Green's tensor and radiation patterns of point sources in general anisotropic inhomogeneous elastic media

Abstract

i Marshall McLuhan, 1958 The elastodynamic ‘ray‐theoretical’ Green's tensor for general anisotropic and inhomogeneous media (GANIMED) is derived in the far‐field high‐frequency approximation. This allows the quantification of the amplitude and phase charac‐teristics of arbitrary point sources. The displacement field is controlled by the phase velocity and the Gaussian curvature of the wave surface. Exploiting the already existing computer codes for dynamic ray tracing in GANIMED, we demonstrate how one may couple it to source theory in order to calculate displacement‐radiation patterns for unipolar and dipolar sources in various earth crustal materials, such as shales, sandstones, and olivine. The existence of a velocity gradient at the source causes asymmetry in the radiation patterns. In contradistinction, anisotropy at the source tends to distort the lobes and in some cases can beam excessive energy in specific directions. Our calculated radiation patterns for shear waves are similar to those observed from some explosions in soil. Copyright © 1991, Wiley Blackwell. All rights reserved