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Community Stress Model (CSM)

CSM WORKING GROUP
CXM Representative
Jeanne Hardebeck
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Introduction

The SCEC Community Stress Model, as presented by Jeanne Hardebeck at the 2021 Dynamic Rupture Workshop.

Crustal stress is a fundamental quantity that is relevant to many aspects of the earthquake problem. The goal of the Community Stress Model (CSM) is to provide the SCEC community with a suite of models and constraints on the stress and stressing rate in the southern California lithosphere. The CSM currently consists of multiple different models of stress and stressing rate, based on different types of data, methodology, and assumptions. There is a range of potential uses for the CSM, including earthquake stress triggering studies and dynamic earthquake rupture modeling.

Research Priorities

  1. Physics-based models of stress in the lithosphere. Most of the current CSM models are upper-crustal models derived empirically from focal mechanism and/or geodetic data. Some of the models are based on modeling of long-term tectonics, and include physical properties such as fault rheology. These models are also primarily fit to earthquake, fault, and geodetic data, and are poorly resolved at depth. Additional work is needed on physics-based models of stress and stressing-rate in the southern California lithosphere, particularly to constrain absolute stress and stressing rate magnitudes below the upper crust.
  2. Borehole Stress Indicators. Direct observations are needed to constrain and/or validate the stress and stressing rate models. The most direct measurement of stress comes from boreholes. The CSM currently includes stress orientations compiled by the World Stress Map project from borehole data, and some additional stress constraints from borehole observations. It is a high priority to compile additional data obtained from industry well logs.
  3. Absolute Stress. Absolute stress in particular exerts strong influence on the outcomes of dynamic rupture simulations and earthquake simulators, but is the parameter of least consensus within the suite of CSM models. We seek constraints on the absolute stress level of the crust from a range of geophysical (e.g. topography support) and geological (e.g. paleo-piezometers) approaches. This topic has strong ties with the goals of the CRM, and will inform broader SCEC priority questions about the effects of short and long-term perturbations to tectonic loading.
  4. Stress Heterogeneity. Stress orientations vary on a range of length scales. The current CSM models mainly attempt to resolve the larger-scale heterogeneity. The resolution of the models needs to be better understood to correctly interpret the modeled variations. At smaller length scales, the stress heterogeneity likely needs to be characterized and modeled stochastically, which is a need that has not yet been formally addressed by the CSM.
  5. Model Validation and Uncertainty. Model validation and the characterization of uncertainty are major goals of the CXM for SCEC5. Therefore, we must validate the CSM against all available data. Most of the current suite of CSM models do not report uncertainty, so we need to develop a quantitative understanding of the accuracy of the models, as well as the sensitivity to modeling assumptions and input data. Comparisons of models may be used to estimate the epistemic uncertainty. Model validation and characterization of uncertainty would also aid in evaluating the consistency between the CSM and other CXM models, such as the CRM and CTM.

Research Accomplishments

The CSM project has compiled the existing stress and stressing rate models developed by the SCEC community. The CSM has put these models into a common format, and sampled them on a common set grid of points covering southern California. The common format and sampling ensures that the models can be easily compared, and that users can easily switch between models. We have compared the different models to gain an understanding of where there is general agreement, and to identify where further work is needed to reconcile differences. Major results include:

  1. Figure 1. Left: Maximum horizontal compressive stress axis (SHmax), in degrees East of North, for a mean stress model generated by averaging the normalized model stress tensors. Right: the RMS difference of the SHmax orientation of the models relative to the mean, in degrees.

    The orientation of the stress tensor. The orientations of the principal stress axes of the stress models are encouragingly similar. The models agree on the direction of the maximum horizontal compressive stress (SHmax) within <15° over almost all of the southern California upper crust (Figure 1). The style of faulting (strike-slip, normal, or reverse) also agrees over most of the region. The largest disagreements tend to occur near the edges of the model area.

  2. Figure 2. Left: Scalar stressing rate (in kPa/yr) for a mean stressing rate model generated by averaging the model stressing rates. Right: the RMS difference of the models relative to the mean, expressed as a fraction of the mean.

    The stressing rate tensor. The stressing rate models generally agree on the scalar stressing rate close to the main faults of the San Andreas system (Figure 2). There are significant disagreements along some faults, however, related to which faults were included in particular models, as well as differences in stressing rate and in the decay of stressing rate away from the faults. Most of the stressing rate models agree well on the orientations of SHmax and the faulting style near the major faults of the San Andreas system. However, off of the major faults, this agreement breaks down. Additionally, the comparison between models is poor at depth, due to the differences in assumptions about locking depths.

  3. The differential stress. Constraining the amplitude of the differential stress at seismogenic depths is a long-standing difficult problem, dating from at least the discovery of the "San Andreas heat-flow paradox." Unsurprisingly, the stress models do not agree on the amplitude of the differential stress. There is an order of magnitude disagreement in the differential stress, and a disagreement as to whether the differential stress increases significantly with depth over the seismogenic zone.

Bibliography

Products

The CSM currently consists of a suite of different models of stress and stressing rate in the southern California lithosphere, in a standardized format on a common grid.

Stress Models

The suite of contributed stress models is available here, along with the associated metadata.

Model Contact(s) Last Updated Description Download
FlatMaxwell Bird, Peter 03/20/2015 Stress field obeying static equilibrium is fit to WSM data and a SHELLS model by weighted least-squares. 26MB
Hardebeck_FM Hardebeck, Jeanne 09/20/2012 The SATSI (Spatial And Temporal Stress Inversion) method of Hardebeck and Michael (JGR, 2006) was used to invert the focal mechanism dataset of Yang, Hauksson, and Shearer (BSSA, 2012) for stress orietation. The focal mechanisms were binned in 3D, in cubes of 2, 4, 8, 16, or 32 km on a side, depending on the spatial density of the data. The inversion includes damping, and linking was done between all adjacent bins, including those of different sizes. 2.3MB
Luttrell-2017 Luttrell, Karen
Smith-Konter, Bridget		 07/31/2017 This model estimates the magnitude of differential stress at seismogenic depth in southern California by balancing in situ orientation indicated by earthquake focal mechanisms against the stress imposed by topography, which tends to resist the motion of strike-slip faults. The orientation of the stress field is taken from Yang and Hauksson (2013, GJI), as the indication of in situ stress orientation derived from earthquake focal mechanisms, but is then scaled so that it has a differential stress magnitude equal to that shown in Figure 3a of Luttrell and Smith-Konter (2017, GJI). 1.6MB
SHELLS Bird, Peter 09/06/2012 A 3-D (isostatic, thermal stready-state) model of the lithosphere is cut by weak faults and deformed by plate motion, driven from the sides. Long-term-average (non-elastic) flow is computed. Stress is controlled by friction at low T and dislocation creep at high T. 22MB
YH14-K Becker, Thorsten 10/01/2016 A simple binning of normalized moment tensors inferred from double couple focal mechanisms. 6MB
YHSM-2013 Hauksson, Egill 10/22/2012 We invert for the state of stress in the southern California crust using the SCSN catalogue of high quality earthquake focal mechanisms (1981–2010). The stress field is best resolved where seismicity rates are high and sufficient data are available to constrain the stress field across most of the region. From the stress field, we determine the maximum horizontal compressive stress (SHmax ) orientations and the style of faulting across southern California. The trend of SHmax exhibits significant regional and local spatial heterogeneities. The regional trend of SHmax varies from north along the San Andreas system to NNE to the east in the Eastern California Shear Zone as well as to the west, within the Continental Borderland and the Western Transverse Ranges. To obtain results with the highest possible spatial resolution and coverage, we perform stress inversions at different spatial scales. We perform four independent 2-D stress inversions at two grid scales (5 km, 10 km), and with two numbers of events per grid node (N = 30, N = 15). For the Spatial And Temporal Stress Inversion (SATSI), we use a damping value of 1.2, which was derived by analysing the trade-off between data misfit and model length, which is a measure of the degree of heterogeneity in the solution. The SATSI software is available from the USGS webpage (Hardebeck & Michael, 2006). See also, Yang and Hauksson (GJI, 2012) for further details. 2.8MB

Stressing Rate Models

The suite of contributed stressing rate models is available here, along with the associated metadata.

Model Contact(s) Last Updated Description Download
LovelessMeade Loveless, Jack 09/26/2012 We calculate interseismic stress rate tensor components analytically using algorithms (Okada, 1992; Meade, 2007) giving strain due to slip on dislocations embedded in a homogeneous elastic half-space (mu = lambda = 3e10 Pa/m^2). Slip rates were calculated using a geodetically constrained elastic block model detailed in Loveless and Meade (2011). The fault geometry used in the block model is based on the SCEC CFM-R and the constraining GPS velocity field is compiled from several publications (McClusky et al., 2001; Shen et al., 2003; Hammond and Thatcher, 2005; McCaffrey, 2005; Williams et al., 2006; Plate Boundary Observatory network velocity field, 2008). The spatial resolution of the stress rate model is technically infinite, as the stress rate due to slip on all dislocations can be calculated analytically anywhere. The GPS velocity fields used to constrain interseismic deformation in the block model span 1993--2008, though some fields were "cleaned" to reduce postseismic signals. 45MB
NeoKinema Bird, Peter
Hearn, Liz		 01/02/2013 NeoKinema is a Fortran code which uses neotectonic kinematic data (geodesy, fault slip rates, stress directions) as additional constraints on a viscous-shell model of the lithosphere with plate-rotation boundary conditions. Outputs are present-day long-term-average horizontal velocities and distributed permanent strain rates (2D model, so horizontal components only)." 6.9MB
SAFPoly3D Cooke, Michele 08/01/2015 Poly3D, a triangular element boundary element method code, is used to simulate the southern San Andreas Fault system. Over 30 active faults with irregular mesh are represented in the model. The inter seismic stresses are determined in two steps. First a long-term model with tectonic loading at the boundaries solves for slip rates along the faults. These slip rates are then applied below the locking depth in an interseismic model. The slip rates and geodetic velocities form the model compare favorably to geologic and geophysical data sets (e.g., Herbert and Cooke, 2012; Herbert et Cooke and Marshall, 2014; Cooke and Dair, 2011; Cooke and Beyer, 2018). 4.1MB
Smith-Konter Smith-Konter, Bridget
Sandwell, David		 N/A N/A Contact Modeler
Strader Strader, Anne
Smith-Konter, Bridget		 N/A N/A Contact Modeler
UCERF3_ABM Johnson, Kaj 12/01/2012 This is the average block model as described in the UCERF3 report which will be released to the public in late 2013 or early 2014 (wgcep.org). It is mostly a traditional block model with backslip on block boundaries using dislocations in an uniform elastic halfspace (uniform 15 km locking depth except creeping faults that creep above 5 km depth). Buried dislocations (extending from 15km to infinite depth) are imposed on smaller faults between block boundaries. 23MB
Zeng Zeng, Yuehua 05/20/2013 This stress rate model is calculated based on a fault-based crustal deformation model with slip rates on all California faults determined by a joint inversion of GPS velocities and field geological slip rate observations. The fault model assumes buried elastic dislocations across the region using fault geometries defined by the UCERF3 project. GPS observations across California and its neighboring states were obtained from the UNAVCO western US GPS velocity model. The geologic slip rates and rupture styles were compiled by the SCEC UCERF3 geologic deformation working group. 17MB
Name of model A fault based model for crustal deformation by Yuehua Zeng and Zhengkang Shen
Preferred acronym Zeng model
Type of model (stress, stressing-rate, other (specify)) stress-rate
Short description of methodology This stress rate model is calculated based on a fault-based crustal deformation model with slip rates on all California faults determined by a joint inversion of GPS velocities and field geological slip rate observations. The fault model assumes buried elastic dislocations across the region using fault geometries defined by the UCERF3 project. GPS observations across California and its neighboring states were obtained from the UNAVCO western US GPS velocity model. The geologic slip rates and rupture styles were compiled by the SCEC UCERF3 geologic deformation working group.
Contact Yuehua Zeng
Contact email zeng@usgs.gov
Date of model completion May 20, 2013
Version number 1
Description of changes from previous version (if applicable)  
Reference  
Link to PDF of reference  
Type of data used (provide reference to datasets, if possible) GPS observation and geologic slip rate data for California
Spatial resolution [km] 1-10 km
Polygon of areal coverage (provide lon-lat pairs [deg])  
Depth range 30 km
OK to make model available to SCEC researchers Yes
OK to make model available to public Yes
Other references (optional)  
Comments (optional)  
Name of model UCERF3 Average Block Model
Preferred acronym UCERF3 ABM
Type of model (stress, stressing-rate, other (specify)) stressing rate
Short description of methodology This is the average block model as described in the UCERF3 report which will be released to the public in late 2013 or early 2014 (wgcep.org). It is mostly a traditional block model with backslip on block boundaries using dislocations in an uniform elastic halfspace (uniform 15 km locking depth except creeping faults that creep above 5 km depth). Buried dislocations (extending from 15km to infinite depth) are imposed on smaller faults between block boundaries.
Contact Kaj Johnson
Contact email kajjohns@indiana.edu
Date of model completion December 2012
Version number 1 (final version)
Description of changes from previous version (if applicable)  
Reference UCERF3 Final Report
Link to PDF of reference  
Type of data used (provide reference to datasets, if possible) Block model uses horizontal GPS velocities, geologic point slip rates and uncertainties, and strict upper and lower bounds estimated from geology (details in UCERF3 Final Report)
Spatial resolution [km] Arbitary -- stressing rates provided at all CSM gridpoints
Polygon of areal coverage (provide lon-lat pairs [deg]) (117,31); (121,33); (128,40); (128,43); (114,43); (114,31)
Depth range 0-15 km
OK to make model available to SCEC researchers Yes
OK to make model available to public Yes
Other references (optional)  
Comments (optional)  
Name of model Poly3D of the southern San Andreas
Preferred acronym SAFPoly3D
Type of model (stress, stressing-rate, other (specify)) stressing rate
Short description of methodology Poly3D, a triangular element boundary element method code, is used to simulate the southern San Andreas Fault system. Over 30 active faults with irregular mesh are represented in the model. The inter seismic stresses are determined in two steps. First a long-term model with tectonic loading at the boundaries solves for slip rates along the faults. These slip rates are then applied below the locking depth in an interseismic model. The slip rates and geodetic velocities form the model compare favorably to geologic and geophysical data sets (e.g., Herbert and Cooke, 2012; Herbert et Cooke and Marshall, 2014; Cooke and Dair, 2011; Cooke and Beyer, 2018).
Contact MIchele Cooke
Contact email cooke@geo.umass.edu
Date of model completion 8/1/2015
Version number 2015
Description of changes from previous version (if applicable)  
Reference Fattaruso, Laura A., Michele L. Cooke and Rebecca J. Dorsey, 2014. Sensitivity of uplift patterns to dip of the San Andreas fault in the Coachella Valley, CA, Geosphere, v. 10; no. 6; p. 1235-1246; doi:10.1130/GES01050.1.
  Herbert, Justin W., Michele L. Cooke and Scott T. Marshall, 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, doi:10.1002/2013JB010472
  Herbert, Justin W., Michele L. Cooke, Michael E. Oskin and Ohilda Difo, 2014. How much can off-fault deformation contribute to the slip rate discrepancy within the Eastern California Shear Zone?, Geology. doi:10.1130/G34738
Link to PDF of reference  
Type of data used (provide reference to datasets, if possible)  
Spatial resolution [km] 2 km
Polygon of areal coverage (provide lon-lat pairs [deg]) -117.652 34.172 -115.916 35.414
Depth range 1, 19
OK to make model available to SCEC researchers yes
OK to make model available to public yes
Other references (optional)  
Comments (optional)  
# The models report the interseismic stressing rates using a two-step backslip approach. The fault slip rates throughout
# the model are determined from a forward model driven by tectonic boundary conditions. In this model, the faults
# are freely-slipping and interact to accommodate the boundary displacement rates.
# These slip rates are applied to an interseismic model (back slip) below the prescribed locking depth 20km.
# See Marshall, Cooke and Owen, JGR 2009 for more details on this implementation of back slip.
#
# The 3D BEM model uses the Community Fault model (CFM) with a few modifications. The Crafton Hills fault is added.
# Inactive portions of the Banning strand of the San Andreas fault are removed.
# Inactive connections between faults in the CFM have also been removed.
# The Helendale and Lockhart faults are disconnected from the Lenwood fault and the Gravel Hills fault is
# disconnected from the Camp Rock fault. Thrust faults in the ecsz are added
# banning has a north dip and merges with ne dipping coachella segment of SAF
# These modifications to the CFM are shown to better match observed fault slip rates.
#
# The stressing rates (MPa/yr) are reported for the dense shallow grid for depth <-19 km. Stress values near or
# below the locking depth (25 km) are not reliable.
#
# PLATE VELOCITY: This model results are for plate velocity of 45 mm/yr oriented N35W.
Name of model NeoKinema.f90 (short for Neotectonic Kinematics, in Fortran 90)
Preferred acronym NeoKinema
Type of model (stress, stressing-rate, other (specify)) Other - stressing rates were computed from output velocities, assuming elastic deformation.
Short description of methodology NeoKinema is a Fortran code which uses neotectonic kinematic data (geodesy, fault slip rates, stress directions) as additional constraints on a viscous-shell model of the lithosphere with plate-rotation boundary conditions. Outputs are present-day long-term-average horizontal velocities and distributed permanent strain rates (2D model, so horizontal components only)."
Contact Peter Bird (for NeoKinema modeling), Liz Hearn (for estimating stressing rates from the velocity field).
Contact email pbird@ess.ucla.edu
Date of model completion 1/2/2013
Version number NeoKinema v. 3.0.
Description of changes from previous version (if applicable)  
Reference Methods See Appendix S1 of Liu, Z. and P. Bird (2008), Geophys. J. Int., 172(2), 779-797, doi 10.1111/j.1365-246X.2007.03640.x.
Link to PDF of reference download
Source code
Type of data used (provide reference to datasets, if possible) Sigma_1 axis orientations from the World Stress Map (2008). Fault geometry is UCERF Fault Model 3.1. Prior (input) geologic offset rates for faults with dated offset features were from UCERF3 fault-data spreadsheet (from Tim Dawson) Prior (input) geologic offset rates for faults with no dated offset features were very broad generic-WUS PDFs from Bird [2007, Geosphere]. Interseismic horizontal GPS velocities from compilation wus5 by Robert McCaffrey, after removal of transient velocities due to transient locking of the Cascadia subduction zone. PA-NA relative rotation for boundary conditions from Gonzalez-Garcia et al. [2003]Ñatest source to include constraint on Guadalupe Island [see Bird, 2009, JGR]."
Spatial resolution [km] CSM grid for 2012.08 modeling exercise (from Jeanne Hardebeck)
Polygon of areal coverage (provide lon-lat pairs [deg]) CSM grid for 2012.08 modeling exercise (from Jeanne Hardebeck)
Depth range 2D FE model. Stressing rates are the same at all depths. The CSM-required file was populated with stressing rates from 1 to 15 km depth are identical at all depths.
OK to make model available to SCEC researchers Yes.
OK to make model available to public Yes.
Notes High stressing rates in narrow elements representing creeping faults should be ignored the high strain rates in these elements are a proxy for inelastic fault zone creep, and the conversion to stressing rates assuming elasticity and NavierÕ equation is not suitable for these elements. Hearn converted velocities to stress rates using the Navier equations and assuming zero for vertical strain rate components. Shear modulus and PoissonÕ ratio were assumed to be 30 GPa and 0.25, respectively. To get strain rates at each CSM point, the point in triangle test was used to determine which element the CSM point was in, then the CSM was populated with that elementÕ strain rate tensor (uniform in these linear elements). No interpolation was done. Element strain rates were computed from element areas, and from velocities using the element shape functions.
Name of model Harvard Crustal Dynamics Group stress rate model
Preferred acronym HCD
Type of model (stress, stressing-rate, other (specify)) Stressing rate
Short description of methodology We calculate interseismic stress rate tensor components analytically using algorithms (Okada, 1992; Meade, 2007) giving strain due to slip on dislocations embedded in a homogeneous elastic half-space (mu = lambda = 3e10 Pa/m^2). Slip rates were calculated using a geodetically constrained elastic block model detailed in Loveless and Meade (2011). The fault geometry used in the block model is based on the SCEC CFM-R and the constraining GPS velocity field is compiled from several publications (McClusky et al., 2001; Shen et al., 2003; Hammond and Thatcher, 2005; McCaffrey, 2005; Williams et al., 2006; Plate Boundary Observatory network velocity field, 2008). The spatial resolution of the stress rate model is technically infinite, as the stress rate due to slip on all dislocations can be calculated analytically anywhere. The GPS velocity fields used to constrain interseismic deformation in the block model span 1993--2008, though some fields were "cleaned" to reduce postseismic signals.
Contact Jack Loveless
Contact email jloveles@smith.edu
Date of model completion 9/26/2012
Version number 1
Description of changes from previous version (if applicable)  
Reference Loveless, J.P. and B.J. Meade (2011), Stress modulation on the San Andreas fault due to interseismic fault system interactions, Geology, 39(11), 1035.1038, doi:10.1130/G32215.1.
Link to PDF of reference LovelessAndMeadeSocalStress.pdf
Type of data used (provide reference to datasets, if possible) GPS
Spatial resolution [km] 2
Polygon of areal coverage (provide lon-lat pairs [deg]) -122.0783, 31.618 to -114.4187, 36.3491
Depth range 1-100 km
OK to make model available to SCEC researchers Yes
OK to make model available to public Yes
Other references Hammond, W. C., and W. Thatcher (2005), Northwest Basin and Range tectonic deformation observed with the Global Positioning System, 1999.2003, Journal of Geophysical Research, 110, B10405, doi:10.1029/2005JB003678.
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, 110(B7), B07401, doi:10.1029/2004JB003307.
McClusky, S. C., S. C. Bjornstad, B. H. Hager, R. W. King, B. J. Meade, M. M. Miller, F. C. Monastero, and B. J. Souter (2001), Present day kinematics of the Eastern California Shear Zone from a geodetically constrained block model, Geophysical Research Letters, 28(17), 3369.3372.
Loveless, J.P. and B.J. Meade (2011), Stress modulation on the San Andreas fault due to interseismic fault system interactions, Geology, 39(11), 1035.1038, doi:10.1130/G32215.1.
Meade, B. J. (2007), Algorithms for the calculation of exact displacements, strains, and stresses for triangular dislocation elements in a uniform elastic half space, Computers and Geosciences, 33, 1064.1075, doi:10.1016/j.cageo.2006.12.003.
Okada, Y. (1992), Internal deformation due to shear and tensile faults in a half-space, Bulletin of the Seismological Society of America, 82(2), 1018.1040.
Plate Boundary Observatory network velocity field (2008), http://pboweb.unavco.org/.
Shen, Z., D. Agnew, R. King, D. Dong, T. Herring, M. Wang, H. Johnson, G. Anderson, R. Nikolaidis, M. van Domselaar, K. Hudnut, and D. Jackson (2003), SCEC Crustal Motion Map, Version 3.0, http://epicenter.usc.edu/cmm3/.
Williams, T. B., H. M. Kelsey, and J. T. Freymueller (2006), GPS-derived strain in northwestern California: Termination of the San Andreas fault system and convergence of the Sierra Nevada-Great Valley block contribute to southern Cascadia forearc contraction, Tectonophysics, 413(3- 4),
Name of model Yang and Hauksson 2013 Stress Model,
Preferred acronym YHSM-2013,
Type of model (stress, stressing-rate, other (specify)) State of stress from inversion of focal mechanisms,
Short description of methodology We invert for the state of stress in the southern California crust using the SCSN catalogue of high quality earthquake focal mechanisms (1981–2010). The stress field is best resolved where seismicity rates are high and sufficient data are available to constrain the stress field across most of the region. From the stress field, we determine the maximum horizontal compressive stress (SHmax ) orientations and the style of faulting across southern California. The trend of SHmax exhibits significant regional and local spatial heterogeneities. The regional trend of SHmax varies from north along the San Andreas system to NNE to the east in the Eastern California Shear Zone as well as to the west, within the Continental Borderland and the Western Transverse Ranges. To obtain results with the highest possible spatial resolution and coverage, we perform stress inversions at different spatial scales. We perform four independent 2-D stress inversions at two grid scales (5 km, 10 km), and with two numbers of events per grid node (N = 30, N = 15). For the Spatial And Temporal Stress Inversion (SATSI), we use a damping value of 1.2, which was derived by analysing the trade-off between data misfit and model length, which is a measure of the degree of heterogeneity in the solution. The SATSI software is available from the USGS webpage (Hardebeck & Michael, 2006). See also, Yang and Hauksson (GJI, 2012) for further details.  
Contact Egill Haauksson,
Contact email Hauksosn@caltech.edu,
Date of model completion 10/22/12,
Version number 1,
Description of changes from previous version (if applicable),N/A  
Reference "Yang, W. and E. Hauksson, The tectonic crustal stress field and style of faulting along the Pacific North America Plate boundary in Southern California,Geophys. J. Int. (July, 2013) 194 (1): 100-117 first published online April 22, 2013 doi:10.1093/gji/ggt113"
Link to PDF of reference N/A,
Type of data used (provide reference to datasets, if possible) Focla mechanisms deermined from first motinos and S/P amplitude ratos
,"Yang, W., E. Hauksson, and P. Shearer, Computing a large refined catalog of focal mechanisms for southern California (1981 _ 2010) Temporal Stability of the Style of Faulting, Bull. Seismol. Soc. Am., June 2012, v. 102, p. 1179-1194, doi
Spatial resolution [km] 5km and 10 km and number of events=30 or 15 respectively. ,
Polygon of areal coverage (provide lon-lat pairs [deg]) --121deg to -115deg and 32deg to 37deg,
Depth range ,average for depth range from 0 to 15 km depth
OK to make model available to SCEC researchers YES,
OK to make model available to public YES
Other references (optional) N/A,
Comments (optional) Most comprehensive model available so far for southern California,
Name of model Normalized Kostrov summation of Yang and Hauksson catalog, including 2014 update
Preferred acronym YH14-K
Type of model (stress, stressing-rate, other (specify)) stress, assuming that the deformation style imaged from normalized co-seismic strain-release corresponds to it
Short description of methodology A simple binning of normalized moment tensors inferred from double couple focal mechanisms.
Contact Thorsten Becker
Contact email twb@ig.utexas.edu
Date of model completion 2016/10
Version number 1
Description of changes from previous version (if applicable)  
Reference for data: Yang, W., E. Hauksson and P. M. Shearer, Computing a large refined catalog of focal mechanisms for southern California (1981 - 2010): Temporal Stability of the Style of Faulting,æBull. Seismol. Soc. Am., June 2012, v. 102, p. 1179-1194, doi:10.1785/0120110311, 2012, for analysis method: Becker, T. W., Hardebeck, J. L., and Anderson, G.: Constraints on fault slip rates of the southern California plate boundary from GPS velocity and stress inversions. Geophys. J. Int., 160, 634-650, 2005.
Link to PDF of reference  
Type of data used (provide reference to datasets, if possible) http://scedc.caltech.edu/research-tools/alt-2011-yang-hauksson-shearer.html
Spatial resolution [km] ~25 km
Polygon of areal coverage (provide lon-lat pairs [deg]) =-R238.5/245.75/31.75/38.25
Depth range Single depth layer (shallow and deep versions available from author)
OK to make model available to SCEC researchers yes
OK to make model available to public yes
Other references (optional)  
Comments (optional) Model uses normalized summation of moment tensors, and as such may approximate the style of strain-release, here assumed to be stress.
Name of model Thin-shell dynamic F-E model SHELLS with faults, 3-D structure, and realistic rheology
Preferred acronym SHELLS
Type of model (stress, stressing-rate, other (specify)) stress
Short description of methodology A 3-D (isostatic, thermal stready-state) model of the lithosphere is cut by weak faults and deformed by plate motion, driven from the sides. Long-term-average (non-elastic) flow is computed. Stress is controlled by friction at low T and dislocation creep at high T.
Contact Peter Bird
Contact email pbird@ess.ucla.edu
Date of model completion 9/6/2012
Version number 1.0
Description of changes from previous version (if applicable)  
Reference Model is new for CSM and unpublished. Methods: Bird, P. [1999] Thin-plate and thin-shell finite element programs for forward dynamic modeling of plate deformation and faulting, Computers & Geosciences, 25(4), 383-394. Also see on-line guide URL below.
Link to PDF of reference Bird_1999_C&G.pdf
  http://peterbird.name/guide/foreword.htm
Type of data used (provide reference to datasets, if possible) ETOPO5 topography; heat-flow map of Blackwell & Steele [1992, GSA map series]; faults of UCERF3 Fault Model 3.1 [Tim Dawson; see UCERF3 OFR in prep., 2013]; NA-PA rotation of Gonzalez-Garcia et al. [2003, GRL]; rheology of Bird et al. [2008, JGR] except: effective fault friction 0.15, and no basal shear traction on lithosphere.
Spatial resolution [km] CSM grid for 2012.08 modeling exercise (from Jeanne Hardebeck)
Polygon of areal coverage (provide lon-lat pairs [deg]) CSM grid for 2012.08 modeling exercise (from Jeanne Hardebeck)
Depth range F-E model extends to top of asthenosphere, which varies from 38 to 108 km depth. Lithostatic stress reported at greater depths (in asthenosphere).
OK to make model available to SCEC researchers Yes.
OK to make model available to public Yes.
Notes Some model predictions of fault slip rates are incorrect (relative to UCERF3 geologic data and NeoKinema kinematic F-E models that use GPS). Spatial variations in fault friction may be needed for better realism. However, a low mean value of effective fault friction is supported by many studies, including Bird & Kong [1984, GSAB], Liu & Bird [2002, GRL], and Bird et al., [2008, JGR].
Additional notes (9/24/15) There are good reasons to conclude that active faults in southern California have lower effective friction (e.g., 0.15) than the crustal continuum between these faults (e.g., 0.85). This causes concentration of long-term-average strain-rates in active faults, elevation of dislocation-creep strain-rates and shear-stresses at all depths, and deeper frictional/dislocation-creep (i.e., 'brittle/ductile') transitions in active faults.

However, these special stress and strain-rate conditions occur only in narrow wedges of the upper crust, which taper to nominal thicknesses of zero at the surface. Therefore, the 3-D sampling grids on which stress models are reported to SCEC CSM are not able to capture these special conditions in the cores of active faults. Instead, the stress tensors reported in both the Shells and the FlatMaxwell stress models at CSM should be regarded as representing the regional or background stresses in strong crust (with 'Byerlee's Law' friction of 0.85) adjacent to, but outside, the active faults.
Name of model 3D Focal Mechanism Inversion
Preferred acronym FM3D
Type of model (stress, stressing-rate, other (specify)) Stress. Absolute value of isotropic and deviatoric stress magnitude are not constrained.
Short description of methodology The SATSI (Spatial And Temporal Stress Inversion) method of Hardebeck and Michael (JGR, 2006) was used to invert the focal mechanism dataset of Yang, Hauksson, and Shearer (BSSA, 2012) for stress orietation. The focal mechanisms were binned in 3D, in cubes of 2, 4, 8, 16, or 32 km on a side, depending on the spatial density of the data. The inversion includes damping, and linking was done between all adjacent bins, including those of different sizes.
Contact Jeanne Hardebeck
Contact email jhardebeck@usgs.gov
Date of model completion 20-Sep-12
Version number 1
Description of changes from previous version (if applicable) N/A
Reference unpublished
Link to PDF of reference N/A
Type of data used (provide reference to datasets, if possible) Focal mechanisms (Yang, Hauksson, and Shearer, BSSA, 2012)
Spatial resolution [km] variable: 2 km to 32 km
Polygon of areal coverage (provide lon-lat pairs [deg]) valid where defined
Depth range valid where defined
OK to make model available to SCEC researchers yes
OK to make model available to public yes
Name of model FlatMaxwell_for_CSM
Preferred acronym FlatMaxwell, or FM
Type of model (stress, stressing-rate, other (specify)) stress
Short description of methodology Stress field obeying static equilibrium is fit to WSM data and a SHELLS model by weighted least-squares.
Contact Peter Bird, UCLA
Contact email pbird@epss.ucla.edu
Date of model completion 2015.03.20
Version number HiRes043
Description of changes from previous version (if applicable)  
Reference P. Bird [2015?] Stress field models from Maxwell stress functions Southern California, to be submitted to Geophys. J. Int., April 2015.
Link to PDF of reference N/A
Type of data used (provide reference to datasets, if possible) World Stress Map, and Shells_for_CSM (<-already in CSM library)
Spatial resolution [km] 10 x 10 x 1.25 km grid for topographic stress, minimum wavelengths 125 x 100 x 12.5 km for tectonic stress
Polygon of areal coverage (provide lon-lat pairs [deg]) 31.2-36.6N, 122-114W (approximately)
Depth range 0-75 km below sealevel
OK to make model available to SCEC researchers Yes
OK to make model available to public Yes
Other references (optional) Bird [2014] Annual Report to SCEC, 11 March 2014
Comments (optional) Shows strong control of stress intensities by the heat-flow map (used in Shells).
This additional information added by TWB from the README included in the original data file, removed, to allow simpler reading from scripts. Original comments follow:

Stress model FlatMaxwell_for_CSM output from source code FlatMaxwell.f90.

General characteristics of FlatMaxwell models:

  • Domain includes crust below sealevel and often mantle lithosphere (if any, depending on heat-flow).
  • Modeling is done in a flat-Earth approximation, but then translated to spherical-Earth.
  • Except for some numerical limitations, output should always satisfy static equillibrium.
  • Models are typically fit by weighted least-squares to multiple target values:

    (1) Boundary conditions of free upper surface and inviscid asthenosphere;
    [Note that side-boundary tractions are left free at lithospheric depths.]
    (2) Principal stress directions (and some magnitudes) from a dataset like WSM.
    (3) Stresses from a dynamic model with realistic rheology such as Shells.

    Specific characteristics of this model HiRes043:

  • Fitted to both the World Stress Map data (449 directions 9 magnitudes) and Shells dynamic model Shells_for_CSM (previously reported to CSM 2013).
  • Equal weight on both of these datasets.
  • Model volume is 750 km x 600 km x 75 km with central point at (-118E 34N).
  • Grid resolution is 10 km x 10 km x 1.25 km.
  • W = 6 so up to 6 wavelengths of variation along each axis of the model.
  • Topographic stress model HiResIso0p50 (isostatic Moho Poisson ratio 0.5).
  • sigma_factor = 0.05 so sigma of each stress datum is MAX(2 MPa 0.05 * datum_value). By Peter Bird UCLA 2015.03.19 (or later)

    Original comments end.
Addtional notes (9/24/15) There are good reasons to conclude that active faults in southern California have lower effective friction (e.g., 0.15) than the crustal continuum between these faults (e.g., 0.85). This causes concentration of long-term-average strain-rates in active faults, elevation of dislocation-creep strain-rates and shear-stresses at all depths, and deeper frictional/dislocation-creep (i.e., 'brittle/ductile') transitions in active faults. However, these special stress and strain-rate conditions occur only in narrow wedges of the upper crust, which taper to nominal thicknesses of zero at the surface.

Therefore, the 3-D sampling grids on which stress models are reported to SCEC CSM are not able to capture these special conditions in the cores of active faults. Another issue is that the limited spatial resolution of the FlatMaxwell model would not be able to represent these local fault conditions even if the CSM grid were refined. Instead, the stress tensors reported in both the Shells and the FlatMaxwell stress models at CSM should be regarded as representing the regional or background stresses in strong crust (with 'Byerlee's Law' friction of 0.85) adjacent to, but outside, the active faults.
Name of model Strader
Name of model Smith-Konter
Name of model Luttrell-2017
Type of model (stress, stressing-rate, other (specify)) stress
Short description of methodology This model estimates the magnitude of differential stress at seismogenic depth in southern California by balancing in situ orientation indicated by earthquake focal mechanisms against the stress imposed by topography, which tends to resist the motion of strike-slip faults. The orientation of the stress field is taken from Yang and Hauksson (2013, GJI), as the indication of in situ stress orientation derived from earthquake focal mechanisms, but is then scaled so that it has a differential stress magnitude equal to that shown in Figure 3a of Luttrell and Smith-Konter (2017, GJI).
Reference Luttrell, K., and B. Smith-Konter (2017), "Limits on crustal differential stress in southern California from topography and earthquake focal mechanisms", Geophys. J. Int., 211, 472-482, doi:10.1093/gji/ggx301.
Luttrell K., B. Smith-Konter, and D. Sandwell (2012), "Investigating absolute stress in southern California How well do stress models of compensated topography and fault loading match earthquake focal mechanisms?", SCEC Annual Meeting poster 039.
Other references (optional) Luttrell, K., X. Tong, D. Sandwell, B. Brooks, and M. Bevis (2011), "Estimates of stress drop and crustal tectonic stress from the 27 February 2010 Maule, Chile earthquake implications for fault strength", J. Geophys. Res., 116, B11401, doi 10.1029/2011JB008509.
  Smith, B. and D. Sandwell (2004), "A 3-D semi-analytic viscoelastic model for time-dependent analyses of the earthquake cycle", J. Geophys. Res., doi 10.1029/2004JB003185.