Reflection of a plane wave from a fluid layer with continuously varying density and sound speed

Abstract

This paper considers the transmission of an acoustic plane wave through a horizontally stratified fluid layer whose density and sound speed both vary continuously with depth. The stratified layer is of finite thickness and lies between two semi-infinite homogeneous fluids. The situation modeled is intended to be representative of an inhomogeneous marine sediment overlying a uniform substrate. Exact solutions of the Helmholtz equation, valid in the stratified layer, are derived for a class of density profiles and a number of classes of sound-speed profile. These include profiles that closely resemble measured density and sound speed variation in marine sediments. The solutions in the stratified layer are matched with solutions in the homogeneous upper and lower layers, to derive analytical expressions for the reflection coefficient of a plane wave, incident from the upper medium. Internal losses are modeled in both the substrate and the sediment layer. The solutions enable assessments to be made of the dependence of reflection coefficient on wavenumber and grazing angle for different shapes of density and sound speed profile in the sediment. The limiting cases of very low and very high frequency are examined, and both limits are shown to give reflection coefficients independent of the shape of the density or sound speed profile in the sediment layer. A number of numerical results are presented, and comparison is made with computed results from a general propagation model.