Afterslip and aftershocks in the rate-and-state friction law

We study how a stress perturbation generated by a mainshock affects a population of faults obeying a rate-state friction law. Depending on the model parameters and on the initial state, the fault exhibits aftershocks, slow earthquakes, or decaying afterslip. We found several regimes with slip rate decaying as a power-law of time, with different characteristic times and exponents. The complexity of the model makes it unrealistic to invert for the friction law parameters from afterslip data. We modeled afterslip measurements for the Southern California Superstition Hills earthquake using the complete rateand-state law, and found a huge variety of model parameters that can fit the observed data. In particular, it is impossible to distinguish the stable velocity strengthening regime (A > B) from the (potentially) unstable velocity weakening regime (B > A and stiffness k < kc). Therefore, it is not necessary to involve small scale spatial or temporal fluctuations of friction parameters A or B in order to explain the transition between stable sliding and seismic slip. In addition to B/A and stiffness k/kc, the fault behavior is strongly controlled by stress levels following an event. Stress heterogeneity can thus explain most of the variety of postseismic behavior observed in nature. Afterslip will induce a progressive reloading of faults that are not slipping, which can trigger aftershocks. Using the relation between stress and seismicity derived from the rate-and-state friction law, we estimate the aftershock rate triggered by afterslip. Aftershock rate does not simply scale with stress rate, but exhibits different characteristic times and sometimes a different power-law exponent. Afterslip is thus a possible candidate to explain observations of aftershock rate decaying as a power-law of time with an Omori exponent that can be either smaller or larger than 1.