To improve the modeling accuracy and adaptability of traditional temporal second-order staggered-grid finite-difference (SFD) methods for 3D acoustic-wave modeling, we propose a modified time-space-domain temporal and spatial high-order SFD stencil on a cuboid grid. The grid nodes on a double-pyramid stencil and the standard orthogonality stencil are used to approximate temporal and spatial derivatives. This stencil can adopt different grid spacing in each spatial axis, and thus it is more flexible than the existing one with the same grid spacing. Based on the time-space-domain dispersion relation, the high-order FD coefficients are generated by using Taylor expansion and least squares. Numerical analyses and modeling examples demonstrate that our proposed schemes have higher accuracy and better stability than other conventional schemes, and thus larger time steps can be used to improve the computational efficiency in 3D case.

为了提高用于 3D 声波建模的传统时间二阶交错网格有限差分 (SFD) 方法的建模精度和适应性，我们提出了一种在长方体上改进的时空域时空高阶 SFD 模板网格。双金字塔模板和标准正交模板上的网格节点用于近似时间和空间导数。该模板可以在每个空间轴上采用不同的网格间距，因此比现有的相同网格间距的网格模板更加灵活。基于时空域色散关系，利用泰勒展开式和最小二乘法生成高阶FD系数。数值分析和建模实例表明，我们提出的方案比其他传统方案具有更高的精度和更好的稳定性，因此可以使用更大的时间步长来提高3D情况下的计算效率。