Perturbations in travel time and ray geometry due to mesoscale disturbances: A comparison of exact and approximate calculations

Exact calculations of the changes in eigenray travel time and geometry, due to range-dependent mesoscale disturbances, are compared to three approximations. In the first approximation, the sound-speed perturbation is integrated along the unperturbed path. In the second approximation, the range average of the sound-speed perturbation is integrated along the unperturbed path. The third approximation uses the range-average raytrace to estimate changes of travel time and geometry. Calculations made both for a measured section through a mesoscale eddy and for a simplified model of an eddy (with variable strength, position, and boundary width) suggest that: (i) while none of the approximations tested is uniformly the best, the first approximation is to be preferred ; (ii) the eddy position relative to the ray path is quite significant; and (iii) the exact travel-time perturbations are not sensitive to whether the eddy boundaries are assumed sharp or gradual. For an eddy perturbation of ±9 m/s (±1.9 °C or Rossby wave displacement of about ∓200 m) at 700-m depth, the travel-time approximations are typically in error by 10%–20%. The associated change in turning depth from the unperturbed state to either the perturbed or the range-average state is typically ±100–200 m. These errors are significant, but not large, and suggest that it will be beneficial to iterate linear inverse schemes used to estimate sound-speed perturbations from travel-time perturbations.