SENSITIVITY OF THE SOUTHERN SAN ANDREAS FAULT SYSTEM TO
North America and Pacific Plate Boundary Velocities
The San Andreas Fault (SAF), San Jacinto Fault (SJF), and Eastern California Shear Zone (ECSZ) significantly contribute to the plate motion between the North American and Pacific plates, with current estimates indicating a movement of approximately 45–50 mm per year This data is supported by various studies utilizing Global Positioning Systems (GPS) and interferometric synthetic aperture radar (InSAR) measurements, which consistently show relative plate motion in the southern section of the study area at rates of 43–47 mm per year, aligning closely with GPS findings.
The mid-ocean ridge velocity model (MORVEL) indicates that the Pacific plate shifts at an angle of 324° in relation to the North American plate, based on seafloor spreading rates and oceanic transform fault orientations, as outlined by DeMets et al (2010) Additional GPS research reveals a variation in these measurements, with orientations ranging from 320° to 330°.
Our research examines how regional deformation responds to tectonic boundary conditions with velocities between 45 and 50 mm/yr and orientations from 320° to 325° This velocity and orientation range captures much of the existing data on plate motion in the area Even slight variations in tectonic loading can considerably influence slip rates along certain faults.
Slip Rates Along Faults
This article summarizes geologic slip-rate data for the San Andreas, San Jacinto, Crafton Hills, Garlock faults, and the Eastern California Shear Zone (ECSZ), highlighting discrepancies between these slip rates and the three-dimensional forward models by Cooke and Dair (2011) While the slip rates from the models generally align with the geological data for most faults in the region, specific areas exhibit mismatches that are explored in detail Our revisions to the fault configurations aim to address these discrepancies, with the goal of accurately modeling regional deformation to align closely with geologic slip rates.
1.3.1 Right-Lateral Strike-Slip and Dip-Slip Rates along the San Andreas Fault
Strike-slip rates along the San Andreas Fault (SAF) in the San Bernardino Mountains exhibit significant variation, decreasing from approximately 24 mm/yr at Cajon Pass to about 5 mm/yr near the southern Big Bend, a distance of 20 km This reduction in strike-slip rates suggests that local deformation is being managed through uplift, off-fault deformation, or the transfer of slip to adjacent faults.
In the southern Big Bend region, slip is transferred from the San Bernardino strand of the San Andreas Fault (SAF) to the north-dipping San Gorgonio Pass thrust and the vertical Banning strand of the SAF Research by Yule and Sieh (2003) indicates a reverse slip rate exceeding 2.5 mm/yr on a northeast-striking segment of the San Gorgonio Pass thrust Currently, the right-lateral Banning strand of the SAF is active primarily near Millard and Potrero canyons, exhibiting a right-lateral strike-slip rate of 1.3–1.6 mm/yr, although its previously active trace can still be mapped throughout the pass.
The eastern end of the San Gorgonio Pass thrust divides into the Banning and north-dipping Garnet Hill strands of the San Andreas Fault These faults trend southeastward towards Biskra Palms, where the Banning strand converges with the Garnet Hill strand.
The Coachella Valley segment of the San Andreas Fault (SAF) exhibits right-lateral strike-slip rates ranging from 12 to 21 mm/yr, according to Behr et al (2010), and between 12.5 and 19.3 mm/yr as reported by van der Woerd et al (2006).
The Cooke and Dair (2011) model generates slip rates that align with many geological rates along the San Andreas Fault (SAF), but it produces left-lateral slip along the San Gorgonio Pass thrust, which contradicts the right-lateral slip evidence presented by Yule and Sieh (2003) This model adheres to the SCEC CFM fault configuration, indicating that the Banning fault is active along its entire mapped trace Given that the Banning fault runs parallel to the San Gorgonio Pass thrust, Cooke and Dair (2011) propose the removal of inactive segments explored in their study.
1.3.2 Normal Slip Along the Crafton Hills Fault Zone
The Crafton Hills fault zone is a series of normal faults between the San
The Crafton Hills fault zone, identified by offset Holocene alluvium, plays a significant role in the tectonic dynamics of the region, as noted by Yule and Spotila (2010) Previous models, such as that of Cooke and Dair (2011), which were based on the SCEC CFM, overlooked this fault zone and inaccurately depicted slip along the San Gorgonio Pass thrust fault Incorporating the Crafton Hills fault zone into tectonic models could reconcile the observed slip-sense discrepancies, as it accommodates local extension while the San Gorgonio Pass fault exhibits reverse-slip motion.
1.3.3 Right-Lateral Strike-Slip Rates Along the San Jacinto Fault
The San Jacinto Fault (SJF) exhibits various overlapping and discontinuous sub-vertical segments that significantly affect the distribution of strike-slip rates along the fault In the northernmost segment of the San Jacinto Valley fault, strike-slip rates vary from 6 to 13 mm/yr, with some measurements exceeding 20 mm/yr The central part of the Anza segment shows strike-slip rates between 7 and 15 mm/yr, while lower rates of 1.8 to 3.7 mm/yr are recorded near the southern Santa Rosa Mountains at the southern end of the Anza segment Additionally, the Coyote Creek segment has a determined strike-slip rate of over 3.2±1.2 mm/yr.
Coyote Creek segment of the SJF and only slips ∼1–3 mm/yr (Sharp, 1981) The model of Cooke and Dair (2011) matches well the right-lateral slip rates along the SJF
1.3.4 Right-Lateral Strike-Slip Within the Eastern California Shear Zone
The Eastern California Shear Zone (ECSZ) primarily features right-lateral slip faults that strike northwest-southeast, contributing between 9% and 23% of the total motion between the North American and Pacific plates (Dokka and Travis, 1990) Research by Oskin et al (2008) indicates that the six major faults in the ECSZ exhibit a cumulative strike-slip rate of approximately 6.2 ± 1.9 mm/yr since the Holocene, with individual fault rates ranging from 0.2 to 2.1 mm/yr.
Geologic slip rates and GPS velocity inversion rates for the Southern ECSZ show discrepancies Studies by Sauber et al (1994), Miller et al (2001), Becker et al (2005), Meade and Hager (2005), and Spinler et al (2010) highlight these differences in slip rate assessments.
The Eastern California Shear Zone (ECSZ) exhibits a right-lateral strike-slip accumulation rate of approximately 12 ± 2 mm/yr, nearly twice the rate derived from geological data (Oskin et al., 2008) A three-dimensional forward model by Cooke and Dair (2011) estimates an average slip rate of 7.5 ± 0.2 mm/yr, which aligns with the cumulative geological slip rate and its uncertainties This study introduces various tectonic boundary conditions, potentially broadening the slip-rate range generated by the forward models.
1.3.5 Left-Lateral Strike-Slip Along the Garlock Fault
Radiocarbon dates of Holocene sediments provide reliable left-lateral strike-slip rates between 4 and 10.7 mm/yr along the Garlock fault (Clark and Lajoie, 1974; McGill
Three-Dimensional Numerical Simulations of Deformation in Southern
Our mechanical models use the three-dimensional BEM code, Poly3D (Thomas,
Boundary Element Method (BEM) models have been effectively utilized to simulate geologic timescale deformation, particularly due to their ability to handle complex fault geometries by discretizing only fault surfaces, unlike finite element method models These models have been instrumental in studying three-dimensional active faulting across various regions, including Southern California, Mexico, Turkey, Utah, and Northern Chile, providing valuable insights into geological processes.
The fault topology in the model is discretized using a triangular mesh with an average segment length of approximately 4 km, effectively capturing variations in fault geometry as small as 10 km, and even smaller in areas of complex fault structures The triangular mesh is favored over rectangular meshes due to its superior ability to accurately represent non-planar, intricate fault shapes, while rectangular meshes can result in gaps and overlaps on curved surfaces, leading to potential local instabilities.
The three-dimensional fault geometries follow the SCEC CFM (Plesch et al.,
In our model, we incorporate 49 faults from the CFM, extending them to a depth of 35 km, where they connect to a horizontal crack This horizontal crack simulates distributed deformation within fault zones beneath the seismogenic crust The chosen depth of the crack aligns with the imaged depth of the Mohorovicic discontinuity in the region, as noted by Magistrale et al (2000), and it is important to note that near-surface deformation remains unaffected by variations in horizontal crack depths below this level.
The study area extends 20 km, utilizing a linear-elastic homogeneous and isotropic material model, which is a valid assumption for crustal rheology over short time frames All faults within this model are considered frictionless, allowing them to slip freely due to applied loads and interactions with adjacent faults To maintain continuous slip at the edges of the study area, vertical patches with specified slip are implemented where faults extend beyond the boundaries.
The modeled fault surfaces exhibit frictionless properties that replicate low-friction conditions during slip events, primarily accumulating slip during earthquakes when dynamic friction is minimal While dynamic models with frictionless faults cannot accurately simulate the initial onset of slip—occurring when the shear-to-normal stress ratio surpasses static friction—they effectively demonstrate the overall accumulation of slip under dynamic-friction conditions Therefore, it is essential to include only active fault surfaces in these models, as inactive faults should be excluded.
This study examines the horizontal crack bounded by patches with specified velocities to mimic the motion between the North American and Pacific plates To replicate the observed plate boundary motions of 45–50 mm/yr at orientations of 320°–325°, we adjust the model edge velocity between 40–45 mm/yr Poly3D Version 2.0 restricts the number of triangular elements to approximately 5760, focusing on accurate deformation in the San Bernardino Mountains region while including elastic deformation west of the San Jacinto Fault (SJF) The faults in this area accommodate about 5 mm/yr of strike-slip movement To address the missing fault slip, we proportionally reduce the plate velocity in the model Our research specifically investigates fault deformation east of the SJF, encompassing the San Andreas and Garlock faults, as well as the Eastern California Shear Zone (ECSZ), by analyzing various plate velocities to assess the sensitivity of fault slip rates and patterns to tectonic loading.
Revisions to Fault Geometry
We have enhanced the three-dimensional models of Cooke and Dair (2011) by incorporating the Big Bear and Crafton Hills faults and modifying the geometry of the Banning fault While the Big Bear fault is included in the CFM (Plesch et al., 2007), it was previously omitted from Cooke and Dair's model Our initial focus is to evaluate whether these modifications reduce the mismatch with geological slip rates Subsequently, we will use the optimized fault geometry to assess the sensitivity of slip rates to tectonic boundary conditions For consistency, all slip rates will be derived from a model employing the same tectonic loading of 45 mm/yr at an angle of 308°, allowing for a direct comparison of the impacts of the altered fault geometries.
When comparing model slip rates to geologic rates, we present the slip rate at the fault trace's surface at the investigation site, as shown in Figure 1.2 and Table 1.2 However, since this surface slip rate may not accurately reflect the entire fault surface, we also provide a weighted average slip rate for the entire fault area, including the standard deviation Discrepancies between the surface slip rate and the weighted average can arise due to variations in fault geometry with depth, which affect the interactions and stresses along the faults.
1.5.1 Addition of the Big Bear Fault
The 1992 Big Bear earthquake, an aftershock of the Landers earthquake, is characterized by a northeast-trending left-lateral strike-slip fault, though no surface trace has been identified The fault's geometry is moderately constrained by aftershock distributions, with a confidence level of 2.5 out of 5 Current models indicate an average left-lateral slip rate of 4.1 ± 1.8 mm/yr and a significant south-side up rate of 2.5 ± 1.5 mm/yr, which are not reflected in the focal mechanisms Complexities in fault shape, such as variations in fault dip with depth, may reconcile discrepancies between the oblique model slip vector and the strike-slip mechanism Additionally, unrecognized contractional features in the San Bernardino Mountains could account for the dip-slip observed on the Big Bear fault Despite its relatively small structure, the fault exhibits high slip rates, likely due to its location within an uplifting area of the restraining bend Further research is essential for a comprehensive evaluation of slip rates on this fault.
1.5.2 Addition of the Crafton Hills Fault
The Hills fault zone, as identified by Matti and Morton (1993) and Yule and Sieh (2003), features a network of normal faults However, our simulation of faulting in this region simplifies the complexity by representing it with a single fault surface in the model.
Incorporating the Crafton Hills fault into our model significantly reduces the unexpected normal slip along the San Gorgonio Pass thrust, decreasing the maximum normal slip rate from 4.3 mm/yr to 1.6 mm/yr Additionally, the weighted average normal slip rate for the western section of the San Gorgonio Pass thrust drops from 1.2 ± 0.1 mm/yr to 0.6 ± 0.9 mm/yr This increase in standard deviation indicates that certain areas of the fault surface experience reverse slip.
The Crafton Hills fault exhibits maximum dip-slip rates on its eastern edge near the San Andreas Fault (SAF), decreasing westward, which corresponds to the rugged topography of the Crafton Hills Normal slip rates along the fault range from 0.7 to 3.3 mm/yr, with a weighted average of 1.0 ± 0.8 mm/yr This fault plays a crucial role in accommodating local extension and mitigating normal slip along the western San Gorgonio Pass thrust The presence of additional faults within the Crafton Hills could further decrease anomalous slip in this area Therefore, incorporating the Crafton Hills fault into the Community Fault Model (CFM) is essential for accurate regional assessments of crustal deformation and earthquake hazards.
1.5.3 Removing the Inactive Strands of the Banning Fault
The Cooke and Dair (2011) model, based on CFM geometry and the Banning strand of the SAF, estimates a right-lateral slip rate of 7.5 mm/yr for the eastern San Gorgonio Pass thrust, while indicating a negligible left-lateral strike-slip rate of less than 0.1 mm/yr on the western part This model also reveals that, at the Earth's surface, there is predominantly left-lateral slip along the San Gorgonio Pass thrust trace Notably, our study excludes inactive segments from this analysis.
The Banning strand west of Millard Canyon has been analyzed, revealing that the inclusion of inactive fault surfaces in models can distort deformation distribution By removing these inactive sections, the model accurately depicts right-lateral strike-slip along the San Gorgonio Pass thrust trace These geometric revisions enhance the accuracy of slip sense along the thrust and align with geological strike-slip rates observed in the active portions of the Banning strand of the San Andreas Fault (SAF) Notably, the reported strike-slip rates for the Banning strand cover different time periods.
Recent studies indicate that the strike-slip rate along the San Andreas Fault (SAF) has varied significantly over time For the last 3,000 years, a slower strike-slip rate aligns more closely with models excluding inactive strands, while a faster rate over the past 100,000 years corresponds to models that include these inactive segments This revised model provides a clearer understanding of the recent deformation patterns along the faults Furthermore, the abandonment of certain Banning strand segments may relate to broader transitions in the SAF's active configuration that occurred around 100,000 years ago, emphasizing the importance of distinguishing between active and inactive segments in geological models.
Sensitivity of Fault Slip Rates to Tectonic Boundary Conditions
Small adjustments in tectonic loading can impact convergence within the restraining bend of the southern Big Bend of the San Andreas Fault (SAF) This study examines the sensitivity of fault slip to tectonic boundary conditions by varying plate velocity and orientation within current uncertainties, specifically between 45 to 50 mm/yr and 320° to 325° The model applied a velocity range of 40–45 mm/yr, correlating to 45–50 mm/yr across the plate boundary Most regional faults exhibit minimal slip rate changes of less than 0.25 mm/yr, indicating a relative insensitivity to tectonic variations However, notable exceptions with significant sensitivity (≥ 0.25 mm/yr) include the Garlock and Garnet Hill faults, the Anza segment of the SJF, the San Bernardino strand of the SAF, and the eastern San Gorgonio Pass thrust Generally, an increase in plate velocity results in higher strike and dip-slip rates for most faults.
1.6.1 Garlock Fault Sensitivity to Tectonic Boundary Conditions
The Garlock fault exhibits high sensitivity to tectonic boundary conditions, with northerly plate velocities (325°) increasing the average left-lateral slip rate by approximately 0.7 mm/yr This sensitivity is reflected in the strike-slip rates along the fault's trace, which respond similarly to tectonic loading The 325° plate velocity, acting obliquely to the fault's average strike, results in greater resolved left-lateral strike-slip compared to the 320° plate velocity In contrast, average dip-slip rates along the vertical Garlock fault remain largely unaffected by tectonic loading.
1.6.2 San Andreas Fault Sensitivity to Tectonic Boundary Conditions
For all segments of the SAF, increased strike-slip rates occur for more westerly (320°) loading, and increased dip-slip rates occur for more northerly (325°) loading
The San Bernardino strand of the SAF exhibits strike-slip rates that are highly sensitive to tectonic loading, with a notable decrease of approximately 0.7 mm/yr when the plate velocity orientation shifts from 320° to 325° In contrast, the modeled dip-slip rates remain unaffected by changes in orientation.
The modeled strike-slip rates along the eastern San Gorgonio Pass thrust, located east of the San Bernardino strand of the San Andreas Fault (SAF), show a decrease of approximately 0.4 mm/yr when the tectonic orientation is more northerly at 325° In contrast, while the right-lateral slip rates along the western San Gorgonio Pass thrust remain largely unaffected by tectonic orientation, the average dip-slip rates increase by about 0.2 mm/yr under the same northerly loading This increase indicates a reversal in slip sense along certain fault segments from normal to reverse slip, aligning more closely with geological observations of slip rates along the western half of the San Gorgonio Pass thrust, as noted by Yule and Sieh (2003).
Modeled strike-slip rates along the Garnet Hill and Banning strands of the San Andreas Fault (SAF) show a decrease of approximately 0.25 mm/yr with more northerly plate orientations (325°) While the sensitivity of slip rates to tectonic loading differs among individual SAF strands, the overall trend indicates decreased strike-slip rates and increased dip-slip rates with increased northerly plate velocity.
1.6.3 San Jacinto Fault Sensitivity to Tectonic Boundary Conditions
Increased northerly plate motion results in a reduction of modeled strike-slip rates along the San Jacinto Fault (SJF), particularly affecting the Anza segment, which experiences a notable decrease of 0.3 mm/yr, while dip-slip rates remain unchanged.
1.6.4 ECSZ Sensitivity to Tectonic Loading
For more northerly plate velocities, the Helendale, Calico–Hidalgo, Pisgah–
The Bullion and Ludlow faults exhibit increased right-lateral strike-slip rates, while more northerly plate velocities reduce modeled strike-slip rates along the Lenwood–Lockhart fault and do not influence the Camp Rock fault's slip rates The highest cumulative strike-slip rates across all faults occur when plate velocity is oriented at 325°, which aligns more closely with the average trace of ECSZ faults, potentially leading to greater strike-slip at this angle.
The Camp Rock fault, situated at the heart of the Eastern California Shear Zone (ECSZ), exhibits strike-slip rates that are largely unaffected by loading orientation, showing only a minimal decrease of 0.1 mm/yr when the plate motion shifts from 320° to 325° In contrast, adjacent faults to the east and west of the Camp Rock fault, which share similar lengths and orientations, demonstrate a greater sensitivity to variations in tectonic boundary conditions.
The Lenwood–Lockhart fault, characterized by its arcuate shape, merges with the Helendale fault to the north, exhibiting an average strike of 314° In contrast, the Helendale fault has a more northerly average strike of 320° Notably, strike-slip rates are higher along the Helendale fault, influenced by tectonic loading; northerly loading favors strike-slip movement along the Helendale fault, while westerly loading is more conducive to strike-slip activity along the Lenwood–Lockhart fault.
1.6.5 Sensitivity of Vertical Deformation Pattern in San Bernardino Mountains
Uplift rate patterns in the San Bernardino Mountains indicate off-fault deformation within mechanical models, allowing for the assessment of uplift and dip-slip rates along range-bounding faults under varying tectonic loading conditions The uplift rates derived from linear elastic boundary element method (BEM) models are adjusted for isostatic compensation In line with the methodology of Cooke and Dair (2011), we utilized a mantle density of 4100 kg/m³, a crustal density of 2700 kg/m³, and a flexural rigidity of 2 × 10²² Pa m³ for our calculations.
Uplift rates in the San Bernardino Mountains increase with both the magnitude of loading and a more northerly orientation of plate velocity The pronounced gradients in uplift across faults indicate that dip-slip movements along these faults significantly control the region's uplift Additionally, variations in plate velocity, such as shifting from 320° to 325°, lead to greater deviations from the San Andreas Fault's overall trend, resulting in reduced strike-slip rates and enhanced dip-slip rates, ultimately causing increased uplift in the area.
The percent change in uplift from 320° to 325° plate velocity orientation for four numbered locations within the San Bernardino Mountains is presented in Figure 8 These
The Morongo, San Gorgonio, and Big Bear blocks exhibit positive percent changes indicating that a northerly oriented plate velocity of 325° leads to increased uplift in these areas The modeled uplift rates demonstrate greater sensitivity to variations in plate velocity orientation, ranging from 0.15 to 0.25 mm/yr, compared to changes in magnitude, which are less than 0.05 mm/yr Additionally, the uplift rates show significantly less sensitivity to the tested range of tectonic loading compared to strike-slip rates along the faults.
1.7 Comparison of Model and Geologic Slip Rates and Vertical Deformation
We enhance the model established by Cooke and Dair (2011) by incorporating the Crafton Hills and Big Bear faults while excluding inactive segments of the Banning fault, resulting in a better alignment between modeled and geological slip rates This refinement reduces inaccuracies, such as the misrepresentation of normal and left-lateral strike-slip on the San Gorgonio Thrust fault However, the tectonic loading rate of 45 mm/yr at 308° used in their study exceeds the range identified by regional geodetic studies Additionally, while Cooke and Dair (2011) provided an average slip rate with a standard deviation reflecting spatial slip variability, they overlooked the sensitivity to tectonic loading By analyzing various tectonic plate velocities and orientations, we can effectively compare the ranges of slip rates influenced by plate motion uncertainties with geological estimates.
1.7.1 Comparison of Model and Geologic Slip Rates on the Garlock Fault
The modeled left-lateral slip rates overlap geologic slip rates of McGill and Sieh
In 1993, analyses at site 6 revealed an overestimation of slip rates by McGill et al (2009) at site 2, while the rates reported by Clark and Lajoie (1974) at site 3 were slightly underestimated Implementing models with westerly oriented and slower plate velocities effectively aligns with the geological slip rate, reducing both the overestimation at site 2 and the underestimation at site 3.
The strike-slip rates along the fault trace are more responsive to the orientation of plate velocity than the average rates along the Garlock fault While average strike-slip rates exhibit a minor variation of approximately 0.7 mm/yr, surface-slip rates can increase significantly, by up to 1 mm/yr, when the plate velocity shifts to a more northerly direction.
1.7.2 Comparison of Model and Geologic Slip Rates on the San Andreas Fault
Discussion
tradeoffs of slip rates between faults within the southern SAF system allows us to explore the evolution and partitioning of strain within the system
1.8.1 Uncertainties of Model Slip Rates Due to Uncertainties in Plate Velocity
Slip rate uncertainties arise from spatial variability along faults and tectonic sensitivity, as detailed in Table 1.2 Spatial variability, determined by the standard deviation of the weighted average slip rate, indicates the range of slip rates along fault segments For instance, a theoretical fault with uniform characteristics would exhibit low standard deviation in slip rates This variability is influenced by topological differences and interactions with adjacent faults, meaning slip rates at one point may not represent those at another location on the same fault Tectonic sensitivity reflects the range of weighted average slip rates based on different models of plate velocity Overall uncertainty combines both spatial variability and tectonic sensitivity, with the latter generally being less significant Notably, the Helendale fault's strike-slip rate shows higher tectonic sensitivity than spatial variability, implying that errors in estimating this rate are more due to tectonic loading uncertainties than geometric variations Neglecting tectonic sensitivity could lead to substantial underestimation of strike-slip rate uncertainty for this fault In contrast, for other faults in the southern SAF system, greater spatial variability compared to tectonic sensitivity underscores the primary role of geometric heterogeneities in controlling fault slip rates.
Slip rates exceeding 0.4 mm/yr of tectonic sensitivity are observed along the Garlock fault and the San Bernardino strand of the San Andreas Fault (SAF), with the latter being the only fault exhibiting dip-slip tectonic sensitivity greater than 0.2 mm/yr The sensitivity of strike-slip rates to spatial variability is approximately 3–35 times higher than the tectonic sensitivity for faults active within the restraining bend of the SAF, where complex fault geometry significantly influences strike-slip rate distribution In contrast, the San Jacinto Fault (SJF) displays spatial variability of strike-slip rates that is about 4–22 times greater than its tectonic sensitivity, with its geometric control stemming from large stepovers between fault segments, particularly near Hemet, California.
The tectonic sensitivity of dip-slip rates is notably relevant for dipping faults, particularly in the San Gorgonio Pass thrust and the north-dipping Garnet Hill strand of the San Andreas Fault (SAF) Although the Mission Creek strand of the SAF is vertical, its dip-slip rate sensitivity may be influenced by its intersection with the dipping Garnet Hill strand Incorporating tectonic sensitivity across all segments of the SAF, the San Jacinto Fault (SJF) systems, the Eastern California Shear Zone (ECSZ), and the Garlock fault significantly amplifies the uncertainty surrounding average strike-slip rates along these faults.
1.8.2 Remaining Mismatch Between Model and Geologic Slip Rates
Comparing model and geologic slip rates validates fault geometries, tectonic boundary conditions, and underlying assumptions This section addresses the discrepancies between geologic and modeled slip rates, highlighting erroneous slip rates Our model results indicate that inaccuracies in fault geometry significantly influence errors in slip rates.
Cumulative strike-slip rates of the modeled ECSZ along a transect at ∼34°45′ latitude are slightly higher than the range of cumulative geologic rates from Oskin et al
The level of geometric detail in the modeled Eastern California Shear Zone (ECSZ) faults significantly influences the accuracy of strike-slip rate estimations While the SCEC CFM models these faults as continuous features, many are actually discontinuous, featuring small bends and stepovers (Oskin et al., 2008) Oversimplifying the fault trace geometry can lead to an overestimation of strike-slip rates By incorporating more geometric detail, particularly along faults like Helendale and Camp Rock, the model could yield strike-slip rates that align more closely with geological data.
Our models indicate that the cumulative strike-slip rates across the Eastern California Shear Zone (ECSZ) range from 7.9 to 9.8 mm/yr, which aligns more closely with the geological cumulative slip rate of 4.3 to 8.1 mm/yr than the geodetic estimates of 12 ± 2 mm/yr This discrepancy may arise from several factors, including the lack of geometric detail in GPS models that typically use simplified fault geometries, potentially leading to an overestimation of slip rates Additionally, post-seismic deformation from recent significant earthquakes in the ECSZ may result in temporarily elevated GPS velocities, contributing to the observed mismatch in measurements.
(Oskin et al., 2008) Additionally, distributed off-fault deformations may contribute to the relative displacement of GPS stations and be erroneously attributed to slip along the faults
The San Gorgonio Pass thrust exhibits both normal and reverse slip characteristics Incorporating the Crafton Hills fault into the model enhanced the findings of Cooke and Dair (2011), yet it did not fully address the unexpected normal slip observed in certain sections of the San Gorgonio Pass thrust This fault, as represented in the CFM and the current model, features a corrugated surface trace that runs east-west and has a dip of 45° to the north.
Steeper faults at depth may lead to reduced dip-slip, while shallower faults could enhance it (Cooke and Dair, 2011) Yule and Sieh (2003) suggest that this fault geometry could explain the extensional features seen in the Cox Ranch and Beaumont Plain fault zones Additionally, the extension accommodation along these structures might decrease normal slip on the western San Gorgonio Pass thrust fault.
1.8.2.3 San Bernardino Strand of the San Andreas Fault
Fuis et al (2012) demonstrated that a 37° northeast-dipping San Bernardino strand of the San Andreas Fault (SAF) aligns more closely with magnetic data compared to a vertical strand, as used in the SCEC CFM and this study In the transpressional environment of the restraining bend, this northeast dip is expected to enhance reverse-slip rates along the fault, contributing to the uplift of the San Bernardino Mountains While future Boundary Element Method (BEM) models can investigate this fault geometry, current data on dip-slip rates is lacking for the distribution of strike-slip rates from Cajon Pass to Burro Flats.
1.8.3 Alternative Loading Along the Southern San Jacinto and San Andreas Fault
At the southern edge of our model, the strike-slip rates for the San Andreas and San Jacinto faults are set at 25 mm/yr and 10 mm/yr, respectively, based on tectonic boundary conditions (Figure 1.3) This approach suggests that the San Andreas Fault (SAF) accommodates more strain compared to the San Jacinto Fault (SJF) However, some studies argue that the SJF may accommodate equal or greater deformation than the SAF To explore this, we evenly distribute the total strain of 35 mm/yr between the two faults and analyze the resulting slip-rate profiles against the initial rates of 25 mm/yr and 10 mm/yr.
Increasing the slip rate from 10 to 17.5 mm/yr along the San Jacinto fault results in a decrease in slip rate to the north, away from the applied load While higher strike-slip rates align better with geological observations at sites 9 and 11, they lead to discrepancies at sites 10, 14, 15, 16, 17, and 18 The modeled strike-slip rates for the San Jacinto Valley segment remain largely unaffected by the increased loading Notably, in the Anza segment, the maximum strike-slip rate surpasses the rate applied at the model's edge, indicating that the strike-slip rates in this region are influenced more by the resistance of the San Andreas fault within the restraining bend than by the partitioning of shear strain between the San Andreas and San Jacinto faults.
The reduction in strike-slip rate along the southern edge of the San Andreas Fault (SAF) significantly impacts three faults: the Coachella Valley segment, Mission Creek strand, and the southern section of the Banning strand Notably, the Coachella Valley strand is directly linked to the vertical patch with the applied slip rate, while the overall change in strike-slip rate from a more distributed loading between the San Andreas and San Jacinto faults is less than 1 mm/year at the surface.
The strike-slip rates along the southern San Andreas and San Jacinto faults are primarily influenced by fault geometry and overall tectonic loading, rather than the distribution of applied slip rates at the model's edge While variations in edge slip rates can impact strike-slip rates, they do not significantly improve the alignment with geological slip rates Additionally, the findings indicate that boundary loading conditions have minimal effect on slip rates in the central region of the model.
1.8.4 Long-Term Change in Plate Boundary Strain Conditions
The southern San Andreas Fault (SAF) is believed to have altered its configuration over 95,000 years ago, with recent luminescence dating indicating that the Mill Creek strand has not experienced any slip during this period Prior to this time, the Mill Creek strand connected to the Mission Creek and San Bernardino strands of the SAF through a gentler bend, unlike the current active system that accommodates greater uplift The evolution of fault systems suggests that more mature faults should exhibit higher strike-slip rates; however, the reason for the SAF's shift from the Mill Creek configuration to a more complex system remains unclear This change may be attributed to a shift in plate motion, with model results indicating that north-south oriented plate motions reduce slip rates along the SAF while increasing uplift rates The transition from northwest-southeast to north-south plate motion before 95,000 years ago could explain the SAF's abandonment of a more efficient fault for a kinked geometry associated with increased uplift Additionally, northerly tectonic loading enhances right-lateral slip along the Eastern California Shear Zone (ECSZ), suggesting that a continued northerly shift in plate motion could lead to the abandonment of the kinked SAF in San Gorgonio Pass and the integration of ECSZ faults with the Coachella Valley segment of the SAF.
Conclusions
BEM models indicate that tectonic boundary conditions significantly influence fault slip rates in the San Bernardino Mountains region, revealing a range of slip rates impacted by fault geometry and plate velocity Higher plate velocities lead to increased fault-slip rates, reinforcing the notion that fault geometry plays a crucial role in deformation Adjustments to fault geometry enhance the alignment of model-slip rates with geological observations The sensitivity of fault slip rates to geometric variations surpasses the uncertainties related to tectonic loading The distribution of strike-slip rates between the San Jacinto and San Andreas faults is likely governed by geometric factors rather than direct loading partitioning A transition from westerly to northerly plate velocities promotes uplift in the San Bernardino Mountains and affects strike-slip dynamics on adjacent faults Conversely, more northerly plate motions reduce strike-slip rates on the San Andreas and San Jacinto faults This relationship between plate motion orientation and slip rates may shed light on the recent changes in the San Andreas Fault configuration over the past 95,000 years, suggesting that a shift towards northerly plate motions could enhance uplift in the San Bernardino Mountains while reducing strike-slip rates along the fault.
Figures
Figure 1.1 Fault trace map of the San Bernardino Mountains region The acronyms denote Cajon Pass (CP), the San Andreas fault (SAF), and the Crafton Hills fault zone (CHFZ)
Figure 1.2 Fault traces within the study area with locations of Quaternary geologic slip- rates indicated by circles (right-lateral) and squares (left-lateral) shaded by slip rate (site
26 is the only reverse-slip rate and indicated by a solid black triangle) Numbers correspond to slip rate investigations listed in Table 1
In the model setup illustrated in Figure 1.3, faults are represented as triangular elements, specifically along the San Jacinto fault (SJF) The model applies half of the plate motion (v) to the southwest and northeast edges, with a gradual decrease in motion towards the center along the northwest and southeast edges For faults extending beyond the model's boundary, slip rates are assigned along the vertical edge cracks.
The modeled strike-slip rates along the San Gorgonio Pass thrust and Banning strand, with a tectonic loading of 45 mm/yr at 308°, indicate the correct sense of slip after removing inactive portions of the Banning strand Additionally, the modeled rates along the Banning strand of the San Andreas Fault remain consistent with geological rates observed at Millard Canyon, as documented by Yule and Sieh (2003) Vertical bars 25a and 25b represent geological slip rates along the Banning strand within Millard Canyon, further supporting these findings.
Figure 1.5 Change in weighted average dip-slip rate (circles) and strike-slip rate
The analysis of plate velocity orientation between 320° and 325° reveals significant changes in slip rates, particularly for triangles and circles outside the horizontal rectangle, indicating variations greater than 0.25 mm/yr The comparison of 40 mm/yr and 45 mm/yr velocities shows that a negative change signifies a decrease in strike-slip and dip-slip rates with a more northerly orientation, while a positive change reflects an increase in slip rates Notably, strike-slip rates along the Garlock fault and the Eastern California Shear Zone (ECSZ) rise with increased northerly plate velocity, whereas they decline along the San Andreas and San Jacinto faults Additionally, a more northerly plate velocity enhances the dip-slip rate along the San Andreas fault (SAF) The term CC-B-SM refers to the Coyote Creek–Borrego–Superstition Mountain segment.
The strike-slip rate profiles for the Garlock, San Andreas, and San Jacinto faults illustrate variations in tectonic loading, with vertical bars indicating the geological slip rates along these faults The profiles in the San Andreas and San Jacinto sections reflect different strands of these significant geological features.
The Eastern California Shear Zone (ECSZ) features significant geologic and modeled strike-slip rates across its six major faults, as illustrated in Figure 1.7 The figure includes cumulative slip rates and highlights various sites of geologic investigations, with gray vertical bars indicating geologic slip rates Modeled strike-slip rates are represented by horizontal lines, with a plate velocity of 45 mm/yr in black and 40 mm/yr in gray Key investigation sites are denoted by acronyms: Helendale (H), Lenwood–Lockhart (LL), Camp Rock (CR), Calico–Hidalgo (CH), Pisgah–Bullion (PB), and Ludlow (L) For detailed site information, refer to Table 1.
The San Bernardino Mountains exhibit contoured uplift rates corrected for isostasy, with maximum uplift observed in models featuring faster and more northerly plate motions A comparison of uplift changes between 320° and 325° models at four distinct locations—Yucaipa Ridge, Morongo, San Gorgonio, and Big Bear—reveals that positive values indicate increased uplift as plate motion shifts to a more northerly orientation Additionally, uplift rates demonstrate less sensitivity to variations in tectonic loading compared to strike-slip rates.
The slip rate profiles for the San Jacinto and San Andreas faults illustrate varying loading along vertical patches on the model's southern boundary The dotted lines indicate the velocity distribution used in the models, with the San Andreas fault set at 25 mm/yr and the San Jacinto fault at 10 mm/yr In contrast, the solid lines show equal velocity of 17.5 mm/yr for both faults Notably, minor changes occur along the faults near the prescribed velocities, with these variations diminishing as one moves north along the faults.
The schematic in Figure 1.10 illustrates the strike-slip magnitude and uplift rates in the San Bernardino Mountains region, highlighting westerly (320°) and northerly (325°) plate motions Faster rates are represented in red and bold, while slower rates are shown in blue and thin Key acronyms include the San Andreas Fault (SAF), San Bernardino Mountains Region (SBMR), San Jacinto Fault (SJF), and Eastern California Shear Zone (ECSZ).
Tables
Recent geologic slip rates in the San Bernardino Mountains region reveal significant tectonic activity, characterized by various motion types including left-lateral (LL), right-lateral (RL), and reverse (RV) movements These findings are visually represented in Figure 1.2, highlighting the specific site locations where these measurements were taken.
Table 1.2 Weighted average fault slip rates with spatial variability (standard deviation of slip) and tectonic sensitivity (Range of Average Slip for the Four Models) Values of slip
HOW MUCH CAN OFF-FAULT DEFORMATION CONTRIBUTE TO THE SLIP
The eastern California shear zone (ECSZ) in southern California features a network of northwest-southeast right-lateral strike-slip faults that account for 12%–25% of the plate motion between the Pacific and North America plates Discrepancies in the ECSZ's contribution to plate boundary deformation arise from varying results in geologic and geodetic studies Geologic estimates indicate a cumulative slip rate of 6.2 ± 1.9 mm/yr across six major faults, while GPS station velocity inversions suggest rates between 13.5 and 18 mm/yr This 7–12 mm/yr difference in slip rates has been linked to temporal variations in the strain field, and inaccuracies in fault geometries used in GPS models may further inflate these slip rate estimates.
Faults with bends, stepovers, or terminations exhibit gradients in slip rates, contrasting with the uniform slip distribution found in long, straight faults The earthquake rebound theory posits that elastic strain should be fully released during seismic events; however, irregularities in faults may prevent complete strain release, leading to measurable off-fault deformation over time Geodetic model inversions that estimate fault slip rates based on kinematic assumptions require these rates to equal the GPS plate boundary velocity, relying on elastic models that disregard permanent off-fault deformation and attribute all observed GPS changes to fault slip.
This study focuses on the Mojave Desert segment of the Eastern California Shear Zone (ECSZ), positioned between the Garlock and San Andreas faults This region is characterized by significant segmentation and discontinuity along the Pacific–North America plate boundary, highlighting a notable difference between geologic and geodetic fault slip rates, as noted by Oskin et al (2008) We aim to enhance the understanding of this area by updating the fault geometry provided by the Southern California Earthquake Center.
The Community Fault Model (CFM; Plesch et al., 2007) enhances the representation of the discontinuous active Earthquake Cycle System Zone (ECSZ) To validate the updated fault model, we compare three-dimensional mechanical simulations with measured geological slip rates Additionally, we analyze the deformation field from the validated model to assess the impact of off-fault deformation throughout the ECSZ.
We utilize the boundary element method (BEM) code Poly3D to model the three-dimensional deformation of the Eastern California Shear Zone (ECSZ), incorporating 52 active faults, including the San Andreas, San Jacinto, and Garlock faults The BEM allows for the discretization of faults into triangular elements, enabling the representation of complex fault geometries Our model extends the faults to a depth of 35 km, where they merge into a horizontal crack that simulates distributed deformation beneath the seismogenic crust Notably, near-surface deformation remains unaffected by horizontal crack depths exceeding 20 km To prevent zero slip at lateral fault tips, we apply known geologic slip rates where faults reach the model boundaries Additionally, we implement plate velocities of 45–50 mm/yr at the basal crack's outer edge, reflecting uncertainties in plate motions The frictionless nature of the faults allows for free slipping in response to loading and interactions with nearby faults, simulating low-strength conditions during earthquakes when slip accumulation occurs Similar BEM models have been effectively employed to study active faulting in southern California.
A comparison of the Fault Activity Map of California (Jennings and Bryant, 2010) and the CFM highlights inaccuracies in the representation of three faulted regions within the central Mojave: the northern Calico fault, the area between the Harper Lake and Camp Rock faults, and the Lockhart and Lenwood faults region The northern 10 km of the Calico fault, located north of Interstate 15, has not experienced right-lateral slip in the past 700,000 years, showing evidence of cutting bedrock but not disrupting late Quaternary alluvial fans The CFM inaccurately connects the Camp Rock and Harper Lake faults with a linear segment lacking a surface trace, while both faults actually terminate within folded Miocene strata Additionally, the CFM suggests a continuous connection between the Lockhart, Lenwood, and Helendale faults, despite many segments being inactive for 700,000 years, indicating that these faults may not connect at all This is particularly evident in the Lenwood fault, which bends and loses slip within the Lenwood anticline To enhance the accuracy of the deformation model in this region, we propose removing the inactive and nonexistent fault segments from the CFM representation of these three faulted areas in the ECSZ.
2.3 Changes in Fault Slip Rates Due to Fault Model Revisions
The geologic slip rates observed at various locations along the Calico, Camp Rock, Lenwood, and Helendale faults are analyzed in comparison to the predicted strike-slip rates from models (Figure 2.2) Utilizing the methodology established by Herbert and Cooke (2012), the variations in slip rates derived from the applied boundary conditions highlight the uncertainties associated with plate motions.
The CFM-based model and the revised model both indicate strike-slip rates along the Calico fault that align with the geologic rate identified by Oskin et al (2007) While the strike-slip rates are comparable, the revised model shows slightly higher slip rates near the geologic investigation site This local increase in slip rates is attributed to the transfer of slip from the disconnection of the adjacent Harper Lake and Camp Rock faults, with the revised model's findings for the Camp Rock fault corroborating Oskin et al.'s geologic rate.
In 2008, a significant enhancement in the alignment between our model and geological slip rates was observed with the removal of a single fault segment between the Harper Lake and Camp Rock faults, underscoring the substantial influence that minor adjustments to fault geometries can exert on crustal deformation.
The removal of three fault segments connecting the Helendale, Lockhart, and Lenwood faults significantly impacts strike-slip rates Disconnecting the Helendale fault from the southern Lockhart fault leads to a notable reduction in the right-lateral slip rate along the Helendale fault, aligning it with previously observed rates Meanwhile, the revised fault geometry results in increased right-lateral slip rates along the Lockhart and Lenwood faults, with the Lockhart fault transitioning from predominantly left-lateral to entirely right-lateral slip Although geologic slip rates for the Lockhart fault are unavailable, the model's right-lateral slip aligns with geological evidence The increase in right-lateral slip along the Lenwood fault arises from the disconnection of the Helendale and South Lockhart faults, which transfers right-lateral slip to the Lenwood fault, resulting in a slip rate that overlaps with previous findings.
The updated geometry of the Calico, Harper Lake, Camp Rock, Lockhart, Lenwood, and Helendale faults more accurately reflects the mapped active traces identified by Jennings and Bryant (2010) and aligns more closely with the available strike-slip rates reported by Oskin et al (2007, 2008).
In the Mojave Desert section of the Eastern California Shear Zone (ECSZ), disconnected faults create localized slip rate gradients that can intensify stress and lead to permanent off-fault deformation This deformation is facilitated by various mechanisms, including cleavage development, granular flow, folding, secondary faulting, pressure solution, and microcracking, which can significantly alter the orientation of features near the faults.
This study examines off-fault deformation patterns in the Eastern California Shear Zone (ECSZ) by analyzing strain energy density, which reflects the mechanical work of deformation in the rock surrounding faults Although the elastic properties of the Boundary Element Method (BEM) model do not directly account for inelastic processes, areas of high strain energy density indicate where such processes are likely to occur Previous research has linked strain energy density from linear-elastic models to the formation of permanent deformation that contributes to fault growth Notably, strain energy density peaks near fault tips and bends within the ECSZ, with significant concentrations observed at locations where multiple faults converge, such as point A in Figure 4A, resulting in a pronounced lobe of high-strain energy density.
Model results indicate that both fault slip and off-fault deformation significantly influence velocity across fault traces Specifically, the contribution of off-fault deformation to total velocity increases from south to north within the study area, with northern regions potentially seeing up to 60% of velocity attributed to off-fault deformation In the Mojave Desert area, off-fault deformation accounts for approximately 40% ± 23% of the overall plate-parallel velocity across the Eastern California Shear Zone (ECSZ), aligning with previous findings that reported up to 25% off-fault deformation near faults in the ECSZ These results corroborate broader deformation models in southern California, which also indicate significant off-fault deformation, particularly within the ECSZ, where prior studies have documented contributions ranging from 28% to 33%.
The Mojave Desert section of the ECSZ exhibits permanent strain through various forms of off-fault deformation, particularly in areas of local transpression, near fault tips, and where slip gradients are pronounced Notably, the northern tips of the Lenwood and Camp Rock faults merge into the south limb of the Lenwood anticline Although the northern Calico fault shows no recent ground rupture, nearby folded pediments and potential active uplift of the Calico Mountains suggest ongoing geological activity Our predictive models indicate considerable off-fault deformation in these regions.
2.5 Potential Role of Off-Fault Deformation on Geodetic Estimates of Slip
INFLUENCE OF FAULT CONNECTIVITY ON SLIP RATES IN SOUTHERN CALIFORNIA: POTENTIAL IMPACT ON DISCREPANCIES BETWEEN
GEODETIC DERIVED AND GEOLOGIC SLIP RATES
Accurate slip rate estimates are crucial for forecasting seismic hazards, particularly in southern California, where discrepancies exist between short-term slip rates from geodetic data and long-term geological slip rates from paleoseismic studies Notable areas of disagreement include the San Bernardino strand of the San Andreas fault and the eastern California shear zone These inconsistencies may stem from errors in either geodetic or geological slip rate data, unaccounted off-fault deformation, or temporal variations in the strain field.
Accurate geodetic data is crucial for estimating slip rates; however, inaccuracies in regional fault geometries within inversion models can introduce significant errors in these estimates (Peltzer et al., 2001; Bennett et al., 2004; Dolan et al., 2007; Freed et al., 2007; Oskin et al., 2008; Chuang and Johnson, 2011; Hearn et al., 2013; Johnson, 2013).
Models that infer slip rates across the Pacific and North American plate boundary
Various studies on tectonic deformation in southern California present differing assumptions regarding long-term internal deformation, with some models neglecting it entirely while others incorporate geologic slip rate constraints Geodetic models often assume steady deformation; however, some utilize viscoelastic earthquake cycle effects to account for increased deformation rates near faults post-large earthquakes While all models simplify the active fault network, block models particularly require a fully connected fault system to create closed-volume fault-bounded blocks These block models directly invert geodetic data using error-minimizing functions, resulting in a strong fit to the observed geodetic data.
Nonuniqueness in block models is influenced by sparse geodetic data and trade-offs between locking depth and slip rates A significant source of uncertainty stems from the fact that block boundaries often do not align with mapped fault traces, and some are arbitrarily defined without corresponding known faults For instance, in southern California, many block models simplify the active fault network by inaccurately connecting the San Jacinto fault to the San Andreas Fault near Cajon Pass, despite a lack of geological evidence supporting this connection.
The study focuses on the Eastern California Shear Zone (ECSZ), examining faults that have not experienced surface rupture in approximately 700,000 years, as noted by Morton (1993) and Jennings and Bryant (2010) Additionally, it aims to exclude faults that were active during the late Pleistocene, as highlighted by Oskin et al (2008).
This study examines the impact of the San Jacinto fault's connectivity to the San Andreas Fault (SAF) and within the Eastern California Shear Zone (ECSZ) on strike-slip rates and interseismic surface deformation patterns We highlight how inaccurate fault connectivity can lead to discrepancies between geological slip rates and those derived from geodetic data when using overconnected fault models To investigate this, we simulate deformation in Southern California utilizing three-dimensional fault geometries that are geologically and geophysically constrained Our fault configuration effectively reproduces the geological slip rates and uplift patterns observed along the southern SAF and ECSZ Additionally, we assess the influence of fault connectivity on slip rates by simplifying and connecting certain faults to reflect the geometries commonly employed in plate boundary-scale block models of Southern California.
California's seismic landscape is characterized by the connection of the San Jacinto fault to the San Andreas Fault (SAF), alongside the integration of individually mapped faults within the Eastern California Shear Zone (ECSZ) This approach reflects the fault network utilized in block models as established by Becker et al (2005) and Meade and Hager (2005).
[2005], Spinler et al [2010], and Loveless and Meade [2011] We show that forward that we tested has far less effect on interseismic velocities than on slip rates
Consequently, using either an overconnected or complex fault geometry in geodetic inversions may provide the same good fit to geodetic data but could produce different geologic slip rates
In southern California, we examine two regions where there are notable differences between geodetic and geologic strike-slip rates Specifically, along the San Bernardino strand of the San Andreas Fault (SAF), geodetic measurements indicate slower strike-slip rates compared to the higher geologic slip rates observed.
In the Eastern California Shear Zone (ECSZ), geodetic strike-slip rate estimates often exceed geological slip rates Notably, the San Jacinto fault significantly influences deformation in our study area, and we present strike-slip rates specifically for the San Jacinto Valley segment, where geodetic and geological rates align more closely.
3.2.1 Strike-Slip Rate Estimates Along the San Bernardino Strand of the SAF
Strike-slip rates along the San Bernardino strand of the SAF determined from geologic investigations decrease southward from Cajon Pass to San Gorgonio Pass from
The observed decrease in slip rates from approximately 25 mm/yr to around 8 mm/yr indicates a transfer of slip to adjacent faults, particularly the San Jacinto fault, or to oblique reverse faults located within the San Gorgonio Pass.
Block models that utilize geodetic data without relying on geological slip rates as constraints tend to predict slower strike-slip rates compared to geological observations along the San Bernardino strand of the San Andreas Fault This discrepancy is highlighted by the findings of Becker et al.
The study by Meade and Hager (2005) reports a slip rate of 5.1 ± 1.5 mm/yr, which overlaps with the lower range of a paleoseismic slip rate, while Loveless and Meade (2011) present the fastest strike-slip rate of 10.2 ± 0.3 mm/yr, aligning with two of the five paleoseismic slip rates This improved accuracy in Loveless and Meade's models may be attributed to enhanced fault geometries, including the incorporation of a north-dipping San Gorgonio Pass thrust, which provides a closer match to mapped fault traces compared to earlier block models Notably, the San Jacinto Valley segment of the San Jacinto fault connects directly to the San Bernardino strand of the San Andreas Fault near Cajon Pass, where the surface traces of these faults run nearly parallel and are only 2 km apart without intersecting.
Inverse models that integrate GPS velocities and geologic slip rates help to minimize the gap between geologic and inversion-derived rates of deformation in the southern California fault system In the northern part of the San Bernardino strand of the San Andreas Fault (SAF), these models indicate a right-lateral slip rate of 12.1–23.8 mm/yr, aligning with established geologic rates Similarly, the southern section of the San Bernardino strand shows strike-slip rates of 11.7–15 mm/yr, which also correspond with geologic observations.
Research indicates that the average strike-slip rate estimates for the San Bernardino strand of the San Andreas Fault (SAF) align with geologic data, showing a range of 5.7–17.8 mm/yr in the northern section and 10.3–13.7 mm/yr in the southern section, as calculated using the "average block model" method (Hammond and Thatcher, 2007; Johnson, 2013; Bird, 2009; Zeng and Shen, 2014).
Johnson (2013) demonstrates that incorporating geological slip rates significantly affects inversion results by comparing kinematic fault network models with and without these constraints The model inversion, which includes geological slip rate constraints, shows substantial increases in slip rates of 5–10 mm/yr along the San Bernardino strand of the San Andreas Fault (SAF) This difference in slip rates underscores the difficulty of reconciling long-term geological slip rates with GPS velocities in the San Bernardino segment of the SAF.
3.2.2 Strike-Slip Rate Estimates Along the San Jacinto Valley Segment of the San Jacinto Fault
THE WORK OF FAULT GENERATION IN LABORATORY SANDBOX
The development and timing of faulting are influenced by the work needed to create new fault surfaces, making the calculation of this work crucial for predicting failures The empirical Coulomb criterion, as outlined by Jaeger et al (2007), characterizes failure based on the normal stress-dependent properties of intact rock, including inherent shear strength and internal friction coefficient derived from laboratory tests on small rock samples However, the Coulomb criterion introduces ambiguity in fault prediction by predicting two potential failure surfaces under the same stress conditions.
The Coulomb criterion for predicting fault failure indicates that fault growth in analog experiments does not always align with the highest Coulomb stresses (Del Castello and Cooke, 2007) Their work budget approach demonstrates that in numerical models of sandbox experiments, fault growth occurs when the reduction in external work from adding a fault surpasses the energy needed to create it Therefore, directly calculating the work needed for fault growth in analog sandbox models could enhance our understanding of both the pathways and timing of fault development.
For centuries, analog models have played a crucial role in studying fault evolution by examining displacements and stresses, while also incorporating accurately scaled material properties that mimic rock-like behavior These models yield quantitative data that enhances our understanding of fault system evolution.
Sandbox experiments are highly effective for studying fault system evolution due to their ability to accurately control boundary conditions and material properties These experiments allow for direct observation of fault growth and provide quantitative data on the evolving displacement field and the total backwall force needed to deform the sand body Recent advancements in sandbox apparatuses, which measure applied stress, enable researchers to directly observe the work involved in fault growth, enhancing our understanding of geological processes (Nieuwland et al., 2001; Cruz et al., 2010; Cubas et al., 2010; Souloumiac et al., 2012).
We determine the work required to grow faults within compressional sandbox experiments conducted at the Université de Cergy-Pontoise (UCP) and Stanford
Research by Cruz et al (2010) highlights the influence of backwall force changes on faulting, while Maillot's (2013) Casagrande shear box experiments at UCP offer valuable measurements of sand strength Our findings indicate that both sandbox and Casagrande shear box tests yield comparable values for the work necessary to develop faults in sand, providing useful insights for fault growth predictions.
The balanced energy budget concept is crucial in Earth sciences for analyzing geologic structures and tectonic deformation, often utilizing a work minimization approach This principle originates from Griffith's 1920 work, which established that, in an equilibrium system, the energy needed for crack growth is countered by an equal change in mechanical energy Irwin (1958) expanded on this by defining the critical energy release rate, linking it to a crack's stress field through critical stress intensity factors, which are material properties independent of crack size, orientation, and normal stress While the critical energy release rate effectively describes colinear crack propagation in various engineering materials, empirical data on the critical values for crack growth in rock remains limited Additionally, frictional failure according to the Coulomb criterion presents a different approach.
Griffith's research highlights the significance of material properties such as inherent shear strength, internal friction, and normal stress on potential failure planes It emphasizes that increased shear stress is necessary to counteract higher normal stresses on incipient faults located deeper within the Earth Conversely, the energy release rate suggests that the work required for fault growth remains consistent, irrespective of the crust's depth.
The fault system work budget comprises five key components that contribute to the total external work (Wext) applied to the system These components include internal work (Wint), work against gravity (Wgrav), work against friction (Wfric), seismic radiated energy (Wseis), and the work of fault propagation (Wprop) The combined losses during faulting, represented as W grow (Wprop + Wseis), are equivalent to the change in force drop, calculated as force times distance.
Wgrow, represented as ΔWext, is calculated using the equation ΔF = ΔFL, where ΔF denotes the difference in force between peak and trough force pairs, and L indicates the change in backwall distance This analysis focuses on determining Wgrow during fault events in both analog sandbox models and Casagrande shear box experiments, examining various layer thicknesses to assess how fault growth is influenced by normal stress.
This study examines data from compressional sandbox wedge experiments conducted at UCP and Stanford University, utilizing similar coarse sand materials Additionally, experiments at UCP employed fine grain sand and spherical glass beads Continuous strain measurements, calibrated to force, along with overhead and side photographs, documented the deformation throughout these experiments.
The UCP sandbox is a rectangular shear box measuring 41 cm in length, 28 cm in width, and 9 cm in height, constructed with 1 cm thick glass walls It features a 0° slope on the basal plate, with an electric screw motor moving the backwall towards the frontwall at a constant speed, ensuring consistent deformation results regardless of varying backwall displacement rates The backwall is equipped with a foam block and strain gauges that measure strain every 0.1 seconds, allowing for conversion to force due to their linear-elastic behavior Two cameras capture images every 5 seconds, while Particle Image Velocimetry (PIV) analyzes sand grain velocity through pixel correlation To minimize friction, Teflon and felt are used where the foam block contacts the glass, and the indentation style sandbox design reduces sidewall friction, which can distort results Additionally, sidewalls treated with Rain-X decrease friction from ~0.27 to ~0.16, further enhancing measurement accuracy.
In UCP experiments, the horizontal layer thickness ranges from 11 to 20 mm, as detailed in Table 4.1 A small protowedge is introduced in front of the moving wall using a sedimentation device, with its slope matching the angle of repose of the granular material This protowedge effectively concentrates the onset of deformation at its toe, distancing it from the moving wall and promoting a uniform sequence of initial faulting across the experiments.
We compare findings from UCP experiments with those from a Stanford University compressional sandbox experiment (Cruz et al., 2010), which features a 28 mm sand layer placed over a 2 mm layer of glass beads.
The technique of material placement significantly influences friction in granular materials, as highlighted by various studies (Krantz, 1991; Lohrman et al., 2003; Panien et al., 2006; Maillot, 2013) Sifting is favored over pouring because it results in consistent, flat, homogeneous, and dense layers (Krantz, 1991; Cubas et al., 2010; Maillot, 2013) Additionally, Maillot (2013) describes a sedimentation device that effectively creates granular material packs for UCP experiments, where material is released from a reservoir above the sandbox and filtered through three sieves before settling in the box.
UCP utilizes granular materials such as Fontainebleau aeolian quartz sand (CV32 and GA39) and glass beads The CV32 sand features a coarse grain size with a median of 250 μm, is poorly sorted, and has a density of 1711 ± 7 kg/m³, as noted by Cubas et al (2010) and Maillot.