标量地震波频率–空间域有限差分法数值模拟

Seismic modeling of scalar seismic wave propagation with finite-difference scheme in frequency-space domain

（同济大学海洋与地球科学学院海洋地质国家重点实验室，上海200092）

State Key Laboratory of Marine Geology, School of Ocean and Earth Science, Tongji University, Shanghai 200092, China

讨论了频率–空间域优化有限差分算子地震波场模拟方法。推导了频率〖CD*2〗空间域双程波高阶有限差分算子，计算了9点有限差分系数；提出了一种节省内存的存储策略，对稀疏矩阵和稀疏矩阵LU分解后的矩阵采用了节省内存的存储策略，使内存空间的需求量大幅度降低，可以利用本方法进行具有生产规模的地震波正演模拟；推导了依赖于频率的最佳匹配层吸收边界条件，获得了很好的吸收效果。洼陷模型和Marmousi模型数值模拟试验表明，方法可行且有效，在节约计算机资源的同时，计算精度也能得到保证。

The seismic wave field simulation method for optimizing finite difference operator in frequency-space domain is discussed. The high-order finite difference operator of two-way wave in frequency-space domain is deduced and the nine-point finite-difference coefficient is calculated. Strategy for saving the inner-memory is proposed. The strategy greatly decreases the requirement of the inner memory for the huge sparse matrixes before and after LU decomposition. Seismic modeling with production scale can be performed based on this work. In addition, the perfectly matched layer absorbing boundary condition depending on frequency is deduced and achieves good absorbing effect. Numerical tests on a depression model and Marmousi model demonstrate that the method is feasible and effective. The computation accuracy can guaranteed with less resource cost.