A training set with sufficient quantity and reliable quality is crucial for achieving satisfactory results in data-driven acoustic impedance inversion. However, effective data augmentation still faces significant challenges when labeled well data are sparse. In this study, it is proposed a novel impedance sequence augmentation strategy based on the SinGAN multiscale generative adversarial networks under few well conditions. SinGAN requires only a single impedance sequence for training and supports two augmentation modes: Random Impedance Generation Mode (RIGM) and Controllable Impedance Generation Mode (CIGM). RIGM controls diversity between synthetic and true impedance by adjusting the Start Generation Scale (SGS), while CIGM synthesizes impedance by fusing a known low-frequency reference model with high-frequency details derived from well data, the SGS determines the proportion of their integration. Three training sets were established through data augmentation using broadcasting, RIGM, and CIGM on the Marmousi2 model, and were subsequently fed into a CNN-GRU fusion network with identical hyperparameters. Experimental results show that the correlation coefficients (R²) between the estimated and true impedance values reach 0.9111, 0.9282, and 0.9423 for the broadcasting, RIGM, and CIGM methods, respectively. Meanwhile, the CIGM-based model achieves the best overall performance, with an MSE of 0.006 and an SSIM of 0.966, and it accurately characterizes impedance variations across stratigraphic layers and clearly delineates the water–strata interface and associated sand bodies. These findings verify that the proposed augmentation strategy effectively expands the training sample space and enhance impedance prediction accuracy, offering a new promising approach for seismic inversion tasks with sparse labeled data.

The inherent non-uniqueness problem challenges acoustic impedance inversion, and thus it is meaningful to explore the possible solutions via advanced strategies, e.g., incorporating uncertainty estimation. At present, several generative adversarial network (GAN)-based inversion methods have been shown to offer advantages in terms of inversion accuracy. However, most of them have primarily focused on deterministic predictions, limiting their ability to explore the range of the solution space. Furthermore, the scarcity of labeled data pairs in field data tasks can reduce inversion accuracy. To address these shortcomings, we introduce a Bayesian GAN (BGAN) based onBayes by Backprop, and integrate it into a closed-loop framework. Synthetic data experiments demonstrate that the closed-loop BGAN performs better than cycle-consistent GAN (cycle-GAN) with insufficiently labeled data pairs. Moreover, unlike the cycle-GAN, the closed-loop BGAN possesses the capability of assessing prediction uncertainties. Compared with the Bayesian linearized inversion (BLI) and Monte Calor (MC) dropout methods, the closed-loop BGAN is more accurate and robust in the inversion of noisy seismic data with lower uncertainty. Therefore, the closed-loop BGAN can achieve high accuracy inversion while estimating potential solutions more reasonably. The field data example also demonstrates that compared with BLI and MC dropout, the closed-loop BGAN can obtain more reasonable inversion results with more reliable uncertainty estimation.

Solutions to the amplitude variation with offset (AVO) inverse problem are inherently nonunique. Thus, estimating the range of potential solutions is crucial. For this reason, uncertainty inversion is more appropriate than deterministic AVO inversion. However, most studies on deep learning (DL)-based inversion focus on deterministic prediction. In general, there are few studies on uncertainty inversion, mainly focused on poststack seismic data. In this study, we propose a DL-based AVO uncertainty inversion method based on an improved variational Bayesian neural network (VBNN) for predicting multiple elastic parameters. Moreover, to mitigate the issue of insufficient labeled data in inversion tasks, we combine the improved VBNN with a semi-supervised learning framework. Synthetic data experiments demonstrate that the proposed method exhibits higher accuracy and robustness to noisy seismic data than the well-known traditional Bayesian linearized inversion (BLI) method. The proposed method also has slightly higher inversion accuracy than the state-of-the-art improved-hybrid-seismic-prior-guided neural network (IHGNN). Moreover, the uncertainty estimation confirms that the proposed method can explore potential solutions to the AVO inverse problem more effectively and reasonably than the comparison methods. Furthermore, field data AVO inverse experiments verify that the proposed method can obtain reasonable predicted results and effectively reveal uncertainty in the inversion results.

Coherent and incoherent noise in seismic data inevitably reduces the quality of subsequent processing, e.g., migration and inversion. Different from random noise, erratic noise follows the non-Gaussian distribution and has high amplitude, which is a challenge to the conventional denoising frameworks based on deep learning (DL). In this study, we propose an unsupervised learning framework with a multi-branch attention mechanism (MANet) to attenuate the erratic and random noise in 2-D and 3-D seismic data. MANet can adaptively attenuate noise in multi-dimensional seismic data without the need to manually generate labels to train the network. MANet integrates global features of waveforms extracted from multiple branches in a weighted way to enhance attention to significant features, thus obtaining a global and comprehensive representation of weights. To enhance the migration ability of shallow-level to deep-level features, we add some skip connections in the corresponding encoder and decoder. We use a robust mean-Huber loss function that is less sensitive to outliers to improve the denoising performance of erratic noise. We apply the proposed network for both 2-D and 3-D synthetic and field data. The denoising results demonstrate that the proposed method has better signal preservation and noise attenuation abilities compared with the conventional denoising methods and the state-of-the-art unsupervised learning framework. We improve the interpretability of the network by visualizing the weight matrices and different encoders. Besides, the visualization schemes proposed in this paper can be applied to more research, such as geological event interpretation, geological resource detection, and surface morphology analysis.

Salt body segmentation is a critical part of structural interpretation and oil and gas exploration for subsalt reservoirs. Existing automatic salt body segmentation techniques mostly use supervised learning strategies. It is challenging to generate a large number of labels by manual labeling, especially for 3-D salt bodies. Here, we propose a self-supervised learning (SSL) framework called Salt3DNet, for 3-D salt body segmentation. This framework is divided into two stages: pretraining and fine-tuning of downstream tasks. In the pretraining stage, we use the Barlow twins (BTs) method to pretrain the encoder and reduce redundancy in a contrastive learning manner to learn high-level data representations. In the fine-tuning stage, we construct two encoders to reconstruct 3-D seismic data and segment salt bodies in a multitask collaborative learning way. The encoder and decoder are composed of the 3-D fully convolutional DenseNet and soft attention mechanism, where the latter represents the selective kernel block (SKB) with multiple kernels of different sizes. Salt3DNet calculates the correlation matrix of features from different perspectives in the pretraining stage and makes it close to the identity matrix to obtain a more prosperous feature representation. Then, Salt3DNet uses a limited number of labeled samples for training. According to the evaluation metrics, the proposed network has demonstrated promising salt segmentation performance in 3-D SEG advanced modeling (SEAM) synthetic data and$F3$block real seismic data. In addition, the proposed network is demonstrated to have higher prediction accuracy than state-of-the-art salt segmentation frameworks through ablation experiments.

The time–frequency analysis methods are powerful tools in seismic interpretation and bright spot identification. The S-transform (ST), as a hybrid of the short-time Fourier transform (STFT) and continuous wavelet transform (CWT), can achieve progressive time–frequency resolution. However, limited by its linear-frequency-dependent term, the ST obtains a deviated frequency distribution. By removing this term, the frequency form of unscaled ST (FUST), as a variation of the ST, is proposed to preserve the reliable frequency distribution. The fly in the ointment is that the FUST decreases the temporal resolution of the low-frequency components, which may not be suitable for seismic reflection interpretation and reservoir location. In addition, the ST cannot tailor the time–frequency resolution for particular applications. To solve these problems, a simple and effective method is proposed by substituting the basis of the FUST. The proposed method can obtain the desired time resolution by adjusting two adjustable parameters. The corresponding inverse transform is also derived to guarantee its energy conservation and inevitable property. Numerical experiments and real data examples show better performance of the proposed method in improving temporal resolution and reservoir location over the ST and FUST.

Neural networks are commonly used for post-stack and pre-stack seismic inversion. With sufficient labelled data, the neural network-based seismic inversion results are more accurate than that use traditional seismic inversion methods. However, in the case of insufficient labeled data, the accuracy of neural networks-based seismic inversion results decreases and is even lower than those based on traditional inversion methods. In addition, the seismic inversion results based on neural networks generally suffer from lateral discontinuity. It further reduces the accuracy of the inversion results. To tackle these problems, we propose a pre-stack seismic amplitude variation with offset (AVO) inversion method based on Closed-Loop Multi-task conditional Wasserstein Generative Adversarial Network (CMcWGAN), which is a GAN-based AVO inversion method. CMcWGAN enables simultaneous and accurate inversion of P-wave velocity (Vp), S-wave velocity (Vs), and density ( ρ ). Moreover, it uses the low-frequency information of elastic parameters as a conditional input to alleviate the problem of lateral discontinuity in inversion results. Experimental results of simulated data show that the inversion results based on CMcWGAN have higher accuracy than those based on traditional AVO inversion methods. In addition, when the seismic angle gather is noisy, CMcWGAN has better robustness than the traditional methods. CMcWGAN can also obtain reasonable AVO inversion results in field seismic angle gather data.inversion results. Experimental results of simulated data show that the inversion results based on CMcWGAN have higher accuracy than those based on traditional AVO inversion method. In addition, when the seismic angle gather is noisy, CMcWGAN has better robustness than traditional method. CMcWGAN can also get reasonable AVO inversion results in field seismic angle gather data.

Accurate estimation of reservoir parameters (e.g., permeability and porosity) helps to understand the movement of underground fluids. However, reservoir parameters are usually expensive and time-consuming to obtain through petrophysical experiments of core samples, which makes a fast and reliable prediction method highly demanded. In this article, we propose a deep learning model that combines the 1-D convo- lutional layer and the bidirectional long short-term memory network to predict reservoir permeability and porosity. The mapping relationship between logging data and reservoir parameters is established by training a network with a combination of nonlinear and linear modules. Optimization algorithms, such as layer normalization, recurrent dropout, and early stopping, can help obtain a more accurate training model. Besides, the self-attention mechanism enables the network to better allocate weights to improve the prediction accuracy. The testing results of the well-trained network in blind wells of three different regions show that our proposed method is accurate and robust in the reservoir parameters prediction task.

Amplitude variation with offset (AVO) refers to the amplitude variation with offset. This relationship can be used to analyze lithology and identify the oil and gas reservoirs in seismic exploration. Traditional AVO inversion is a typical ill-posed problem. When deep learning is directly used for seismic inversion, there are three main issues. First, the label data are insufficient. Second, a network trained for one working area is not applicable to other working areas. Third, there are spatial discontinuities and instability problems in the inversion results. In this letter, we propose the AVO inversion method that combines transfer learning and low-frequency component constraints. Transfer learning strategy is introduced to solve two main problems: The label data are insufficient to train the network, and the trained network is not applicable to other regions. Taking the low-frequency component as the constraint term makes the solution easier to converge to the true value. The experimental results of a typical example show that our method not only effectively improves the prediction accuracy and spatial continuity of the inversion results, but also reduces dependence on logging data.

Effective random noise attenuation is critical for subsequent processing of seismic data, such as velocity analysis, migration, and inversion. Thus, the removal of seismic random noise with an uncertainty level is meaningful. Attenuating 3-D random noise in a supervised way based on deep learning (DL) is challenging because clean labels are difficult to obtain. Therefore, it is necessary to develop an adaptive unsupervised-based method for random noise attenuation. In this article, we propose a deep-denoising unsupervised learning (DDUL) network to attenuate random noise in 2-D/3-D seismic data. A patching technique is used to split 2-D/3-D seismic data into several patches to be fed into the network, which helps to expand the number of samples for training. We use the fully symmetrical structure of the autoencoder to construct the network. In each corresponding encoder and decoder layer, skip connections are added to enhance the learning of seismic data features. We construct three blocks to extract waveform features in seismic data, i.e., encoder, decoder, and skip blocks. Among them, the skip is connected between the encoder and decoder blocks of each hidden layer. The use of multiple blocks not only improves the network’s ability to extract seismic data features but also solves the problem of excessive training parameters caused by hidden layer stacking. Five 2-D/3-D synthetic and field seismic datasets are used to test the denoising performance of our proposed method. The denoising results demonstrate that our proposed method has good signal-preserving and noise attenuation capabilities in real-world applications.

Absorption attenuation compensation is an important part of seismic data processing. It enhances the resolution of non-stationary seismic data by compensating the amplitude energy and correcting phase distortion. The stabilized inverseQ-filter method, a widely used attenuation compensation method, constructs compensation operators based on stratigraphy-related assumptions and compensates seismic data using time-window analysis, which is computationally complex and sensitive to noise. The essence of attenuation compensation lies in the establishment of a nonlinear mapping relationship between attenuated and non-attenuated seismic traces, which strongly benefits from deep learning. This paper proposes a new method for attenuation compensation based on an end-to-end deep neural network to reduce the hand-crafted step of time-window analysis. Instead, the convolutional blocks of the network automatically learn and process seismic data features to achieve simultaneous amplitude and phase compensation. We have constructed two end-to-end network architectures for attenuation compensation: a fully convolutional network (FCN) and a U-Net. As an effective spectrum-broadening method, the compensation method based on the U-Net is shown to enhance vertical resolution with good lateral continuity, to provide reliable compensation results without complex calculations, and to exhibit high noise robustness. Synthetic data tests indicate that the compensation results from the U-Net are better than those from either the FCN or the stabilized inverseQ-filter method at different noise levels. Moreover, the correlation coefficient between the U-Net compensation results of the synthetic profile and the reference non-attenuated profile is higher than that of the FCN and the stabilized inverseQ-filter method. A field data application further verifies the effectiveness of this method.

The distance-separated simultaneous-sourcing (DSSS) technique can make the smallest interference between different sources. In a distance-separated simultaneous-source acquisition with two sources, we propose the use of a novel iterative seislet-frame thresholding approach to separate the blended data. Because the separation is implemented in common shot gathers, there is no need for the random scheduling that is used in conventional simultaneous-source acquisition, where random scheduling is applied to ensure the incoherent property of blending noise in common midpoint, common receiver, or common offset gathers. Thus, DSSS becomes more flexible. The separation is based on the assumption that the local dips of the data from different sources are different. We can use the plane-wave destruction algorithm to simultaneously estimate the conflicting dips and then use seislet frames with two corresponding local dips to sparsify each signal component. Then, the different signal components can be easily separated. Compared with the FK-based approach, the proposed seislet-frame-based approach has the potential to obtain better separated components with less artifacts because the seislet frames are local transforms while the Fourier transform is a global transform. Both simulated synthetic and field data examples show very successful performance of the proposed approach.

Interpolating regularly missing traces in seismic data is thought to be much harder than interpolating irregularly missing seismic traces, because many sparsity-based approaches cannot be used due to the strong aliasing noise in the sparse domain. We propose to use the seislet transform to perform a sparsity-based approach to interpolate highly undersampled seismic data based on the classic projection onto convex sets (POCS) framework. Many numerical tests show that the local slope is the main factor that will affect the sparsity and antialiasing ability of seislet transform. By low-pass filtering the undersampled seismic data with a very low bound frequency, we can get a precise dip estimation, which will make the seislet transform capable for interpolating the aliased seismic data. In order to prepare the optimum local slope during iterations, we update the slope field every several iterations. We also use a percentile thresholding approach to better control the reconstruction performance. Both synthetic and field examples show better performance using the proposed approach than the traditional prediction based and the F-K-based POCS approaches.