The Slow Slip of Viscous Faults

摘要

We examine a simple mechanism for the spatiotemporal evolution of transient, slow slip.We consider the problem of slip on a fault that lies within an elastic continuum and whose strength is proportional to sliding rate. This rate dependence may correspond to a viscously deforming shear zone or the linearization of a nonlinear, rate-dependent fault strength.We examine the response of such a fault to external forcing, such as local increases in shear stress or pore fluid pressure.We show that the slip and slip rate are governed by a type of diffusion equation, the solution of which is found using a Green's function approach.We derive the long-time, self-similar asymptotic expansion for slip or slip rate, which depend on both time t and a similarity coordinate η = x∕t, where x denotes fault position. The similarity coordinate shows a departure from classical diffusion and is owed to the nonlocal nature of elastic interaction among points on an interface between elastic half-spaces.We demonstrate the solution and asymptotic analysis of several example problems. Following sudden impositions of loading, we show that slip rate ultimately decays as 1∕t while spreading proportionally to t, implying both a logarithmic accumulation of displacement and a constant moment rate.We discuss the implication for models of postseismic slip as well as spontaneously emerging slow slip events.