Dynamically orthogonal equations for stochastic underwater sound propagation

Abstract

Grand challenges in ocean acoustic propagation and inference are to accurately capture the dynamic environmental uncertainties and to predict the evolving probability density distribution of stochastic acoustic waves, all efficiently and rigorously, using the governing partial differential equations (PDEs). To start addressing these needs, the stochastic dynamically orthogonal (DO) PDEs for the parabolic wave equation are derived and numerical schemes for their integration are obtained. Within the parabolic approximation, these equations are the optimal reduced-order representation of stochastic acoustic waves within the uncertain sound speed environment. The DO equations govern the propagation of the mean field, the DO modes, and their stochastic coefficients. Examples are provided for a set of idealized test cases as well as for more realistic ocean environments, and predictions are contrasted with those of other uncertainty quantification schemes. The utilization of DO equations for end-to-end uncertainty prediction within oceanographic-seabed-acoustic-sonar dynamical systems is discussed.