ASA 127th Meeting M.I.T. 1994 June 6-10

3aUW6. An alternative wide-angle PE formalism and hybrid split-step/finite-difference solution algorithm.

David Yevick

Dept. of Elec. Eng., Queen's Univ., Kingston, ON K7L 3N6, Canada

David J. Thomson

Defence Res. Establishment Pacific, FMO Victoria, BC V0S 1B0, Canada

The split-step Fourier algorithm is widely used in underwater acoustics to solve parabolic equations (PEs) resulting from split-operator approximations to the one-way wave equation. Recently, Porter and Jensen [J. Acoust. Soc. Am. 94, 1510--1516 (1993)] reported on a seemingly benign propagation problem in which two wide-angle split-operator PEs performed poorly compared to the standard PE. For a source and a receiver located within a leaky surface duct, each of the wide-angle approximations gave rise to anomalously high values of transmission loss at ranges where the leakage energy is refracted back into the duct. Moreover, the two wide-angle PEs were more sensitive to the choice of reference wave number than the standard PE. This behavior is contrary to previous experience with such split-operator approximations in underwater acoustics applications. In this paper, we present a higher-order PE formulation that retains most of the efficiency of the split-step algorithm while improving the accuracy of the propagated solutions. In its simplest form, the new formulation modifies the standard split-step Fourier method by additionally solving a tridiagonal system of equations at each range step. The accuracy of our algorithm is illustrated with several numerical examples.