An optimized staggered variable-grid finite-difference scheme and its application in cross-well acoustic survey

In this paper, an optimized staggered variable-grid finite-difference (FD) method is developed in veloc- ity-stress elastic wave equations. On the basis of the dispersion-relation-preserving (DRP), a fourth-order finite-difference operator on non-uniform grids is constructed. The proposed algorithm is a continuous variable-grid method. It does not need interpolations for the field variables between re- gions with the fine spacing and the coarse one. The accuracy of the optimized scheme has been veri- fied with an analytical solution and a regular staggered-grid FD method for the eighth order accuracy in space. The comparisons of the proposed scheme with the variable-grid FD method based on Taylor series expansion are made. It is demonstrated that this optimized scheme has less dispersion errors than that with Taylor’s series expansion. Thus, the proposed scheme uses coarser grids in numerical simulations than that constructed by the Taylor’s series expansion. Finally, the capability of the opti- mized FD is demonstrated for a complex cross-well acoustic simulation. The numerical experiment shows that this method greatly saves storage requirements and computational time, and is stable.