  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.
