Ray travel times at long ranges in acoustic waveguides

The Hamiltonian formalism in terms of the action-angle variables is applied to study ray travel times in a waveguide with a smooth sound speed profile perturbed by a weak range-dependent inhomogeneity. A simple approximate formula relating the differences in ray travel times to range variations of action variables is derived. This relation is applied to study range variations of the timefront (representing ray arrivals in the time-depth plane). Widening and bias of timefront segments in the presence of perturbations are considered. Qualitative and quantitative explanations are given to surprising stability of early portions of timefronts observed in both numerical simulations and field experiments. This phenomenon is interpreted from the viewpoint of Fermat's principle. By ray tracing in a realistic deep water environment with an internal-wave-induced perturbation it has been demonstrated that our approach can be used at ranges up to, at least, 3000 km.