Dynamic Shear Cracks with Friction as Models for Shallow Focus Earthquakes

Abstract

Summary In this paper a dynamical model of an earthquake source is investigated. This necessarily idealized model consists of a uniform elastic half space under a shearing pre-stress which tends to produce strike slip on a vertical fault plane. The fault plane is a plane of weakness across which the material is not welded but is initially inhibited from moving by a static frictional resistance which increases with depth. At a certain instant in time and depth in the half space a region of relative slip across the fault plane is initiated which spreads upwards and downwards so as to occupy at all times an infinite strip. Thus we shall be concerned only with two-dimensional SH motion (anti-plane strain). Once slipping occurs only reduced tractions act across the region of slip and it is the resulting stress drop which drives the mechanism. This model is almost the same as that considered by Berg and Weertman but goes further in that the dynamical problem is solved. We here extend previous work by Burridge and Burridge & Willis, in that we now find as part of the solution how the zone of slip spreads as well as the relative displacements, how the increasing friction prevents the crack (zone of slip) from penetrating very deeply, and eventually how it brings the whole mechanism to rest. Finally we calculate the pulse shapes in the far-field radiation and the residual displacements and stresses on the fault plane.