Homogenization of fault frictional properties

SUMMARY The frictional properties of large faults are expected to vary in space. However, fault models often assume that properties are homogeneous, or nearly so. We investigate the conditions under which the details of variations may be neglected and properties homogenized. We do so by examining the behaviour of nonlinear solutions for unstably accelerating fault slip under frictional heterogeneity. We consider a rate- and state-dependent fault friction in which the characteristic wavelength for the property variations is a problem parameter. We find that homogenization is permissible only when that wavelength shows scale separation from an elasto-frictional length scale. However, fault models also often include property transitions that occur over distances comparable to the elasto-frictional length. We show that under such comparable variations, the dynamics of earthquake-nucleating instabilities is controlled by the properties’ spatial distribution.