3-DIMENSIONAL WAVE-PROPAGATION ANALYSIS OF A SMOOTHLY HETEROGENEOUS SOLID

A method of analysis is presented for three-dimensional wave propagati on problems of a vertically-heterogeneous half-space with a linear she ar wave velocity profile. With the aid of a displacement-polential rep resentation, Hankel transforms and Fourier decompositions, the dynamic response of the semi-infinite solid to an arbitrarily distributed bur ied source is shown to admit integral representation in terms of modif ied Bessel functions. Specific aspects of the problem such as the mult iple poles along the inversion path on the complex plane and the chara cteristics of the wave propagation in the vertical direction are eluci dated. Apart from its intrinsic interest, the solution can be degenera ted to ring-load and point-load Green's functions which are fundamenta l to boundary integral equation formulations.