Simple illustrations of range-dependence and 3-D effects by normal-mode sound propagation modelling

TL;DR

This paper uses normal-mode sound propagation models to illustrate how horizontal variations in underwater environments affect wave behavior, including reflections and transmissions at interfaces, with simple assumptions that keep mode shapes constant horizontally.

Contribution

It introduces a straightforward approach to model horizontal parameter variations where mode shapes are unchanged, simplifying the analysis of complex 3-D effects in underwater acoustics.

Findings

Mode reflection and transmission can be computed separately without mode coupling.

Frequency-dependent effects like reflections from ridges are demonstrated.

Pulse and continuous-wave simulations illustrate 3-D effects such as shadow zones.

Abstract

As is well known, the sound-speed profile has significant effects on underwater acoustic sound propagation. These effects can be quantified by normal-mode models, for example. The basic case is a laterally homogeneous medium, for which the sound speed and the density depend on depth only and not on horizontal position. Effects of horizontal medium-parameter variation can be quantified by coupled-mode models, with coupling between mode expansions for laterally homogeneous parts of the medium. In the present paper, these effects are illustrated for media with a particularly simple horizontal parameter variation such that mode shapes do not vary with horizontal position. The modal wavenumbers depend on horizontal position, however. At a vertical interface between regions with laterally homogeneous medium parameters, each mode is reflected as well as transmitted. For the media considered, reflection and transmission coefficients can be computed separately for each mode without mode coupling, and this is done recursively, stepping through the laterally homogeneous regions in appropriate order. Continuous-wave as well as pulse computations are used to illustrate frequency-dependent reflections from ridges and diffraction into shadow zones behind islands, for example.