Dynamic motions near an earthquake fault: a three-dimensional so ution

The rupture process occurring during an earthquake is described here in terms of one of the few known solutions to a problem of brittle fracture, in which rupture originates at a point, and spreads over a fault plane, initiating shearing motions. Using a stress-relaxation model with a particular geometry of rapture growth, stresses and displacements can readily be found throughout the medium in which rupture is taking place. The qualitative and quantitative properties of this fracture solution can give considerable assistance in interpreting records of strong ground motion, and provides insight into the processes taking place at an earthquake source. It is shown that rupture speeds are likely to lie between the Rayleigh-wave and shear-wave speeds, that temperatures can be raised substantially by faulting, and that the ratio of particle velocity to stress drop is approximately proportional to rupture velocity. In order to obtain the rupture velocity in rock mechanics experiments, measurement of displacement normal to the fracture surface is recommended