Models of Stochastic, Spatially Varying Stress in the Crust Compatible with Focal-Mechanism Data, and How Stress Inversions Can Be Biased toward the Stress Rate

Evidence suggests that slip in earthquakes and the resultant stress changes are spatially heterogeneous. If crustal stress from past earthquakes is spatially heterogeneous, then earthquake focal mechanisms should also be spatially variable. We describe the statistical attributes of simulated earthquake catalogs, including hypocenters and focal mechanisms, for a spatially 3D, time-varying model of the crustal stress tensor with stochastic spatial variations. It is assumed that temporal variations in stress are spatially smooth and are primarily caused by plate tectonics. Spatial variations in stress are assumed to be the result of past earthquakes and are independent of time for periods between major earthquakes. It is further assumed that heterogeneous stress can be modeled as a stochastic process that is specified by an autocorrelation function. Synthetic catalogs of earthquake hypocenters and their associated focal mechanisms are produced by identifying the locations and times at which the second deviatoric stress invariant exceeds a specified limit. The model produces a seismicity catalog that is spatially biased. The only points in the grid that exceed the failure stress are those where the heterogeneous stress is approximately aligned with the stress rate. This bias results in a focal-mechanism catalog that appears less heterogeneous than the underlying stress orientations. Comparison of synthetic focal-mechanism catalogs with catalogs of real earthquakes suggests that stress in the crust is heterogeneous. Stochastic parameters are estimated which generate distance dependent spatial variations in focal mechanisms similar to those reported by Hardebeck (2006) for southern California.