Optimal Explicit and Implicit Rotated Staggered-Grid Finite-Difference Schemes for Seismic Modeling in Elastic TTI Media

The explicit rotated staggered-grid finite-difference method (ERSG-FDM) has been successfully applied to simulate seismic wave propagation in viscoelastic and anisotropic media. Nevertheless, the implicit stencils can effectively increase the accuracy and the stability of the explicit finite-difference (FD) stencils in numerical modeling. In this paper, in order to improve the accuracy of seismic modeling in elastic tilted transversely isotropic (TTI) media without increasing the computational resources, we optimal the coefficients of the ERSG-FDM and extend the globally optimal implicit staggered-grid finite-difference method (ISG-FDM) based on least-squares method (LSM) to the implicit rotated staggered-grid finite-difference method (IRSG-FDM). Also, the boundary reflections are absorbed by the first-order hybrid absorbing boundary condition (1st-HABC) for TTI elastic wave equations. Dispersion analysis and modeling results reveal that the new method can achieve same accuracy with shorter operator and thus is more efficient.