The implementation of an accurate and efficient forward/backward modeling approach plays a very important role in full waveform inversion (FWI), in which the finite difference method (FDM) with rectangular grid is mostly adopted. However, the FDM has the ripple-shaped divergence/scattering problem when dealing with uneven interface. On the contrary, a meshless method called generalized FDM (GFDM) is suitable for the flexibility of simulation region and can be of interest for solving the above problem. Hence, we develop a meshless frequency-domain acoustic modeling method with GFDM to improve the accuracy and eliminate the divergence. Then, we apply the GFDM to inverse problem and propose a meshless FWI method. The proposed method reduces lots of the computations and memory usage of frequency-domain FWI and successfully suppresses the ripple-shaped scattering. Numerical examples demonstrate that our method can efficiently improve numerical accuracy and recover an accurate velocity model, which is helpful for high-precision seismic exploration through the complex Earth.

中文翻译：

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基于广义FD方法的频域全波形反演


准确高效的前向/后向建模方法的实现在全波形反演（FWI）中起着非常重要的作用，其中大多采用矩形网格的有限差分法（FDM）。然而，FDM在处理不均匀界面时存在波纹状发散/散射问题。相反，一种称为广义 FDM (GFDM) 的无网格方法适合模拟区域的灵活性，并且可以对解决上述问题感兴趣。因此，我们开发了一种使用 GFDM 的无网格频域声学建模方法，以提高精度并消除发散。然后，我们将GFDM应用于反问题，提出了一种无网格FWI方法。该方法减少了频域 FWI 的大量计算量和内存使用量，并成功抑制了波纹状散射。数值算例表明，该方法可以有效提高数值精度，恢复准确的速度模型，有助于复杂地球的高精度地震勘探。