A Nonbalanced Staggered-Grid FDTD Scheme for the First-Order Elastic-Wave Extrapolation and Reverse-Time Migration

In this study, an efficient and accurate staggered-grid finite-difference time-domain method to solve the two-dimensional (2-D) first-order stress–velocity elastic-wave equation is proposed. In the conventional implementation of the staggered-grid finite-difference (SGFD) method, the same SGFD operator is used to approximate the spatial derivatives. However, we propose a numerical method based on the mixed SGFD operators that are more efficient but similar in accuracy when compared with a uniform SGFD operator. We refer to the proposed method as the nonbalanced SGFD numerical scheme that combines the high-order SGFD operators with the second-order SGFD operators. The suitability of the proposed scheme is verified by dispersion analysis. Through SGFD modeling and reverse-time migration examples, we demonstrate that the proposed nonbalanced scheme offers a similar level of accuracy with a lower computational cost compared with the time-consuming conventional SGFD method.