Seismic Radiation from a Kink on an Antiplane Fault

Abstract

We study radiation and energy balance for an antiplane fault containing a kink. A semi-infinite crack with a sharp rupture front propagates along the flat portion of a kinked crack. At time t � 0, the crack reaches the kink located at the origin of coordinates and continues propagating beyond the kink at a different speed. We com- pute the exact solution for this problem using a Chaplygin transformation, a variation of the well-known Cagniard-de Hoop method. We first establish an integral equation for the computation of stress intensity factor after the kink and then we solve numeri- cally for the velocity and stress field around the crack. We find that the propagation of the crack across the kink produces a sharp change in energy balance that in turn pro- duces a circular SH wave centered at the kink that we call the kink wave. Across the wavefront of this wave there is a sudden jump in particle velocity and radial stress. At the same time, a local stress concentration appears on the external side of the kink. We establish an exact energy balance for this problem in terms of energy rates per unit crack advance. Radiated energy is shown to maintain the balance between elastic en- ergy released by the bulk and energy used to make the crack advance. The kink wave- front is the boundary between a field dominated by the initial flat portion of the crack and a region dominated by radiation from the kink.