Present finite-difference (FD) algorithms for modeling seismic wave propagation in 3D acoustic media are mainly based on the traditional orthogonal stencil and can achieve spatial high-order but temporal second-order accuracy. Therefore, these approaches may result in visible temporal dispersion and even instability for relatively large time sampling intervals. In this paper, we develop an advanced FD stencil with temporal and spatial arbitrary even-order accuracy to solve the 3D acoustic wave equation. The temporal derivative is approximated by an octahedron stencil with the operator length N together with the traditional second-order FD. Meanwhile, the spatial derivatives are calculated by the orthogonal stencil with the operator length M. The plane-wave theory is introduced to derive the time-space-domain dispersion relation and estimate the corresponding high-order FD coefficients by Taylor expansion. To achieve higher accuracy, we further optimize FD coefficients by applying least-squares (LS) to minimize the relative error of the time-space-domain dispersion relation. Dispersion and stability analyses show that our new schemes have higher modeling accuracy and propagation stability than the conventional method. Numerical examples demonstrate that the proposed FDs can generate greater temporal accuracy on the prerequisite of preserving satisfactory spatial accuracy. Our new temporal high-order FD stencil by incorporating larger time step, shorter operator lengths, LS-based coefficients and variable-length operators can be regarded as a kind of accurate and efficient tool for seismic wave modeling.

当前的建模3D声波介质中地震波传播的有限差分（FD）算法主要基于传统的正交模板，可以实现空间高阶但时间上的二阶精度。因此，这些方法可能会导致可见的时间分散，甚至在相对较大的时间采样间隔内也可能导致不稳定。在本文中，我们开发了一种具有时间和空间任意偶数精度的高级FD模具，以求解3D声波方程。时间导数由八面体模具（带有算子长度N）和传统的二阶FD近似。同时，空间导数由带有操作符长度M的正交模板计算得出。引入平面波理论以推导时空域色散关系，并通过泰勒展开估计相应的高阶FD系数。为了获得更高的精度，我们通过应用最小二乘法（LS）进一步优化FD系数，以最小化时空域色散关系的相对误差。色散和稳定性分析表明，与传统方法相比，我们的新方案具有更高的建模精度和传播稳定性。数值算例表明，在保持令人满意的空间精度的前提下，提出的FD可以产生更高的时间精度。我们的新型临时高阶FD模板，具有更大的时间步长，更短的操作员长度，