An optimized staggered variable-grid finite-difference scheme and its application in cross-well acoustic survey |
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Authors: | HaiBo Zhao XiuMing Wang |
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Institution: | (1) Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100080, China |
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Abstract: | In this paper, an optimized staggered variable-grid finite-difference (FD) method is developed in velocity-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 regions with the fine spacing and the coarse one. The accuracy of the optimized scheme has been verified
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 optimized 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.
Supported by the Key Program of National Natural Science Foundation of China (Grant No. 10534040) and the National Natural
Science Foundation of China (Grant No. 10674148) |
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Keywords: | finite-difference variable-grid elastic waves DRP cross-well acoustic simulation |
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