Reflection and Transmission at an Interface Separating Transversely Inhomogeneous Acoustic Half-Spaces

摘要

The problem of reflection and transmission at a vertical interface separating two stratified half-spaces is solved exactly, in principle, in the context of one-way propagation theory. The solution requires a generalization of the usual notions of reflection and transmission coefficients. These coefficients become (formally) pseudo-differential operators. For homogeneous half-spaces the operator symbols are recognized as the usual plane wave reflection and transmission coefficients. For stratified half-spaces the operator symbols should be calculated using approximate formulae that are consistent with whatever algorithm is to be used in the associated propagation problem. Formulae are derived that are consistent with a high-frequency algorithm that has already been shown to be superior to other extended parabolic (one-way) theories. The connection between the exact theory and a number of other extended parabloic theories is explored by means of perturbation series.