A stochastic response surface formulation for the description of acoustic propagation through an uncertain internal wave field

Abstract

A modeling and simulation study is performed in a littoral ocean waveguide subject to uncertainty in four quantities: source depth, tidal forcing, initial thermocline structure, and sediment sound speed. In this partially known shelf-break environment, tidal forcing over a density-stratified water column produces internal tides and solitary wave packets. The resulting uncertainty in the space-time oceanographic field is mapped into the sound speed distribution which, in turn, introduces uncertainty into the acoustic wave field. The latter is treated as a stochastic field whose intensity is described by a polynomial chaos expansion. The expansion coefficients are estimated through constrained multivariate linear regression, and an analysis of the chaos coefficients provides insight into the relative contribution of the uncertain acoustic and oceanographic quantities. Histograms of acoustic intensity are estimated and compared to a reference solution obtained through Latin Hypercube sampling. A sensitivity analysis is performed to illustrate the relative importance of the four contributions of incomplete information about the environment. The simulation methodology represents an end-to-end analysis approach including both oceanographic and acoustic field uncertainty where the latter is quantified using stochastic basis expansions in the form of a polynomial chaos representation.