Response of rate-and-state seismogenic faults to harmonic shear-stress perturbations

Field and laboratory observations show that seismicity has non-trivial period-dependent response to periodic stress perturbations. In Nepal, seismicity shows significant variations in response to annual monsoon-induced stress variations but not to semidiurnal tidal stresses of the same magnitude. Such period dependence cannot be explained by the Coulomb failure model and spring-slider rate-and-state model (SRM). Here, we study seismicity response to periodic stress perturbations in a 2-D continuum model of a rate-and-state fault (that is, a finite rate-and-state fault). We find that the resulting seismicity indeed exhibits nearly periodic variations. Their amplitude is maximum at a certain period, T_a, and decreases with smaller and larger periods to the SRM predictions, remaining much larger than the SRM predictions for a wide range of periods around T_a. We attribute the higher sensitivity of finite faults to their finite nucleation zones which vary in space and have a different slip-velocity evolution than that of the SRM. At periods T ≫ T_a and T ≪ T_a, the seismicity-rate variations are in phase with the stress-rate and stress variations, respectively, consistent with the SRM, although a gradual phase shift appears as T increases towards T_a. Based on the similarities with the SRM and our simulations, we propose a semi-analytical expression for T_a. Plausible sets of model parameters make T_a equal to 1 yr, potentially explaining Nepal observations and constraining the fault properties. Our finite-fault findings indicate that aσ, where a is a rate-and-state parameter and σ is the effective normal stress, can be severely underestimated based on the SRM.