Simulating elastic wave using temporal high accuracy and implicit spatial rectangular staggered-grid finite-difference approaches

The existing temporal high-order Finite-Difference (FD) methods for simulating elastic wave propagation are mainly based on the explicit differencing and square grid cell, thus they may encounter strong numerical dispersion and poor adaptability. In view of these problems, we develop an Implicit Staggered-Grid FD (ISFD) using a modified rectangular grid-based operator, which is the combination of cross and rhombus stencils, to solve the elastic wave equation. In this scheme, the modified FD stencil and temporal second-order FD are incorporated to approximate temporal derivatives, the spatial derivatives are computed by the implicit FD formula. The high-order FD coefficients are estimated by using Taylor-Series Expansion (TE) and Least-Squares (LS) optimization. A combination of the high-order FD and wavefield separation technique is applied to produce high accuracy elastic wavefield. We also compare the developed methods with several available FDs : explicit and implicit temporal second-order FDs, and explicit temporal high-order FD. Numerical analyses and simulated examples prove that our proposed schemes have higher accuracy and flexibility than other ones.