Equivalent staggered-grid (ESG) as a new family of schemes has been utilized in seismic modeling, imaging, and inversion. Traditionally, the Taylor series expansion is often applied to calculate finite-difference (FD) coefficients on spatial derivatives, but the simulation results suffer serious numerical dispersion on a large frequency zone. We develop an optimized equivalent staggered-grid (OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3D elastic wave equation. On the one hand, we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave, S-wave, and converted-wave (C-wave) terms. On the other hand, a novel plane wave solution for the 3D elastic wave equation is derived from the matrix decomposition method to construct the time–space dispersion relations. FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method. Finally, we construct a new objective function to analyze P-wave, S-wave, and C-wave dispersion concerning frequencies. The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method. The synthetic examples demonstrate the effectiveness and superiority of the presented method.

中文翻译：

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优化的等效交错网格有限差分法进行3D弹性波形建模

等效交错网格（ESG）作为新的方案系列已被用于地震建模，成像和反演中。传统上，通常使用泰勒级数展开来计算空间导数上的有限差分（FD）系数，但是仿真结果在较大的频率区域上遭受严重的数值离散。我们开发了一种优化的等效交错网格（OESG）FD方法，该方法可以同时抑制时间和空间色散，以解决3D弹性波方程的二阶系统。一方面，我们考虑了弹性波方程中波速与空间导数之间的耦合关系，并针对P波，S波和转换波（C波）项给出了三组FD系数。 。另一方面，通过矩阵分解方法推导了一种新颖的3D弹性波方程平面波解，以建立时空色散关系。可以通过基于牛顿迭代法求解新的色散方程来获得OESG方法的FD系数。最后，我们构造一个新的目标函数来分析与频率有关的P波，S波和C波色散。色散分析表明，与传统的ESG方法相比，该方法产生的建模误差较小。综合实例证明了所提出方法的有效性和优越性。我们构造了一个新的目标函数来分析有关频率的P波，S波和C波色散。色散分析表明，与传统的ESG方法相比，该方法产生的建模误差较小。综合实例证明了所提出方法的有效性和优越性。我们构造了一个新的目标函数来分析有关频率的P波，S波和C波色散。色散分析表明，与传统的ESG方法相比，该方法产生的建模误差较小。综合实例证明了所提出方法的有效性和优越性。