An Efficient Difference Scheme for Wide-Angle Shift-Map Parabolic Equation

In this article, a highly efficient difference scheme for solving parabolic equations (PEs) is proposed. The scheme is achieved by transforming <tex-math notation="LaTeX">∂ /∂ x </tex-math> into <tex-math notation="LaTeX">∂ /∂ z </tex-math> with the Taylor expansion of the forward wave equation. This transformation allows the truncation errors to be converted into a series of <tex-math notation="LaTeX">∂ /∂ z </tex-math> , enabling the design of a high-accuracy difference scheme. To evaluate the effectiveness of the new scheme, numerous numerical results are provided. In particular, when the terrain profile is 15°, the proposed scheme is at least ten times faster than the original scheme of second-order approximation of the wide-angle equation for terrain for most propagation angle range from −10° to 10°. The presented results help to explain why decreasing the horizontal and vertical step leads to a decrease in accuracy in the original scheme.