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The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots’ reconstruction. The spatial reciprocity of Green’s function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization. [ABSTRACT FROM AUTHOR]

The Radon transform (RT) has been widely used as a powerful tool, especially in exploration geophysics fields, such as multiple removal, interpolation, and velocity analysis. However, the existing strong outlier effects can seriously decrease the accuracy of the traditional RT. Therefore, a robust time-invariant RT (TIRT) is proposed in the mixed time–frequency domain to attenuate the outlier effects by using double L1-norm sparse constraints performed on the data misfit and the Radon model in the time domain. For the TIRT, the forward RT and its adjoint can be implemented in the frequency domain efficiently. Only one matrix inversion for each frequency component is involved in all iterations to speed up the iterations. Then, the 1-D alternating split Bregman (ASB) algorithm is introduced and improved for 2-D Radon model updating efficiently. It involves matrix-vector multiplication operators and two proximity operators. These two proximity operators can guarantee the robustness and sparseness of the proposed method. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of the proposed method. The proposed method is also used for interpolation to decrease the trace interval. After interpolation, seismic data are more continuous with less serrations along the spatial direction and the frequency-wavenumber spectrum is more focused. The interpolated data have wider potential applications in improving the accuracy of the following seismic processing. It should be noted that the proposed robust and efficient RT can also be used in remote sensing and computerized tomography fields instead of the traditional RT. [ABSTRACT FROM AUTHOR]