Stochastic sound propagation using dynamically orthogonal parabolic equations

Abstract

Accurate modeling of underwater acoustic propagation is challenging due to the complex ocean physics and acoustic dynamics and the need for resolving the wavelength of the propagating acoustic wave over large distances. These challenges are further amplified by the incomplete knowledge of the ocean environment and the acoustic parameters. These complexities thus lead to many sources of uncertainties in the governing models. In this work, we use our stochastic Dynamically Orthogonal (DO) framework to represent these uncertainties probabilistically in the acoustic Parabolic Equation (PE). These equations optimally represent the dominant uncertainties in the sound speed, density, bathymetry, and acoustic pressure fields. Starting from the governing PE, we derive range-evolution DO differential equations for the mean field, stochastic modes, and coefficients, hence preserving the nonlinearities and capturing the non-Gaussian statistics. The DO equations are implemented for the narrow-angle PE and higher-order Padé wide-angle PEs and are applied in range-dependent canonical test cases and realistic ocean environments with uncertain source location, source frequency, sound speed, and/or bathymetry fields. We highlight the computational advantages of our framework by comparing it to Monte Carlo predictions and show convergence of the probability density functions as the number of samples and/or modes is increased.