Optimization of staggered grid finite-difference coefficients based on conjugate gradient method

The implementation of difference coefficients optimization strategy can effectively suppress numerical dispersion and improve the modeling accuracy. The conventional difference coefficients calculation method based on Taylor-series Expansion exists serious numerical dispersion. In this paper, we derive a new dispersion error function from the dispersion relation, and the optimal difference coefficients are obtained iteratively by using the conjugate gradient method, thus a staggered-grid difference coefficients optimization method based on the conjugate gradient is developed. We compare dispersion curves, snapshots and single shot records using low-velocity model, high-velocity model and Marmousi model, the results show that the new method can effectively reduce the numerical dispersion compared with the difference coefficients of the conventional Taylor-series Expansion method. The 8th-order optimized difference operators can achieve the modeling precision of 12th-order Taylor-series Expansion difference operators, which can effectively save calculation time and internal storage. The optimization method performs well for both simple model and complex model forward modeling.
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