Dynamically orthogonal ray equations with adaptive reclustering

Abstract

The vast size of the ocean coupled with the Nyquist criterion often makes high-frequency ocean acoustics computationally intractable without approximation. A common approach is to employ ray theory to develop an approximate Green’s function for the acoustic wave equation. But due to the dynamic nature of ocean fields and the many sources of uncertainty in the temperature, salinity, density, sea surface, bathymetry, neither the sound speed nor the source and receiver locations are precisely known, and a single deterministic solution of the ray equations is often insufficient. In place of Monte Carlo simulations, we develop and numerically solve dynamically orthogonal ray equations to efficiently approximate solutions to the stochastic acoustic wave equation. The Lagrangian nature of the ray equations introduces a new computational challenge for reduced-order models; a naive approach requires realizations to be reconstructed at each time step. To remedy this, we employ a Taylor expansion of the sound speed around “mean rays” and propose a novel, adaptive algorithm to determine when the modes and coefficients of the reduced-order model must be reclustered and/or augmented to preserve accuracy. This offers a unique methodology for uncertainty quantification in the presence of non-Gaussian statistics which may be utilized in forward modeling as well as in acoustic inverse problems.