Mathematical aspects of space-time horizontal ray method

TL;DR

This paper extends the space-time horizontal ray method for acoustic wave propagation in shallow water, enabling prediction of signal characteristics like amplitude and frequency modulation through a decomposition based on vertical modes.

Contribution

It introduces a novel approach to analyze acoustic signals in underwater waveguides using space-time horizontal rays derived from vertical mode decomposition.

Findings

Analysis of space-time caustics in underwater waveguides

A simple method for predicting signal form and parameters

Enhanced understanding of acoustic wave propagation in shallow water

Abstract

The following development of the well-known "vertical modes and horizontal rays" approach for acoustic waves propagation in shallow water, introduced in different works, is studied. In this approach we study so-called space-time horizontal rays, constructed on the base of decomposition of the sound field, depending on time, over adiabatic vertical modes (solutions of the Sturm-Liouville problem). Using this technique we obtain different properties of signals, propagating in underwater waveguide, such as space-time caustics, and provide rather simple method for the prediction of the form of the signal and all its parameters (amplitude and frequency modulation, different front angles, etc.) at some point of observation.