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Seismic Radiation from a Kink on an Antiplane Fault

Laboratoire de Physique Statistique de l’École Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France

R. Madariaga

Laboratoire de Géologie de l’École Normale Superieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France

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 compute 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 numerically 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 produces 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 energy released by the bulk and energy used to make the crack advance. The kink wavefront is the boundary between a field dominated by the initial flat portion of the crack and a region dominated by radiation from the kink.