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

We study how a stress perturbation generated by a main shock affects a fault obeying the rate-state friction law using a simple slider block system. Depending on the model parameters and on the initial stress, 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 behavior of the rate-state friction law is thus far more complex than described by the "steady state'' approximation frequently used to fit afterslip data. The fault reaches steady state only at very large times, when slip rate has decreased to the tectonic loading rate. The complexity of the model makes it unrealistic to invert for the friction law parameters from afterslip data. We modeled afterslip measurements for three earthquakes using the complete rate-and-state law and found a huge variety of model parameters that can fit the data. In particular, it is impossible to distinguish the stable velocity-strengthening regime (A > B) from the ( potentially) unstable velocity-weakening regime (A < B). 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, the fault behavior is strongly controlled by stress levels following an event. Stress heterogeneity can thus explain part of the variety of postseismic behaviors observed in nature. Afterslip induces 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 coseismic and postseismic slip. 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. Progressive unloading due to afterslip can also produce delayed seismic quiescence.