On the plane-wave reflection coefficient and nonspecular reflection of bounded beams for layered half-spaces underwater

Abstract

We study the recently derived reflection coefficient for plane waves in a liquid that are incident on the liquid–solid interface of a solid half-space, which consists of a single layer of one elastic material bonded to a substrate of a different material. Plots of the magnitude of the reflection coefficient versus the incident angle are presented for many sets of material parameters and values of frequency f and layer thickness d. The use of the results presented for the study of nonspecular reflection of bounded acoustic beams is of primary interest. We therefore seek to identify all the critical incidence angles for nonspecular reflection. We find that nonspecular reflection can occur, not only in connection with surface waves that are purely propagating modes in the absence of the liquid, but also for leaky modes on a layered half-space, provided the leakage is not too great. We also investigate, in particular, the surface wave propagation for the case of a stiff layer on a soft half-space, and we find that the purely propagating mode cuts off with increasing fd when its speed reaches the shear wave speed of the substrate, as reported in the literature. However, as fd increases further, a leaky mode appears that approaches the Rayleigh wave for the layer. This leaky mode is also associated with nonspecular reflection for large enough fd.