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. 17, 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.