A model of foreshock occurrence

SUMMARY We have constructed a model for the occurrence of foreshocks and foreshock sequences. The foreshocks as well as the main shock are assumed to occur because of the abrupt coalescence of pre‐existing cracks. Coalescence occurs if the stress intensity factors at the crack tips exceed a certain critical value. In the sub‐critical state each crack undergoes accelerated extension quasi‐statically due to stress corrosion, until it reaches the critical state, at which point growth becomes catastrophic. The rate of foreshock occurrence increases as the time of the main shock approaches and is described by a power law function of time. The exponent in the power law is independent of the distributions of crack sizes, spacings and fracture strengths. This universality implies that foreshock patterns should be useful identifiers for the prediction of the occurrence times of large earthquakes. However, we find that there is considerable diversity in the patterns of energy release. Nevertheless, there is some hope that the magnitudes of large earthquakes can be predicted from the magnitudes of the events in the foreshock sequences if one has a priori information describing the distributions of barrier strengths and geometries.