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 $\partial /\partial x$ into $\partial /\partial {z}$ with the Taylor expansion of the forward wave equation. This transformation allows the truncation errors to be converted into a series of $\partial /\partial {z}$ , 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 degrees, 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 degrees to 10 degrees. The presented results help to explain why decreasing the horizontal and vertical step leads to a decrease in accuracy in the original scheme.