Acoustic wave propagation in horizontally variable shallow water

Abstract

A unique normal mode solution which approximates sound speed variation with depth by a sequence of isovelocity layers is verified for a sample of range independent environments. Within each layer, two closed-form fundamental solutions which satisfy the separated depth-dependent wave equation are formulated with complex analogues to be used in evanescent regions. Piecewise-continuous potential mode solutions are constructed by satisfying an upper boundary condition and extending through isovelocity layers to the bottom. The value of the Wronskian for the Green’s function thus obtained is used to locate the eigenvalues of the normal modes comprising the propagating field. A closed form solution in a modified two-layer Pekeris waveguide with step-wise changes in the upper layer sound speed with range is used to study horizontal mode coupling through a series of such environments and to predict propagation loss as a function of range.