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Stochastic Acoustic Ray Tracing with Dynamically Or Equations

Michael Humara, S.M., 2020
Pierre Lermusiaux, Advisor

Developing accurate and computationally efficient models for ocean acoustics inherently challenging due to several factors including complicated physical mechanisms and the need to produce results on varying resolution scales. In this work, we explore the acoustic computation through first understanding the basics of wave equation and its derivation and then explaining several deterministic methods for acoustic computation. We also explore methods for computing stochastic realizations with Monte Carlo, Empirical Orthogonal Functions, and Dynamically Orthogonal (DO) Equations implementations. We then explore the potential for computing stochastic acoustic Reduced-Order Models by deriving and implementing Dynamically Orthogonal differential equations from the differential equations for acoustic Ray Tracing (DO-Ray). With a DO-Ray implementation we can insert environmental uncertainties and compute the stochastic acoustic ray fields in a reduced order fashion, all while preserving the statistics of the ocean environments. We begin by outlining a deterministic Ray-Tracing model and validate the model to perform Monte Carlo stochastic computation as a basis for comparison. We then present the methodology with detailed deviations and implementation challenges. By applying it to three idealized cases of stochastic sound-speed profiles (SSPs), we observe the ability to represent the stochastic ray trace field in a reduced order fashion.