Random matrix theory for underwater sound propagation

¹ Department of Physics and Astronomy, Washington State University - Pullman, WA, 99164-2814, USA
² Department of Physics, Indian Institute of Technology Madras - Chennai, 600036, India

^a tomsovic@wsu.edu

Received: 30 September 2011
Accepted: 14 December 2011

Abstract

Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep-ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.