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speculative. However, agreement of the rate- and state-dependent model for seismic activity with observations of aftershocks and earthquake clustering (28) lends support to the use of the formulation over the time-scale aftershock phenomena (months to years). This includes apparent confirmation of a predicted independence of aftershock duration ta on earthquake magnitude and an inverse dependence of ta on stressing rate. Alternative mechanisms for aftershocks and clustering, based on viscoelastic stress transfer or diffusion processes that alter fault stress, lead to characteristic aftershock times that are insensitive to stressing rates but depend on a characteristic length of the mainshock disturbance.

Both foreshock models provide comparable fits to the data. Model 1 is more specific than model 2, and the parameters used for the model 1 computation appear consistent with other results. The value (∆τe/)=40 is based on the aftershock analysis of Dieterich (28). Assuming a typical laboratory value of A=0.001 and earthquake stress drop ∆τe=4 MPa, this gives σ=10 MPa. In turn, these values and years give a stressing rate MPa/year. Model 2 is nonspecific and demonstrates only that the shape of the predicted temporal decay of foreshock-mainshock pairs is consistent with the data. The large value of the stress coupling parameter, C=9300, indicates strong coupling between slip during mainshock nucleation and stresses at regions of foreshock nucleation. This suggests the model 2 mechanism can work only if foreshocks nucleate at the edges of the mainshock nucleation zone or perhaps as small patches embedded within the slipping region for mainshock nucleation.

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