Epicentral Displacement Caused by Elastic Waves in an Infinite Slab

Abstract

The displacement is determined at the epicenter of a homogeneous isotropic infinitely long elastic slab containing a point source of pressure waves. The source is centrally located between the slab surfaces and is taken to have a step function time dependence. The formal solution for the Laplace transform of the displacement is obtained as an infinite integral. The integration and the inversion are simultaneously accomplished by an infinite series expansion of the integrand and transformation of variables for each term of the expansion. The resultant integrated series consists of terms having the mathematical form of reflected waves which diverge individually but combine to give a finite resultant. In view of the fact that the expansion of the integrand is not valid at the upper limit of integration, a justification of the method and of the results is given.