A stochastic representation of environmental uncertainty and its coupling to acoustic wave propagation in ocean waveguides

It is argued that a quantitative measure of incomplete environmental knowledge or information (i.e., environmental uncertainty) should be included in any simulation-based predictions linked to acoustic wave propagation. A method is then proposed to incorporate environmental uncertainty directly into the computation of acoustic wave propagation in ocean waveguides. In this regard, polynomial chaos expansions are chosen to represent uncertainty in both the environment and acoustic field. The sound-speed distribution and acoustic field are therefore generalized to stochastic processes, where uncertainty in the field is interpreted in terms of its statistical moments. Starting from the narrow angle parabolic approximation, a set of coupled differential equations is derived in which the coupling term links incomplete environmental information to the corresponding uncertainty in the acoustic field. Propagation of both the field and its uncertainty in an isospeed waveguide is considered as an example, where the sound speed is described by a random variable. The first two moments of the field are computed explicitly and compared to those obtained from independent Monte Carlo solution of the conventional (deterministic) parabolic equation that describes the acoustic wave properties.