Role of fault geometry on the spatial distribution of the slip budget

Report for SCEC Award #16164 Submitted March 15, 2017

Investigators: Phillip G. Resor (Wesleyan University), Michele L. Cooke (University of Massachusetts), Scott T. Marshall (Appalachian State University)

I. Project Overview .................................................................................................................................... iA. Abstract ............................................................................................................................................ iB. SCEC Annual Science Highlights ..................................................................................................... iC. Exemplary Figure ............................................................................................................................. iD. SCEC Science Priorities .................................................................................................................. iiE. Intellectual Merit .............................................................................................................................. iiF. Broader Impacts .............................................................................................................................. iiG.Project Publications ......................................................................................................................... ii

II. Technical Report ................................................................................................................................... 1A. Objectives ........................................................................................................................................ 1B. Methodology .................................................................................................................................... 1C.Results ............................................................................................................................................ 2D.References ...................................................................................................................................... 6

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I. Project Overview

A. Abstract In the box below, describe the project objectives, methodology, and results obtained and their signifi-cance. If this work is a continuation of a multi-year SCEC-funded project, please include major research findings for all previous years in the abstract. (Maximum 250 words.) A fundamental problem in earthquake physics is how stress is transferred from plate motion to faults. Kinematic models assume that long-term fault slip rates will sum to the plate velocity; however, in a number of locations in southern California slip rates determined from modeling geodetic data differ sig-nificantly from geologic estimates. In this study we use mechanical models to investigate how releasing steps may affect estimates of fault slip over geologic time. A suite of 2D models reveals how fault length, friction and step geometry affect kinematic efficiency and the distribution of slip rate for idealized fault systems. We find that although systems with longer segments are more efficient, accommodating ~55-86% of plate displacement, geologic studies are unlikely (p<50%) to yield representative slip rate esti-mates. Systems with short segments are less efficient, but more likely to yield representative rates, par-ticularly when summing slip on overlapping segments. A 3D model of the San Jacinto fault illustrates how fault system geometry may impact slip rate estimates along a real fault system. Modeled slip rates are faster in the middle of fault segments and slower within releasing steps, consistent with published geologic estimates. The mean slip rate along the modeled fault trace, however, is significantly slower than the average of the geological rates. Our results suggest that the location of geologic slip rate stud-ies may govern their suitability for hazard estimates and that models can be used to put point measure-ments of slip into the context of slip distribution throughout a fault system.

B. SCEC Annual Science Highlights Each year, the Science Planning Committee reviews and summarizes SCEC research accomplishments, and presents the results to the SCEC community and funding agencies. Rank (in order of preference) the sections in which you would like your project results to appear. Choose up to 3 working groups from be-low and re-order them according to your preference ranking.

1. Stress and Deformation Through Time (SDOT) 2. Earthquake Geology 3. Tectonic Geodesy

C. Exemplary Figure Select one figure from your project report that best exemplifies the significance of the results. The figure may be used in the SCEC Annual Science Highlights and chosen for the cover of the Annual Meeting Proceedings Volume. In the box below, enter the figure number from the project report, figure caption and figure credits. Figure 3. Results from 3D mechanical model of the San Jacinto Fault and vicinity. A. Surface traces of faults from 3D model. B. Slip distribution at the Earth’s surface along faults of the San Jacinto Valley, Anza and Coyote Creek sections segments of the San Jacinto fault from a 3D mechanical model of the region. Blue shaded region corresponds to uncertainties in tectonic loading and white line shows aver-age slip distribution. The black dashed line shows the averaged model surface dextral slip summed across the overlapping faults. The grey band shows the geodetic range from Lindsey and Fialko (2013). The red line shows the 40 km wide average of slip rates at all depths along the modeled fault. Bars show geologic estimates of slip rates from 1) Prentice et al. (1986), 2) Rockwell (2008), 3) Sharp (1981), 4) Janecke et al. (2011), 5) Blisniuk et al. (2010) and 6) Blisniuk et al. (2013).

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D. SCEC Science Priorities In the box below, please list (in rank order) the SCEC priorities this project has achieved. See https://www.scec.org/research/priorities for list of SCEC research priorities. For example: 6a, 6b, 6c 4b, 1a, 4a

E. Intellectual Merit How does the project contribute to the overall intellectual merit of SCEC? For example: How does the research contribute to advancing knowledge and understanding in the field and, more specifically, SCEC research objectives? To what extent has the activity developed creative and original concepts? This project contributes toward a better understanding of how stress is transferred from plate motion to crustal faults where it is released during fault slip (priority for SCEC 4). Specifically, the project explores how along strike variation in fault complexity may lead to spatially variable slip rate (SCEC Science Pri-ority 4b) with implications for our ability to extract representative slip rates from geologic and geodetic observations (SCEC Science Priority 1a). Although several previous studies have proposed methods for better estimating uncertainty of geologic slip rates, little attention has been given to characterizing how representative geologic slip rates may be. Specific contributions include: 1) a 2D parametric modeling study of releasing steps that highlights which fault geometries are most, and least, likely to yield representative slip rate estimates from geologic and geodetic studies based on measures of their slip rate distribution and kinematic efficiency. 2) A quantifi-cation of the effects of summing slip across overlapping segments in stepovers. 3) A 3D modeling study of the San Jacinto fault and vicinity that illustrates how segmentation along this fault system may lead to spatially variable slip rates that are locally consistent with geological estimates (SCEC Science Priority 4a). Our results suggest that the location of geologic slip rate studies may govern their suitability for hazard estimates and that models can be used to put point measurements of slip into the context of slip distribution throughout a fault system.

F. Broader Impacts How does the project contribute to the broader impacts of SCEC as a whole? For example: How well has the activity promoted or supported teaching, training, and learning at your institution or across SCEC? If your project included a SCEC intern, what was his/her contribution? How has your project broadened the participation of underrepresented groups? To what extent has the project enhanced the infrastructure for research and education (e.g., facilities, instrumentation, networks, and partnerships)? What are some possible benefits of the activity to society? This project has continued to foster collaborations between researchers at Wesleyan University, the University of Massachusetts, and Appalachian State University. The project provided support for a grad-uate student (John Hossain) at Wesleyan University to attend the SCEC annual meeting. The results of this project will benefit society by helping geoscientists to better characterize slip rates and seismic haz-ard of active strike slip faults.

G. Project Publications All publications and presentations of the work funded must be entered in the SCEC Publications data-base. Log in at http://www.scec.org/user/login and select the Publications button to enter the SCEC Pub-lications System. Please either (a) update a publication record you previously submitted or (b) add new publication record(s) as needed. If you have any problems, please email web@scec.org for assistance.

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II. Technical Report

A. Objectives One of the fundamental problems in earthquake physics (and a priority for SCEC4) is how stress is trans-ferred from plate motion to crustal faults where it is released during fault slip. Kinematic models assume that the long-term fault slip rates will sum to the plate velocity; however, in a number of locations in southern California the slip rates determined from modeling geodetic data in this manner differ significant-ly from geologic estimates of slip rate (e.g. Meade and Hager, 2005; Oskin et al., 2007). This discrepancy may reflect temporal variations in slip rate, such that geodetic rates measured over decades are truly dif-ferent from geologic rates measured over thousands to millions of years (Dolan et al., 2007). Alternative-ly, the discrepancies may reflect inconsistencies in the way that we interpret or model the data to deter-mine slip rates. Several authors have explored how the assumptions of geodetic models may lead to un-realistic slip rate estimates. In particular, it has been noted that the kinematic assumption outlined above only holds true for parallel planar faults with no permanent deformation of the intervening crustal blocks (Herbert et al., 2013). Models that allow permanent off-fault strain may thus be able to fit both geodetic and geologic observations (Johnson, 2013). In this study, we investigate how geometric complexity of fault systems and off-fault strains may similarly affect estimates of fault slip over geologic time scales. Although several previous studies have proposed methods for estimating uncertainty of geologic slip rates (e.g. Bird, 2007; Zechar and Frankel, 2009), little attention has been given to characterizing how representative geologic slip rates collected at one site may be for the fault segment (see Dolan and Haravitch (2014) for a recent notable exception). Recent geologic investigations along the San Andreas and San Jacinto faults reveal the variability of slip rate along these structures. Blisniuk et al. (2010) show a trade off in slip rates between two fault seg-ments of the San Jacinto fault within their stepover region. McGill et al. (2013) show a reduction of strike-slip rate associated with the restraining bend of the San Andreas through the San Gorgonio Pass. We expect other faults in southern California have similar spatial variability of slip rate but most other faults have fewer than two site investigations. For structures with a few slip rate investigations, we don’t know if the average of these values accurately represents the slip accommodated over the entire structure and thus the seismic potential of the fault (e.g. Marshall et al., 2008). We have taken a two-pronged approach to addressing this problem. First, we use two-dimensional (2D) parametric models to explore the effects of stepovers on the probability that a geologic point measure-ment of slip rate will be representative of the average fault slip and thus the fault’s role in relieving crustal stress and accommodating far-field plate velocities. These results may be used to identify published esti-mates of geologic slip rate that may be unrepresentative as well as to design strategies for future geologic sampling to minimize the impact of fault geometry. Second, we use three-dimensional (3D) mechanical models of southern California, focusing on the well-studied releasing stepovers along the San Jacinto fault to investigate the impact of specific fault geometries on existing estimates of fault slip rate. The re-sults of the parametric models can be directly applied to the releasing stepovers of this fault, which have abundant geologic slip rate data (Blisniuk et al., 2010; Janecke et al., 2011; Rockwell, 2008; Sharp, 1981) and slip rates inferred from GPS studies of the region (Becker et al., 2005; Loveless and Meade, 2011; Lundgren et al., 2009; McCaffrey, 2005). The comparison of these rates provides a test for the potential reconciliation of geologic and geodetic estimates of slip rate (averages of ~10 and 16 mm/yr respectively) with consideration of the complete slip distribution along the fault. In 2016 we built on the results of our 2015 work by adding an analysis of the impact of specific sampling strategies and biases on the probabil-ity distributions and will soon submit a manuscript for publication.

B. Methodology Both our 2D and 3D models use Boundary Element Methods (BEM) to simulate faulting and fault-related deformation. In the BEM, faults are represented as linear (2D) or triangular (3D) elements that are inter-connected to simulate curvilinear or curviplanar fault geometries, respectively. The BEM provides an effi-

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cient tool to model the effects of fault geometry on stress and deformation as only the fault surface, itself, is discretized. Furthermore, the 3D formulation with triangular elements is adept at approximating the complex fault networks of southern CA because the branching and curving fault surfaces with incomplete intersections such as within the Community Fault Model (Plesch et al., 2007) can be simulated without compromising the accuracy of the modeled fault geometry. To simulate 3D deformation in southern California, we apply plate boundary velocities along the far edges of the base of the model while leaving the center of the base freely-slipping so that faults interact without prescribed rates of slip. The low friction of the faults simulates dynamic conditions during rupture when most fault slip occurs. The quasi-static model simulates deformation in the crust over several earthquake cycles. The good match between the slip rates from the frictionless fault models and geologic slip rates (Cooke and Dair, 2011; Cooke and Marshall, 2006; Herbert and Cooke, 2012; Herbert et al., 2014; Marshall et al., 2008) supports the analysis of Bird (2009) that many of the faults in southern California may slip with low dynamic frictional strength. Our parametric exploration of fault geometry uses the 2D BEM code, Fric2D, which incorporates fault strength properties, including cohesion and sliding friction (Cooke and Pollard, 1997; Savage and Cooke, 2010). The 2D nature of the code permits rapid exploration of a range of fault system geometries and calculation of full deformation and stress fields. The extended frictional functionality facilitates investiga-tions that the 3D code does not include.

C. Results Releasing (extensional) stepovers are a common target of geologic investigations into strike-slip fault his-tory due to their tendency to accumulate sediments, including organic-rich strata that can be dated using C-14 methods. In our project, we targeted fault systems with releasing steps to explore their efficiency at accommodating far-field loading as well as the probability that a geologic sampling site along the fault will reveal a representative rate. Within the 2D parametric models, we simulate fault slip accumulation over multiple earthquake cycles (Fig. 1). Models are loaded with far field fault parallel and normal displacements that simulate a uniform stress field (in the absence of faulting). We simulate both frictionless and frictional faults (mu=0.1, con-sistent with estimates of coseismic values) to assess a range of plausible fault conditions. A suite of 2D models reveals how fault length, friction and step geometry (fault overlap and stepover distance) affect fault slip and off-fault strain over geologic time scales. We calculate each system’s kinematic efficiency (ratio of mean slip to applied displacement, Fig 2A) and determine the probability that a site along the fault will reveal a representative rate (i.e. mean ± 1 mm/yr, Fig 2B). Faults with longer segments are most efficient, accommodating ~55-86% of plate displacement. Systems with short segments, large overlap and large spacing are the least efficient, accommodating as little as 23% of the total plate displace-ment. We find that the probability of sampling a representative slip rate is greater along short faults, due to the low overall slip magnitudes relative to typical geologic slip rate errors, and is inversely correlated with the kinematic efficiency of the system. For longer faults, the probability of sampling a representative rate is much lower and is most strongly controlled by the shape of the slip distribution rather than the overall efficiency. In situations where overlapping faults are recognized in stepovers, geological studies may attempt to ob-tain more representative slip rate estimates by measuring slip on overlapping strands and summing the measurements to obtain a total slip rate for the fault system. We have simulated this approach by sum-ming slip for all geometries that include overlapping segments. For segments with large overlap relative to segment size and small stepover distance this approach results in near-average slip rates for much of the stepover region (e.g., Fig. 1D), but for other geometries summing may result in slip rate estimates that are below or above (e.g., Fig. 1E) average. Overall, summing the slip across stepovers results in higher aver-age slip rate as well as a much greater probability that a randomly selected site will yield this slip rate (Fig. 2C). The increased probability is greatest for short fault segments, large overlap distance, and small stepover distance.

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Figure 1. Examples of 2D models of idealized releasing stepovers. For each model (A-E) the figure shows (left to right) map view model geometry, along fault slip distribution, and a histogram of slip magnitude. Models A-C treat slip on individual segments separately, while models D and E sum slip on overlapping segments. Bold black dashed line and thinner gray dashed line are mean and median slip values, respec-tively. Red regions have slip values within the interval of the mean slip +/- 1 mm/yr. All slip values are normalized to the far field displacement.

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A

B

C

Figure 2. Color-shaded plot of A. kinematic effi-ciency and B. Probability that a site will yield a representative rate for the entire suite of models when overlapping segments are treated sepa-rately. C. Probability that a site will yield a repre-sentative rate when slip is summed on overlap-ping segments (In shaded regions segments do not overlap and results are unchanged from B). Hachured areas are geometries that result in touching or physically coincident faults and were not modeled.

Next, we use 3D models to explore the effect of stepovers along the San Jacinto fault (Fig. 3). Geologic investigations along the San Jacinto fault have determined strike-slip rates ranging from 2 to 20 mm/yr. The average slip rate from all geologic studies of the San Jacinto fault is about 10 mm/yr. Variations in slip rate estimates, however, correlate with their location along the fault’s segmented geometry. Specifi-cally, slip rates slow within stepovers between fault segments. It is thus unclear which measurements are representative of the average slip rate for the fault system. To address this question we constructed a 3D BEM model of the San Jacinto and San Andreas faults in southern California that incorporates geometric aspects of the fault system down to ~4 km in scale. The near-surface strike-slip rates this model predicts

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provide a good fit to the spatial variation observed in the geologic measurements, including lower rates within each of the stepovers (Fig. 3). The mean slip rate along the modeled fault trace is 6.4 mm/yr, which is significantly slower than the simple average of the geological rates and the average of the geodetic es-timates for slip rate. The probability density distribution of the modeled surface slip has two peaks, one associated with the Coyote Creek segment and one with the San Jacinto Valley-Anza segments. A ran-domly chosen site along the fault has a relatively high (~75%) probability of sampling a location where the slip rate is significantly higher or lower than the mean. Furthermore, slip rates may vary with depth along the fault (Marshall et al., 2008) so that rates measured at the Earth’s surface do not represent the aver-age slip rate on the fault. Analysis of modeled slip rate along the entire structure of the San Jacinto fault, not just at shallow depths, gives a strike-slip rate of 7.5±3 mm/yr. This value has 1.5 mm/yr greater slip rate than the mean near the Earth’s surface and better represents the seismogenic potential for the fault. Interestingly, the model-predicted seimsogenically representative slip rate is expressed near the stepover that was investigated in detail by Blisniuk et al. (2010). This example demonstrates that the location of geologic slip rate studies may govern the suitability of their results for hazard estimates and that model results can be used to put point measurements of slip into the context of slip distribution throughout the fault system.

Figure 3. Results from 3D mechanical model of the San Jacinto Fault and vicinity. A. Surface traces of faults from 3D model. B. Slip distribution at the Earth’s surface along faults of the San Jacinto Valley, An-za and Coyote Creek sections segments of the San Jacinto fault from a 3D mechanical model of the re-gion. Blue shaded region corresponds to uncertainties in tectonic loading and white line shows average slip distribution. The black dashed line shows the averaged model surface dextral slip summed across the overlapping faults. The grey band shows the geodetic range from Lindsey and Fialko (2013). The red line shows the 40 km wide average of slip rates at all depths along the modeled fault. Bars show geologic es-timates of slip rates from 1) Prentice et al. (1986), 2) Rockwell (2008), 3) Sharp (1981), 4) Janecke et al. (2011), 5) Blisniuk et al. (2010) and 6) Blisniuk et al. (2013).

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References Becker, T. W., Hardebeck, J. L., and Anderson, G., 2005, Constraints on fault slip rates of the southern

California plate boundary from GPS velocity and stress inversions: Geophysical Journal International, v. 160, no. 2, p. 634-650.

Bird, P., 2007, Uncertainties in long-term geologic offset rates of faults: General principles illustrated with data from California and other western states: Geosphere, v. 3, no. 6, p. 577.

Bird, P., 2009, Long-term fault slip rates, distributed deformation rates, and forecast of seismicity in the western United States from joint fitting of community geologic, geodetic, and stress direction data sets: Journal of Geophysical Research-Solid Earth, v. 114.

Blisniuk, K., Oskin, M., Mériaux, A.-S., Rockwell, T., Finkel, R. C., and Ryerson, F. J., 2013, Stable, rapid rate of slip since inception of the San Jacinto fault, California: Geophysical Research Letters, v. 40, no. 16, p. 4209-4213.

Blisniuk, K., Rockwell, T., Owen, L. A., Oskin, M., Lippincott, C., Caffee, M. W., and Dortch, J., 2010, Late Quaternary slip rate gradient defined using high-resolution topography and10Be dating of offset landforms on the southern San Jacinto Fault zone, California: Journal of Geophysical Research, v. 115, no. B8.

Cooke, M., and Pollard, D., 1997, Bedding-plane slip in initial stages of fault-related folding: Journal of Structural Geology, v. 19, no. 3-4, p. 567-581.

Cooke, M. L., and Dair, L. C., 2011, Simulating the recent evolution of the southern big bend of the San Andreas fault, Southern California: Journal of Geophysical Research-Solid Earth, v. 116.

Cooke, M. L., and Marshall, S. T., 2006, Fault slip rates from three-dimensional models of the Los Angeles metropolitan area, California: Geophysical Research Letters, v. 33, no. 21.

Dolan, J. F., Bowman, D. D., and Sammis, C. G., 2007, Long-range and long-term fault interactions in Southern California: Geology, v. 35, no. 9, p. 855-858.

Dolan, J. F., and Haravitch, B. D., 2014, How well do surface slip measurements track slip at depth in large strike-slip earthquakes? The importance of fault structural maturity in controlling on-fault slip versus off-fault surface deformation: Earth and Planetary Science Letters, v. 388, p. 38-47.

Herbert, J. W., and Cooke, M. L., 2012, Sensitivity of the Southern San Andreas Fault System to Tectonic Boundary Conditions and Fault Configurations: Bulletin of the Seismological Society of America, v. 102, no. 5, p. 2046-2062.

Herbert, J. W., Cooke, M. L., and Marshall, S. T., 2014, Influence of fault connectivity on slip rates in southern California: Potential impact on discrepancies between geodetic derived and geologic slip rates: Journal of Geophysical Research-Solid Earth, v. 119, no. 3, p. 2342-2361.

Herbert, J. W., Cooke, M. L., Oskin, M., and Difo, O., 2013, How much can off-fault deformation contribute to the slip rate discrepancy within the eastern California shear zone?: Geology, v. 42, no. 1, p. 71-75.

Janecke, S. U., Dorsey, R. J., Forand, D., Steely, A. N., Kirby, S. M., Lutz, A. T., Housen, B. A., Belgarde, B., Langenheim, V. E., and Rittenour, T. M., 2011, High Geologic Slip Rates since Early Pleistocene Initiation of the San Jacinto and San Felipe Fault Zones in the San Andreas Fault System: Southern California, USA, v. 475, p. 1-48.

Johnson, K. M., 2013, Slip rates and off-fault deformation in Southern California inferred from GPS data and models: Journal of Geophysical Research: Solid Earth, v. 118, no. 10, p. 5643-5664.

Lindsey, E. O., and Fialko, Y., 2013, Geodetic slip rates in the southern San Andreas Fault system: Effects of elastic heterogeneity and fault geometry: Journal of Geophysical Research: Solid Earth, v. 118, no. 2, p. 689-697.

Loveless, J. P., and Meade, B. J., 2011, Stress modulation on the San Andreas fault by interseismic fault system interactions: Geology, v. 39, no. 11, p. 1035-1038.

Lundgren, P., Hetland, E. A., Liu, Z., and Fielding, E. J., 2009, Southern San Andreas-San Jacinto fault system slip rates estimated from earthquake cycle models constrained by GPS and interferometric synthetic aperture radar observations: Journal of Geophysical Research, v. 114, no. B2.

Marshall, S. T., Cooke, M. L., and Owen, S. E., 2008, Effects of nonplanar fault topology and mechanical interaction on fault-slip distributions in the Ventura basin, California: Bulletin of the Seismological Society of America, v. 98, no. 3, p. 1113-1127.

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McCaffrey, R., 2005, Block kinematics of the Pacific–North America plate boundary in the southwestern United States from inversion of GPS, seismological, and geologic data: Journal of Geophysical Research, v. 110, no. B7.

McGill, S. F., Owen, L. A., Weldon, R. J., and Kendrick, K. J., 2013, Latest Pleistocene and Holocene slip rate for the San Bernardino strand of the San Andreas fault, Plunge Creek, Southern California: Implications for strain partitioning within the southern San Andreas fault system for the last 35 k.y: Geological Society of America Bulletin, v. 125, no. 1-2, p. 48-72.

Meade, B. J., and Hager, B., 2005, Block models of crustal motion in southern California constrained by GPS measurements: Journal of Geophysical Research, v. 110, no. B3.

Oskin, M., Perg, L., Blumentritt, D., Mukhopadhyay, S., and Iriondo, A., 2007, Slip rate of the Calico fault: Implications for geologic versus geodetic rate discrepancy in the Eastern California Shear Zone: Journal of Geophysical Research, v. 112, no. B3.

Plesch, A., Shaw, J. H., Benson, C., Bryant, W. A., Carena, S., Cooke, M., Dolan, J., Fuis, G., Gath, E., Grant, L., Hauksson, E., Jordan, T., Kamerling, M., Legg, M., Lindvall, S., Magistrale, H., Nicholson, C., Niemi, N., Oskin, M., Perry, S., Planansky, G., Rockwell, T., Shearer, P., Sorlien, C., Suss, M. P., Suppe, J., Treiman, J., and Yeats, R., 2007, Community fault model (CFM) for southern California: Bulletin of the Seismological Society of America, v. 97, no. 6, p. 1793-1802.

Prentice, C. S., Weldon, R. J., and Sieh, K. E., 1986, Distribution of slip between the San Andreas and San Jacinto faults near San Bernadino, southern CA: GSA abstracts with programs, v. 18, no. 2, p. 172.

Rockwell, T., 2008, Observations of mode-switching from long paleoseismic records of earthquakes on the San Jacinto and San Andreas faults: Implications for making hazard estimates from short paleoseismic records: Paper presented at International Geological Congress, Int. Union of Geol. Sci., Oslo.

Savage, H. M., and Cooke, M. L., 2010, Unlocking the effects of friction on fault damage zones: Journal of Structural Geology, v. 32, no. 11, p. 1732-1741.

Sharp, R. V., 1981, Variable Rates of Late Quaternary Strike Slip on the San-Jacinto Fault Zone, Southern-California: Journal of Geophysical Research, v. 86, no. Nb3, p. 1754-1762.

Zechar, J. D., and Frankel, K. L., 2009, Incorporating and reporting uncertainties in fault slip rates: Journal of Geophysical Research, v. 114, no. B12.