Constructing acoustic timefronts using random matrix theory

TL;DR

This paper extends the application of random matrix theory to construct and analyze acoustic timefronts in the ocean, providing an efficient statistical method that aligns with traditional propagation models and reveals environmental information embedded in the data.

Contribution

It introduces a novel method for constructing acoustic timefront ensembles using random matrix theory, enhancing analysis of ocean acoustic propagation and environmental information retrieval.

Findings

The method accurately reproduces timefront statistics at various ranges.

It reveals which environmental features are preserved in the acoustic data.

The approach aligns well with traditional parabolic equation simulations.

Abstract

In a recent letter [Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. This work gives a more complete account of that approach and extends the methods to the construction of an ensemble of acoustic timefronts. The result is a very efficient method for studying the statistical properties of timefronts at various propagation ranges that agrees well with propagation based on the parabolic equation. It helps identify which information about the ocean environment survives in the timefronts and how to connect features of the data to the surviving environmental information. It also makes direct connections to methods used in other disordered wave guide contexts where the use of random matrix theory has a multi-decade history.