Stochastic basis expansions applied to acoustic propagation in an uncertain, range, and depth-dependent, multi-layered waveguide.

Abstract

We study the utility of stochastic basis expansions in acoustic propagation through a multi-layered ocean waveguide in the presence of environmental uncertainty. Environmental uncertainty means that the parameters that describe the waveguide are treated probabilistically. Specifically, in the differential equation governing propagation, the uncertainty appears in the sound speed profile as an explicit dependence on a set of random variables. This implies that the acoustic field itself is a random field. Stochastic basis expansions are attractive because of their often exponential convergence. We use a complete set of multivariate orthogonal polynomials to compute the acoustic field’s statistics. The field propagates by a wide-angle parabolic equation through a rectangular waveguide comprised of three layers separated by two horizontal interfaces. A pressure release surface and hard bottom bound the waveguide. The water’s sound speed is a constant perturbed by a small, random range, and depth-dependent term that models a frontal zone, the middle sedimentary layer is stratified and modeled to represent uncertainty in sound speed measurements, and the bottom layer is a deterministic attenuating layer. We compare the field’s statistics generated by the stochastic basis to those generated by Monte Carlo simulations.