An approach to computing acoustic wave propagation in shallow water

Abstract

A shallow water mode solution is presented, which approximates the water column sound speed variation using isovelocity layers. Within a layer, two fundamental solutions are seen to satisfy the separated depth-dependent wave equation and complex analogs apply in evanescent regions. Solutions which satisfy an upper boundary condition are extended continuously through isovelocity layers to the bottom, matching functions and derivatives at layer boundaries. 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. Acoustic mechanisms which are dominant in shallow water such as forward scattering and range dependence are incorporated as matrix multiplications to implement horizontal coupling between modes. Agreement between the shallow water approach and a benchmark deep water mode solution is shown for a number of shallow environments.