Deep learning has been successfully applied to image denoising. In this study, we take one step forward by using deep learning to suppress random noise in poststack seismic data from the aspects of network architecture and training samples. On the one hand, poststack seismic data denoising mainly aims at 3-D seismic data. We designed an end-to-end 3-D denoising convolutional neural network (3-D-DnCNN) that takes raw 3-D cubes as input in order to better extract the features of the 3-D spatial structure of poststack seismic data. On the other hand, denoising images with deep learning require noisy-clean sample pairs for training. In the field of seismic data processing, researchers usually try their best to suppress noise by using complex processes that combine different methods, but clean labels of seismic data are not available. In addition, building training samples in field seismic data has become an interesting but challenging problem. Therefore, we propose a training sample selection method that contains a complex workflow to produce comparatively ideal training samples. Experiments in this study demonstrate that deep learning can directly learn the ability to denoise field seismic data from selected samples. Although the building of the training samples may occur through a complex process, the experimental results of synthetic seismic data and field seismic data show that the 3-D-DnCNN has learned the ability to suppress the Gaussian noise and super-Gaussian noise from different training samples. Moreover, the 3-D-DnCNN network has better denoising performance toward arc-like imaging noise. In addition, we adopt residual learning and batch normalization in order to accelerate the training speed. After network training is satisfactorily completed, its processing efficiency can be significantly higher than that of conventional denoising methods.

The concept of simultaneous source has recently become of interest in seismic exploration, due to its efficient or economic acquisition or both. The blended data overlapped between shot records are acquired in simultaneous source acquisition. Separating the blended data and recovering the single-shot seismic signals (the recovery) are of great importance in the scenario of current workflows, which can be called seismic simultaneous source separation. In the context of general random time-dithering firing, we propose an alternative method to separate the blended data by combining patchwise dictionary learning with sparse inversion, in which the dictionary is directly learned from the measured blended data. Apart from the sparse coding used for the coefficients, an additional regularization term on the dictionary is particularly designed to remove the severe interference noise. The efficient and flexible alternating direction method of multipliers (ADMM) is used to update the dictionary in the used alternating optimization scheme. The results obtained from the synthetic and real examples reasonably suggest that the separated seismic signals by using dictionary learning are more accurate and robust compared with that using the fixed transform basis, such as the local discrete cosine transform. The learned dictionary tailors for the recovery and is similar to the local seismic waveform, which improves the sparsity of the recovery substantially and is highly advantageous for producing the promised results.

Five-dimensional seismic reconstruction is receiving increasing attention and can be viewed as a tensor completion problem, which involves reconstructing a low-rank tensor from a partially observed tensor. Tensor train (TT) decomposition and tensor ring (TR) decomposition are two powerful tensor networks for solving this problem. However, updating core tensors leads to high computational costs in practical applications. We propose two efficient methods to exploit low TT rank and low TR rank structures by theoretically establishing the relationship between tensor ranks and matrix unfoldings, respectively. Specifically, the former uses a well-balanced matricization scheme, and the latter uses a tensor circular unfolding. Furthermore, we use the randomized parallel matrix factorization (PMF) to accelerate the solution of these problems. Both synthetic and real data experiments demonstrate that the proposed algorithm can also achieve remarkable reconstruction performance; in the meantime, the computational cost is significantly reduced.

Deep-learning-based methods have been successfully applied to seismic data random noise attenuation. Among them, the supervised deep-learning-based methods dominate the unsupervised ones. The supervised methods need accurate noise-free data as training labels. However, the field seismic data cannot meet this requirement. To circumvent it, some researchers utilized realistic-looking synthetic data or denoised results via conventional methods as labels. The former ones encounter the problem of weak generalization ability because it requires the same distribution of test and training data. The latter ones encounter the issue of insufficient denoising ability because its denoising ability is difficult to significantly exceed the conventional methods which were used to generate labels. To avoid preparing noise-free labels, we propose a novel deep learning framework for attenuating random noise of prestack seismic data in an unsupervised manner. The prestack seismic data, such as common-reflection-point (CRP) gathers and common-midpoint (CMP) gathers after normal moveout (NMO) correction, have high self-similarity. It is because their events are coherent in the time–space domain and approximately horizontal from shallow to deep layers. The generator convolutional neural network (GCN) first learns self-similar features before any learning. The useful signals are more self-similar than random noise, which is incoherent and randomly distributed. Therefore, the GCN extracts features of useful signals before random noise. We select the specific training iteration and adopt the early stopping strategy to suppress random noise. Both synthetic and field prestack seismic data examples demonstrate the validity of our methods.

Recent years have witnessed many practical applications of supervised deep learning in seismic processing. However, a weak generalization behavior prevents widespread implementation on large-scale prestack data sets for coherent noise attenuation. This is particularly true when addressing strong near-surface scattered noise in land seismic data. To alleviate this problem, we have combined deep learning with an offset-vector tile (OVT) partitioning method to suppress strong scattered noise. With the OVT partitioning method, seismic data are spatially uniformly sampled, offering a favorable foundation for network learning. Specifically, the reflection probability distribution is more stationary than the noise distribution, making it easier for the network to learn the reflections. Accordingly, we use the direct signal learning strategy rather than the commonly used residual learning strategy to train the network. To construct high-quality training labels, we adopt the 3D continuous wavelet transform (3D CWT), which can exploit the 3D spatial correlation in OVT gathers. General use of these labels can produce results similar to 3D CWT but is highly efficient. To further improve denoising performance, we propose a training sample construction approach that leverages middle-offset OVT volumes with varying azimuths in light of midoffset relatively high signal-to-noise ratio characteristics. The field data experiment demonstrates that our proposed method also has an excellent generalization ability. Despite only using six middle-offset gathers for training, the trained network is able to effectively process 1260 OVTs in a timely manner.

As one type of important seismic geometric attributes, the seismic volumetric dip is extensively used to assist interpretation of horizons, faults, and other geologic structures in 3-D seismic data. In this paper, we mainly focus on estimating seismic volumetric dip robustly and try to reduce the influences of amplitude's lateral changes, faults, and other discontinuous structures. We first use the instantaneous phase (IP) as one fundamental data set to reduce the influence of amplitude's lateral variation. Second, we construct structure tensor (ST) on IP and apply eigendecomposition on corresponding ST covariance matrix to obtain three eigenvalues and corresponding eigenvectors. Then, the seismic volumetric dip can be calculated from the dominant eigenvector, and a similarity measure can be constructed based on these three eigenvalues. Third, based on the similarity measure, we reduce the influence of fault on dip estimation by using multiwindow technology if the analyzing window spans a fault. Finally, we applied our method to three synthetic data examples and two field data examples. The results of seismic volumetric dip and curvature estimation verify that the proposed method has better antinoise and antifault performance comparing with the corresponding sophisticated method in commercial software and the conventional ST-based method.