Supervised seismic data reconstruction methods are often limited by the quality and quantity of labels in practical applications, and some self-supervised and unsupervised methods suffer from higher computational cost. In addition, most deep models trained with clean datasets possess weak noise robustness. To address the above challenges, we develop a method that makes a trade-off in reconstruction precision, efficiency, demand for labels, and noise robustness. Specifically, we propose a deep model (W-KAN) integrating wavelet and Kolmogorov-Arnold Network (KAN) for regularly missing seismic data reconstruction, which employs discrete wavelet transform (DWT) downsampling to preserve more critical details information and KAN blocks to capture high-level feature representations, which effectively improves the reconstruction precision. We also give a Bernoulli sampling (BS)-based semi-supervised learning strategy that avoids the need for a large number of high-quality labels and enhances noise robustness. We evaluate the proposed method on synthetic as well as field data. Numerical experiments demonstrate the effectiveness and real-time capability of the proposed method, and reveal its competitiveness as well as superiority compared to three deep learning (DL)-based benchmark methods.

Unsupervised methods for single 3-D seismic data reconstruction, such as deep image prior (DIP) and Bernoulli sampling (BS) frameworks, have achieved promising results. However, they suffer from expensive computational costs caused by a large number of iterations. Moreover, in the absence of labels, the final reconstructed results often require visual inspection to pick out, which inevitably introduces subjective errors. To address the above problems, we introduce local Pearson correlation coefficient (LPCC) and local mean absolute error (LMAE) to assess the correlation and difference between seismic traces. The mean values of LPCC (MLPCC) and LMAE (MLMAE) for all nonedge traces in the reconstructed result can evaluate the quality of the reconstructed result based on the internal similarity and internal difference of 3-D seismic data without labels. We further develop an MLPCC-MLMAE-based early stopping strategy. The training process will stop once the number of values behind the highest MLPCC has reached the patience value, and the MLMAE is used as one of the indispensable constraints for the highest MLPCC. We apply the proposed early stopping strategy to the DIP and BS frameworks and demonstrate that it has the ability to significantly reduce computational costs through experiments on synthetic and field data, which makes the DIP and BS frameworks a major step toward practical production. Furthermore, the quantitative evaluation metrics allow the network to automatically and intelligently monitor the training process, and the prediction at the end of iteration is used as the final reconstructed result, thus eliminating the need for human intervention.

The field acquired seismic data are often irregular, which affects the accuracy of subsequent processing algorithms. We develop a framework based on a dual-attention-based wavelet integrated convolutional neural network (DAWCNN) constrained via stochastic structural similarity (S3IM) for reconstruction of seismic data with regularly as well as irregularly missing traces. The proposed method utilizes discrete wavelet transform (DWT) and inverse wavelet transform (IWT) to preserve the valid information. It also leverages skip connections based on the group multiaxis Hadamard product attention (GHPA) mechanism and spatial attention (SA) mechanism to perform the fusion of more critical and refined multiscale features and subband feature recalibration, respectively. Additionally, a hybrid loss function is designed, which reduces the pixel differences through mean square error (MSE) loss and the differences in local structures and stochastic nonlocal structures via S3IM loss. We evaluate the proposed method on synthetic and field data. The numerical experiments demonstrate the effective and superior reconstruction capability of the proposed method, which outperforms four traditional and deep learning (DL)-based benchmark algorithms. The proposed method can also perform reconstruction and denoising simultaneously.

Seismic data acquisition is an indispensable step in seismic exploration, whose cost takes up a large proportion of seismic exploration. The cost of seismic data acquisition has limited the development of industrial manufacturing. The compressed sensing method can obtain high-quality seismic data with less random sampling. Recently, deep learning (DL) based compressed sensing methods have achieved outstanding performance in the reconstruction of seismic data with randomly missing traces. However, most existing DL-based methods focus on the 2D seismic data. The obstacle to applying deep learning to the reconstruction of 3D seismic data is the lack of high-quality training data. Self-supervised learning can overcome the lack of high-quality training data. Nevertheless, the time cost is the biggest obstacle preventing the application of self-supervised learning methods. To solve the above issues, we propose a fast self-supervised learning method for the reconstruction of 3D seismic data. The proposed method learns from the observed seismic data directly by sub-sampling. Besides, 3D lightweight gated convolution layers are utilized for highly efficient reconstruction of the input seismic data with randomly missing traces. Meanwhile, the proposed method employs a global waveform extractor based on a fast Fourier transform to extract global waveform. The synthetic and field experiments have demonstrated that the proposed method has a remarkable reconstruction performance with high efficiency.

Quality factor (Q) estimation is critical for the processing of nonstationary seismic data and is an important indicator of oil and gas. Traditional methods for Q value estimation require the identification of the top and bottom of each constant Q layer, which can be challenging in the processing of field seismic data. Deep-learning (DL)-based Q inversion methods leverage the powerful nonlinear fitting capabilities of deep network to automatically obtain interval Q estimates directly from the input seismic data. However, these methods possess so-called “black box” characteristics and lack interpretability, thereby limiting their practical application. To address these issues, this study proposes a physics-driven neural network (PDNN) that integrates physical knowledge with deep neural networks, embedding the frequency-shift method for Q value calculation into the computational layers of the network. Our approach uses nonstationary seismic signals and their corresponding logarithmic time-frequency amplitude spectrum (LTFAS) as input. The neural network decouples the dynamic wavelets and reflection coefficients to obtain the LTFAS of dynamic wavelets. Furthermore, a network layer is designed based on the frequency-shift method to generate the interval Q curve. Experiments on both synthetic and field data demonstrate that the neural network constrained by physical knowledge can alleviate the instability in interval Q calculations, yielding more stable Q estimates. Additionally, this approach enhances the interpretability and generalization capabilities of DL methods, offering significant practical value.

Most previous studies focus on using complex deep neural networks to learn diverse features of massive synthetic data. In more realistic situations with a limited number of data pairs, complex networks not only have higher computational complexity, increasing training time and reducing inference speed, but also tend to over-fit a small amount of training data, thus having weak generalization capability. To address the aforementioned problem, we propose a lightweight architecture for real-time velocity inversion in realistic situations, the bilateral inversion network (BiInNet). BiInNet uses lightweight ResNet18, ShuffleNetV2, and modified MobileNetV2 as backbones, taking into account the inversion accuracy and inference speed. To reduce the redundant information in common shot gathers and focus on graphical property features which are strongly correlated with velocity, the intermediate results of velocity analysis, semblances, and interval velocity models are prepared as data pairs. Numerical experiments show that BiInNet can infer interval velocity models in real-time, with frames per second (FPS) up to 76.90 when ResNet18 is used as the backbone. Moreover, BiInNet achieves the best inversion accuracy on more realistic fold models, fault models, salt models, and noisy dataset (NFOMD) when adopting ShuffleNetV2 as the backbone, which illustrates that BiInNet can be applied to velocity inversion tasks of different geological structures and is robust to noise. Adopting transfer learning to fine-tune pretrained model, BiInNet is effectively applicable to velocity reversal models and field data, which further demonstrates the reliability of the proposed method and provides a practical velocity inversion scheme when the field data pairs are insufficient.

Most existing traditional and deep learning (DL)-based methods used for random noise attenuation or reconstruction of seismic data typically only process two-dimensional (2-D) data. Very few methods are able to perform both denoising and reconstruction tasks for three-dimensional (3-D) seismic data. We develop a framework based on a self-supervised 3-D partial convolutional neural network (3-DPCNN) for multi-task processing of single 3-D seismic data volume, including random noise attenuation, reconstruction, and simultaneous denoising and reconstruction. The proposed method utilizes 3-D spatial structure information via 3-D convolution kernels and exploits Bernoulli sampling to generate training data pairs and test data. Attributed to Bernoulli sampling, the 3-DPCNN can be trained with only one noisy and/or corrupted seismic data volume; therefore, all supervised information is derived from the original data, and no external supervised information is required. The data augmentation strategy does not always boost the performance of the 3-DPCNN. Therefore, whether it is used and which transform is randomly employed are determined by the task type and the data. In addition, a double ensemble learning strategy is employed to boost 3-DPCNN performance and avoid randomness in the predictions. We evaluate the proposed method using multiple synthetic and field data. The experiments show that the proposed method has remarkable denoising and reconstruction abilities and is competitive with and even superior to a variety of traditional and DL-based benchmark algorithms.