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Blended acquisition improves the efficiency of seismic data acquisition sharply, and deblending algorithms are still open to prepare separated data. Most deblending methods are suitable for on-the-grid blended data. However, blended data in field cases are always at off-the-grid samples which pose great challenges in providing accurate deblended results. A binning strategy can assign an off-the-grid sample at its nearest on-the-grid sample approximately with the amplitude and phase bias caused by the existing distance between them. However, the subsequent deblending accuracy is low, especially when the amplitude and phase biases are large. With true off-the-grid data constraints, we introduce a Kaiser window tapered $\mathrm{sin}c$ interpolator to link off-the-grid samples and on-the-grid samples during the procedure of compressive sensing-based functional construction. Full expressions of the interpolator and its adjoint operator are provided to generate an iterative thresholding algorithm for off-the-grid blended data deblending. Separated on-the-grid data can be obtained accurately in an iterative manner. The deblending performance of artificially off-the-grid blended data demonstrates the validity of the proposed method quantitatively no matter whether the amplitude and phase biases are large or small. Field examples of off-the-grid blended data further prove the effectiveness of the proposed method to provide accurate on-the-grid separated data. [ABSTRACT FROM AUTHOR]

The blended acquisition can help improve the seismic data quality or enhance the acquisition efficiency. However, the blended seismic data should first be separated for subsequent traditional seismic data processing steps. The signal is coherent in the common receiver domain, and the blending noise shows randomness when the blending operator is constructed using a random time delay series. The seismic data can be characterized sparsely by the curvelet transform which can be used for deblending. However, it has a high computational cost, especially for large-volume seismic data. The spectrum of the seismic data is band-limited with the conjugate symmetry property, and thus the principal frequency components can characterize the signal accurately. The size of the principal frequency components is at least halved. Thus, we propose to implement the curvelet transform on the principal frequency wavenumber (PFK) domain data instead of the time-space (TX) domain data. The size of the PFK domain data is at least halved compared with the TX domain data, which can improve the deblending efficiency reasonably. The related formulae are fully derived and the efficiency enhancement analysis is provided in detail. One synthetic and two field artificially blended data are provided to demonstrate the validity and flexibility of the proposed method in the efficiency improvement and the deblending performance. The separated gathers can be beneficial for subsequent traditional seismic data processing procedures. [ABSTRACT FROM AUTHOR]

The blended acquisition allows multiple sources to be simulated simultaneously in a narrow time interval, which can improve the acquisition efficiency and reduce the acquisition cost tremendously. However, the overlapped information from multiple sources poses challenges for traditional seismic data migration or inversion algorithms. Thus, accurate and efficient deblending should be implemented as a pre-requisite. Traditional inversion-based deblending algorithms can provide deblended data with a high computational burden, especially for a large volume of seismic data. As a deep learning strategy can match seismic data accurately in a nonlinear way through supervised learning, we propose a U-net-based accurate deblending algorithm, which incorporates transfer learning and an iterative strategy. A set of labeled synthetic data with a blending fold of 2 are classified into the training and validation data for U-net training and validation. Field data are regarded as the test data to assess the performance of the trained U-net. To guarantee the deblending performance of the field data to some extent, parts of field data with labels are used to fine-tune the trained U-net based on transfer learning. The fine-tuning procedure is relatively fast within several minutes. To further improve the deblending performance, we incorporate an iterative strategy with the fine-tuned U-net. The deblending performance is promising in the quality and computational efficiency compared with the curvelet-thresholding-based deblending method, which demonstrates the validity of the proposed intelligent deblending method. [ABSTRACT FROM AUTHOR]

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]