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.

Gravity inversion is the pioneer in exploring the structural characteristics of the Earth, the Moon, and other celestial bodies. Classical gravity inversion methods aim to estimate the 3D subsurface density distribution from the observed 2D surface gravity anomalies, which is an ill-posed problem. Constraints can provide vertical resolution and reduce uncertainty. However, these methods significantly increase the cost of data acquisition. This manuscript presents a novel joint inversion method to estimate subsurface density anomaly via a physics-inspired neural network. The observed signals in the proposed method are the gravity anomalies on multiple altitudes and their vertical gradients, which provide vertical resolution for gravity inversion. The proposed joint inversion method contains two stages. The proposed inversion model is initially pre-trained on the synthetic data. Self-supervised transform learning with a closed loop between inversion and forward models is applied to the target gravity anomalies and their gradients. The loss function is defined by mean absolute error, cross-gradient loss, and total variation. Experiments on independently and identically distributed synthetic data, as well as out-of-distribution field data, demonstrate the effectiveness of the proposed method.

Magnetic inversion aims to estimate the subsurface susceptibility distribution from surface magnetic anomaly data. Recently, supervised deep learning (DL) methods have been widely utilized in lots of geophysical fields including magnetic inversion. However, these methods rely heavily on synthetic training data, whose performance is limited since the synthetic data is not independently and identically distributed with the field data. Thus, we proposed to realize magnetic inversion by self-supervised learning. The proposed self-supervised knowledge-driven method for 3D magnetic inversion (SSKMI) learns on the target field data by a closed loop of the inversion and forward models. Given that the parameters of the forward model are preset, SSKMI can optimize the inversion model by minimizing the difference between observed and re-estimated surface magnetic anomalies. Besides, there is a knowledge-driven module in the proposed inversion model, which makes the DL-based method more explicable. Meanwhile, comparative experiments demonstrate that the knowledge-driven module can accelerate the training and achieve better results. Since magnetic inversion is an ill-pose task, SSKMI proposed to constrain the inversion model by a guideline from a well log, seismic waves, or electromagnetic signals. The experimental results demonstrate that the proposed method is a reliable magnetic inversion method with outstanding performance.

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.

Three-dimensional inversion of magnetic data can obtain the distribution of subsurface magnetic targets. Deep learning is an effective way to achieve 3-D inversion, which trains a neural network to learn the features of magnetic anomaly data and then generates a 3-D model based on these features. Large training samples are required to achieve persuasive results due to the limited observational data and the multisolution nature of the inverse problem. To reduce the nonuniqueness of the inversion, this article proposes a multivariate magnetic data-based deep learning 3-D inversion strategy. With the proposed strategy, more domain knowledge is incorporated into the training data of the neural network to improve the inversion accuracy. The input data of the neural network adopt multivariate observation data, including multiscale data and multitype data such as magnetic three-component data, magnetic gradient tensor data, and so on, and output a 3-D model to realize 3-D to 3-D mapping. Then, the neural network structure uses the 3-D convolution to extract 3-D spatial information. Both tests on simulation and measured data verify that the proposed strategy can effectively improve the accuracy of the 3-D magnetic inversion.

Seismic inversion is a critical research area in seismic data interpretation. Given the powerful feature extraction and representation capabilities of deep neural network (DNN), it has been widely adopted in the seismic reservoir parameters inversion. However, the majority of DNN-based inversion methods use 1-D models due to the scarcity of well-logging labels, which are only 1-D time series. The performance of higher-dimensional DNN-based inversion methods depends on the quality of the initial inversion results, leading to an interdependence between the model and data in the time and space dimensions. Here, we propose a model and data co-evolution method for seismic reservoir parameters inversion. It employs a 1-D DNN model-based closed-loop model to generate initial reservoir inversion results. Then, the evolutionary 2-D model learns spatial structural features constrained by the initial reservoir inversion results to improve the spatial continuity. We tested the proposed method on synthetic seismic data with multiple fault structures, achieving the lowest inversion error and highest inversion accuracy. It also exhibits the highest accuracy in real seismic data with the structural features of underground rivers being more pronounced.

Seismic stratigraphic interpretation plays an important role in geophysics and geosciences. Recently, deep learning has been explored for seismic stratigraphic interpretation. However, deep learning-based interpretation methods usually require sufficient labeled samples. This is often too hard to be satisfied in field seismic interpretation. In this paper, we propose a deep active learning-based method to address this issue. Active learning typically exploits prediction uncertainty to reduce labeling effort. We found that uncertainty of prediction is easily obtained in the field of seismic interpretation. Since adjacent seismic images are very similar, they should have similar predictions. When the model performs poorly, the predictions of adjacent images will differ significantly. Thus, the uncertainty can be easily obtained by measuring the similarity of the predictions of adjacent seismic images. Then, data with the highest uncertainty is annotated by geological expert and used for the next round of training. For few-shot active learning, initial models obtained by different initial training sets are quite different. We combine deep clustering and uncertainty sampling to select initial training datasets, with which a good initial model can be obtained. To improve generalization, we introduce a random thin plate spine transformation to simulate changes of terrain. We apply the proposed method to the F3 field seismic data. The results demonstrated that the proposed method can effectively improve performance of learned seismic interpretation network with very limited labeled samples.

Seismic stratigraphic interpretation plays an important role in geophysics and geoscience. Recently, deep learning has been widely applied to seismic stratigraphic interpretation. These deep learning-based stratigraphic interpretation methods have shown greater potential than traditional methods. Despite the promising results achieved by deep learning-based methods, it is still necessary to enhance their generalization capabilities and the reasonability of stratigraphic interpretation. Therefore, we propose a semi-supervised deep learning-based method to improve the accuracy and reasonability of interpretation results. First, we quantitatively describe the correlation of adjacent seismic data using the dynamic time warping algorithm. The correlation of all seismic data can be regarded as the spatial structure of seismic data. The interpretation results of seismic data should conform to such spatial structure. Then, we train a deep learning model to interpret seismic stratigraphic units under the constraints of seismic spatial structure. The performance of the proposed seismic stratigraphic interpretation method is evaluated on the Netherlands F3 data. We build two scenarios to interpret the stratum: 1D scenario for the one seismic profile and 2D scenario for the whole seismic volume. The results on the field data demonstrate that the proposed method has better generalization ability and the interpretation results are more reasonable. Therefore, the proposed method can be a useful tool for seismic stratigraphic interpretation.

The difficulty of 3D magnetic inversion is to use 2D magnetic anomaly data to obtain 3D 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 paper, artificial intelligence (AI) technology is applied to 3D magnetic inversion to predict the susceptibility model corresponding to magnetic anomaly. The inversion network built in this paper 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 3D refiner behind the decoder. The 3D refiner converts the 2D feature map from the decoder into 3D data. Based on the typical complex medium theory, this paper constructs a diverse sample set of complex 3D 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 paper can achieve high-precision 3D underground susceptibility imaging in this area. The susceptibility distribution is in good agreement with the borehole data and the proved deposit distribution.

Magnetotelluric (MT) inversion constitutes a pivotal research domain within the purview of electromagnetic data interpretation, characterized by its inherent nonlinearity and illposed problem. Traditional MT inversion algorithms often require introducing an initial model as a prior constraint, and then drawing the electrical distribution of the structure based on the observed data, which has limitations such as low computational efficiency and high computational costs. This paper proposes an efficient and high-quality MT intelligent joint inversion method based on artificial intelligence (AI) control strategy to address the issues in MT inversion problems. Capitalizing on the strong nonlinear fitting capabilities of convolutional neural networks (CNNs), the closed-loop network composed of forward and inversion subnetworks is constructed to enable the closed-loop network to train in the absence of labels, thereby solving the restrictive problem of the small number of label samples faced by MT inversion. Simultaneously, the reciprocal constraint between forward and inversion subnetworks can suppress inversion multiplicity, leading to improved inversion accuracy. In addition, the uncertainty in inversion can be further reduced by mutual constraints between apparent resistivity and phase data. Finally, this paper tests and verifies the effectiveness of the closed-loop network using synthetic and measured data. The results demonstrate that the closed-loop network significantly enhances the depth resolution of inversion and elevates the reliability of inversion results. Moreover, the closed-loop network can also effectively predict the apparent resistivity and phase response data that are close to those simulated via the finite element method.

Seismic elastic parameters inversion is a method to predict geophysical reservoir parameters, including P-wave velocity, S-wave velocity and density, by using pre-stacked seismic data. Deep learning (DL) techniques have been utilized to establish complex and nonlinear inversion model. However, these DL-based inversion methods have some limitations. For instance, they often overlook the complementary observation distance information in pre-stacked seismic data at different incident angels, and they do not always consider the spatial structure and physical information conditions. As a result, the inversion solutions may be prone to falling into local minima. In order to alleviate this issue, we propose a spatial pattern learning method for pre-stacked seismic inversion. First, multi-view convolutional neural network is used to extract more complementary high-dimensional features of pre-stacked seismic data, which implies the spatial observation distance pattern of the input data. Second, the dip structure loss item is used to ensure the structural consistency between inverted results and seismic data, which constrains the spatial continuity. Third, forward physical constraint item improves the physical interpretability of inversion results. In addition, forward reconstruction result and estimated dip structure result can be used to automatically evaluate inversion results on unlabeled data. The proposed approach has been proven in enhancing the inversion accuracy and spatial continuity based on experimental results from both synthetic pre-stacked seismic data and real pre-stacked seismic data.

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.

The traditional method to improve the resolution in electromagnetic inversion is increasing the number of iterations, which displays poor non-linear mapping and strong non-uniqueness. To meet this challenge, a new strategy is proposed via reconstructing the geoelectric model for traitional inversion results through a deep neural networks (DNN). DNN possesses the advantage on establishing an uncertain mapping between low-resolution images and high-resolution target images. In order to recover the high-precision geoelectric model, we propose an end-to-end electromagnetic recovery network (EMRNet) with novel components to adequately utilize the geoelectric model data of traditional inversion. Specifically, EMRNet uses the codec structure from U-Net, whereby a cross-scale feature attention module (CSFA Block) is incorporated into the decoding process to make full use of feature information of different scales. The superiority of EMRNet are validated on both synthetic and measured data, The predicted geoelectric models of EMRNet are more consistent with the target from the aspects of resistivity values, overall structure, and resolution. In addition, the geoelectric model predicted by EMRNet agree well with the real geological background data and corresponding response data is closer to the measured data.

The gravity method is one of the non-destructive geophysical methods, which aims to estimate the 3D subsurface density distribution of geological bodies from the observed 2D surface gravity anomalies. Recently, deep learning has achieved great success in solving ill-posed problems including gravity inversion. The limitation of the current deep learning methods for gravity inversion is the difference between synthetic and field data. Thus, we introduce a self-supervised estimation method for 3D gravity inversion (SSGI). SSGI learns the field data directly by closed-loop of the inversion model and forward model. The proposed inversion model contains an encoder, an expander, a decoder, and a 3D refiner. Since the forward model is built according to the law of universal gravitation, SSGI can optimize the inversion model by minimizing the mean absolute error of the original and reconstructed gravity anomalies. Besides, SSGI constrains the inversion model by a guide-line in the auxiliary loop. Since the guide-line corresponds to the sampling or average of the density matrix, minimizing the mean absolute error between the original guide-line and the generated guide-line can reduce the uncertainty of inversion. The experimental results demonstrate that the proposed SSGI achieves state-of-the-art performance in 3D gravity inversion.

Recently, a multitask learning framework named M: multitask, R: global residual skip connection structure, U: encoder–decoder structure of U-Net, D: dense skip connection structure, and SR: super-resolution (M-RUDSR) has successfully improved the accuracy of full-waveform inversion (FWI) results by enhancing the resolution of the seismic velocity model. However, M-RUDSR does not make full use of seismic data even though it contains high wavenumber information, which can help enhance the resolution of the velocity model. Moreover, the effects of employing seismic data realized by simply increasing the model’s input and output channels are limited since the seismic velocity model and seismic data are in different frequency bands. Therefore, we propose to consider super-resolution (SR) of seismic data and its edge images as supplementary auxiliary tasks of the seismic velocity model SR. Besides, the proposed method named M-RUDSRv2 improves the resolution of the seismic velocity model leveraging a three-step learning strategy. First, the model in M-RUDSRv2 is trained preliminarily on the specific data where the seismic velocity model and seismic data are in the same blurring levels. Then, the pretrained model is fine-tuned on the extensive data, where the seismic velocity model and seismic data are in various kinds of blurring levels, to achieve strong generalization ability. Finally, the fitted model focuses on improving the resolution of the seismic velocity model by adjusting the parameters in the loss function. Comparative experiments on synthetic and field data validate the superior performance of M-RUDSRv2 compared with M-RUDSR in SR of the seismic velocity model.

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.