Geometric stochastic ray propagation using the special Euclidean group

This paper describes a stochastic model of ray trajectory propagation through a medium-such as the ocean-which has an uncertain sound speed profile. We frame ray propagation as a geometric fractal Brownian motion process on the special Euclidean group of dimension two, SE(2). The framing includes diffusion parameters to describe how the stochastic rays deviate from the expected rays, and these diffusion parameters are a function of the uncertainty in the sound speed profile. We demonstrate this framing for the classical Munk profile and a double-ducted profile in the Beaufort.