Propagation of Sound from a Fluid Wedge into a Fast Fluid Bottom

Abstract

The ocean waters lying above the continental shelf often can be modeled with a fair degree of accuracy by a fluid wedge overlying a bottom. In those cases where the bottom consists of unconsolidated sediments, it is also an admissible approximation to treat the bottom as a fluid. See Fig. 1. If the speed of sound in the bottom exceeds that in the water layer (a fast bottom), the wedge can support trapped normal-mode propagation. Let acoustic energy from a distant source propagate up the slope towards the apex of the wedge. As the apex is approached and the local thickness of the wedge decreases, the modes carrying the energy will experience the condition for cutoff at varying distances from the apex. We can estimate the depth at which a given normal mode would be cut off by calculating the depth H for which the equivalent mode would just be cut off in a layer of constant depth. If the wedge angle is 3 the lowest mode of propagation would experience cutoff when the distance from the apex decreases to a dump distance X = H/β, the next mode at the distance 3X, the third at 5X, and so forth. Thus, as the acoustic energy propagates towards the apex, successively lower modes will be cut off and the energy contained in each of them transmitted into the bottom.