Rate State Seismicity Equations Applied to 3D Spatially Heterogeneous Stress to Study Aftershock Sequences: Implications for Crustal Stress

3D models of stress heterogeneity [Smith and Heaton, submitted 2008] are combined with a formulation for seismicity based on rate-state friction [Dieterich, 1994] to examine aspects of aftershock seismicity: 1) Spatial patterns as a function of time, 2) seismicity rates, and 3) changes of focal mechanism statistics in aftershock sequences. Some key observed features for the simulated aftershock period are: 1) Approximately 1/t, Omori Law behavior, 2) initial clustering of aftershocks in regions of greatest Coulomb stress then transitioning to a more even spatial distribution with time, and 3) some seismicity in stress shadow areas due to the pre-existing heterogeneous stress. With regard to focal mechanism statistics, we find that stress inversions of aftershock focal mechanisms with the spatially heterogeneous stress yield large "apparent" rotations of the inferred maximum horizontal compressive stress, SH, that are far in excess of the "true" SH rotations. Also, focal mechanism inversions for simulations with spatially variable stress perturbations due to slip on finite geometrically complex faults can produce transient increases in the stress inversion mean misfit angle, β, (generally thought to correlate with stress heterogeneity). Both the apparent changes in stress orientation and increase in misfit angles decay during the aftershock period. These results generally agree with previous conclusions [Smith 2006; Smith and Heaton, submitted 2008] that failures in a heterogeneous stress field are biased toward the stressing rate or stress perturbation. Biasing arises because failure surfaces that are well oriented with respect to stress perturbations experience larger transient seismicity rate changes than surfaces that are misaligned. Perhaps the most important conclusion is that one can generate this "apparent" rotation of SH, much larger than the "true" rotation, for a moderately strong crust (mean stress 50 MPa) if stress is heterogeneous. Consequently, estimates of crustal strength from aftershock studies may significantly underestimate the mean crustal stress state for the region; i.e., one cannot directly use rotations of, SH, from stress inversions, to conclusively demonstrate low crustal strength (< 10 MPa). Understanding to what degree biasing effects create rotations of the inferred stress orientations and increase the stress inversion parameter, beta, is important if one wishes to better parameterize stress in the Earth's crust. Indeed, we explore the potential extent of the biasing and its implications for crustal stress, by comparing our models to a few aftershock sequences.