The Combined Compact Difference Scheme Applied to Shear-Wave Reverse-Time Migration

Abstract

In this paper, the combined compact difference scheme (CCD) and the combined supercompact difference scheme (CSCD) are used in the numerical simulation of the shear-wave equation. According to the Taylor series expansion and shear-wave equation, the fourth-order discrete scheme of the displacement field is established; then, the CCD and CSCD schemes are used to calculate the spatial derivative of the displacement field. Additionally, the accuracy, dispersion, and stability of the CCD and CSCD are analyzed, and numerical simulation analyses are carried out using 1D uniform models. Lastly, based on the processing of artificial boundary reflection using PML boundary conditions, shear-wave reverse-time migrations are carried out using synthetic data. The results show that (1) CCD and CSCD have smaller truncation errors, higher simulation precision, and lower numerical dispersion than other normal difference schemes; (2) CCD and CSCD can use the coarse grid and larger time step to calculate, with less memory and high computational efficiency; (3) finally, the result of the shear-wave reverse-time migration of the 2D synthetic data model show that the reverse-time migration imaging is clear, and the proposed method for shear-wave reverse-time migration is practical and effective.