Theory of three-dimensional acoustic propagation in a wedgelike ocean with a penetrable bottom

Abstract

A new analytical solution is presented for the three-dimensional acoustic field due to a monotonic point source in an ocean wedge with a penetrable bottom. The field consists of a sum of normal modes which depend weakly on range (out from the apex) and frequency. The mode coefficients depend strongly on range, on z (cross range parallel to the apex), and on frequency. A dispersion relation is derived which gives the range-dependent mode shapes. Then a notional ‘‘effective’’ wedge is constructed with perfectly reflecting boundaries whose apex is displaced from that of the penetrable wedge. The offset is such that the range-independent modes in the effective wedge match the range-dependent modes in the penetrable wedge. A known solution for the perfect wedge is then modified, by excluding rays which intersect the bottom at greater than the critical grazing angle, to give the spatial and frequency dependence of the mode coefficients in the penetrable wedge. The new solution, which satisfies the Helmholtz equation and the boundary conditions, exhibits prominent 3-D features uniquely associated with the penetrable bottom. These features conform with ray-theoretic predictions. Toward the end of the article the transient field in the penetrable wedge due to an impulsive point source is derived by Fourier transforming the cw solution. The Green’s function for the velocity potential is a transient of extended duration which contains evidence of image smearing, a phenomenon due directly to the phase shift experienced by rays undergoing total internal reflection from the penetrable interface.