A model for frictional sliding instability on a heterogeneous fault

An instability of frictional sliding driven by tectonic stress is assumed to be the source of earthquakes. Empirical slip laws indicate that, under constant ambient conditions, friction depends on time, slip rate and slip history. Regular stick slip behaviour is induced by velocity weakening, a decrease of friction with slip rate. Velocity weakening is introduced into a model for a propagating Somigliana dislocation under slowly increasing shear stress in an elastic space. Two distributions of static friction are considered, characterized by asperities with sharp borders and smooth borders respectively. The instability occurs when the rate at which friction decreases becomes greater than the rate at which the applied stress must increase to produce an advance of fault slip. The possibility that this condition is fulfilled depends on the velocity dependence and on the spatial distribution of friction on the fault. In the case of sharp asperity borders, instability can take place only when some amount of slip has occurred on the fault, while this condition is not required in the case of smooth borders.