  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
rate-and-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 a different characteristic time and power-law exponent.
