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.