ABSTRACT Finite‐difference modeling with a cross‐rhombus stencil with high‐order accuracy in both spatial and temporal derivatives is a potential method for efficient seismic simulation. The finite‐difference coefficients determined by Taylor‐series expansion usually preserve the dispersion property in a limited wavenumber range and fixed angles of propagation. To construct the dispersion‐relationship‐preserving scheme for satisfying high‐wavenumber components and multiple angles, we expand the dispersion relation of the cross‐rhombus stencil to an over‐determined system and apply a regularization method to obtain the stable least‐squares solution of the finite‐difference coefficients. The new dispersion‐relationship‐preserving based scheme not only satisfies several designated wavenumbers but also has high‐order accuracy in temporal discretization. The numerical analysis demonstrates that the new scheme possesses a better dispersion characteristic and more relaxed stability conditions compared with the Taylor‐series expansion based methods. Seismic wave simulations for the homogeneous model and the Sigsbee model demonstrate that the new scheme yields small dispersion error and improves the accuracy of the forward modelling.

中文翻译：

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使用交叉菱形模板的离散关系保持地震建模，有限差分系数由超定线性系统求解

摘要 在空间和时间导数上具有高阶精度的交叉菱形模板的有限差分建模是一种有效的地震模拟的潜在方法。由泰勒级数展开确定的有限差分系数通常在有限的波数范围和固定的传播角度内保持色散特性。为了构建满足高波数分量和多角度的色散关系保持方案，我们将交叉菱形模板的色散关系扩展到超定系统，并应用正则化方法获得稳定的最小二乘解有限差分系数。新的基于色散关系保持的方案不仅满足几个指定的波数，而且在时间离散化方面具有高阶精度。数值分析表明，与基于泰勒级数展开的方法相比，新方案具有更好的色散特性和更宽松的稳定性条件。均质模型和 Sigsbee 模型的地震波模拟表明，新方案产生的色散误差小，提高了正演建模的准确性。