Normal-mode program with N2 linear layers

Abstract

Normal-mode expansions provide a low-frequency complement to the high-frequency ray theoretic methods. These methods are useful in environments where the sound speed and density profiles are essentially stratified, i.e., these parameters have a weak dependence on range. They also provide a means of confirming the validity of other approximate methods for which a direct error analysis is not possible. The theory of such expansions is well established, but their implementation is sometimes difficult. In the present program, the sound speed and density profiles in the ocean and the bottom are approximated and the resulting approximation is solved exactly. The nature of the profile approximation is as follows: The depth coordinate is partitioned into N layers such that in each layer the square of the index of refraction may be approximated by a straight line and the density by a constant. The Z-dependent portion of the pressure field can then be expressed in terms of Airy functions. The results are compared with a modified NRL program [A. V. Newman and F. Ingenito, “A Normal Mode Computer Program for Calculating Propagation in Water with an Arbitrary Velocity Profile,” NRL Rep. 2381 (Jan. 1972)] and with the FFP program [F. DiNapoli, “Fast Field Program for Multilayered Media,” NUSC Rep. No. 4103 (1971)] for a set of examples presented at the recent ONR Non-Ray Tracing Workshop, May 1973. In addition, the effects of the continuous spectrum are considered. [Supported by Naval Ordnance Systems Command.]