Viscoelastic relaxation of cyclic displacements on the San Andreas Fault

Abstract

It is recognized that displacements on major plate margin faults such as the San Andreas Fault in California occur episodically. In this paper we construct a mathematical model of the fault as the boundary between two semi-infinite lithosphere plates of finite thickness, moving in opposite directions parallel to their common boundary with constant velocities at infinity but locked together on the boundary except during great earthquakes. The surface plates behave elastically but the underlying asthenosphere, although elastic in the short term, behaves as a viscous fluid on geological time scales and is treated as a viscoelastic half space linked to the lithosphere by continuity of stress and displacement. An analytic solution is obtained for the anti-plane displacement and shear stress on the surface in terms of the displacement on the fault. We apply the solution to compute the response to an infinite sequence of stepwise offsets on the fault, and to periodic displacements. The interaction of the plates with the asthenosphere damps out the time-dependence at large distances from the plate boundary, the relaxation process being characterized by a time scaleT=η/G(η= Newtonian viscosity,G= shear modulus). The results should be applicable to understanding the time dependence of the strain as a function of distance from the San Andreas Fault.