Diffraction of SH-Waves in a Spherically Isotropic Medium by a Rigid or Fluid Spherical Core

Abstract

Suininary In this paper we have considered the diffraction of SH-waves from a point source by a rigid or fluid spherical core. The medium outside the core is assumed to be spherically isotropic about the centre of the core. It is found that the propagation of SH-waves in such a medium is characterized by two elastic parameters associated with the phase velocities C1 and C, along and perpendicular to a radius, respectively. Depending on the ratio l/a of these two velocities and the distance of the source from the centre, the region of space outside the core can be separated into three different regions: (i) an illuminated zone which is reached either by the rays going left or right from the source and their reflections from the sphere; (ii) a shadow zone, which may be bounded; and (iii) if the shadow is bounded, then there is a third zone which may be reached by both rays going left and right and their reflections. This classification is true provided c1 is greater than one, which is true in most geophysical applications. Furthermore, if c1 is 2 2, then there is no shadow when the distance b of the source from the centre is large enough. We have discussed the solutions for 1 < c1 < 2 and have given simple geometrical interpretations to these solutions.