A stochastic model for fracture growth on a heterogeneous seismic fault

We present a model for the propagation of seismic fracture on a heterogeneous fault on which the strength and applied stress vary locally along the fault plane in a random fashion. The propagation of fracture is controlled by three macroscopic parameters: the average of the difference between the applied stress and fault strength, a measure of fault heterogeneity and the average coupling between elementary faults. Evolution of fracture can then be represented by an epidemics model, whose domains of slip are obtained from percolation theory. The geometry of these domains contains the principal features of both barrier and asperity models.