Stochastic ray theory for long-range sound propagation in deep ocean environments

The motion of sound ray trajectories in deep ocean environments, including internal wave induced scattering, is considered. Using the empirical Garrett-Munk internal wave spectrum and results from the study of stochastic differential equations, a framework for studying and modeling stochastic ray motion is developed. It is argued that terms in the ray equations involving internal wave induced sound speed perturbations delta c can be neglected, but those involving partial derivative delta c/partial derivative z cannot. It is then shown in that the (Markov) approximation that spatial variations of partial derivative delta c/partial derivative z are delta correlated is remarkably good. These results lead naturally to an extremely-simple system of coupled stochastic ray equations (in ray depth z, ray slowness p and travel time T) in which stochasticity enters the system only through the equation for p. Solutions to the stochastic ray equations-or the corresponding Fokker-Planck equation-describe approximately the density of acoustic energy in range, depth, angle and time. Two dimensionless parameters are introduced: (1) an acoustic Peclet number which is a measure of the ratio of the strength of deterministic ray refraction to that of stochastic scattering induced ray diffusion; and (2) a measure of the ratio of the strength of scattering induced ray diffusion to that of wave diffraction. Numerical solutions to the stochastic ray equations are compared to full wave simulations. These results show that, even in the weak scattering regime (large acoustic Peclet number), the inclusion of internal wave induced scattering may lead to important qualitative corrections to predictions of distributions of acoustic energy. (C) 1998 Acoustical Society of America. [S0001-4966(98)01810-4]