A staggered-grid lowrank finite-difference method for elastic wave extrapolation

Abstract

Elastic wave extrapolation in the time domain is significant for an elastic wave equation-based processing. To improve the simulation reliability and accuracy of decoupled elastic P- and S- waves, we propose the staggered-grid lowrank finite-difference method based on the elastic wave decomposition. For elastic wave propagation, a lowrank finite-difference method based on the staggered grid is derived to improve the accuracy. Regarding the application of the decoupled elastic wave equation, we derive the finite-difference scheme coefficients which are dependent on velocity. Based on the elastic wave decomposition and plane wave theories, we formulate the elastic wave-extrapolation operators, which contain trigonometric adjustment factors. Accordingly, by applying the lowrank method to approximating the operators, the finite- difference scheme is designed to discretize the decoupled wave equation. The derivation processing implies the combination of elastic wave-mode decomposition and extrapolation. The proposed method enables elastic P- and S-waves to extrapolate in the time-space domain separately and produces accurate P-and S-wave components simultaneously. Dispersion analysis suggests that our proposed method is reliable and accurate in a wide range of wavenumber. Numerical simulation tests on a simple model and the Marmousi2 model validate the accuracy and effectiveness of the method, showing its ability in handling complex structures. Although the operators are accurate only when the medium is homogeneous, they are of high accuracy when the velocity gradient is quite small and are applicable when the velocity gradient is large. The subsequent results of reverse time migration for the Marmousi2 model also suggest that the proposed method is enough to serve as an extrapolator in elastic reverse time migration.