An Efficient Finite-Difference Stencil with High-Order Temporal Accuracy for Scalar Wave Modeling

Solving a scalar wave equation by the finite-difference (FD) method is a key step for advanced seismic imaging, in which the numerical accuracy is significantly affected by the FD stencil. High-order spatial and temporal approximations of the FD stencil can effectively improve the numerical accuracy and mitigate dispersion error. However, the huge costs of high-order stenciling in computation and storage hinder the application of large-scale modeling. In this paper, we propose a new efficient FD stencil with high-order temporal accuracy for numerical seismic modeling. The new stencil has a radial shape, including a standard cross-stencil and a rotated cross-stencil with a (pi/4) degree, and it can reach sixth-order accuracy in the time approximation. Compared with the well-known temporal high-order cross-rhombus stencil, the new stencil involves fewer grid nodes and thus has higher computational efficiency, especially in high-order cases. Dispersion and stability analyses show that the new stencil has great improvements in mitigating the dispersion error and stability problem compared with the conventional methods. Numerical accuracy and execution time analyses show that the new stencil is an economical and feasible method for large-scale modeling.