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.