Numerical evaluation of near-field, high-frequency radiation from quasi-dynamic circular faults

abstract We compute the near-field, high-frequency radiation from a circular crack expanding with constant rupture velocity and discuss the characteristics of the stopping phases. We then introduce rupture velocity jumps in the fracture process. The computed accelerations show the dominant role played by the rupture front kinematics. The high acceleration pulses are associated with sudden changes of the rupture velocity. For a sudden jump (or a sudden stop), there is no theoretical high-frequency limit to the spectral density of acceleration. In order to account for fmax, we introduce a smooth deceleration of the rupture front over a time t′ in place of a sudden stop. This results in a spectral fall-off for frequencies greater than 1/t′ and supports the interpretation of fmax as a source effect.

On the ratio of P-wave to S-wave corner frequencies for shallow earthquake sources

abstract We construct a theoretical three-dimensional kinematical model of shallow-focus earthquake faulting in order to investigate the ratio of the P- and S-wave corner frequencies of the far-field elastic radiation. We attempt to incorporate in this model all of the important gross kinematical features which would arise if ordinary mechanical friction should be the dominant traction resisting fault motion. These features include a self-similar nucleation at a single point, a subsonic spreading of rupture away from that point, and a termination of faulting by smooth deceleration. We show that the ratio of the P-wave corner frequency to the S-wave corner frequency for any model which has these features will be less than unity at all points on the focal sphere.