Ray Chaos in the Long-Range Propagation of Sound in the Ocean

We develop an approximate analytical approach for a description of the stochastic behavior of sound rays in deep-sea acoustic waveguides with paths up to 3 to 5 thousands of kilometers. The ray dynamics is studied using the Hamiltonian formalism in terms of the action–angle canonical variables. A realistic model of underwater waveguide with internal-wave-induced perturbations of the sound speed field is applied. We point out a small parameter of the problem, which allows one to linearize the Hamilton (ray) equations and approximate the action variable by a Wiener process representing the simplest model of diffusion. The stochastic ray theory based on this approximation is applied to an analysis of ray travel times, i.e., the travel times of sound pulses coming to a receiver via different ray paths. The formation of compact clusters of the chaotic-ray travel times is explained quantitatively.