Gaussian ray bundles for simulating shallow-water torpedo reverberation

Abstract

A range-dependent propagation model was developed to simulate shallow-water torpedo reverberation. The model is based on Gaussian ray bundles in the form ‖P(r,z)‖2=[β/√2πσ(r)prr]exp(−0.5[(z−zr)/ σ(r)]2), where r is the horizontal range from the source to the field point, z is the vertical depth of the field point, zr is the vertical depth along a central ray, pr is the horizontal slowness along a central ray, β depends on the source, and σ(r) is an effective standard deviation given by σ(r)=(1/2)max(Δzr,8λ). Here, Δzr is the vertical distance between two adjacent rays and λ is the wavelength at the field point. [Work supported by the Naval Sea Systems Command (PMS-402 and PMS-406) and the Office of Naval Research (ONR-321).]