Travel‐time perturbations due to internal waves: Equivalence of modal and ray solutions

Abstract

In a recent paper, Lynch et al. used modal and ray based perturbation techniques to compare predicted variances of acoustic travel times due to internal waves to measured variances in the Barents Sea Polar Front experiment [Lynch et al., J. Acoust. Soc. Am. 99, 803–821 (1996)]. One of the interesting results of this work is that the modal and ray travel‐time variances are substantially different for rays and modes with the same grazing angle. Specifically, the maximum modal travel‐time variance shows a resonant effect in which the variance increases with increasing frequency. Unlike the modal solution, the ray travel‐time variance has a geometrically constrained maximum, independent of frequency. In this paper, the linear first‐order solutions for the ray and modal variances due to the internal waves are reviewed, and in an Appendix the effects of the linearizing assumptions are examined. The ray and mode solutions are then shown to be consistent by considering a truncated sum of modes that constructively interfere along a geometric ray path. By defining the travel‐time perturbation due to a truncated sum of modes, the travel‐time variance of the modal sum is derived. With increasing frequency the maximum value of this variance converges to a frequency‐independent result with a similar magnitude to the ray maximum variance.