In the process of seismic data acquisition, there are often missing seismic traces in seismic records, so it is necessary to reconstruct the missing data to provide high-quality data for subsequent seismic data migration and reservoir inversion. Traditional interpolation methods for post-stack seismic data are based on the sparse constraint in the frequency-wavenumber (f-k) domain. However, the data completed using the interpolation method usually leads to the loss of some weak signals when the dip of the post-stack seismic profile is complex. In this paper, the missing data could be regarded as the result of irregular noise with the same waveform and the original signal but with the opposite polarity. The non-local similarity in the denoising algorithm is introduced as a low-rank promoting transform of the low-rank regularization term, and an interpolation method based on non-local similarity is proposed (NLS-WNNM). Furthermore, a fast matching algorithm is developed to search and match the non-local similarity of missing seismic traces (abbreviation FNLS-WNNM), which reduces the loss of weak signals during interpolation. The traditional interpolation method based on f-k domain is compared with the NLS-WNNM to highlight the advancement of the method. Finally, the interpolation test applied to field data confirmes the robustness of the proposed method.

在地震数据采集过程中，地震记录中经常存在缺失的地震道，因此需要对缺失的数据进行重建，为后续的地震数据偏移和储层反演提供高质量的数据。叠后地震数据的传统插值方法基于频率波数（fk）域中的稀疏约束。然而，当叠后地震剖面倾角复杂时，采用插值方法完成的数据通常会导致一些弱信号的丢失。本文中，丢失的数据可以看作是波形与原始信号相同但极性相反的不规则噪声的结果。引入去噪算法中的非局部相似度作为低秩正则化项的低秩提升变换，提出一种基于非局部相似度的插值方法（NLS-WNNM）。此外，还开发了一种快速匹配算法来搜索和匹配缺失地震道的非局部相似性（简称FNLS-WNNM），从而减少了插值过程中弱信号的损失。将传统的基于fk域的插值方法与NLS-WNNM进行比较，突显该方法的先进性。最后，应用于现场数据的插值测试证实了所提方法的鲁棒性。