Travel time stability in weakly range-dependent sound channels

Travel time stability is investigated in environments consisting of a range-independent background sound-speed profile on which a highly structured range-dependent perturbation is superimposed. The stability of both unconstrained and constrained (eigenray) travel times are considered. Both general theoretical arguments and analytical estimates of time spreads suggest that travel time stability is largely controlled by a property $\omega ^{\prime}$ of the background sound speed profile. Here, $2\pi/\omega (I)$ is the range of a ray double loop and $I$ is the ray action variable. Numerical results for both volume scattering by internal waves in deep ocean environments and rough surface scattering in upward refracting environments are shown to confirm the expectation that travel time stability is largely controlled by $\omega ^{\prime}$.