Three-dimensional diffraction of elastic waves by a spherical cavity in an elastic half-space, I: Closed-form solutions

Abstract

The three-dimensional scattering and diffraction of elastic waves at an arbitrary angle of incidence in a homogenous, perfectly elastic and isotropic half-space due to the presence of an embedded spherical cavity is analysed. The closed form solutions of the multiple boundary-valued problems for incident elastic waves are developed. Two methods for the development of the solution are used: the iterative method of successive constructions and a one-step method with an infinite matrix. Explicit expressions for the coefficients in the series solutions can be derived both at each step of the iteration and also from the infinite matrix. This problem has valuable applications in the theory of earthquake engineering and related problems in seismology.