Variability of earthquake nucleation in continuum models of rate-and-state faults and implications for aftershock rates

Using two continuum models of rate-and-state faults, one with a weaker patch and the other with rheological transition from steady state velocity-weakening to velocity-strengthening friction, we simulate several scenarios of spontaneous earthquake nucleation plausible for natural faults, investigate their response to static shear stress steps, and infer the corresponding aftershock rates. Overall, nucleation processes at weaker patches behave similarly to theories based on spring-slider models, with some notable deviations. In particular, nucleation and aftershock rates are affected by normal stress heterogeneity in the nucleation zone. Nucleation processes at rheological transitions behave differently, producing complex slip velocity histories, nonmonotonic responses to static stress changes, and aftershock rates with pronounced peaks and seismic quiescence. For such processes, positive stress steps sometimes delay nucleation of seismic events by inducing aseismic transients that relieve stress and postpone seismic slip. Superposition of the complex aftershock response for spatially variable stress changes results in Omori's law for a period of time followed by seismic quiescence. Such behavior was observed at the base of the seismogenic zone near the 1984 Morgan Hill earthquake. We show that the computed aftershock rates are linked to unperturbed slip velocity evolution in the nucleation zone and construct simplified analytical scenarios that explain some features of the response. The qualitative differences that we find between the two nucleation models indicate that aftershock response of rate-and-state faults to static stress changes would depend on the conditions under which nucleation occurs on natural faults and may be different from predictions based on spring-slider models.