 
Summary: Seismic Radiation from a Kink on an Antiplane Fault
by M. AddaBedia and R. Madariaga
Abstract We study radiation and energy balance for an antiplane fault containing a
kink. A semiinfinite 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 wellknown Cagniardde 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.
Introduction
