Laplace-Fourier (L-F) domain finite-difference (FD) forward modeling is an important foundation for L-F domain full-waveform inversion (FWI). An optimal modeling method can improve the efficiency and accuracy of FWI. A flexible FD stencil, which requires pairing and centrosymmetricity of the involved gridpoints, is used on the basis of the 2D L-F domain acoustic wave equation. The L-F domain numerical dispersion analysis is then performed by minimizing the phase error of the normalized numerical phase and attenuation propagation velocities to obtain the optimization coefficients. An optimal FD forward modeling method is finally developed for the L-F domain acoustic wave equation and applied to the traditional standard 9-point scheme and 7- and 9-point schemes, where the latter two schemes are used in discontinuous-grid FD modeling. Numerical experiments show that the optimal L-F domain FD modeling method not only has high accuracy but can also be applied to equal and unequal directional sampling intervals and discontinuous-grid FD modeling to reduce computational cost.

拉普拉斯傅立叶 (LF) 域有限差分 (FD) 正演建模是 LF 域全波形反演 (FWI) 的重要基础。优化的建模方法可以提高 FWI 的效率和准确性。在 2D LF 域声波方程的基础上使用了一个灵活的 FD 模板，它需要所涉及的网格点的配对和中心对称性。然后通过最小化归一化数值相位和衰减传播速度的相位误差来执行 LF 域数值色散分析，以获得优化系数。最后针对LF域声波方程开发了一种最优FD正演建模方法，并将其应用于传统的标准9点方案和7、9点方案，其中后两种方案用于不连续网格FD建模。