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传统上,有限差分的差分系数一般可以通过泰勒级数展开法或优化方法来极小化频散误差得到。基于泰勒级数展开的差分法在有限的波数范围内精度较高,但在这个范围之外会产生较强的数值频散;基于最小二乘的优化有限差分法能在更大的波数范围内达到较高的精度,并可以在较小的计算需求内获得全局最优解。本文将基于最小二乘的优化有限差分法从二维正演模拟推广到三维,形成了计算效率高、高精度范围宽、适合并行计算的三维声波优化有限差分方法。频散分析及正演模拟表明本文发展的有限差分方法可以很好地压制数值频散。最后,将本文发展的有限差分方法应用到三维逆时偏移的震源波场延拓和检波点波场延拓中,并结合有效边界存储策略与checkpointing技术在GPU集群上实现三维逆时偏移以提高计算效率、减少存储量。三维逆时偏移试算结果表明本文三维优化有限差分方法与传统的有限差分法相比可以获得更高精度的偏移成像结果。
Traditionally, the finite difference differential coefficient can be obtained by minimizing the dispersion error by the Taylor series expansion method or optimization method. The difference method based on the Taylor series expansion has higher precision in the limited wavenumber range, but produces stronger numerical dispersion outside this range. The least squares-based optimal finite difference method can be used in a larger wavenumber range Achieve higher precision, and get the global optimal solution within the smaller calculation requirement. In this paper, the optimal finite difference method based on least squares is extended from two-dimensional forward modeling to three-dimensional, which forms a three-dimensional finite-difference method for sonic optimization with high computational efficiency, wide range of high precision and suitable for parallel computing. Dispersion analysis and forward simulation show that the finite difference method developed in this paper can suppress the numerical dispersion well. Finally, the finite difference method developed in this paper is applied to the three-dimensional inverse time migration source wavefield continuation and detector wavefield continuation, combined with the effective boundary storage strategy and checkpointing technology to achieve three-dimensional inverse time migration To improve the computational efficiency and reduce the storage capacity. The experimental results of three-dimensional inverse time migration show that the three-dimensional finite difference method in this paper can obtain more accurate migration imaging results than the traditional finite difference method.