Among many seismic inversion methods, the sparse spike inversion for post-stack seismic data uses the migrated and stacked seismic data which is regarded as zero offset reflection seismic data in the case of normal incidence to extract reflectivity and impedance of underground rocks. The seismic reflectivity and impedance can reflect underground rocks’ lithology, petrophysical property, oil–gas possibility, and so forth. However, the common used post-stack seismic inversion adopts single trace in the process of inversion and completes the whole data cube’s inversion through trace by trace. It cannot use lateral regularization. Hence, the lateral continuity of single trace inversion result is poor. It is difficult to represent the lateral variation features of underground rocks. Based on the conventional sparse spike inversion, the nuclear norm of matrix in the matrix completion theory is introduced in the process of post-stack seismic inversion. At the same time, the strategy of multi-trace seismic data simultaneous inversion is used to carry out lateral regularization constraint. Numerical tests on 2D model indicate that the inversion results obtained from the proposed method can clearly represent not only the vertical variation features but also the lateral variation features of underground rocks. At last, the inversion results of real seismic data further show the feasibility and superiority of the proposed method in practical application.

在许多地震反演方法中，用于叠后地震数据的稀疏峰值反演使用的是迁移和堆叠的地震数据（在法向入射情况下被视为零偏移反射地震数据），以提取地下岩石的反射率和阻抗。地震反射率和阻抗可以反映地下岩石的岩性，岩石物性，油气可能性等。但是，常用的叠后地震反演在反演过程中采用单迹，并通过逐迹完成了整个数据立方体的反演。它不能使用横向正则化。因此，单迹线反演结果的横向连续性很差。很难表示地下岩石的横向变化特征。基于常规的稀疏峰值反演，在叠后地震反演过程中，介绍了矩阵完备理论中矩阵的核范数。同时，采用多道地震资料同时反演的策略进行横向正则约束。在二维模型上的数值试验表明，该方法获得的反演结果不仅可以清楚地表示地下岩石的垂直变化特征，而且可以清楚地表示地下岩石的横向变化特征。最后，实际地震数据反演结果进一步证明了该方法在实际应用中的可行性和优越性。采用多道地震资料同时反演的策略进行横向正则约束。在二维模型上的数值试验表明，该方法获得的反演结果不仅可以清楚地表示地下岩石的垂直变化特征，而且可以清楚地表示地下岩石的横向变化特征。最后，实际地震数据反演结果进一步证明了该方法在实际应用中的可行性和优越性。采用多道地震资料同时反演的策略进行横向正则约束。在二维模型上的数值试验表明，该方法获得的反演结果不仅可以清楚地表示地下岩石的垂直变化特征，而且可以清楚地表示地下岩石的横向变化特征。最后，真实地震数据反演结果进一步证明了该方法在实际应用中的可行性和优越性。