Results of stability analyses for spring and slider systems, with state variable constitutive properties, are applied to slip on embedded fault patches. Unstable slip may nucleate only if the slipping patch exceeds some minimum size. Subsequent to the onset of instability the earthquake slip may propagate well beyond the patch. It is proposed that the seismicity of a volume of the earth's crust is determined by the distribution of initial conditions on the population of fault patches that nucleate earthquake slip, and the loading history acting upon the volume. Patches with constitutive properties inferred from laboratory experiments are characterized by an interval of self-driven accelerating slip prior to instability, if initial stress exceeds a minimum threshold. This delayed instability of the patches provides an explanation for the occurrence of aftershocks and foreshocks including decay of earthquake rates by time-1. A population of patches subjected to loading with a periodic component results in periodic variation of the rate of occurrence of instabilities. The change of the rate of seismicity for a sinusoidal load is proportional to the amplitude of the periodic stress component and inversely proportional to both the normal stress acting on the fault patches and the constitutive parameter, A1, that controls the direct velocity dependence of fault slip. Values of A1 representative of laboratory experiments indicate that in a homogeneous crust, correlation of earthquake rates with earth tides should not be detectable at normal stresses in excess of about 8 MPa. Correlation of earthquakes with tides at higher normal stresses can be explained if there exist inhomogeneities that locally amplify the magnitude of the tidal stresses. Such amplification might occur near magma chambers or other soft inclusions in the crust and possibly near the ends of creeping fault segments if the creep or afterslip rates vary in response to tides. Observations of seismicity rate variations associated with seasonal fluctuations of reservoir levels appear to be consistent with the model. ?? 1987.
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Nucleation and triggering of earthquake slip: effect of periodic stresses