Seismic interpolation is a widely adopted method to improve the resolution of seismic images. During the interpolation of regularly downsampled seismic data, the aliasing problem highly deteriorates the quality of the interpolation results. Nowadays, deep learning has shown great potential in extracting features from data and achieved significant improvement compared with traditional interpolation methods. However, only a few of them have addressed the aliasing problem. In this article, we propose a novel self-adaptive antialiasing framework for seismic data interpolation. We theoretically analyze the aliasing problem in the frequency domain and adopt the shear transform to turn the severely aliased data into less aliased data. Moreover, a closed-loop framework is proposed to automatically evaluate the interpolation results and select the optimal parameter of the shear transform. The experimental results demonstrate that the proposed method can significantly improve the interpolation quality and suppress the aliasing problem.

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.

Seismic inversion is aimed at building a mapping from low-resolution seismic data to high-resolution impedance data. Most of the traditional methods have satisfactory interpretability, and most parameters tend to have specific physical definitions. On the other hand, deep learning-based methods present poor interpretability as their prediction performance is not always clearly explainable. One of the significant challenges of the deep learning-based methods is to quantify the uncertainty of the model. The uncertainty includes aleatoric uncertainty and epistemic uncertainty, and epistemic uncertainty can be used to evaluate the predicted accuracy of the trained model. In this paper, we propose a new deep learning model called uncertainty backpropagation network (UB-Net) to perform impedance inversion. The proposed UB-Net is based on a closed-loop framework and can predict the impedance and the epistemic uncertainty simultaneously. UB-Net has three closed-loop data flows, whereby the predicted uncertainty is utilized as the weight of loss functions to improve the inversion accuracy. Experimental analyses demonstrate that UB-Net presents advanced inversion accuracy on both synthetic and real examples. Specifically, the mean absolute error (MAE) on synthetic examples drops by 40%, and the Pearson correlation coefficient (PCC) on real examples increases by 2%. Besides, compared with existing approaches, UB-Net presents superior spatial continuity and preserves more geological structures such as little faults in real examples.

Reservoir prediction is a significant issue in seismic interpretation, and it is difficult to reach a tradeoff point for the reservoir prediction accuracy and spatial continuity. Nowadays, though numerous machine learning methods have been widely applied in reservoir prediction, so few available well-logging labels are still a major obstacle for improving prediction performance. Considering for such a critical factor, we propose a semisupervised deep-learning framework, in which the closed-loop convolutional neural network (CNN). and virtual well-logging labels are used. The closed-loop CNN, which is consisting of the predictive and generative subnetworks, can be trained directly by using the seismic attribute data not only with well-logging labels but also without well-logging labels. The virtual well-logging labels (Vl) are generated by fusing the results of two existing reservoir predicting methods, one based on polynomial linear regression and the other based on CNN. Vl contributes to improve the spatial continuity and accuracy of the predicted reservoir as constraint items in network training process. Finally, cross-validation experiments on real-field data are carried out, and 3-D field reservoir prediction results show that the proposed method outperforms several existing machine-learning-based methods.

Deep learning (DL) methods have been widely applied in seismic inversion. However, one of the major challenges for DL-based seismic inversion is the time-shifted well-logging labels, which is resulted by the inaccurate time–depth relationship estimation during seismic well tie. Also, time-indexed phenomena of time-shifted well-logging labels may be squeezed, stretched, time ahead, or time lag, which can be considered as a typical noisy label problem in the DL field. In order to tackle the problem, we propose a dynamic time warping (DTW) loss-based closed-loop convolutional neural network (CNN) for seismic impedance inversion. First, DTW loss and cycle-consistency loss together constrain the closed-loop CNN training to optimize the weights of neural network. Second, the well-logging label will be corrected by warping the original well-logging label with the aligned path matrix during the iteration learning procedure, and the iteration termination criterion is reached if the similarity between the corrected well-logging label of the last iteration and that of the current iteration is larger than a given threshold. Third, the DTW error is suggested as the reasonable evaluation index in the blind-well test due to the time shift phenomena inevitably existed in the blind well. The experimental results on both synthetic data and real data demonstrate that the proposed method can effectively improve the inversion accuracy and spatial continuity.

Deep learning has been applied to tackle the seismic inversion problem, bringing more efficiency and accuracy. However, bad spatial continuity and poor generalizability limit the practical application. To solve these problems, we propose a 2D end-to-end seismic inversion method based on domain adaption. Firstly, the proposed 2D network learns the inversion mapping of seismic data under the constraint of domain adaption layer, which can reduce the difference between the features of real seismic data and synthetic seismic data, improving the generalization ability on real seismic data. Then, the trained model is finetuned with well logging data. In the first process, the spatial continuity of the inversion result is guaranteed by the 2D training scheme. Meanwhile, due to the constraint of the domain adaption layer, our model not only performs well on the synthetic data but also has good generalization ability on the real seismic data. And we carefully discuss the mechanism of domain adaption layer. In the second process, finetuning introduces well logging information, which can further improve the ability to invert details. Moreover, in order to improve the inversion accuracy on real seismic data, we develop a new training data generation method that can generate the synthetic samples close to the real samples, and a 2.5D training strategy is adopted to improve the continuity of the 3D data. The experiments on both synthetic and real seismic data show that our method performs better than both the recursive inversion method and the 1D closed-loop CNN methods.

For seismic random noise attenuation, deep learning has attracted much attention and achieved promising performance. However, compared with conventional methods, the denoising performance of supervised learning-based methods heavily depends on massive training samples with high-quality labeled data, which makes their generalization capabilities limited. Even though deep neural networks (DNNs) usually outperform the conventional denoising methods, their performance is not guaranteed since neural networks still lack good mathematical interpretability at present. To alleviate the dependency on labeled data and explore insights into the denoising system, we proposed an unsupervised denoising method based on model-based deep learning, which combined domain knowledge and a data-driven method. We designed a network based on the modified iterative soft threshold algorithm (ISTA), which omitted the soft threshold to alleviate uncertainties introduced by empirically selected thresholds. In this network, we set the dictionary and code as trainable parameters. A loss function with a smooth penalty was designed to ensure that the network training can be implemented in an unsupervised manner. In the proposed method, we set the denoised result by$f-x$deconvolution as the input for our network, and the further denoised data can be obtained after each epoch of the training, which means that our method does not need the testing procedure. Experiments on synthetic and field seismic data demonstrate that our method exhibits competitive performance compared to the conventional, supervised, and unsupervised methods, including$f-x$deconvolution, curvelet, the Denoising Convolutional Neural Network (DnCNN), and the integration of neural network and Block-matching and 3-D filtering method (NN + BM3D).

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.