CSM WORKING GROUP

CXM Representative Karen Luttrell CSM Contributors Brad Aagaard Thorsten Becker Peter Bird Michelle Cooke Jeanne Hardebeck Egill Hauksson Elizabeth Hearn Kaj Johnson Jack Loveless Karen Luttrell Scott Marshall Brendan Meade Patricia Persaud David Sandwell Bruce Shaw John Shaw Zheng-Kang Shen Joann Stock Anne Strader Bridget Smith-Konter Wenzheng Yang Yuehua Zeng SCEC Software Team Tran Huynh  Edric Pauk Mei-Hui Su Phil Maechling

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DATA ACCESS TOOL A web-based data access tool that provides 2D map view of the SCEC CSM contributed models at different depths within the lithosphere. GO TO CSM VIEWER CONTRIBUTED MODELS Have a new model you would like to contribute to the SCEC CSM? Use the CSM Grid format and submit it through the Model Contribution Form for review. CONTRIBUTE A MODEL

SCEC COMMUNITY MODELS Community Fault Model Community Geodetic Model Community Rheology Model Community Stress Model Community Thermal Model Community Velocity Model Unified Community Velocity Model

RELATED RESEARCH Unified Structural Representation Ground Motion Simulation Validation SCEC Broadband Platform

WORKSHOPS January 15-16, 2019 September 13, 2015 October 27, 2014 May 29, 2013 October 15, 2012 September 14, 2011

Above: Predicted Aphi values associated with contributed stress and stressing rate models that make up the SCEC Community Stress Model. Aphi indicates whether the faulting regime is normal (blue), strike-skip (yellow), or reverse (red).

Overview

Understanding the state of lithospheric stress and how it changes over time is critical to advancing earthquake research. Stress quantifies the fundamental forces that cause faults to slip and the ground to shake. Researchers use stress to describe how faults are loaded, how faults interact, and as initial conditions in ground motion simulations. A working group of the Southern California Earthquake Center (SCEC) has developed the Community Stress Model (CSM) to study the stress and stressing rate within the southern California lithosphere. The SCEC CSM is a suite of models that fall into two broad categories: 

1. “stress” models simulate the 3-D symmetric stress tensor (6 components), describing the forces present within a volume of subsurface material.  
2. “stressing rate” models simulate how the 3-D stress tensor changes over time, for example due to stress accumulating along a tectonic plate boundary.

The CSM differs from other SCEC Community Models in that it compiles a group of models (of stress and stressing rate) rather than providing a single consensus model.

The SCEC CSM v2023 includes 11 distinct models: 6 of stress, and 5 of stressing rate. Table 1 summarizes the basic attributes of each contributed model. The model techniques, assumptions, and input datasets vary, so no two models provide the exact same result.

The SCEC CSM web tool allows users to visualize and explore different model contributions at different depths within the lithosphere. Users can compare model orientation (SHmax or Aphi) and magnitude (isotropic or differential), download model values from a region of interest, or upload their own data (in kml/kmz format) for visualization and comparison with the SCEC CSM. The full model information is available in the SCEC CSM archive.

Download and View Current SCEC CSM

• SHmax: maximum horizontal compression azimuth (describes stress tensor orientation)
• Aphi: Anderson modified shape parameter (describes stress tensor orientation)
• Isotropic pressure: (S1+S2+S3)/3 (describes stress tensor magnitude)
• Differential stress: (S1-S3) (describes stress tensor magnitude)​

Use the SCEC CSM web tool to interactively compare these four metrics for different stress or stressing-rate models at different depths.

Contributed Models

Contributed models in the current SCEC CSM are summarized below.  We welcome new and updated contributions of models of stress, stressing rate, or stress observations.  See the SCEC CSM Model Contribution Form for more details.

What are the CSM models based on?

For CSM stress models, the orientation of the stress tensor is typically derived from the inversion of earthquake focal mechanisms. Some of the models are based solely on earthquake focal mechanisms, and thus do not provide information on stress magnitude. Some models provide an estimate of the deviatoric stress required to support existing topography. Some models provide an estimate of the full absolute stress tensor, based on forward physics-based modeling of the tectonic loading of the southern California fault system.

CSM stressing rate models are typically based on kinematic or mechanical models constrained by geodetic data. Some are based on estimates of geodetic velocity field or strain rate that are then translated into stressing rate. Others involve forward physics-based modeling of tectonic loading of the fault system, but focus on deriving stressing rate rather than the absolute stress tensor.

Note that even when sampled “on” a major fault surface, these model values should be regarded as estimates of stress in the adjacent continuum rather than estimates from “within” fault gouge zones or directly on a fault surface.

For the details of all model contributions, see the README files in the SCEC CSM archive.

Long-Term Research Priorities for CSM development

Lithospheric stress is a fundamental quantity that is relevant to many aspects of the earthquake problem, including fault loading and dynamic rupture simulations.  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.

The CSM has made considerable progress in building a suite of stress and stressing rate models for the upper crust.  Five research themes have been identified as key for future progress: 

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 can be compared with stress orientations compiled by the World Stress Map project from borehole data, and includes some additional stress constraints from borehole observations (download Table S1 from Luttrell and Hardebeck 2021). 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.

SCEC CSM Model Comparison Exercise (2012-2016)

From 2012-2016, the SCEC CSM working group undertook a series of comparison exercises to understand where the contributed models agree and disagree about the orientation and magnitude of stress and stressing rate, 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.

Additional Resources

• Hardebeck, J. L. (2021) SCEC Community Stress Model, oral presentation at SCEC Workshop on Dynamic Rupture and Stress Conditions, recording available on CSM website, December 2021.
• Hardebeck, J.,  Becker, T. W., Bird, P., Cooke, M. L., Hauksson, E., Hearn, E. H., Johnson, K. M., Loveless, J. P., Luttrell, K., Meade, B. J., Shen, Z., Smith-Konter, B. R., Yang, W., and Zeng, Y. (2023). SCEC Community Stress Model (CSM) (Version 2023) [Data set]. Zenodo, https://doi.org/10.5281/zenodo.8270631.
• Luttrell, K., and Hardebeck, J. (2021), A unified model of crustal stress heterogeneity from borehole breakouts and earthquake focal mechanisms, J. Geophys Res. Solid Earth, 126, e2020JB080817, https://doi.org/10.1029/2020JB020817.
• Luttrell, K., Hardebeck, J., and Marshall, S. T. (2023), Unboxing the Community Stress Model: Progress, Challenges, and Opportunities in Describing the Fundamental Forces Behind Earthquakes, Invited Plenary Speaker, Session  6: How to extend Community Earth Models Statewide, SCEC Annual Meeting, September 2023, Palm Springs, CA.
• Luttrell, K., Marshall, S. T., Su, M., Huynh, T. T., Pauk, E., and Maechling, P. J. (2023), Broadening Access to the SCEC Community Stress Model Through a Queryable Web-based Visualization Tool, SCEC Annual Meeting poster 205.