REFLECTION AND REFRACTION OF SPHERICAL COMPRESSIONAL WAVES AT ARBITRARY PLANE INTERFACES *

Abstract

A bstract The exact expressions for the reflection and refraction of homogeneous spherical compressional waves at the plane contact between two semi‐infinite media are obtained by a new simple method. Whilst its general ideas were outlined in a previous paper (Bortfeld 1962) dealing with some special interfaces, this method is now applied to all kinds of contact (solid‐solid, solid‐fluid, fluid‐solid, solid‐free, fluid‐fluid, fluid‐free). By some improvements, the treatment of the general case is even more simple than the previous one of the special cases. Integrating the potentials for sinusoidal excitation over the circular frequency and adding the static potentials yields expressions for the step‐response which consist of (infinite) single integrals of elementary functions. By a single application of Cauchy's theorem, the complete set of wavefronts is obtained and the step‐response is put into forms suitable as a basis for numerical calculations. The responses for arbitrary source excitations are given in the usual way by superposition integrals.