An efficient algorithm for calculating depth dependent modal phase and for mode identification in normal-mode models based on the Airy equation

Abstract

The underwater acoustic normal modes of multichannel environments may exhibit closely spaced eigenvalues that require a fine horizontal wave-number sample in models based on the Airy equation. Also, for broadband applications the maximum frequency difference that permits accurate interpolation is limited by the frequency difference of the modal depth functions. A straightforward and numerically efficient algorithm to construct a monotonic depth-dependent phase using the properties of the Airy functions is presented that significantly reduces the computational burdens imposed by these constraints. The total phase change of a mode across the depth of the waveguide gives the mode number, modulo π, which is essential in adiabatic normal-mode calculations for range variable environments because the acoustic field must be propagated from one environment to the next mode by mode. [Work supported by the Advanced Surveillance and Prediction System (ASAPS) Program of the Space and Naval Warfare Systems Command (SPAWAR, PMW 181-14).]