km and 1.25 km, respectively. Double-couple focal mechanisms with qualities ranging from A to D are taken from the catalog of Yang et al. (2012), including fault plane uncertainties between 5 and 55 degrees with a median value of 31 degree. Larger background seismicity rates on the fault are found in the depth range 9-15 km, but the distribution of hypocenter locations and seismicity rates vary considerably along the SJFZ. The catalog is declustered using the nearest-neighbor distance method of Zaliapin and Ben-Zion (2013) to minimize effects of local earthquake interactions and reflect the large-scale background stress field (e.g., Martínez-Garzón et al., 2016a). This is done by detecting clusters of seismicity without magnitude dependence (i.e., considering only inter event times and distances), using hypocentral locations for distances, and retaining only the largest event in each cluster. The declustered events are referred to in the text also as background seismicity. From more than 26,000 earthquakes with calculated focal mechanisms around the SJFZ in the initial catalog between the years 2000 and 2012, the declustered catalog contains 14,543 events with focal mechanisms. Figure 1.1 shows the locations of the declustered events used in the analyses of stress and strain fields along with the main faults in the area. The thickness of the seismogenic crust is often defined from seismicity as the depth above which 90% of the events occurs. At the SJFZ, the seismogenic thickness decreases toward the southeast (Figure 1.1b), likely because of the increasing heat flow in this direction (Doser and Kanamori, 1986). Three regions with dense seismicity are selected (Figure 1.1) as focus study areas: (1) Crafton Hills (CH), (2) Hot Springs (HS) and (3) Trifurcation area (TR). The three selected regions have different background seismicity 10 rates, fault structural complexity, seismogenic thickness and topography (Table 1.1). The CH region in the northwestern portion of the SJFZ contains the Crafton Hills fault zone. The main SJFZ is intersected in this region with orthogonal faults accommodating some normal faulting. It has a background seismicity rate of ~3.2 events per year per km along the fault and a seismogenic thickness of ~17.4 km. The HS region is located in the central part of the SJFZ and northwest of Anza. This region has the highest background seismicity rate of ~8.2 km -1 yr -1 among the study areas and a seismogenic thickness of ~17.5 km. The TR region located southeast of Anza displays the largest structural complexity, with three main fault branches as well as smaller orthogonal faults and seismicity lineation (e.g., Ross et al., 2017a; Cheng et al., 2018). It has a background seismicity rate of 6.85 km -1 yr -1 and seismogenic thickness of ~13.7 km (~4 km shallower than the other two areas). The topography of these regions is variable and includes areas adjacent to the San Jacinto and Santa Rosa Mountains, with the highest elevations at the Hot Springs fault (the northern fault strand in the HS) and the Buck Ridge fault (the northern fault strand in the TR). Inbal et al. (2017) suggested that the EMC event and a following Mw5.4 Collins Valley earthquake in the TR area produced transient aseismic slip in the HS and TR regions. First, we analyze the distribution of stress parameters along the SJFZ (section 1.4.1). This is done by using 10,827 background events that occurred during the years 2000- 2009 to suppress potential transient effects associated with the 2010 Mw 7.2 EMC earthquake in Baja California. Then, we describe the distribution of faulting styles, b- values and variations of stress and strain parameters through the seismogenic thickness using the same dataset (sections 1.4.2, 1.4.3 and 1.4.4). Finally, we investigate spatio- 11 temporal changes of stress parameters in relation to the EMC earthquake (Section 1.4.5). For this purpose, we select events from approximately two years prior to the EMC earthquake, from January 2008 to December 2009, and two years following the EMC event from October 2010 to December 2012. These two data subsets have 2901 and 2429 declustered events with focal mechanisms, respectively. Table 1.1 Average seismic and stress parameters for the SJFZ, CH, HS and TR areas, estimated based on the 2000-2009 declustered seismicity. The angle θ is the angle between S Hmax and main fault strike direction (N55°W). Seismogenic Thickness * (km) Seismicity Rate (km -1 .yr -1 ) Stress Ratio S Hmax θ SJFZ 16.7 ~4 0.50±0.10 5°±4.0° 60°±4.0° CH 17.5 ~3.2 0.20±0.10 18°±5.5° 73°±5.5° HS 17.4 ~8.2 0.59±0.08 10°±2.5° 65°±2.5° TR 13.7 ~6.85 0.48±0.08 0°±3.5° 55°±3.5° 12 Figure 1.1 (a) Spatial distribution of seismicity in the San Jacinto fault zone (SJFZ) used in the study. Declustered earthquakes from 2000 to 2012 are shown in purple circles. Red rectangles denote three focus study areas, Crafton Hills (CH), Hot Springs (HS) and Trifurcation area (TR). Black lines indicate mapped surface traces of the SJFZ, San Andrea fault (SAF) and Elsinore fault (EF). The upper right inset shows the study area in a larger scale (southern California) view. The red star marks the epicenter of the 2010 M W 7.2 El Mayor-Cucapah Earthquake. (b) Distribution of seismicity with depth along the SJFZ (Profile A-A’). Red rectangles mark depth sections of the three focus areas. 13 1.3 Methodology 1.3.1 Stress tensor inversion of focal mechanisms The formal stress inversion utilizes double-couple earthquake focal mechanisms to estimate the orientations of the three principal stresses σ 1 , σ 2 and σ 3 (from most to least compressive) and the stress ratio, R, defined as R= σ 1 −σ 2 σ 1 −σ 3 (1.1) The stress ratio, R, has values between 0 and 1. In strike-slip stress regime, larger stress ratios correspond to a stress regime closer to transpression (i.e., mixed strike-slip and reverse faulting), while smaller stress ratios represent a transition toward a transtensional stress field (i.e., mixed strike-slip and normal faulting). The majority of stress inversion techniques are based on the following assumptions: (1) The stress field is homogeneous within a considered rock volume. (2) Earthquakes occur on pre-existing faults with varying orientations. (3) Slip on each fault occurs parallel to the direction of tangential traction (Wallace, 1951; Bott, 1959). This is equivalent to assume that at the time that an earthquake occurs, the stress and strain fields are consistent. The stress inversion further assumes that the seismicity is driven by the background tectonic stress and not by the stress interaction between the seismicity. For that reason, we decluster the seismicity catalog to only consider the background seismicity (see Martínez-Garzón et al., 2016a). Using the refined methodology of Martínez-Garzón et al. (2016a), we invert the focal mechanisms of the background seismicity for spatial and temporal variations of the stress field in the SJFZ region. The analysis employs the MSATSI software (Martínez-Garzón et al., 2014), which is an 14 updated version from SATSI algorithm (Michael, 1984; Hardebeck and Michael, 2006), applying a linear damped stress inversion to the earthquake focal mechanisms. Uncertainty assessments of 95% confidence intervals are done by bootstrap resampling of the original set of focal mechanisms (Michael, 1987). The resulting stress field orientation is classified according to the three Andersonian stress regimes - normal, strike-slip and reverse - based on the trend and plunges of the principal stresses (Zoback, 1992). From the orientation of the principal stress axes, the orientation of maximum horizontal compressional stress, S Hmax , is computed following Lund and Townend (2007). The stress inversion selects one of the two available fault planes from each source mechanism solution. Considering the fault plane ambiguity, previous studies show that the choice of the main fault plane does not affect the estimation of the principal stress orientation (Michael, 1984; Vavryčuk, 2015), but can affect the resolution of the stress ratio. The linear inversion procedure of Michael, (1984; 1987) selects one of the nodal planes randomly. Another approach is to use an iterative procedure. In each iteration, the stress field orientation is calculated and the fault plane with the largest instability coefficient I is selected for the next iteration (Vavryčuk, 2011; 2014; Martínez-Garzón et al., 2016b). The parameter I is defined as I = τ−µ(σ −1) µ+ 1+µ 2 , (1.2) where µ is the apparent coefficient of friction and τ and σ are scaled shear and normal stresses, respectively. The values of I range between 0 and 1 indicating the least and most optimally oriented faults to failure within the given deviatoric stress field, respectively. When evaluating the fault instability, a grid search is applied over values of µ ranging 15 between 0.2 and 0.8 and the value that produces the highest overall instability for the inverted data is selected (Vavryčuk, 2014). As this is selected in relation to the inversions, we call it an apparent coefficient of friction. Stress inversion methods cannot constrain the stress orientation of a region with a single focal mechanism (McKenzie, 1969), and a minimum number of focal mechanisms is required to invert for stress parameters. Synthetic tests with focal mechanisms having realistic uncertainties are performed to estimate how many focal mechanisms are needed to retrieve the stress field orientation with an accuracy of ±10° (Martínez-Garzón et al., 2016a). Based on these tests, ~60 events are the optimum in a strike-slip regime to converge on a stable stress tensor. In this analysis, the study volume is discretized into Voronoi cells containing the minimum number of events required for stable inversion. The Voronoi cells are implemented using the k-means technique (Hartigan and Wong, 1979; Seber, 1984; Martínez-Garzón et al., 2016a). The Voronoi cell sizes vary in relation to the density of seismicity and provide estimates for the spatial resolution of the inversion. In this study, the grid cells have dimensions in the range of ~1 to 5 km as an approximate radius of the grid cells. Therefore, the present study aims to resolve the stress field in the SJFZ region with a finer discretization than previous studies (e.g., Jones, 1988; Hardebeck and Hauksson, 2001; Yang and Hauksson, 2013), which investigated spatial changes of stress parameters in southern California with a variable resolution between 5 and 20 km and larger. 1.3.2 Coseismic strain parameters from focal mechanisms Unlike the estimation of the stress field, the estimation of the coseismic (i.e., inelastic) strain field does not require a formal inversion. The inelastic strain tensor in the 16 faulting region defines the seismic potency density tensor per unit volume: P ij = d ij P dV V ∫ , (1.3) where d P is the inelastic strain tensor, V is the source volume and subscripts i and j denote the three Cartesian directions (Ben-Zion, 2003; 2008). The tensor P ij is directly related to the strike, dip and rake of the source mechanisms of each event. The orientation of the principal strain axes, ˆ d 1 > ˆ d 2 > ˆ d 3 d ! > d ! > d ! , can be calculated from the normalized sum of earthquake potencies, ˆ P ij SM , in each of the grid cells (Bailey et al., 2009) using P ij SM = P ij (k) k=1 N ∑ , (1.4) where N is the number of all earthquakes per grid cell, and ˆ P ij SM = P ij SM P ij SM P !" !" = P !" !" P !" !" (1.5) The use of normalized potencies equally distributes the effects of all events on the computed strain quantities and eliminates dominance of the largest events. The principal strain orientations are used to estimate a strain ratio parameter, D, defined as (Twiss and Unruh, 1998): D= ˆ d 1 − ˆ d 2 ˆ d 1 − ˆ d 3 (1.6) This parameter is a scalar invariant of the strain tensor related to the shape of the strain ellipsoid, and it is analogous to the stress ratio, R, defined in the previous section. 17 The orientation of maximum horizontal compressional strain, D Hmax , is estimated following Lund and Townend (2007). The calculations of the potency and strain tensors require choosing one of the two possible fault planes in the earthquake focal mechanism. As done in the stress analysis, the strain tensor is calculated for each focal mechanism using the fault plane with the highest instability coefficient. 1.3.3 Estimation of magnitude of completeness and b-values The b-value of the frequency-magnitude distribution has often been used as an indicator of the differential stress level (Scholz, 2015) as well as the fault damage (Amitrano, 2003). Here, the magnitude of completeness M c and b-values of the Gutenberg-Richter statistics of earthquakes are estimated using the goodness of fit method (Wiemer and Wyss, 2000). In each of the focus study areas, we calculate b-value changes with depth (from 3 to 18 km) by considering the entire declustered seismicity catalog within the analyzed time period (2000 to 2009) and dividing the seismicity into moving windows of 3 km depth bins. We also group the declustered seismicity in the different faulting styles (normal, reverse, strike-slip) to investigate how the different faulting styles may affect the magnitude-frequency distribution. Only bins containing 60 or more earthquakes with M>M c , and b-value error estimation of less than 0.1 are analyzed. 1.4 Results Applying the refined methodologies for stress inversion, coseismic strain estimation and b-values, we obtain detailed information on the background stress and coseismic strain fields in the San Jacinto fault zone. In the following, we first analyze the 18 distribution of stress parameters along the SJFZ. Then we describe the distribution of faulting styles, b-values and variations of stress and strain parameters for the three focused study regions (CH, HS, TR, see Table 1.1) through depth. Finally we investigate spatio-temporal changes of stress parameters in relation to the EMC earthquake. 1.4.1 Variations of stress parameters along the SJFZ The declustered catalog of 10,827 events distributed along the entire SJFZ, having focal mechanisms and occurring between the years 2000 to 2009, is discretized into 111 groups of seismicity (grid cells) containing between 60 and 110 focal mechanisms in each group. Focal mechanisms from each grid cell are inverted for the stress field orientation and stress ratio, R, following the methodology discussed in section 1.3.1. Figure 1.2 shows the distribution of maximum horizontal compressional stress (S Hmax ) in the entire SJFZ and the focus areas CH, HS and TR. As expected from the general tectonic setting and the previous larger-scale stress inversion study of Yang and Hauksson (2013), the main stress regime in the fault zone is strike-slip. Oblique faulting styles with a mixture of strike-slip and dip-slip deformation are prominent in the HS and CH, and in the northwest part of TR. The only region with a tendency towards transtension is CH that includes sub-volumes dominated by normal faulting. This can be explained in terms of extension associated with motion on both the SJFZ and the nearby San Andreas fault (Wesnousky, 1986; Jennings, 1994). Figure 1.3 presents inverted values of the stress ratio, R, along the different regions of the SJFZ. The stress ratio distributions are consistent with a main faulting style of strike-slip, superposed with some transtensional and transpressional components. In agreement with Figure 1.2, the main recovered stress regime in the CH area is transtensional (strike-slip and normal faulting), 19 while in HS area the obtained oblique faulting represents a transpressional environment (strike-slip and reverse faulting). The fine data discretization allows us to observe detailed changes of stress parameters along the fault zone. Table 1.1 lists the stress ratios and S Hmax values averaged across the entire depth range for the three focused areas. From the northwest to the southeast portions of the SJFZ, the median trend of S Hmax rotates by >15°. The angle between the S Hmax and the main fault trace is larger in the CH area than in the other two regions, suggesting that the CH portion of the SJFZ could be mechanically weaker. In agreement with this, the estimated apparent friction coefficients (Eq. 2) generated by the iterative inversion (Vavryčuk, 2014) are 0.45 for CH, 0.6 for HS and 0.55 for TR areas. We performed additional high-resolution inversions discretizing separately events that are within 1-2 km from the main faults, off-fault events with distance from the nearest major fault larger than 2 km, as well as events that are on the opposite sides of the SJFZ. These inversions show significant variations of stress ratios when a main fault is crossed (Figure S1.1), but there are no significant changes between on- and off-fault events. Additional results for different depth sections are described in section 1.4.3. 20 Figure 1.2 Maximum horizontal compressional stress orientations (S Hmax ) along the (a) SJFZ, (b) CH, (c) HS and (d) TR areas. The S Hmax orientations are color-coded with red, green, blue, and brown denote reverse, strike-slip, normal and oblique faulting, respectively. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. Purple dashed lines mark the Voronoi cells used in the analysis of seismicity. 21 Figure 1.3 Seismicity along the (a) SJFZ, (b) CH (c) HS and (d) TR areas, color-coded with values of the stress ratio R. Purple dashed lines mark the used Voronoi cells. In a strike-slip faulting environment, R-values around 0.5, 0 and 1 indicate pure strike-slip, transtension and transpression, respectively. 22 1.4.2 Seismicity parameters and faulting styles in the focused study areas For b-value estimation, the used seismicity is divided into moving windows of 3 km depth bins. This choice of depth bins is based on the distribution of events and the overall depth uncertainty (~1.25 km) of the hypocenter locations. Tables S1.1 to S1.3 list the magnitude of completeness M C and b-values of various subsets of the employed declustered seismicity (different depth sections and different faulting styles) in the selected study regions. Higher b-values represent relatively larger proportions of lower magnitude events. The HS area displays the lowest average b-value of ~0.72, while the CH and TR areas have average b-values of ~0.95 and ~0.96. Numerical and laboratory experiments have shown that the b-value tends to decrease with increasing confining pressure (Amitrano, 2003). Spada et al. (2013) inferred that b- values in fault regions decreases in the seismogenic zone up to a given depth, considered to reflect the brittle-ductile transition, and then increases below that depth. Figure 1.4 presents variations of b-values with depth in the three focus study areas along the SJFZ. Among the three regions, only the TR area clearly displays a minimum b-value at a given depth. In this area the overall b-value distribution and the one related to the strike-slip events reach a minimum value at 7-10 km (black and green line in Figure 1.4c), suggesting that this may reflect the brittle-ductile transition depth. At CH, the b-value from all events as well as the one calculated only from normal faulting have minima at 11-14 km (black and blue line in Figure 1.4a), but the uncertainties imply that this is not significant. At HS, there is not enough seismicity shallower than 9-12 km depth section. The overall b-value shows two local minima at 10-13 km and at 12-15 km (black line in Figure 1.4b). In principle, either of these two minima could be associated to the brittle- 23 ductile transition. The ternary plots (Frohlich, 1992) in Figure 1.5 show the distribution of events with different sizes and faulting types within 3 km depth bins through the seismogenic thickness. In all focus study areas strike-slip faulting is seen to dominate in the shallow crust. However, in the HS area deeper than 9-12 km and the CH and TR regions deeper than 6-9 km there is substantial increase in the relative amount of dip-slip faulting. The changes in faulting style occur at similar depths where b-values show minima in the TR area. Comparing b-values associated with different faulting types, b-values related to normal faulting events are on average ~0.2 larger than for strike-slip events in CH and HS regions. Larger b-values related to normal faulting have been observed to be a common feature of the southern California catalog (Schorlemmer et al, 2005). These results indicate that the largest events in the CH and HS have strike-slip mechanisms, while normal faulting events tend to be associated with smaller events. This is not observed in the TR area, where the b-value distributions from strike-slip and normal faulting appear to closely overlap (Tables S1.1 to S1.3). 24 Figure 1.4 Variations of b-values with depth in the (a) CH, (b) HS, and (c) TR areas. Green and blue lines display b-values associated with strike-slip and normal faulting, respectively, while black line shows b-value of all events. 25 Figure 1.5 Ternary plots showing faulting type distribution vs. depth for the three focus areas. The P, T and B sides represent normalized plunge angles of the maximum, minimum and intermediate compressional stresses, respectively. Red circles show events with circle size denoting the earthquake magnitude. 26 1.4.3 Variations of stress parameters through the seismogenic thickness The dataset described in section 1.4.1 (10,827 background events with focal mechanisms for the years 2000-2009) is divided into 3 km bins in the depth range of 3 to 18 km. As mentioned, the choices of depth bins are based on the distribution of events and the overall depth uncertainty (~1.25 km) of the resolved hypocenter locations. The data at the different depth bins are discretized into Voronoi cells and inverted for the orientation of the principal stresses, S Hmax and the stress ratio in the three focus areas (Figures 1.6 to 1.8). The variation of the stress regime with depth appears to be different for each of the focus study areas. The CH area displays an overall transtensional regime (i.e., Figure 1.2b). At shallow depths, seismicity is driven by strike-slip stress regime, changing to normal and oblique faulting at deeper fault sections (Figure 1.6). In the CH area, events in the depth bins of 9-12 km and 12-15 km appear to be mostly located off-fault. However, in the deepest bin of 15-18 km, earthquakes are localized within the main trace of the SJFZ. In contrast, in the HS area the stress field orientation slightly changes towards transpression with depth (Figure 1.7). This may be the result of higher topography related to the San Jacinto Mountains (Fialko et al., 2005). The event locations at 12-15 km depth in the HS area appear more localized than for the same depth range at CH. Within the HS, seismicity in the 15-18 km section appears to be localized both on the Clark fault (main strand of the SJFZ) and also on Hot Springs fault in the northern section of HS region. In the TR area, strike-slip faulting is prevalent across the entire seismogenic zone. In the deepest section (12-15 km) the stress field includes a region with higher transpressional regime in the northern section adjacent to the Buck Ridge 27 fault and the high topography associated with Santa Rosa Mountains. The seismicity distribution changes significantly with depth (Figure 1.8). The seismicity in range 6-9 km covers both the mapped fault traces and the regions between (and also slightly outside) the main traces. With increasing depth the seismicity becomes more localized. The majority of seismicity in the depth range 12-15 km is bounded by the main fault traces. The event distributions with depth, median orientations of S Hmax , principal stress plunges and stress ratios in the three study areas are shown in Figure 1.9. The CH and HS areas have maximum background seismicity in the depth range 15-18 km, while region TR with thinner seismogenic zone has maximum seismicity at a shallower depth range of 9-15 km. In all regions, the peak background seismicity is located near the bottom of the seismogenic zone (Figure 1.9a). This can be explained by a strong gradient of slip and high stress concentration at this depth section, which, consequently, produce high rate of seismicity. A significant clockwise rotation in the S Hmax orientation is observed in the entire SJFZ from the depth range 3-6 km to 15-18 km, with an average rotation value of 13 degrees. The largest S Hmax rotation angle of about 23 degrees is observed for the CH region, where the largest S Hmax variation occurs close to the inferred brittle-ductile transition zone (below 11-14 km). At the TR region, a rotation of approximately 15 degrees is observed and appears to be uniformly distributed across all the sampled depths. Finally, at the HS area only a rotation of ~5 degrees is visible below 9 km, which is comparable to the uncertainty of the estimated S Hmax (Figure 1.9b). In all study regions, the stress at shallow depth sections follows Andersonian faulting showing a strike-slip regime with the intermediate principal stress axis oriented vertically and the other two horizontally (Figure 1.9c). However, below the estimated brittle-ductile 28 transition zone at each region, the results show mixed faulting regimes toward transtension or transpression. The principal stress plunges in all the areas rotate considerably below 9-12 km depth. This is in agreement with the observed increase in mixture of focal mechanisms in the ternary plots of Figure 1.5. It is noteworthy that the grid cells in the eastern part of CH, containing only events off the SJFZ in all depths, do not show variations in either S Hmax orientations or the principal stress plunges (Figure 1.6). The median stress ratios, R, in all regions also reflect variations of the stress field with depth. The stress ratio tends to first decrease with depth, reaching minima at 9-12 km and increasing at deeper sections (Figure 1.9d). The CH area has the lowest stress ratios (R< 0.5) among the focus study areas, consistent with a transtensional regime. The HS area has higher stress ratios than in the CH and TR regions, especially in the deepest section, consistent with a transpressional region. The TR area has stress ratios around 0.5 close to pure strike-slip faulting. The stress regime in TR changes only slightly with depth. The estimated instability coefficients of the employed fault planes in the stress inversions (Eq. 2) indicate that strike-slip (I ≥ 0.9) and normal faulting events are better oriented for failure than the reverse faulting events. 29 30 Figure 1.6 Distribution of stress parameters in the Crafton Hills area through depth sections of (a, b) 9 to 12 km, (c, d) 12 to 15 km, (e, f) 15 to 18 km. Left plots (a, c, e) indicate the stress ratio distributions while right plots (b, d, f) display the S Hmax orientations (fan symbols) and the principal stress orientations (stereonets) in the Voronoi cells (purple dashed lines). The colors of fan symbols denote different fault types. The maximum, intermediate and minimum principal stresses in the stereonets are indicated with red, green and blue, respectively. Figure 1.7 Same as Figure 1.6 for the Hot Springs area. 31 Figure 1.8 Same as Figure 1.6 for the Trifurcation area. 32 Figure 1.9 Variations of (a) seismicity rate, (b) S Hmax orientation, (c) plunges of principal stress orientations and (d) stress ratios through depth in the three focus areas for the period 2000-2009. The three rows display the results from the CH, HS and TR areas, respectively. Purple and blue bars in the left panels show seismicity rates from the entire and declustered catalogs, respectively. Black arrows indicate the depth interval with enough data for analysis of the stress field orientation. In (b), S Hmax values show the angle between the S Hmax direction and the main fault strike direction of N55°W. In (c), plunges of principal stresses are color coded with red, green and blue as maximum, intermediate and minimum principal stresses, respectively. The median values of derived parameters from different grid cells within given depth intervals are shown in (b, c, d) with colored dots and error bars mark the 90% confidence interval. 33 1.4.4 Variations of coseismic strain parameters through the seismogenic zone The dataset and Voronoi cell discretization described in section 1.4.3 are used to estimate the coseismic strain parameters: maximum horizontal compressional strain (D Hmax ), principal strain plunges and strain ratio, D (Eq. 5). The derived strain parameters for equivalent depth bins as for the stress analysis are in good agreement with corresponding stress parameters in each region (Figure S1.3). D Hmax shows the same rotations with depth as S Hmax , with the CH area displaying the largest rotation of ~24 degrees followed by the TR and HS areas with ~20 and ~8 degrees, respectively. The principal strain plunges vary with depth in all three regions, changing from pure strike- slip in the shallow crust to oblique faulting for deeper sections. The CH area displays a large rotation of maximum and intermediate principal strain axes below 6-9 km. In the HS area, all three principal strain plunges rotates below 9-12 km. The TR area has only a slight rotation in the plunges deeper than 9-12 km, but the variation is significant. The strain ratios show slight changes within seismogenic thickness, with changes mostly within the estimated uncertainty error and therefore not significant. To quantitatively compare the stress and strain results for same regions, the median of the minimum rotation angle (i.e., the Kagan angle) between the stress and strain tensors and median differences in each corresponding stress and strain parameter are analyzed (Figure 1.10). To be statistically comparable, we only compare results for depth sections including more than two grid cells. The estimated Kagan angle between stress and strain tensors in all areas and depth sections is less than 20 degrees. The differences between S Hmax and D Hmax are smaller than 5 degrees, and the differences in the principal stress and strain plunges are smaller than 10 degrees. The TR and CH areas have stress 34 and strain ratio parameters that differ by less than 0.1, while in the HS area the difference is less than 0.2. In summary, the results indicate high consistency between the recovered stress and strain parameters in regions with sufficient seismicity. Figure 1.10 Variation of differences between (a) maximum horizontal compressional stress and strain, (b) plunges of principal stress and strain tensors, (c) stress and strain ratio, and (d) minimum rotation (Kagan) angle between the stress and strain tensors through the depth in the CH, HS and TR areas. At all depth sections, median values are marked with circles and the error bars show 90% confidence interval. Differences in the plunges of principal stresses in (b) are color coded as in Figure 1.9. 35 1.4.5 Spatio-temporal variations of stress parameters Analyzing the entire catalog, rather than the declustered background seismicity as done here, can lead to apparent temporal changes of various inverted stress parameters across the time of the EMC event (Martínez-Garzón et al., 2016a). These changes are produced by internal stress variations associated with aftershocks and they do not reflect changes in the background stress field operating on the study areas. To examine possible temporal changes of the background stress in the TR, HS and CH study regions, we use data from approximately two years before and after the 2010 Mw 7.2 EMC earthquake (see section 1.2 for details). The data sets are divided in 3 km depth bins from 3 km to 18 km depth (Figure 1.11, Figures S1.4 to S1.10), discretized horizontally with Voronoi cells containing 60 to 110 events per cell, and inverted for stress parameters as discussed. The obtained principal stress axes before and after the EMC earthquake have generally consistent orientations in all the three focus areas and for all depth sections. The changes in S Hmax after the EMC event (3 degrees) are smaller than the uncertainties and hence insignificant (Figure S1.11 and S1.12). However, stress ratios show a significant increase after the EMC event at specific regions. The maximum variation of stress ratio is at 6-9 km depth in the TR area, increasing from a median value of 0.52 before the EMC event to 0.79 afterward. This changes the local stress regime from strike- slip toward transpressional (Figure 1.11 and 1.12). It should be noted that the largest event in the period 2008-2012, the Mw5.43 Collins Valley earthquake with a strike-slip focal mechanism, occurred in the TR area on 7 th July 2010 at depth ~12 km. Hauksson et al. (2011) and Meng and Peng (2014) estimated a positive Coulomb stress change of ~10kPa from the EMC earthquake near the TR area, and noted increase in seismicity 36 along the SJFZ that is consistent with both dynamic and static stress increase from the EMC event. The observed stress variations in the TR can be produced in part by the positive Coulomb stress transfer from the EMC, along with changes generated by the Mw5.4 Collins Valley earthquake and triggered moderate events and aseismic slip northwest of the EMC rupture (Ross et al., 2017b) and along the SJFZ (Inbal et al., 2017). 37 Figure 1.11 Temporal changes of stress ratios (left) and S Hmax (right) in the TR area between 6 and 9 km depth using focal mechanisms from 2 years before the EMC earthquake (top panels) and 2 years after the event (bottom panels). The symbols and notations are the same as in Figure 1.6. Figure 1.12 Variations of stress ratio (left) and S Hmax (right) with depth in the TR area using data 2 years before (top panels) and 2 year after (bottom panels) the EMC earthquake. Color circles and error bars denote the same as in Figure 1.9. 38 1.5 Discussion This study aims to characterize spatio-temporal variations of crustal stress and strain in the San Jacinto fault zone region and to clarify the main sources of stress-strain variations. We examine data from the entire SJFZ and look in detail at three focus areas (CH, HS, TR) associated with abundant seismicity (Figure 1.1). The derived quantities include stress inversion results along the main fault and depth sections in the focus areas, direct analysis of coseismic strain (based on earthquake potency tensors) and calculations of frequency-size event statistics. In the following, we discuss some of the most important results and elaborate on their implications. The finer selection of grid cell distribution, and improved data preprocessing (Martínez-Garzón et al., 2016a) lead to higher resolution of our results on stress parameters in the SJFZ than the earlier study of Yang and Hauksson (2013) in the same region. The results from Yang and Hauksson (2013) show primarily strike-slip regime along the SJFZ, with a few grid cells displaying tensional stress regime adjacent to the CH area. Our results indicate strike-slip as the main faulting type in the focus study areas, superposed with some variations. The stress ratios show a transtensional stress field near the CH area, which can be associated with an extensional region adjacent to the San Andreas and San Jacinto fault intersection. The stress ratios in the HS area indicate a transpressional stress environment, which may be the result of higher topography involving the San Jacinto Mountains in the northern section of the HS area closer to the Buck Ridge fault (Fialko et al., 2005). The TR area is in general consistent with a strike- slip stress regime (Figure 1.3, Table 1.1). The recovered S Hmax orientation is mostly in NNE-SSW (Figure 1.2), in agreement with Yang and Hauksson (2013). 39 The apparent coefficient of friction is estimated for each of the analyzed regions, as a by-product of the stress tensor inversion. The CH area displays the smallest average apparent coefficient of friction (~0.45) among the three study areas. This region also displays the largest angle between the maximum horizontal compressional stress and the main fault trace. These observations suggest that the CH area may have a weaker crust than the other two focus study areas (Table 1.1). The employed stress inversion methodology selects the fault plane best oriented for failure out of each focal mechanism (Vavryčuk, 2014). Focal mechanism heterogeneity has been observed to be dominated by spatial or structural factors rather than by time or event magnitude (Bailey et al., 2010). Our analysis of the updated focal mechanisms and stress field with depth indicate increased proportion of dip-slip faulting with depth, suggesting larger focal mechanism heterogeneity in the deeper sections of the fault zones for all the focus areas (Figure 1.5). The increased diversity with depth may be related to the changes of structural properties (e.g., Allam et al., 2014; Qiu et al., 2017; Qin et al., 2018), variations of rheology such as weak crustal layers (e.g., Bokelmann and Beroza, 2000) or localized creep below the fault (e.g., Wdowinski, 2009; Cooke et al, 2018). The relation between the dominant fault strike direction, N55°W, and the asymmetry in the distribution of focal mechanism orientations is considered to correlate with the direction of the fault strike relative to the plate loading (Bailey et al., 2010). Based on this, when the plate motion direction deviates from a main fault strand, it can lead to second-order normal faulting (Bailey et al., 2010). Increased number of dip-slip faulting through depth includes a higher proportion of smaller normal events according to the b- value analysis (Table S1.1 to S1.3). This can result from variations of the plate motion 40 direction relative to the main SJFZ fault strike, and may hold for the CH area having significant larger b-values associated with normal events compared with strike-slip events. As mentioned, the three focus study areas show similar trends with depth for the estimated stress parameters, with different degrees of variations. The stress inversion results show a clear clockwise rotation of S Hmax with increasing depth, increasing the angle between the S Hmax and the main fault trace at the surface. At the same time, the stress regime appears to change with depth from more pure strike-slip to oblique (transtensional or transpressional) faulting depending on the region. All the observed rotations appear to be deeper than ~9 km. Stress ratios have their minimum value at ~9 km depth and slightly increases getting deeper (Figure 1.9). The average locking depth along the SJFZ are estimated from geodetic data and seismogenic thicknesses to be 11±2 km and 17±3 km, respectively. These provide two independent reference values associated with mechanical changes through depth (Wdowinski, 2009). The ~10-17 km depth is assumed to be the transition zone between the brittle crust to the ductile lower crust (Wdowinski, 2009; Inbal et al., 2017). This depth section includes high seismic activity, but the elastic strain may be released both seismically and aseismically (Inbal et al., 2017). Proposed explanations for the mechanical changes in the transition zone include lower frictional strength at depth or higher pore pressure leading to a reduction in the effective normal stress acting on the fault (Wdowinski, 2009). Further, rheology variations with depth may lead to decreasing horizontal shear traction at the brittle-ductile transition zone and related variations of focal mechanisms (Bokelmann and Beroza, 2000). The stress field rotations and stress 41 ratio increases resolved in this study appear to occur within the transition zone at ~10-17 km depth, coinciding with the increased seismicity rates and mechanism heterogeneity. To invert for the stress field orientation, we utilized focal mechanisms with qualities A to D representing fault plane uncertainties in the range 5-55 degrees with a median value of 31 degree. To test the robustness of the results with respect to the focal mechanism uncertainties, the stress inversions were repeated selecting only focal mechanisms of quality A and B having <35° of fault plane uncertainty. The corresponding results confirm that the reported stress rotations and main changes with depth are robust and are not affected strongly by the uncertainty of the input data. However, due to the reduced number of available focal mechanisms, the resolution is lowered. The coseismic strain distributions with depth for all focus areas show highly consistent patterns with the inverted stress field. The differences in principal stress and strain plunges, and maximum horizontal compressional stress and strain, are less than 10° in all cases. The difference in the stress ratio, R, and the analogous strain parameter, D, is less than 0.1, and the Kagan angle between the stress and strain tensors are less than 20° at all depth sections (Figure 1.10), implying that the stress and strain orientations are nearly parallel in the study areas. One of the stress inversion assumptions is that the fault slip during an earthquake occurs in the direction of the shear traction vector (Wallace, 1951; Bott, 1959). This implies that at the time of occurrence of an earthquake the strain and stress fields are parallel. The general agreement between the obtained stress and strain results validates this assumption, and indicates that the velocity structure at the depth of the used seismicity is on the average approximately isotropic (e.g., Twiss and 42 Unruh, 1998). This also provides some validation of the stress inversion results, since the strain results reflect more directly the earthquake data with no additional assumptions. Small secondary faults near the major faults in southern California do not accommodate large displacements, but they are important for non-fault-parallel displacements related to transpressional and transtensional areas (Ghisetti, 2000). Seismic sequences in southern California have indicated slip heterogeneity and occurrence of dip- slip faulting on planes parallel to the major strike-slip fault (Ghisetti, 2000). This is in accordance with our observations of increased dip-slip faulting and increased heterogeneity with depth in the SJFZ. Ghisetti (2000) founds that slip along a large proportion of small-scale faults is compatible with S Hmax , and inferred that the estimated stress and strain tensors are oriented coaxially based on shallow M<5 earthquakes. Our results extend these conclusions to deeper sections of the SJFZ. The large events occur on the main faults and have mainly right-lateral strike-slip mechanisms, while the numerous off-fault smaller events with mixed faulting types accommodate geometrical variations of the faults in relation to the regional stress regime. These results are also consistent with observations of Bailey et al. (2010) and Cheng et al. (2018). 1.6 Conclusions The analyses performed in this study allow us to obtain information on (1) the distribution of background stress field and coseismic strain in SJFZ regions with high resolution and (2) variations in the state of stress from shallow crust to the brittle-ductile transition region. Three focused areas, CH, HS and TR, are analyzed in higher detail and compared. The main findings can be summarized as follows: 43 (1) The b-value analysis provides some constraints on the brittle-ductile transition depth in the analyzed areas. In all regions, the brittle crust extends down to 9-12 km and the seismicity in that depth section displays mainly strike-slip events. A change towards dip-slip is observed through the brittle-ductile transition zone to 15- 18 km. This depth appears to be shallower at the TR than at other two regions. (2) At least for the CH and TR areas, a significant clockwise rotation of S Hmax with depth is observed. The angle between S Hmax and the fault trace at the surface appears to increase especially at the depth interval of the inferred brittle-ductile transition depths (10-17 km). This may indicate a progressive weakening of the fault with depth. This may also reflect partially changing dip of the main fault in the region (e.g., Ross et al., 2017a). (3) The distribution of stress and coseismic strain parameters appear to be largely consistent. This provides some validation of the stress inversion results with the direct input data and indicates that the velocity structure is on average approximately isotropic. (4) The stress parameters before and after the El Mayor Cucapah earthquake do not show significant rotation of S Hmax . The stress ratios move toward transpressional regime after the EMC event in the TR area. However, an event with magnitude > 5.4 occurred in the TR area in 2010 adjacent to the maximum variations of the stress ratio. This event could have potentially affected the observed stress ratio (e.g., Martínez-Garzón et al., 2016a). 44 1.7 Acknowledgments The study was supported by the Southern California Earthquake Center (based on NSF Cooperative Agreement EAR-1600087 and USGS Cooperative Agreement G17AC00047). P. M. G. acknowledges funding from the Helmholtz Association under the Helmholtz Postdoc Programme and the Helmholtz Young Investigators Group SAIDAN. The manuscript benefitted from useful comments by two anonymous referees. 45 2. Variations of stress parameters in the Southern California plate boundary around the South Central Transverse Ranges (Abolfathian et al., in review) 2.1 Introduction The boundary between the North American and Pacific plates in Southern California consists of multiple active fault zones with different total offsets, slip rates and seismic activities (Figure 2.1). Most of the plate boundary motion and seismic hazard are associated with the San Andreas Fault (SAF) and San Jacinto Fault Zone (SJFZ). The plate boundary in the South Central Transverse Ranges (SCTR) with high topography of ~3 km associated with the San Gabriel and San Bernardino Mountains has a complex set of thrust and strike-slip faults (e.g., Matti et al., 1993; Spotila et al., 2001; Yule and Sieh, 2003), especially between Cajon Pass (CP) and San Gorgonio Pass (SGP). The Crafton Hills (CH) area between the SAF and SJFZ has significant seismicity that is relatively deep (Figure 2.1). Improved characterization of the stress field within and around the SCTR area can provide useful information on tectonic deformation and earthquake processes in the region. This is done in the present paper with stress inversion analyses of earthquake focal mechanisms on regional and local scales. Previous studies examined the stress field around the SCTR and other regions in Southern California. Hardebeck and Hauksson (2001) performed stress inversion of focal mechanisms and showed that a homogeneous background stress field is not able to explain the complex faulting system and stress variations in the region. They also studied the temporal changes of stress variations in 5-year time periods between 1980 and 1999. 46 Their results show significant changes in the orientations of the maximum horizontal compressional stress in the vicinity of major earthquakes, and no significant changes detectable within the noise level of the data related to the tectonic loading. Yang and Hauksson (2013) studied stress field on regional (100-500 km resolution) and local scales (less than 100km) and discussed the importance of local scale stress variations that can affect rupture zones of major M7 type earthquakes. (add more on background) In the present study we use earthquake fault plane solutions from 1981 to 2017 (Yang et al., 2012; extended to later years) to examine the 3D background stress field in a larger (regional) scale (Figure 2.1) extending from the Eastern California Shear Zone (ECSZ) to the LA basin (section 2.4.1), and more detailed spatiotemporal variations of the stress field near the SCTR (section 2.4.2). Compared with previous studies, we employ a refined stress inversion methodology developed by Martínez-Garzón et al. (2016a) over a larger data set and obtain a robust stress parameters, including the principal stress orientations and the stress ratio, in an average resolution of ~5 km (resolution varies with the seismicity distribution) that provide information on the local stress field and associated loadings in more detail than earlier works. Various studies indicate that focal planes of aftershocks are generally consistent with the orientation of the major geological structures (McCloskey et al., 2003; Hardebeck, 2014). The total crustal stress field (𝜏 ! ) can be written as the sum 𝜏 ! = 𝜏 ! +𝜏 ! +∆𝜏 !" . (2.1) where 𝜏 ! is the regional far field loading, 𝜏 ! represents additional loading due to local features such as topography, and ∆𝜏 !" is stress transfer from earthquakes in the considered crustal volume. 47 Inversions of focal mechanisms of declustered seismicity (mainshocks) provide information on the background stress field associated with the loading compoenents (𝜏 ! +𝜏 ! ), while inversions of the aftershock mechanisms reflect the background stress field together with the internal stress transfers of the mainshocks and these events (𝜏 ! +𝜏 ! +∆𝜏 !" ). Comparing the stress fields produced by these two types of inversion can provide information on the dominant loading mechanisms of the mainshocks that drive the aftershocks. In section 2.4.3 we compare the estimated stress parameters from the mainshocks and the aftershocks in the focused study area around the SCTR. 2.2 Data and the study area For the purpose of this study, the earthquake hypocenters are selected from the Southern California relocated catalog of Hauksson et al. (2012, extended to later years) (Figure 2.1) with horizontal and vertical location errors of 0.75 km and 1.25 km, respectively. The fault plane solutions are selected from the Yang et al. (2012, extended to later years) focal mechanism catalog for the total time period of 1981-2017. The selected focal mechanisms have qualities from A to D, in accordance with 5° to 55° degrees of uncertainty, where with the mentioned uncertainty range, inversions with ~40 events per grid cell, resolves a stable stress field (Martínez-Garzón et al., 2016a). The selected focal mechanism catalog is declustered using the nearest-neighbor proximity approach developed by Zaliapin and Ben-Zion (2013, 2020), separating the mainshock events from the aftershocks and the foreshocks. The declustered seismicity makes it possible to focus on the background tectonic stress, and separately on the stress field associated with internal stress transfers resulting from the aftershocks (Martínez- Garzón et al., 2016a). The declustered events are also referred to as background 48 seismicity. The background hypocenters show notable variations in the selected focused area near the SCTR. The area between the main two faults of SAF and SJFZ includes 52% of all the selected background seismicity and has the deepest seismogenic thickness (defined as the depth above which 90% of the events are located) of 17.8 km (Figure 2.1). The background seismicity from east of the SAF comprises 34% of the selected events and displays a seismogenic thickness of 11.9 km, while the western section of the SJFZ includes 14% of the background seismicity and has a seismogenic thickness of 14.9 km. Based on the mentioned background seismicity hypocentral variations and the geological structures such as mountain ranges and the main faults we divided the area into six sub- regions (Figure 2.2). The sub-regions are as follows: (1) San Gabriel Mountains (SGM), (2) San Bernardino Mountains (SBM), two areas in the (3) northern and (4) eastern sections of the SBMs including parts of the ECSZ and fault system near Landers, (5) between the two main fault strands of SAF and SJFZ, and (6) Western region of the SJFZ. We separately analyze the background stress field of the mentioned sub-regions in the entire seismogenic thickness. The stress parameters are estimated independently for the mainshocks’ and aftershocks’ mechanisms. Aftershocks comprise the majority of events in the SCTR (~65%), while mainshocks (background events) are only ~21% of the earthquakes in the selected focused study area. Foreshocks comprise ~14% of the total seismicity in the selected study area, which is not utilized for the purpose of this study. It should be noted that the seismogenic thickness of the mainshocks is ~16.9 km, whereas the aftershocks show a shallower seismogenic thickness of ~13.5 km in the focused study area. The ~3.4 49 km average hypocentral difference of the mainshocks and aftershocks is correlated with the difference in their associated main loadings. Table 2.1 summarizes statistical information on the distribution of the mainshocks and the aftershocks. Figure 2.1 Distribution of declustered seismicity with focal mechanisms in the selected region in Southern California, between 1981 to 2017 used for the stress inversion. Each event is color-coded with its hypocentral depth. The brown rectangle denotes a selected region around the South Central Transverse Ranges (SCTR). The yellow squares show focused regions of study, Cajon Pass (CP), and San Gorgonio Pass (SGP). Faults are marked in black lines. Stars show events larger than magnitude 6 in the region during the selected time period. SCTR and yellow text in the figure shows regions of study, while black text defines geology of the area. (SGM: San Gabriel Mountains; SBM: San Bernardino Mountains; SJM: San Jacinto Mountains; CH: Crafton Hills; HS: Hot Springs). 50 Table 2.1 Seismic statistics in SCTR, comparing foreshocks, mainshocks, and aftershocks. Figure 2.2 Seismicity distribution in six sub-regions in the selected region around the South Central Transverse Ranges: (1) San Gabriel Mountains (SGM) in purple, (2) San Bernardino Mountains (SBM) in red, (3) northern part in yellow, (4) eastern section of the SBM in cyan, (5) between the San Andreas Fault (SAF) and San Jacinto Fault Zone (SJFZ) in green, (6) western section of the SJFZ in blue. 51 2.3 Methodology 2.3.1 Stress tensor inversion of focal mechanisms In this study, we apply the refined stress inversion method developed by Martínez- Garzón et al. (2016a) on double-couple earthquake focal mechanism catalog in Southern California. The inversion method employs the refined MSATSI software (Martínez- Garzón et al., 2014; 2016a), which is an updated version from SATSI algorithm (Michael, 1984; Hardebeck and Michael, 2006). The assumptions of the stress inversion include: (1) The stress field is homogeneous within a considered rock volume, (2) Earthquakes occur on pre-existing faults with varying orientations, and (3) Slip on each fault occurs parallel to the direction of its tangential traction (Wallace, 1951; Bott, 1959). The implied method includes discretizing the events based on an optimum required number of focal mechanisms per grid cell to constrain a stable stress orientation of an area (McKenzie, 1969), which in this study, the optimum number of mechanisms per grid cell is estimated to be ~40 (Martínez-Garzón et al., 2016a). The study volume is discretized using the k-means technique (Hartigan and Wong, 1979; Martínez-Garzón et al., 2016a) into Voronoi grid cells containing the mentioned optimum number of events. The cell sizes vary in relation to seismicity density and provide estimates for the spatial resolution of the inversion. The linear damped stress inversion estimates the orientations of the three principal stresses σ 1 , σ 2 and σ 3 (from most to least compressive) and the stress ratio parameter, R, defined as (2.2) R= σ 1 −σ 2 σ 1 −σ 3 52 The stress ratio (R value) ranges between 0 and 1, with smaller and larger stress ratios in a strike-slip environment corresponding to stress regimes closer to transtensional (i.e., mixed strike-slip and normal faulting) and transpressional (i.e., mixed strike-slip and reverse faulting) fields, respectively. The orientation of maximum horizontal compressional stress, S Hmax , is computed from the orientation of the principal stress axes following Lund and Townend (2007) and the estimated trends and plunges of the principal stresses are classified into Andersonian stress regimes: normal, strike-slip and reverse, and oblique faulting types (Zoback, 1992). Uncertainty estimations of the inversion outputs are obtained by bootstrap resampling of the original set of focal mechanisms (Michael, 1987) and provide 95% confidence intervals. The method applies an iterative procedure to select the nodal plane that is optimally oriented for failure in the estimated stress field. During each iteration, the stress field orientation is calculated and the fault plane with the largest instability coefficient I is selected for the next iteration (Vavryčuk, 2011; 2014; Martínez-Garzón et al., 2016b). The parameter I is defined as , (2.3) where µ is the apparent coefficient of friction. τ and σ are scaled shear and normal stresses, respectively. The parameter I takes values between 0 and 1, representing the least and most optimally oriented faults to failure within a given deviatoric stress field. When estimating the fault instability, a grid search is applied over values of coefficients of frictions, ranging between 0.2 and 0.8. For each grid cell, the estimated µ produces the I = τ−µ(σ −1) µ+ 1+µ 2 53 highest overall instability coefficient (Vavryčuk, 2014). Since µ is selected based on iterative computations in the inversion procedure, we refer it as an apparent coefficient of friction. 2.4 Results 2.4.1 Regional stress variations in Southern California Initially, we analyze the background stress distribution in a volume extending over the plate-boundary region in Southern California, from the ECSZ to the LA basin, using ~6,800 focal mechanisms from the declustered catalog between 1981-2017. To examine the 3D spatial changes of stress parameters, the selected focal mechanisms in the study area are divided into 5 km depth bins. The bin width is chosen considering the overall depth uncertainty of ~1.25 km of the resolved hypocentral locations and the optimum number of seismicity, ~40 per grid cell, in a strike-slip regime to converge to a stable stress tensor (Martínez-Garzón et al., 2016a). Focal mechanisms in each grid cell are inverted and the S Hmax direction, the stress field orientations, and the stress ratio R are estimated following the methodology discussed in section 2.3. The spatial distribution of S Hmax of the selected declustered seismicity over the regional scale can be divided into regions near the ECSZ, San Bernardino Mountains (SBM), the area between the SAF and SJFZ, and near the WTR (Figure 2.3). In the ECSZ, the S Hmax is oriented toward NNE, with average azimuths of ~10º, ~15º and ~12º in the depth sections 0-5 km, 5-10 km, and 10-15 km, respectively. In the SBM, the S Hmax orientation rotates towards the north and slightly NNW, with average S Hmax trend of N7ºW. Between the SAF and SJFZ, S Hmax generally points toward the north and NNE. In this area, near Crafton Hills, a large clockwise rotation in the S Hmax direction is observed. 54 Near the WTR and the LA basin, the S Hmax directions rotate back towards NNE similar to the orientation in the ECSZ, with the difference that the WTR includes lower spatial resolution and higher uncertainty in the inferred S Hmax orientation. The stress regimes are estimated based on the relative position of the σ 1 , σ 2 , and σ 3 axes. The regional background stress regime is in general strike-slip with deviations near the WTR deeper than 10 km showing reverse faulting and in the ECSZ, at the 5-10 km depth section, showing oblique faulting with a mixture of strike-slip and normal faulting (Figure 2.3). The variations of the estimated stress ratio R represent the deviation from the regional strike-slip faulting towards transtensional and transpressional stress regimes. In general, clear variations from transtension near the ECSZ to transpression near the WTR are observed at all depth ranges (Figure 2.4). Deviations from the regional strike-slip stress field near the SCTR include patches of higher transpressional components near CP and SGP (Figure 2.4c) and higher transtensional stress regimes observed near the CH (Figure 2.4, b to d). The CP, SGP, and CH areas are considered to display local stress components related to the local geological structures, which are discussed in more detail in the following section, 2.4.2. 2.4.2 Stress variations near the South Central Transverse Ranges We focus on the area near the SCTR using ~3,300 focal mechanisms from the declustered catalog in the selected time period (brown box in Figure 2.1). We analyze the 3D variations of the stress parameters dividing the selected focal mechanisms into 5 km depth bins and the 2D spatial variation of the stress parameters dividing the background focal mechanisms based on geological features near the SCTR. 55 The S Hmax orientations near the SCTR are generally towards the north and NNE direction (Figure 2.5), with significant variation in the CH area at 15-20 km depth, where the S Hmax direction rotates ~23° clockwise from the surface to the bottom of the seismogenic thickness (Abolfathian et al., 2019). The orientations of the estimated principal stresses (shown as stereonets in Figure 2.5) indicate the main background stress regime of strike-slip faulting, which based on the Andersonian theory of faulting has vertical intermediate principal stress and parallel least and most compressional stress orientations with the Earth surface as the reference. The Andersonian theory for strike-slip faulting holds overall from the surface to 15 km depth in the focused study area. However, below 15 km depth, the most compressive and intermediate principal stresses’ plunge angles rotates about ~30° in the CH area, and all principal stresses’ plunge angles in the southern part of SGP area and close to the Hot Springs (HS) area rotate about ~15° to ~30° (Figure 2.5). In addition, in this depth section, the hypocenters of the selected focal mechanisms are mainly located between the two main faults of SAF and SJFZ. Significant variations in the stress ratios are observed in the focused study area near the SCTR. In the shallowest depth bin, 0-5 km, the stress ratios follow the regional overall strike-slip faulting, varying from slightly transtensional in the most eastern section towards transpression in the most western part (Figure 2.4a). The same variations are observed in 5-10 km depth with amplified components of transtension and transpression in the eastern and western sections, respectively (Figure 2.4b). At 10-15 km depth, the higher transpressional component appears near the highest peaks of the San Bernardino Mountains near SGP, and San Gabriel Mountains close to CP (Figure 2.4c). 56 At the same depth range, transtensional components emerge in the CH area. Below ~5 km, the stress ratio near the CP area changes sharply from transpression in its northwest to transtension in its southeast, even though the inversions utilized damping to smooth stress variations between the neighbor cells. The CP area is located where the SJFZ branches from the SAF and the strong change in topography exists at the edge of the San Gabriel Mountains. The region between the SJFZ and SAF near the SCTR is highly seismically active (more than 50% of the background events in the SCTR region are between the two fault strands), and the hypocenters of the declustered seismicity are on average ~5 km deeper than the ones located outside of this region. In an effort to clarify stress variations related to fault-system interactions and topographic variations, we separately divide selected declustered mechanisms into six sub-regions (see section 2.2) and invert independently for stress parameters in each sub-region within its entire seismogenic thickness. Seismicity from each sub-region is color-coded in Figure 2.2. The results from the independent inversions of the 6 sub-regions indicate the overall strike-slip faulting near the SCTR, with deviations including amplified reverse faulting close to the CP area and oblique/normal faulting in the ECSZ area (Figure S2.1). The stress ratio variations from the 6 sub-regions (Figure 2.6) show the compressional components near CP and the sharp stress ratio changes between the NW and SE of the junction of the SAF and SJFZ, where the compressional component is likely associated with the higher topography. The transtensional stress components close to the junction could be explained in terms of the extension associated with the right-lateral strike-slip motion on the SJFZ and the nearby SAF. This region also includes sub-volumes dominated by normal faulting near CH. The 57 areas near SGP and SBM show clear transpressional components. The spatio-temporal variations of background stress field are also examined and found to be in general in agreement with the discussed spatial background stress field variations (Figure S2.2). For this purpose, we divide the entire selected declustered focal mechanisms into 5 time periods of ~8 years, namely 1981-1985, 1986-1993, 1994-2001, 2002-2009, 2010-2017, and estimate the stress parameters independently. The estimated stress parameters do not show any significant changes within these time periods. 58 Figure 2.3 Regional distribution of the maximum horizontal compressional stress orientations (S Hmax ) at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. The orientations are color-coded in red, green, blue, and brown denoting reverse, strike-slip, normal and oblique faulting, respectively. Purple dashed lines indicate the used Voronoi cells. WTR: West Transverse Ranges; SGM: San Gabriel Mountains; CP: Cajon Pass; CH: Crafton Hills; SJM: San Jacinto Mountains; SGP: San Gorgonio Pass; SBM: San Bernardino Mountains; ECSZ: Eastern California Shear Zone. Figure 2.4 Regional seismicity distribution color-coded with values of the stress ratio R at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. In a strike-slip faulting environment, R-values around 0.5, 0 and 1 indicate pure strike-slip, transtensional and transpressional stress regimes, respectively. Purple dashed lines indicate the used Voronoi cells. 59 Figure 2.5 Distribution of the maximum horizontal compressional stress orientations (S Hmax ) in fan symbols and the principal stress orientations (Stereonets) in the selected region around SCTR at (a) 0 to 5 km, (b) 5 to 10 km, (c) 10 to 15 km, (d) 15 to 20 km depth sections. The variations in S Hmax orientations show the uncertainty of 95% confidence interval. The maximum, intermediate and minimum principal stresses in the stereonets are indicated with red, green, and blue, respectively. Purple dashed lines indicate the used Voronoi cells. CP and SGP shown in pink rectangles. 60 Figure 2.6 Seismicity color-coded with values of the stress ratio R in the selected region around SCTR. Background seismicity distributed in 6 sub-regions based on Figure 2.2. Signs are as in Figure 2.4. 61 2.4.3 Stress variations in the SCTR — aftershocks and depth dependency In the last part, we compare the background stress variations with results obtained from the inversion of aftershock mechanisms. The focused study area near the SCTR has ~3,300 focal mechanisms from the declustered catalog, while ~9,600 aftershock mechanisms are available in the selected area within the same time period. We divide the aftershock mechanisms in 5 km depth bins as applied on the background seismicity and invert for their stress parameters (Figure 2.7). The transtensional component of background stress near the CH area is amplified between ~5 to 15 km depth in the stress field inverted from the aftershocks. The transpressional stress components near the SGP are also amplified in the results obtained from the aftershock mechanisms, with the difference that the areas with transpressional stress fields are located shallower compared with the ones obtained from the mainshocks. The aftershocks show the overall thinner seismogenic thickness and amplified shallower transtensional and transpressional stress components in the CH and SGP areas, respectively. In contrast, no evidence of the transpressional stress components near the CP area is observed in the aftershock results. Considering that in the CP area comprises sparse aftershock distribution, we might not have enough resolution to resolve properly the stress field from the aftershocks. The comparison of the estimated stress field from the background declustered seismicity and aftershocks help to understand the main loading in the selected area that reflect local loadings, as discussed below. 62 63 Figure 2.7 Seismicity color-coded with values of the stress ratio R, at (a,b) 0 to 5 km, (c,d) 5 to 10 km, (e,f) 10 to 15 km, (g,h) 15 to 20 km depth sections. Subplots (a,c,e,g) show the variation of the stress ratio regarding to the mainshocks while (b,d,f,h) are estimated inverting the aftershock events. Signs are as in Figure 2.4. 2.5 Discussion We examine spatio-temporal variations of the stress field in the plate-boundary region around the SCTR based on inversions of earthquake focal mechanisms, and attempt to interpret the results in relation to different loadings, fault properties, topography, and crustal depth. The primary analyzed data is a declustered catalog of the focal mechanisms of Southern California earthquakes from 1981 to 2017, and is used to derive the background stress fields in different scales of space and time. We also invert separately focal mechanisms of aftershocks that are generally triggered by stress transfers from the mainshocks. Comparisons between inversion results based on the declustered seismicity and aftershocks allow us to infer dominant local loading mechanisms that exist in different crustal volumes in addition to the large-scale tectonic loading. On a regional scale, the background stress fields inverted from the declustered catalog (Figures 2.3 and 2.4) are generally consistent with previous studies, showing transtensional stress regime in the ECSZ moving towards strike-slip regime near the SCTR and further transpressional stress regime in the WTR and LA basin (Hardebeck and Hauksson, 2001; Yang and Hauksson, 2013). The S Hmax trends show NNE direction near the ECSZ and the WTR (Figure 2.3) in agreement with the regional S Hmax directions in Southern California (Yang and Hauksson, 2013). Various sub-volumes with clear transpressional and transtensional stress components near the SBM, CH, SGP, and CP in the SCTR do not follow the expected regional strike-slip loading and indicate additional loadings associated with local structures. 64 The stress inversion results based on the declustered catalog in the SBM show an average S Hmax trend of N7ºW (Figure S2.1). Yang and Hauksson (2013) estimated S Hmax variations towards the NNW in this area and presented a schematic model of the ECSZ and SAF movements near the CP, with a wedge-shaped area of SBM having counter clock-wise loading. This scenario can induce compressional stress components near SBM that are observed (R ~ 0.6) in the inversion results of this study (Figure 2.6). However, the stress field estimated from the aftershocks does not show the NNW rotation of the S Hmax direction and the transpressional stress components, indicating that the proposed loading in the SBM accounts only for a small fraction of the total background loading in this area. Previous observations indicated tensional stress near the CH area (Hardebeck and Hauksson, 2001; Yang and Hauksson, 2013; Abolfathian et al., 2019). Several studies connected the deeper seismicity and increase of normal faulting in the northern SJFZ with deep creeping below the seismogenic fault (Wdowinski, 2009; Cooke and Beyer, 2018). Our inversion results based on the declustered mechanisms are consistent with these inferences. The results of the background stress field provide the following lines of evidence that the SJFZ is weak near the bottom of the seismogenic zone in the CH area: (1) The inversion results indicate that the S Hmax of the background stress field rotates clock-wise below 10 km depth, with maximum rotation at 15 km where the S Hmax trend is almost perpendicular to the main surface fault trace. (2) The estimated apparent coefficient of friction indicates a weak zone with an average µ of ~0.4 below 10 km depth compared to an average value of ~0.55 in the focused study area (brown box in 65 Figure 2.1) (Abolfathian et al., 2019). (3) The maximum and intermediate principal stress plunges rotate more than 45º below ~12 km depth (Abolfathian et al., 2019). The stress inversions of aftershocks’ mechanisms indicate transtensional 0<R<0.2 stress components in the CH area (Figure 2.7). The aftershock results are consistent with the local background stress field estimated for the CH area rather than the regional strike- slip stress field. This suggests that the dominant loading in the CH area is associated with a local structure that may be associated, as suggested in previous studies, with creep below the seismogenic fault. Evidence for a wide damage zone below 10 km in this area (Ben-Zion and Zaliapin, 2019) suggests that the deep creep may be associated with a wide shear zone rather than aseismic slip on a fault interface. In the SCTR region, the SAF is associated with significant bending of the main fault by about ~20º-30º and elevated terrain. The fault bending and topography are associated with perturbations in the intermediate (vertical) stress on the non-optimally oriented fault (dipping fault) at seismogenic depth (Fialko et al., 2005). The CP and SGP areas located near elevated topography in the SCTR are associated with transpression stress fields. In the SGP area, the strike-slip faulting regime is dominant from the surface to 10 km depth, while transpressional stress components are significant below 10 km. The same stress pattern exists in the CP area, with significant transpressional stress components below ~5 km (Figure 2.4). The observed transpressional stress fields imply that the parts of the SAF passing through the SGP and CP may be dipping within the seismogenic depth. This is consistent with seismological observations of Fuis et al. (2012) and others. The stress field estimated from the aftershock mechanisms in the SGP indicates higher compressional, 0.8<R<1, stress components (Figure 2.7) and is in agreement with 66 the loading from the topography rather than the regional strike-slip stress field, suggesting that the dominant stress field near SGP is associated with the topography (e.g., Fialko et al., 2005). In contrast, no evidence of compressional stress components is observed in the stress field inverted from the aftershock mechanisms near CP; this may be due to the fewer available aftershock mechanisms in this area. Large contrasts in the stress fields and seismicity depth are observed across the junction between the SAF and SJFZ near Cajon Pass. To the northwest of the junction in the San Gabriel Mountains the dominant stress field is transpressional (R~0.9), while to the southeast, the dominant stress field is transtensional (R~0.2) and the average S Hmax direction rotates more than 15º. The seismogenic depth varies by ~7 km from northwest to southeast of the SAF and SJFZ junction. These variations occur over a distance less than 20 km, implying strong effects of fault properties on the stress field and the importance of high-resolution analysis of the stress field of the type done in this study. Results of stress ratios inverted from the background seismicity in 5 separate time intervals of ~8 years between 1981 and 2017 are overall consistent with the discussed stress ratio variations for the combined 1981 and 2017 data, showing compressional stress components near high topography and tensional stress components near CH. The time interval 1986-1993 produces the largest transpressional stress components near the SGP area, where two transpressional events with magnitudes M w 5.6 and 5.0 occurred in 1986 and 1988 (Figure S2.2). Earthquake ruptures produce rock damage in their source volume (e.g., Lyakhovsky et al., 1997; Lockner et al., 1992; Aben et al., 2019). The evolution of rock damage can modify the properties and dynamics of fault zones on a geological time scale (e.g., Ben- 67 Zion and Sammis, 2003). Estimated rock damage production by ongoing background seismicity in Southern California shows several prominent damage zones (Ben-Zion and Zaliapin, 2019). The SJFZ and the SCTR, especially near major fault junctions (CP and SGP), are among the regions with the highest relative damage production, and the seismicity and rock damage become more pronounced and continuous with depth. The depth ranges with high concentration of seismicity and rock damage near CH, SGP, and CP areas are consistent with the depth range of the highest transpressional and transtensional stress components. The Moho has significant depth variations below the SCTR (Zhu and Kanamori, 2000; Ozakin and Ben-Zion 2015) and several studies discussed the association of Moho depth changes with enhanced generation of rock damage and reduced ability of faults to localize in the upper brittle crust (Lyakhovsky and Ben-Zion, 2009; Zaliapin and Ben- Zion, 2019). Earthquakes in such areas are expected to be distributed in space and exhibit a high diversity of mechanisms as observed near the SCTR. All three faulting types (strike-slip, reverse and normal) estimated from focal mechanisms of the declustered events exist in the entire SCTR, with increased number of normal and reverse faulting around CH and CP areas, respectively (Figure S2.3). The dip-slip events near the SCTR comprise a smaller fraction of the background seismicity than the strike-slip events and have mostly M w < 3.5. The relatively small magnitudes of the dip-slip events suggest that they are mainly associated with off-fault damage zones rather than the main strike-slip plate-boundary faults. Another manifestation of complexity in the SCTR is that strike angles of the declustered focal mechanisms are distributed in a range of directions (Figure S2.3) with no clear relationship between the strike angles and faulting types. 68 2.6 Acknowledgments The earthquake and focal mechanism catalogs used in the paper are available in the Southern California Earthquake Data Center (https://scedc.caltech.edu/). The study was supported by the Southern California Earthquake Center (based on NSF Cooperative Agreement EAR-1600087 and USGS Cooperative Agreement G17AC00047) and the U.S. Department of Energy (award DE-SC0016520).. PMG acknowledges funding from the Helmholtz Association in the frame of the Young Investigators Group VH-NG-1232 (SAIDAN). 69 3. Numerical simulations of stress variations with depth of a strike-slip fault 3.1 Introduction The state of stress within the fault-systems is a fundamental component of fault mechanics and crustal deformations. Recent enhancements in data acquisition instruments and improvements in the measurement’s coverage developed high-resolution spatiotemporal distributions of the stress fields within the crust. Southern California provides a well-recorded earthquake catalog for the past ~40 years and its spatial stress variation is studied in detail (Jones, 1988; Hardebeck and Hauksson, 2001; Yang and Hauksson, 2013; Abolfathian et al., 2019; Abolfathian et al., in review). Abolfathian et al. (2019) studied the depth variations of the stress field along the San Jacinto Fault Zone (SJFZ) up to ~2 km spatial resolution. This study indicated the rotation of the S Hmax direction and the principal plunge angles with increasing depth in the seismogenic crust near the Crafton Hills (CH), Hot Springs (HS), and Trifurcation (TR) areas. In the CH area, extreme rotation of the S Hmax , ~23º, is observed with depth. The HS area did not show large S Hmax rotation and in the TR area, the S Hmax rotates ~15º in its entire seismogenic depth. The plunge angle of the three areas rotates up to ~30º below ~9 km depth. All the three areas indicate the minimum stress ratio and maximum seismicity rates around the same depth section, deeper than ~9 km, where it is inferred to be the depth range that the mechanical behavior of the seismogenic crust changes (Abolfathian et al., 2019). Models attempt to explain the depth distribution of earthquakes in fault zone areas and associated crustal deformations and faulting types (Sibson, 1983; Scholz, 1988; 70 Bürgmann and Dresen, 2008). In general, crustal models include a seismogenic brittle layer including frictional discontinuous faulting overlying a ductile layer with mostly aseismic shearing (Sibson, 1977). The sharp change from the brittle to ductile behavior is unrealistic and the earthquake cycle should be extended some distance below the brittle upper crust, which makes the transition area spread over a depth interval of brittle to ductile shearing (Sibson, 1980). This large-scale change in the crustal behavior is dominantly correlated to the quartz response to the deviatoric stress in higher temperatures in deeper layers (Sibson, 1983). The brittle-ductile transition (BDT) zone comprises the bottom of the seismogenic regime. The shear resistance in this area is maximized and the larger earthquake ruptures nucleate near this area (Sibson, 1983). The overall shape of the fault zone structure, extending downward to the layer below the brittle upper crust, is one of the unresolved problems, which is crucial for understanding crustal deformation and associated earthquake nucleation. In the case of the strike-slip faulting, three modes of fault extension below the brittle upper crust are suggested. The initial mode includes the localized fault extending downward to the lower crust and the second mode includes the fault extending to the horizontal shear zone and third a mixture of both end-member cases with the favor of one (Sibson, 1983). In this study, we develop numerical simulations to describe the transition zone deformation for the end member scenarios. Our hypothesis is that the observed rotation in the stress field in Southern California (Abolfathian et al., 2019) is able to constrain the geometric and mechanical features of the BDT zone. Fluid pressure, rock type, temperature, and heat flow variations largely affect the crustal rheology and the depth of the seismogenic regime. Studies in Southern California 71 indicate that the temperature is the dominant factor defining the depth of the seismogenic zone in the crust (Sibson, 1983; Bürgmann and Dresen, 2008). In this study, we assume that the fluid pressure, temperature and rock type are inherited in the selected input velocity model and viscosity and we only focus to examine the effects of the end-member BDT zone models on the stress field variations with depth. 3.2 Model We design a simple model of a vertical strike-slip fault. The initial model setup includes horizontal crustal layers in a block of 80 km by 60 km with 25 km depth extension (Figure 3.1). The elastic upper crust extends for 0-10 km depth lying over the viscoelastic lower crust, extending between 15-25 km with a Maxwell viscosity of 7.1*10 20 Pa s (Bürgmann and Dresen, 2008). The BDT zone is located from 10 to 15 km depth. The velocity model is obtained from the SCEC Community Velocity Model- Harvard (CVM-H) and averaged for the values within 10 km from the TR area along the San Jacinto Fault Zone (Shaw et al., 2015). Far-field loading of 2 cm/yr is applied 30 km distance from each side of the fault in order to make a right-lateral fault slip. Initial normal stress corresponding to the gravitational forces is applied on the fault surface, and the entire block is under isotropic initial stresses. Boundary conditions including fixed surface normal to the fault and bottom surface are applied (Figure 3.1). The fault zone is represented by a localized surface in the elastic upper crust. We set up a quasi-static model to simulate the fault with a frictional model resulting in stick-slip behavior. The slip weakening frictional model has been applied in our model in the layer from 0-10 km depth. The fault is extended in the BDT zone with the same frictional model. The parameters are selected in a way that no friction being applied on the fault in 72 the lower crust and the fault creeps in this layer. Selected parameters for the frictional model are collected in Table 3.1. The two modeled end-member scenarios includes models with a BDT zone that comprises the elastic parameters as in the brittle upper crust and a viscoelastic shear zone with a viscosity of an order of magnitude larger than the selected viscosity of the lower crust (Figure 3.2). Figure 3.1 A schematic representation of the block model, initial stress distribution, boundary conditions and far field loading applied on the model. 73 Table 3.1 Selected frictional model parameters in upper and lower crust Figure 3.2 A schematic representation of the cross section perpendicular to the fault surface of the models changing in the rheology of the BDT zone. Models are meshed with the 1500 m mesh size. The FEM software package PyLith is used for solving the partial differential equations describing the tectonic deformation. The code solves the conservation of momentum and formulates a set of algebraic equations, which are solved in the absence of inertial forces, suited for the quasi-static case (Aagaard et al., 2017a; 2017b). The models are run initially for more than 10,000 years to Model 1 Depth (km) Friction Parameters Upper Crust (Discontinuous fault slip) 0 -10 µs = 0.6 ; µd = 0.58 Slip weakening parameter = 0.2 Cohesion = 0 Transition Zone 10-15 As in the upper crust Lower Crust (Creeping Section) 15-20 µs = 1e-12 ; µd = 1e-12 Slip weakening parameter = 0.2 Cohesion = 0 74 estimate for the best initial stress distribution inside the block. Applying the initial stress distribution, the models will be run for ~1000 years, in order to have at least three earthquake cycles for each model. 3.3 Results and discussion Depth dependent crustal stress field in a strike-slip faulting environment is attempted to be explored. The results obtained for this section are not provided since the computational setup of the models has to be largely improved. Model 1 is simulated in 10-year timesteps. The simulations of this model show the shear traction changes at different depths on the fault surface indicating earthquake cycles of ~200 years (Figure 3.3 a). The maximum shear traction is happening at the bottom of the brittle crust at 15 km depth as expected (Figure 3.3 c). Moreover, the best-obtained simulation for Model 2 is simulated in the 50-year timesteps. The 50-year time step is larger than the model relaxation time and by this means it is not possible to resolve the earthquake cycle. The simulation for Model 2 including the viscoelastic BDT zone, with the requisite relaxation time of ~10 years, requires more than 30 CPU hours per 100 years for model evolution, with the warm-up period larger than 4000 years, making this model computationally very expensive. The updated versions of Pylith and adjustments in the solver setup of the code can be helpful in decreasing this computational time. Further improvements in Model 2 and stress analysis can be a potential topic for future studies. 75 Figure 3.3 Shear traction variation on the fault surface at selected depths (a). Snapshots of depth variations of the fault slip (b) and the shear stress (c) in the direction parallel to the fault surface in the points from the middle of the fault. The time interval between lines are 10 years. a) b) c) 76 Discussion I examine the spatiotemporal variations of the background stress field near the selected areas along the San Jacinto Fault Zone (SJFZ) and the South Central Transverse Ranges (SCTR) in Southern California up to ~2 km spatial resolution using a refined stress inversion method (Martínez-Garzón et al., 2016a). The obtained background stress field variation in the study areas provide constraints on fault and crustal structure and are inferred to be associated with fault-system interactions, topography, fault geometry (dipping), and deep creep below the brittle crust. The main background stress field around the SJFZ in Southern California (Chapter 1: Abolfathian et al., 2019) is strike-slip, although the northwest portion near Crafton Hills (CH) area displays significant transtensional field. The S Hmax rotates clockwise with respect to the main fault trace through the depth. This rotation is significant at the depth interval of the inferred brittle-ductile transition zone (10-17 km) along the SJFZ, and maximizes (~23 degrees) near the CH area. The stated rotation of the S Hmax with depth indicates a progressive weakening of the fault (Wdowinski, 2009; Inbal et al., 2017) and potential change in the main fault dipping (e.g., Ross et al., 2017a). The principal stress plunges rotate largely below ~9 km along the SJFZ, near the depth section with the highest seismicity rates and inferred brittle-ductile transition zone. The rotations are associated with the observed increased dip-slip faulting of relatively deep small events and produce significant deviations from Andersonian strike-slip faulting in the bottom of the seismogenic thickness in this region. The stress ratio parameters and b-value estimations are consistent with the increasing number of dip-slip faulting below ~9 km. Moreover, the derived coseismic strain field agrees well with the 77 stress inversion results, which provides some validation for the stress analysis and indicates that the velocity structure is on average approximately isotropic. Further temporal stress analysis regarding the EMC earthquake shows an increase in the stress ratio near the Trifurcation area (TR) area after the event. The TR area is the closest analyzed study area to the EMC hypocenter. The increase in the stress ratio is expected to be produced by the local M w 5.4 event or an aseismic slip. This study shows no significant temporal rotation in the stress field across the SJFZ due to the EMC event. The stress field in the region near the SCTR is examined independently inverting the declustered and aftershock focal mechanisms (Chapter 2: Abolfathian et al., in review). Comparing the two stress fields provides information on the local dominant loading in the area. Over the regional scale, the S Hmax trends towards the NNE and the stress ratios vary from transtensional stress regime near the Eastern California Shear Zone (ECSZ) to strike-slip faulting near the SCTR, and towards transpression near the Western Transverse Ranges. Detailed examination of the stress field near the SCTR indicates deviations from the regional stress regime. The San Bernardino Mountain indicates transpressional stress components and the S Hmax directs towards NNW that is likely associated with the relative motion of the San Andreas Fault and ECSZ (Yang and Hauksson, 2013). The Cajon Pass (CP) and San Gorgonio Pass (SGP) show transpressional stress regime near the bottom of their seismogenic zones that is inferred to be correlated with the elevated topography (Fialko et al., 2005). In the CH area, rotation of the principal stress plunges and S Hmax direction and transtensional stress regime below ~10 km, along with lower estimated apparent frictional coefficient suggest a weak fault possibly associated with deep creep 78 (Wdowinski, 2009; Cooke et al, 2018). The results reveal effects of local loadings resolved by the performed multi-scale analysis. The study does not show significant temporal variations of stress variations near the SCTR from the average stress parameters in the past 37 years. Depth dependent crustal stress orientations in strike-slip faulting environments are explored using quasi-static numerical simulations with variations of rheology of a layered substrate, to compare model predictions with stress inversion of focal mechanisms from the TR area in SJFZ (Chapter 3). It is attempt to understand observed rotations up to ~30 ̊ of the principal stress axes below ~9 km depth in this region performing a model consisting of a vertical right-lateral frictional fault in a solid with horizontal crustal layers, constant tectonic loading, and gravitational forces. The model design incorporates different scenarios with a fault in an elastic upper crust atop a transition zone and a viscoelastic lower crust. This study is potential for future research as follows. Additional insights on dominant loading mechanisms and crustal stress field in different areas can be obtained by comparing the stress inversion results with strain-rate variations obtained from geodetic observations (e.g. Townend and Zoback, 2006). Deriving focal mechanisms for smaller events will allow stress inversions to be done using smaller sub-volumes and time intervals, leading to better resolution of stress variations in space and time. Numerical simulations of stress/strain evolution in crustal models with different loadings, fault geometries, and viscoelastic structures can aid the interpretation of results. 79 A1. Chapter 1 supplementary figures and tables Figure S1.1 Seismicity along the HS area comprising (a) on-fault and (b) off-fault events, and along the TR area comprising (c) on-fault and (d) off-fault events, all color- coded with the stress ratio parameter R. 80 Figure S1.2 Variation of S Hmax and strike angles through depth. The diagram shows polar histogram of strike angles in 10° bins. The left, middle and right diagrams indicate depth variations of CH, HS and TR, respectively. S Hmax is indicated with purple dashed line and its variations show the uncertainty. Main fault strike direction is N55°W, shown in dashed black line. Polar histograms of strike angles divided by faulting types are indicated with red, green and blue indicating normal, strike-slip and reverse faulting types, respectively. 81 Figure S1.3 Variations of (a) D Hmax orientation, (b) plunges of principal strain orientations and (d) strain ratios through depth in the three focus areas for the period 2000-2009. The three rows display the results from the CH, HS and TR areas, respectively. In (a), D Hmax values show the angle between the D Hmax direction and the main fault strike direction of N55°W. In (b), plunges of principal strains are color coded with red, green and blue as maximum, intermediate and minimum principal stresses, respectively. The median values of derived parameters from different grid cells within given depth intervals are shown in (a, b, c) with colored dots and error bars mark the 90% confidence interval. 82 Figure S1.4 Same as Figure 1.11 for the 9 to 12 km depth at the Crafton Hills area. 83 Figure S1.5 Same as Figure 1.11 for the 12 to 15 km depth at the Crafton Hills area. 84 Figure S1.6 Same as Figure 1.11 for the 12 to 18 km depth at the Crafton Hills area. 85 Figure S1.7 Same as Figure 1.11 for the 12 to 15 km depth at the Hot Springs area. 86 Figure S1.8 Same as Figure 1.11 for the 15 to 18 km depth at the Hot Springs area. 87 Figure S1.9 Same as Figure 1.11 for the 9 to 12 km depth at the Trifurcation area. 88 Figure S1.10 Same as Figure 1.11 for the 12 to 15 km depth at the Trifurcation area. 89 Figure S1.11.Same as Figure 1.12 for the Crafton Hills area. 90 Figure S1.12 Same as Figure 1.12 for the Hot Springs area. 91 Table S1.1 Estimated b-values for all events and for each separate faulting type in the CH area at different depth bins. The magnitudes of completeness related to each b-value are shown in parentheses in each cell. Table S1.2 Same as Table S1.1 for the Hot Springs area. Table S1.3 Same as Table S1.1 for the Trifurcation area. 92 A2. Chapter 2 supplementary figures and tables Figure S2.1 Distribution of the maximum horizontal compressional stress orientations (S Hmax ) in the selected region around SCTR based on data distribution in six sub-regions as in Figure 2.2. Signs are as in Figure 2.3. CP SGP 93 Figure S2.2 Temporal Variations of stress ratios near CP and SGP areas in the entire seismogenic thickness. Signs are as in Figure 2.4. Stress Ratio (R) 94 Figure S2.3 Distribution of the strike angles of the events from the declustered catalog, color-coded with the main types of faulting in the selected region around SCTR based on data distribution in six sub-regions as in Figure 2.2. CP SGP 95 References Aagaard, B., M. Knepley, C. Williams (2017a), PyLith v2.2.1rc1. 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Abstract (if available)

Abstract Knowledge of the state of stress in the brittle crust is crucial to understand fault mechanics, crustal deformations, and further to assess the potential for large earthquakes. I estimate and examine the spatiotemporal background stress field variations in selected regions in Southern California with higher seismicity rates and geological complexities, including the South Central Transverse Ranges (SCTR) and the San Jacinto Fault Zone (SJFZ). The analysis employs the refined stress inversion methodology and the available seismicity catalog of the region including focal mechanisms for the past ∼40 years. The background stress field is compared with the stress field obtained from the aftershock focal mechanisms to provide information on the local dominant stress field. Background stress field analysis is generally consistent with previous studies showing that strike-slip faulting is the main faulting type in the study area. Detailed examinations indicate deviations towards transpressional and transtensional stress regimes and rotations in the principal stress orientations as follows. Along the SJFZ, principal stress plunges and the SHₘₐₓ trend rotates significantly with depth. These rotations are maximized below ∼9 km along SJFZ, near the depth section with the highest seismicity rate and inferred brittle-ductile transition zone. The Crafton Hills area, located in the northwest of the SJFZ, shows the largest rotation of the SHₘₐₓ direction (∼23°). Together with the increased transtensional stress regime below ∼9 km, and lower estimated apparent friction coefficient, the Crafton Hills area is suggested to be a weak fault associated with a deep creep. Mountain ranges near the Cajon Pass, San Gorgonio Pass, and the Hot Springs area indicate higher transpressional stress components that are likely associated with elevated topography. The temporal background stress field variation near the SCTR does not show any significant changes from the average background stress field of the past 37 years. The 2010 Mw 7.2 El Mayor–Cucapah (EMC) event also does not show any implied large-scale background stress rotation along the SJFZ. The only observed temporal background stress field variation is across the time of the EMC earthquake, showing an increase in the stress ratio towards a higher transpressional stress regime after this event near the Trifurcation area. The increase in the stress ratio has potentially resulted from the nearby Mw 5.4 event or aseismic slip. In future studies, to improve the spatiotemporal variations of the stress field and giving an insight to hazard analysis, enhancing the incorporated modeling tools and integrating the seismic and geodetic observation are suggested.

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Asset Metadata

Creator Abolfathian, Niloufar (author)

Core Title Spatiotemporal variations of stress field in the San Jacinto Fault Zone and South Central Transverse Ranges

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Geological Sciences

Publication Date 07/21/2020

Defense Date 04/16/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,San Jacinto fault zone,Southern California,spatiotemporal stress changes,stress inversion,Transverse Ranges

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ben-Zion, Yehuda (committee chair), Haldar, Justin (committee member), Platt, John (committee member)

Creator Email nabolfat@usc.edu,niloufar.abolfathian@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-336041

Unique identifier UC11663575

Identifier etd-Abolfathia-8719.pdf (filename),usctheses-c89-336041 (legacy record id)

Legacy Identifier etd-Abolfathia-8719.pdf

Dmrecord 336041

Document Type Dissertation

Rights Abolfathian, Niloufar

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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