abstract

We study the near-field generated by Haskell's rectangular fault model used extensively to interpret seismic data. By means of the Cagniard-de Hoop method we have been able to find an exact solution for the near-field particle velocities in the case of a step-function source slip history. The results show that there are two distinct regions of radiation. One is a cylindrical region in front of the fault where two-dimensional approximations are valid and result in a substantial reduction of computation. In the rest of space the field is dominated by spherical waves radiated from the corners of the dislocation. These waves are much more complicated to calculate. First motion approximations demonstrate that the cylindrical waves are stronger than the spherical waves; in particular, infinite accelerations at the cylindrical wave fronts are predicted even for ramp sourcetime functions.

The stress field on the fault plane generated by this dislocation is also calculated. Strong stress singularities of type r−1 are found all around the edges of the fault. These singularities are a consequence of the assumption of constant dislocation across the fault width. They may only be eliminated by smoothing the dislocation near the fault edges. These singularities are so strong that an infinite averaged stress drop on the fault is predicted independently of any source parameters. As a consequence, the Haskell model is essentially a long-period model of faulting.

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