We study models of seismicity rate changes caused by the application of a static stress perturbation to a population of faults and discuss our results with respect to the model proposed by Dieterich ( 1994). These models assume a distribution of nucleation sites ( e. g., faults) obeying rate-state frictional relations that fail at constant rate under tectonic loading alone, and predicts a positive static stress step at time t(0) will cause an immediate increased seismicity rate that decays according to Omori's law. We show one way in which the Dieterich model may be constructed from simple general ideas, illustrated using numerically computed synthetic seismicity and mathematical formulation. We show that seismicity rate changes predicted by these models ( 1) depend on the particular relationship between the clock-advanced failure and fault maturity, ( 2) are largest for the faults closest to failure at t(0), ( 3) depend strongly on which state evolution law faults obey, and ( 4) are insensitive to some types of population heterogeneity. We also find that if individual faults fail repeatedly and populations are finite, at timescales much longer than typical aftershock durations, quiescence follows a seismicity rate increase regardless of the specific frictional relations. For the examined models the quiescence duration is comparable to the ratio of stress change to stressing rate &UDelta;τ/(τ) over dot, which occurs after a time comparable to the average recurrence interval of the individual faults in the population and repeats in the absence of any new load perturbations; this simple model may partly explain observations of repeated clustering of earthquakes.
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