Random matrix theory for underwater sound propagation

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.