Application of the Method of Generalized Rays to Acoustic Waves in a Liquid Wedge Over Elastic Bottom

Abstract

A range-dependent problem of shallow water acoustics is modeled by a liquid wedge over fast-speed elastic substratum, and the solution is derived based on the method of generalized rays, where the total acoustic field is decomposed into a sum of partial waves, comprising the wave emitted from the point source and the multi-reflected waves. The contribution of each partial wave at a given time is represented by a single integral. The diffracted waves arising from scattering at the apex of the wedge are neglected in this otherwise exact solution. The pressure records are evaluated at the downslope receiver when the pressure pulse applied at a point situated within the wedge has impulsive or harmonic time history. It was found that the arrival of the source pulse is preceded by the group of head wave arrivals, and this early portion of the record (the ground wave) includes considerable pressure build-ups. For a Heaviside source-pulse, we have found that the pressure records of the partial waves exhibit a singular behavior such as the logarithmic singularity at the arrival time of the totally reflected spherical wave. This singular behavior was not found for less sharp input, that is, a triangular source-pulse. We have also found that for a causal harmonic input of lower frequency the ground wave stands out very clearly, whereas for that of higher frequency it is almost suppressed, and for both frequencies the response becomes more or less steady-state soon after the arrival of a few partial waves.