A highly efficient implicit finite difference scheme for acoustic wave propagation

The accuracy of a numerical derivative has a significant effect on any numerical simulation. Long stencils can provide high accuracy as well as reduce the numerical anisotropy error. However, such a long stencil demands extensive computational resources and with their growing size, such derivatives may become physically non-realistic since contributions from very far offset whereas the derivative is local in nature. Further, the application of such long stencils at boundary points may introduce errors. In this paper, we present a very efficient, accurate and compact size numerical scheme for acoustic wave propagation using implicit finite difference operator, which utilizes a lesser number of points to estimate derivatives in comparison to the conventional central difference derivative operator. The implicit derivative operator, despite its several advantages, is generally avoided due to its high computational cost. Therefore in this paper, we discuss a method which can dramatically reduce the computational cost of this scheme to almost half. This strategy is useful particularly for 2D and 3D case. Spectral characteristics of the derivative operator and the numerical scheme are compared with several other central difference schemes. We have also demonstrated an application of this scheme for seismic wave propagation in 2D and 3D acoustic media. (C) 2019 Elsevier B.V. All rights reserved.