ACOUSTIC PROPAGATION IN AN UNCERTAIN WAVEGUIDE ENVIRONMENT USING STOCHASTIC BASIS EXPANSIONS

Abstract

A generalization of acoustic propagation in an uncertain ocean waveguide environment is described using a probabilistic formulation in terms of stochastic basis expansions. The problem is studied in the context of wave propagation in random media, where environmental uncertainty and its interaction with the acoustic field are described by stochastic, rather than deterministic parameters and fields. This representation, constructed explicitly in terms of Karhunen-Loève (KL) and polynomial chaos (PC) expansions, leads to coupled differential equations for the expansion coefficients from which the stochastic acoustic field can be obtained as a random process. The equations are solved in the narrow-angle parabolic approximation using a split-step method to compute moments of the random acoustic field at any point in the waveguide. Results are compared with Monte-Carlo computations of the acoustic field in the same environment to study the convergence of the truncated stochastic basis expansion representing the acoustic field. The rate of convergence of the truncated chaos expansion was found to be dependent on the particular moment computed. For the first and second moments corresponding to the mean field and the field intensity, convergence was achieved rapidly, only requiring low order expansions. Another second moment, the acoustic spatial coherence, converged more slowly due to the relative phase information that, in this formulation, is described by polynomial approximation. While stochastic basis expansions show promise for the development of compact representations of the acoustic field in the presence of environmental uncertainty, accelerated convergence schemes will be needed to allow for practical applications.