Seismic data interpolation is a longstanding issue. Most current methods are only suitable for randomly missing cases. To deal with regularly missing cases, an antialiasing strategy should be included. However, seismic survey design using a random distribution of shots and receivers is always operationally challenging and impractical. We have used deep-learning-based approaches for seismic data antialiasing interpolation, which could extract deeper features of the training data in a nonlinear way by self-learning. It can also avoid linear events, sparsity, and low-rank assumptions of the traditional interpolation methods. Based on convolutional neural networks, eight-layers residual learning networks (ResNets) with a better back-propagation property for deep layers is designed for interpolation. Detailed training analysis is also performed. A set of simulated data is used to train the designed ResNets. The performance is assessed with several synthetic and field data. Numerical examples indicate that the trained ResNets can help to reconstruct regularly missing traces with high accuracy. The interpolated results in the time-space domain and the frequency-wavenumber (f-k) domain demonstrate the validity of the trained ResNets. Even though the accuracy decreases with the increase of the feature difference between the test and training data, the proposed method can still provide reasonable interpolation results. Finally, the trained ResNets is used to reconstruct dense data with halved trace intervals for synthetic and field data. The reconstructed dense data are more continuous along the spatial direction, and the spatial aliasing effects disappear in the f-k domain. The reconstructed dense data have the potential to improve the accuracy of subsequent seismic data processing and inversion.

Seismic inversion is a process of predicting high-resolution stratigraphic parameters from low-resolution seismic data. Traditional inversion methods tend to impose human prior knowledge, such as sparsity, to the modeling of the seismic inversion process. Nowadays, with the development of deep learning, the idea of modeling by learning from data has gained great attention in varieties of research fields. As a data-driven method, an artificial neural network (ANN) has already been explored by many researchers in the field of seismic inversion. Compared to ANN, a convolutional neural network (CNN) has a stronger learning ability attributing to its sophisticated structures. However, the development of CNN is limited by the amount of labeled data in many industrial fields including the field of seismic inversion. In order to mitigate the dependence of CNN on the amount of labeled data, we propose a closed-loop CNN structure in this article. The proposed closed-loop CNN can model the seismic forward and inversion process simultaneously from the training data set. Compared to traditional CNN, which is in an open-loop form, closed-loop CNN can not only learn from labeled data but also extract information contained in unlabeled data. The experimental results show that the closed-loop CNN has a better performance than both traditional methods and other deep learning-based methods on the synthetic data set and also can be efficiently applied on the real seismic data set.

Deep learning has been widely adopted in seismic inversion. One of the major obstacles when adopting deep learning in seismic inversion is the demand for labeled data sets. There are mainly two approaches to address this problem. One is to generate massive numbers of synthetic data and then transfer the trained model to real data. The other is to introduce theoretical constraints and reduce the parameter spaces of deep learning. In this letter, we propose a physics-constrained seismic impedance inversion method based on deep learning. Robinson convolution model is adopted to model the seismic forward process and provide theoretical constraints for the inversion process. Bilateral filtering is further combined to constrain the spatial continuity of the inversion results. The experimental results on both synthetic examples and real examples demonstrate that the proposed method can effectively improve the prediction accuracy and the spatial continuity of the inversion results.

Full waveform inversion (FWI) is a powerful tool for estimating the underground velocity model. However, it is computationally expensive and the resulting models tend to be not accurate enough. Thus, to improve the efficiency and accuracy of FWI, we propose a super-resolution (SR) method based on deep learning to enhance the resolution of the seismic velocity model. Since the edge images of the seismic velocity model are also widely used in geophysics, a multitask learning (MTL) network with hard parameter sharing is applied to perform the SR of the seismic velocity model and its edge images. The proposed MTL model dubbed M-RUDSR includes a global residual skip connection, an encoder-decoder structure of U-Net, and a dense skip connection structure. Besides, two networks for comparison, namely, RUDSR and M-RUSR, are proffered. RUDSR is a single-task version of M-RUDSR, whereas M-RUSR is a simplified version of M-RUDSR without a dense skip connection structure. Compared with RUDSR and M-RUSR, M-RUDSR produced the best results for all kinds of blurring levels and achieved better visual details. We found that FWI followed by SR can help reduce the computational cost of FWI in the high-frequency part of the spectrum, as well as achieve better high-frequency details recovery. The experimental results show that M-RUDSR is a practical recovery scheme in SR of the seismic velocity model and can be applied to a real data set efficiently.

The difficulty of 3-D magnetic inversion is to use 2-D magnetic anomaly data to obtain 3-D magnetic susceptibility structure. The contribution of the underground medium to the magnetic anomaly decreases rapidly with the increase of the depth, which leads to the rapid attenuation of the inversion resolution with the depth. In this article, artificial intelligence (AI) technology is applied to 3-D magnetic inversion to predict the susceptibility model corresponding to magnetic anomaly. The inversion network built in this article uses the method of down-sampling in the encoder to increase the receptive field and realize the feature extraction of magnetic anomaly data. In the decoder, attention fusion modules are added to fuse feature maps from different sources. Finally, we added a 3-D refiner behind the decoder. The 3-D refiner converts the 2-D feature map from the decoder into 3-D data. Based on the typical complex medium theory, this article constructs a diverse sample set of complex 3-D susceptibility models. The inversion experiment of synthetic data verifies the feasibility and versatility of the proposed network. Compared with the other methods, the distribution of susceptibility prediction obtained by our method is more accurate and more reliable in determining the magnetic body boundary. In the field example of Jinchuan Copper-nickel sulfide deposit in China, the network constructed in this article can achieve high-precision 3-D underground susceptibility imaging in this area. The susceptibility distribution is in good agreement with the borehole data and the proved deposit distribution.

The time-invariant Radon transform (RT) is commonly used to regularize and interpolate sparsely sampled or irregularly acquired prestack seismic data. The sparseness of the Radon model significantly influences the results of regularization. We have developed an effective and efficient method for the regularization and interpolation of 2D as well as 3D prestack seismic data. We used an accelerated sparse time-invariant RT in the mixed frequency-time domain to improve the performance of RT-based seismic data regularization. This 2D sparse RT incorporated the iterative 2D model shrinkage algorithm instead of the traditional iteratively reweighted least-squares (IRLS) algorithm in the time domain, and we computed the forward and inverse RTs in the frequency domain to solve the sparse inverse problem, which dramatically reduced the computational cost while obtaining a high-resolution result. The 2D synthetic and real data examples revealed that our 2D approach can better interpolate beyond aliasing a 2D prestack seismic record that contains a large gap, compared with the least-squares-based RT and the frequency-domain sparse RT methods. To extend the 2D technique to 3D more efficiently, we first formulate the 3D RT as a problem of solving a special matrix equation. Next, we use the iterative 3D model shrinkage algorithm to obtain a high-resolution 3D Radon model. The proposed 3D sparse RT method can be applied in the regularization of 3D prestack gathers, such as in the cable interpolation in a 3D marine survey. We achieved robustness and effectiveness with our 3D approach with successful applications to 3D synthetic and real data.