THE METHOD OF GENERALIZED REFLECTION AND TRANSMISSION COEFFICIENTS

Abstract

The objective of this work is to provide a method for predicting the surface response of a stratified half space to the radiation from a localized source when neither the assumptions of the plane wave theory nor the assumptions of the normal mode theory are valid. The earth model consists of a finite number of perfectly elastic, homogeneous, isotropic layers separated by interfaces which are plane and parallel to one another. The method leads to an infinite series for the Laplace transform of the response function (displacement, velocity, stress, etc.) in a multi‐interface system. Each term in the series describes all the energy which traverses a particular generalized ray path between the source and the receiver. The specification of the mode of propagation across each stratum (either as an irrotational wave or as an equivoluminal wave) and of the sequence in which the strata are traversed serve to define a generalized ray path. A prescription is given for constructing the integral representation for the disturbance which has traversed such a path directly from the integral representation for the source radiation. The method therefore obviates the necessity for solving a tedious boundary value problem. The time function associated with each term can be obtained by using Cagniard’s method.