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Community Stress Model (CSM)

CXM Representative
Jeanne Hardebeck


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.



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