A two-way parabolic equation for acoustic backscattering in the ocean

Abstract

The parabolic equation (PE) method is generalized to handle backscattered acoustic energy in the ocean. The two-way PE is based on the single-scattering approximation and the approach of two-way coupled modes in which range-dependent environments are approximated by a sequence of range-independent regions. At the vertical boundaries between regions, the solution of the two-way PE is required to satisfy two continuity conditions. The range derivative in one of the conditions is replaced by a higher-order PE depth operator. The reflected and transmitted fields that satisfy these conditions are computed with an efficient iteration scheme. The outgoing and incoming fields are propagated by two-way range marching. The two-way PE, which is presently implemented for two-dimensional problems, is a practical method for solving large-scale reverberation problems. The accuracy of the two-way PE is demonstrated by comparisons with reference solutions. The two-way PE is applied to simulate the localization of a source of backscattering using the method of back propagation.