Transient Elastic Plane P- and SV -wave Diffraction by a Semi-Infinite Fluid-Filled Crack in an Isotropic, Dispersive Solid.

摘要

The canonical problem of the diffraction of a transient elastic plane P- and SV-wave by a semi-infinite fluid-filled crack in an unbounded, homogeneous, isotropic, dispersive solid is considered. The dispersion properties of the solid (and its associated loss mechanism) are accounted for by general, global relaxation functions that meet the causality criterion and encompass the influence of frictional forces and a Maxwell-type visco-elasticity that can be used to describe the temporal dispersion of seismic waves. The problem is solved by a combination of the Wiener-Hopf and modified Cagniard techniques, together with an appropriate correspondence principle that interrelates the transient elastic wave motion in a solid with global relaxation functions and the one in a perfectly elastic solid. Closed-form analytic expressions are obtained for the particle velocity in the wave motion. Several examples are discussed and numerical results are presented.