Ray travel times in range-dependent acoustic waveguides

An approximate analytical approach to describe the stochastic motion of sound rays in deep ocean is developed. This is done for a realistic propagation model with an internal wave induced perturbation imposed on the smooth background sound speed field. The chaotic ray dynamics is analyzed using the Hamiltonian formalism taken in terms of the action-angle canonical variables. It is shown that even at ranges of a few thousands km, the magnitude of range variations of the action variable is still small enough to be used as a small parameter in the problem. A simple expression for the difference in travel times of perturbed and unperturbed rays and approximate analytical solutions to stochastic ray (Hamilton) equations are derived. These relations are applied to study range variations of the timefront (representing ray arrivals in the time-depth plane). Estimations characterizing the widening and bias of timefront segments in the presence of perturbations are obtained. Qualitative and quantitative explanations are given to surprising stability of early portions of timefronts observed in both numerical simulations and field experiments.