The method of generalized ray applied to plastic sources

摘要

The expansion into plane waves of cylindrical or spherical waves propagating in a layered elastic half-space proves to be quite efficient for short observation times at a fixed receiver. Even the divergence effects of dipping interfaces of wedge-type layers are perfectly included by proper coordinate rotations and the exact "seismograms" are observed at a point receiver from any source located at the hypocenter. These nontrivial technique relies on invariance of the phase function and of the infinitesimal amplitude of the plane waves in the ray expansion. Recently, the concept of the elastic background was explored for the elastic-viscoplastic waves propagating in thin rods and extended to the 3-D problem of spherical waves with point symmetry. In that context and in an incremental formulation, the notion of plastic sources was used, which emit elastic waves in the background. Further, the dynamic generalization of Maysel's formula of thermo-elasticity to include all kinds of eigenstrains connected the dynamic stress Green's function of the background with the eigenstrain distribution by a convolution and the domain integral. The novel contribution of that paper to acoustic emission and monitoring of (layered) structures is the formulation of the full 3-D problems and the introduction of the generalized rays in the background considering an instantaneous oblique force point source. Taking into account the progress in symbolic manipulation with integrated numeric such a formulation seems timely and may be competitive to the entirely computational Finite Element Method of analysis of signals received from plastic sources.