Point source in a layer overlying a semi-infinite solid with special reference to diffracted waves

Abstract

The problem of a point source of dilatational waves in a homogeneous, isotropic, perfectly elastic layer overlying a homogeneous, isotropic, perfectly elastic halfspace has been discussed. The terms corresponding to various reflected waves are obtained from the representation of the point source as a summation of plane waves by making use of reflection coefficients. These are then integrated along the modified Sommerfeld contour and various minimum-time-path and diffracted waves are obtained. Numerical values of the elastic constants are inserted and the dependence of the amplitudes of these waves on frequency and sourcedepth observed. The amplitudes of the diffracted waves are compared with those of the minimum-time-path waves and it has been found that the contribution due to the former is always small as compared to that due to the latter. In fact the former are appreciable only when the frequency is small.