Constructing acoustic timefronts using random matrix theory

Abstract

In a recent letter [Hegewisch and Tomsovic, 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 can be deduced from the timefronts and how to connect features of the data to that environmental information. It also makes direct connections to methods used in other disordered waveguide contexts where the use of random matrix theory has a multi-decade history.