A wide-angle split-step algorithm for the parabolic equation

Abstract

In this paper we describe a new wide‐angle parabolic equation based on an operator‐splitting that permits the use of a marching‐type Fourier transform solution method. The equation was first presented by Feit and Fleck [Appl. Opt. 1 7, 3990–3998 (1978)] for studying propagation within optical fibers. Existing computer codes which numerically solve the standard parabolic equation of ocean acoustics by the split‐step algorithm of Tappert and Hardin are easily modified to accommodate the wide‐angle capability of the new equation. In addition, since the new wide‐angle equation is less sensitive to the value of the reference wavenumber, the effects of phase errors are greatly reduced. The results of a simple error analysis indicate that improved accuracy can be achieved by the new wide‐angle equation for propagation conditions typical of deep ocean environments. This is supported by our numerical experience, a summary of which is presented in the paper. For test cases, where the variation of the acoustic index of refraction was large, the new wide‐angle equation gave results superior to those of the standard parabolic equation. Moreover, even for conditions which support long range, low‐angle propagation in the deep ocean, the predictions based on the new equation are a significant improvement over those obtained with the standard equation.