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.

Seismic image segmentation is important in geological interpretation. In recent years, numerous studies have leveraged texture features to analyze seismic images. However, traditional texture feature extraction methods are computationally intensive and cannot be updated through back-propagation. To address these challenges, we propose a model named Lightweight Segmentation Network based on Co-occurring Matrix (LSCM-Net). The overall architecture of LSCMNet employs an asymmetric encoder-decoder structure. The encoder mainly consists of a lightweight bottleneck that integrates the Parametric Co-occurrence Matrix model based on the Convolutional Neural Network (CNN) for Segmentation (S-PCMCNN) module, along with channel shuffle and split for feature fusion, enhancing the model representational capacity. The pyramid decoder encompasses a spatial attention mechanism. This design significantly reduces the parameters while maintaining accuracy in seismic image segmentation. In the application of igneous rocks, an ablation experiment was conducted to validate the effectiveness of the S-PCMCNN module. Moreover, compared with other classical segmentation models, LSCMNet demonstrates superior segmentation accuracy in few-shot scenarios while having fewer parameters and floating point operations (FLOPs).

Logging-while-drilling (LWD) azimuthal imaging is a widely used well-logging technique in modern geological resource exploration. However, due to the measurement principles and data transmission capacity, the circumferential resolution of current techniques is very limited. In this article, we propose a deep convolutional network-based algorithm called azimuthal image super-resolution (AzSR), which is capable of reconstructing high-resolution borehole images with 128 fans from noisy azimuthal responses of 4/8/16 fans. To make the proposed algorithm more suitable for AzSR, techniques such as sample synthesis, circular padding, and special loss terms are introduced. The advantages and effectiveness of the proposed AzSR algorithm are demonstrated through systematic experiments and real-world applications. The results show that the proposed AzSR has significant advantages over existing algorithms in terms of noise robustness, detail reconstruction, and resolution improvement. With the super-resolution results of AzSR, detailed information about lithological interfaces, local structure, and thin layers can be clearly revealed. This will be of great value for decision-making during geosteering drilling and for fine-scale geological interpretation after drilling.

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.

High-resolution characterization of subsurface hydrocarbon reservoirs critically depends on the integration of seismic and well log data. However, the precision of well-to-seismic tie procedures is often compromised by inaccuracies in time-depth conversion curves, stemming from imprecise migration velocity errors, scale discrepancy and the inherent domain disparity between seismic data (time-domain) and well log data (depth-domain). Traditional methods rely on iterative wavelet estimation and manual adjustments, leading to wavelet-depth curve coupling problems, reduced accuracy, and significant time consumption. To address these limitations, we propose a novel automated time-depth conversion curve correction method. This approach leverages key feature matching in the time-frequency domain of well log reflection coefficients and borehole-side seismic traces, incorporating dual constraints: stratigraphic constraints in the time domain and spectral notch points in frequency domain. By directly aligning with well log reflection coefficients, this time-frequency joint analysis eliminates the need for wavelet estimation as well as iterative and interactive processes. Experiments performed using both synthetic and field data demonstrate the validity and effectiveness of the proposed method compared to traditional iterative matching method and interactive commercial software.

In this paper, we investigate the multiple autonomous underwater vehicles (AUVs) collaborative data collection and tra- jectory planning scheme in integrated sensing and communication for underwater acoustic networks (ISAC-UANs). To collect data efficiently, AUVs traverse the overlapping communication region of sensor nodes instead of accessing every sensor node. In addition, the sensing function is required to enable obstacle avoidance. To this end, we first propose the time division multiple access (TDMA)-based communication and mono-static sensing strategy for ISAC-UANs. Secondly, we formulate the data collection and trajectory design problem into a min-max problem to minimize energy consumption and enhance the network throughput. To solve this problem, we decouple it into three sub-problems: the sensor node clustering problem, the cluster traversal problem, and the trajectory planning problem. The first sub-problem is to determine the AUV traversal area to collect data, which is solved by an overlapping communication regions based clustering algorithm. The second sub-problem is to determine the AUVs' cluster traversal sequence minimizing the traversal length, which is solved by an min-max ant colony optimization (ACO)-based algorithm. The third sub-problem involves planning the optimal trajectory for AUVs to reach the data collection area while avoiding obstacles, which is solved by the soft actor-critic (SAC)-based online trajectory planning algorithm. Extensive simulations demonstrate that the proposed scheme outperforms benchmarks in terms of trajectory length, energy consumption, and network throughput.

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.

As an important elastic parameter, seismic acoustic impedance is usually obtained through poststack inversion. However, there are usually two problems that limit the quality of the inversion results. First, conventional inversion methods typically use regularization terms to enhance the stability of the inversion results, and effective regularization terms are particularly important for accurately inverting seismic impedance. Second, most inversion methods adopt a trace-by-trace inversion strategy, resulting in poor lateral continuity when connecting the inversion results of all traces into a 2-D profile, especially for processing noisy data. To address these two problems, we propose a structure-oriented minimum entropy stabilizer for acoustic impedance inversion that enhances the lateral continuity of the inversion results while restoring the blocky structures of the strata and improving the resolution of the inversion results. The stabilizer consists of a structure-oriented regularization (SOR) operator and the minimum entropy norm. The SOR operator is constructed using the local dip estimated from the seismic data by the plane-wave destruction (PWD) algorithm and constrains the inverted impedance along the structural trend, making it more consistent with geological features. The minimum entropy norm restores the blocky structures and enhances resolution by imposing sparse constraints on the temporal and spatial derivatives of the impedance. Based on synthetic and field seismic data, we compare the inversion results of the proposed method with those of conventional Tikhonov regularization and total variation (TV) regularization methods. The results show that the proposed method exhibits superior performance, especially in processing noisy data.

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.

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.

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.

Inversion of seismic data, particularly full waveform inversion (FWI), allows for high-resolution subsurface velocity estimation. However, the inversion of subsurface velocities using only seismic data typically involves severe non-uniqueness. Electromagnetic exploration, due to its broad detection range and low cost, can effectively complement seismic exploration. Although electromagnetic data give a lower resolution resistivity information, they are sensitive to subsurface anomalies. Hence, the joint inversion of electromagnetic and seismic data effectively integrates the complementary information in both data sets to reduce the inversion non-uniqueness to improve accuracy and reliability of the inversion results. Nevertheless, current joint inversion techniques are confronted with issues such as the complexity of objective function design, challenges in achieving convergence, and insufficient coupling between seismic and electromagnetic data. To address these challenges, we propose a Seismic-Electromagnetic joint Inversion Network (SEMI Net) based on joint learning. Our approach leverages the powerful nonlinear fitting capabilities of neural networks for efficient multi-objective optimization. Moreover, we establish coupling between seismic and electromagnetic data across multiple sampling scales. Harnessing the frequency band complementarity of seismic and electromagnetic data, i.e. the low-frequency of the electromagnetic data and the mid-to-high frequency of the seismic data, we obtain high-resolution resistivity and velocity models by SEMI Net. Results on synthetic data and the Overthrust model demonstrate the effectiveness of our approach.

Seismic imaging technology, which analyzes seismic wave propagation and reflection to gather data on underground geological structures, is vital for geological exploration. Due to factors such as the anisotropy of subsurface media, migration velocity errors, and drift of seismic streamers in marine environments, observation points at the same position exhibit horizontal and vertical displacements in different common offset gathers (COGs), thereby diminishing stacking coherence and compromising imaging quality. Consequently, the nonflattened seismic events in common image gathers (CIGs) extracted from COGs can lead to false amplitude variations with offset. Traditional CIG enhancement methods like cross-correlation matching encounter challenges such as slow inference speed, limited accuracy, the capability to predict only a single directional displacement, and difficulty in parameter tuning. Therefore, based on optimizing local normalized cross-correlation matching, an interpretable deep learning method to enhance CIGs using a self-supervised optical flow estimation network is proposed. Experiments performed using both synthetic and field data demonstrate the validity and effectiveness of the method.

Ground-roll is a typical Rayleigh-type interference noise in field seismic data, which is characterized by low frequency, low velocity and high amplitude. Since it will interfere effective seismic signals and severely degrade the signal-to-noise ratio of observed seismic records, many approaches have been developed for ground-roll attenuation or separation. In this letter, we proposed an improved ground-roll separation algorithm through the combination of deep learning based low-frequency generation and dictionary learning based low-frequency reconstruction. Moreover, to utilize the inter-band morphological similarity prior in seismic response, we introduce the morphological similarity constraint into the learning approach of pseudo low-frequency generation networks. Experiments demonstrate that compared to previous methods, the introduced the morphological similarity loss can effectively improve the quality of generated pseudo low-frequency signals, which results in better low-frequency reflection reconstruction and ground-roll separation performances.

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 multiple is one of the most common noises in marine seismic data, which heavily affects subsequent processing and interpretation. To eliminate the influence of seismic multiples, many methods have been developed, while surface-related multiple elimination (SRME) is one of the most widely deployed methods. However, results of SRME always contain a few strong residual diffracted multiples (RDMs) in practice because of the unprecise prediction of diffracted multiples compared to reflection multiples. If we try to apply further multiple suppression methods to SRME results, it not only tends to damage the signals, but also spends lots of unnecessary computations where there is no RDM. In this article, we propose an improved RDM suppression method based on object detection and image segmentation. First, we employ an object detection network to locate bounding boxes containing RDMs in the SRME results. Then a threshold-based image segmentation method is utilized to identify regions of strong RDMs in the detected boxes. According to the segmentation results, parameters for weak multiples and strong multiples are provided for the adaptive multiple subtraction (AMS) in different regions to generate different results. At last, we combine the suppression results of strong RDMs and weak RDMs as the final results. Application on field data demonstrates that our method is able to suppress RDMs with little loss of signal.

Known for its great potential for determining subsurface properties quantitatively, full-waveform inversion (FWI) is a hot topic in the field of exploration seismology. The success of FWI depends significantly on the accuracy of the starting model. Given that both the migration and velocity profiles originate from the same geological structure, the two should be morphologically consistent. Starting from the velocity-reflector depth tradeoff, we propose a deep learning approach with a new training paradigm for building a good starting model. A velocity model and the corresponding migration image are used to form two-channel inputs, and the generative adversarial network (GAN) is trained to minimize the difference between the output and the true velocity model. After the training, the velocity generator network becomes a plug-in component to enhance the FWI performance. The network can be well generalized to unseen data by training with only the synthetic data. We perform extensive experiments on our test dataset, the Marmousi model, the salt velocity model, and field data to demonstrate the effectiveness of our method. Besides, we briefly give an explanation of why our model produces such outputs in this article, making the proposed method more controllable and credible.

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 techniques can help minimize inter-physician analysis variability and the medical expert workloads, thereby enabling more accurate diagnoses. However, their implementation requires large-scale annotated dataset whose acquisition incurs heavy time and human-expertise costs. Hence, to significantly minimize the annotation cost, this study presents a novel framework that enables the deployment of deep learning methods in ultrasound (US) image segmentation requiring only very limited manually annotated samples. We propose SegMix, a fast and efficient approach that exploits a segment-paste-blend concept to generate large number of annotated samples based on a few manually acquired labels. Besides, a series of US-specific augmentation strategies built upon image enhancement algorithms are introduced to make maximum use of the available limited number of manually delineated images. The feasibility of the proposed framework is validated on the left ventricle (LV) segmentation and fetal head (FH) segmentation tasks, respectively. Experimental results demonstrate that using only 10 manually annotated images, the proposed framework can achieve a Dice and JI of 82.61% and 83.92%, and 88.42% and 89.27% for LV segmentation and FH segmentation, respectively. Compared with training using the entire training set, there is over 98% of annotation cost reduction while achieving comparable segmentation performance. This indicates that the proposed framework enables satisfactory deep leaning performance when very limited number of annotated samples is available. Therefore, we believe that it can be a reliable solution for annotation cost reduction in medical image analysis.

The success of modern deep learning algorithms for image segmentation heavily relies on the availability of high-quality labels for training. However, obtaining accurate labels is time-consuming and tedious, and requires expertise. If directly trained with dataset with noisy annotations, networks can easily overfit to noisy labels and result in poor performance, which might lead to serious misinterpretation. To this end, we propose a noisy pixel estimation approach based on deep neural network, which helps correct the noisy annotations resulting in better prediction performance. First, a deep neural network is trained to detect noisy pixels from image annotations. Then, the estimated noisy pixels are used to correct the noisy annotations. Finally, the corrected annotations are used to train the deep learning model. Our proposed framework is validated on the breast tumor segmentation task. The obtained experimental results show that our proposed method can improve the robustness of deep learning model under noisy annotations while achieving favorable performance against existing noisy label correction methods.

Noisy labels seriously degrade the performance of the deep learning models. Especially on segmentation tasks, labels are represented at pixel level, and therefore, it is easier to generate them as noisy labels. In this letter, we aim to cleanse the dataset which contains noisy labels using Kullback–Leibler (KL) divergence algorithm and noise robust loss function. Here, we regard the whole dataset as noisy labels and separate noisy labels into two different parts. One is the strong noisy labels where there are the most noisy labels, which is referred to as incorrect labels, and the other is The weak noisy labels where pixels are incorrect in some parts of the image. The KL algorithm is more efficient in removing the labels which contain the most noise. At the same time, we use noise robust model to remove the labels where pixels are inaccurate only in small parts of the image. Noise robust loss function is robust to noisy labels, and thus, we consider noisy labels when intersection over union (IoU) is lower than a constant threshold despite using noise robust loss function. The effectiveness of our proposed method is assessed using Kaggle’s TGS Salt Identification Challenge dataset. We have demonstrated that using our method, segmentation performance is increased without heavy noisy labels.

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.

Accurate estimation of volumetric seismic dip is of great significance for subsequent seismic processing and interpretation works. Recently, with the development of deep learning techniques, convolutional networks are also applied for seismic dip estimation. Compared with traditional approaches, estimating dips with convolutional networks is not only more efficient but also shows great promise in accuracy and robustness. However, if we take dips estimated by traditional approaches as labels and train networks on the field seismic data directly, the accuracy and robustness of learned networks are influenced due to the error in dip labels. An alternative solution is synthesizing realistic seismic samples with accurate dip labels. However, we find that due to the differences in seismic responses and structural patterns between the synthetic and field seismic data, networks directly learned from synthetic samples cannot guarantee their generalization on the field seismic data. To overcome these drawbacks, we develop a transfer learning approach for improvement. The proposed approach pretrains the dip estimation network on synthetic seismic samples at first and then transfers it to the targeted field seismic data with a domain knowledge-inspired fine-tuning process. Moreover, the proposed approach also highlights the combination of deep learning techniques and domain knowledge in seismic processing—several subtle realizations, such as knowledge-driven sample augmentation, knowledge constrained loss function, and knowledge motivated transfer learning strategy, are introduced, which greatly enhance the learning of the seismic dip estimation network. The advantages of the proposed approach in accuracy, robustness, and resolution are validated by applying the estimated dips for structural filtering and curvature extraction on the Netherlands F3 and Kerry3D seismic data, which further confirms its practicality in the real-world application. We believe that the proposed approach has provided an effective improved way for further seismic dip estimation practices, and the present domain knowledge constrained deep learning case will also inspire researchers in the same discipline.

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.

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.

In seismic exploration, seismic data usually contain anomalous amplitude noise whose high energy may affect the results of subsequent processing steps. In industry, this kind of noise is generally suppressed using the anomalous amplitude attenuation (AAA) method. The AAA method essentially suppresses abnormal amplitude noise using a median filter in the time–frequency domain. This makes its performance heavily dependent on the parameters, especially the window width of the median filter. Thus, we propose an improved anomalous amplitude attenuation (IAAA) method based on deep neural networks. The IAAA method contains two steps. In the first step, deep neural networks are used to detect the locations and the widths of noise regions. In the second step, the noise information (locations and widths) obtained at the previous step is exploited to apply the AAA method with more appropriate parameters to each noisy region. Compared with the conventional AAA method, the IAAA method can suppress the noise more effectively and preserve signals better. The experiments on both synthetic data and field data demonstrate that our method outperforms the conventional AAA method.

Dynamic wavelet amplitude spectra extraction (DWASE), which is an ill-posed problem, is of great importance for nonstationary seismic data processing. The most difficult challenge is how to decouple the dynamic wavelets and reflection coefficients. The traditional DWASE methods solve the ill-posed problem depending on some prior information, such as the piecewise stationary hypothesis or estimation of the attenuation factor$Q$. In this article, we propose a multitask learning-based DWASE method and apply the method for$Q$estimation. Our proposed method can reduce the multiplicity of the ill-posed problem by estimating the logarithmic time–frequency amplitude spectrum (logarithmic TFAS) of both reflection coefficients and dynamic seismic wavelets, simultaneously. In our method, a parameter-sharing U-net is used to extract the logarithmic TFAS of the reflection coefficients and dynamic wavelets from the logarithmic TFAS of the nonstationary seismic data. To verify the accuracy of the DWASE results of our method, we make a quantitative analysis of the synthetic seismic data, which are obtained by our method and some traditional methods. We also apply the DWASE results of our method for$Q$estimation and attenuation compensation in both synthetic and field seismic data, to prove the effectiveness of the method. Also, comparisons with some traditional methods are given.

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.

Transverse relaxation T2 spectrum obtained by nuclear magnetic resonance (NMR) logging tools is an intuitive reflection of the pore size distribution for subsurface formation, which is valuable for petroleum reservoir characterization. However, the deployment of NMR logging tools is constrained by financial and operational factors, while NMR data are only available in very limited wells. This seriously limits its application in practices. Therefore, researchers try to synthesize NMR T2 spectra from more widely measured conventional logging data with the help of machine learning technologies. In the article, we propose the spectrum regression forest (SRF) algorithm for the prediction of NMR T2 spectra from conventional logging responses. Based on the experiment on the real-world well data of carbonate reservoir, the proposed algorithm is proved to provide effective NMR T2 spectrum predictions with accuracy amplitudes and consist morphology, which is believed to enhance the understanding of formation pore structures for future reservoir characterization practices.

Hyperspectral image (HSI) classification is of vital importance in remote sensing-related applications. Various approaches, including the recently popular convolutional neural network (CNN)-based models, are proposed to tackle the problem of exploitation of the spatial and spectral features in the HSIs for the use of training classifier. In this letter, we design a simple but innovative end-to-end deep U-net-based model for HSI classification task. Unlike the previous CNN based models that mainly use CNN for spatial feature extraction and process the HSI data locally in small patches, our model takes the whole HSI as network input directly and outputs the predicted classes corresponding to each pixel location. Classification loss in the train data set and spatial constraint loss for the predicted result are combined as the loss function in the training stage to learn the mapping from HSI data to classification map and enhance the spatial continuity and consistency of the predicted result. Benchmark HSI data sets are used to evaluate the performance of the proposed method. Experimental results show that our model can achieve promising results comparing with the existing CNN-based methods.

External source interference noise (ESIN) is a common kind of noise in marine seismic data acquisition. According to the noise-to-signal ratio (NSR), a shot gather can be divided into a low NSR part and a high NSR part. The existing ESIN attenuation methods work well in high NSR parts of shot gathers. However, because the signals in low NSR parts are much stronger than ESINs, these methods cannot suppress the ESINs in low NSR parts, and they usually damage the signals. In this letter, we propose a deep-learning method to suppress the ESINs in low NSR parts based on a convolutional neural network (CNN). The end-to-end fully convolutional network needs labeled training samples; however, the real data are unlabeled, i.e., the ESINs in low NSR parts are unknown. To obtain the labeled training data, we propose a sample generation method based on real data. The ESINs in high NSR parts extracted by the traditional methods and the signals of the clean shot gathers are added together to synthesize training samples. We then use the synthesized data and its ESINs to train the network. The experiments prove that the proposed method can suppress the ESINs in low NSR parts properly and protect the signals as well.

Structural curvatures are widely used seismic attributes that help interpreters to understand both structural and stratigraphic features. Traditional structural curvature extractions are mainly calculated from dip estimations through lateral scanning of seismic events, which is not only a very time-costing approach but also influenced by parameter settings, seismic frequency, and data quality. In this article, we propose a deep learning-based volumetric curvature extraction approach that directly derives structural curvature volumes from the seismic response. To realize the above approach, we develop a suite of sample generation and augmentation methods to synthesize seismic samples with accurate curvature labels. Then, a multitask end-to-end convolutional neural network architecture and a geometric loss function are proposed to establish the volume mapping model from complex seismic responses to the most positive and negative curvature volumes. The performance of the proposed curvature extraction approach is evaluated on both the synthetic data and the Netherlands F3 field seismic data. Extensive experiments demonstrate that curvature volumes extracted with the proposed approach are not only more accurate and less influenced by the noises of poststack seismic data but also more friendly for structure interpretation. Therefore, we believe that our proposed deep learning curvature extraction approach can be a useful tool for further seismic structure interpretation practices.

Seismic image, especially for the prestack image, performs a blurred version of the reflectivity image due to spatial aliasing, poor acquisition aperture, and nonuniform illumination. The blurring effects can be quantified by the point spread function (PSF). We herein adopt an explicit space-variant PSF formula, which can be defined as a sequential application of the modeling and migration operators with the asymptotic Green's function. The deblurred images are restored using the nonstationary deconvolution with total variation regularization in which the blurred images are described by the convolution between the space-variant PSF and the reflectivity image. However, nonstationary deconvolution is computationally challenging. We introduce an extending primal-dual hybrid gradient (E-PDHG) method to decompose the complex problem into a sequence of simple subproblems that have closed-form solutions. Numerical results on synthetic data and field data demonstrate that the proposed E-PDHG method outperforms the basic PDHG method in the prestack seismic image deblurring.

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.

In the seismic exploration, recorded data contain primaries and multiples, where primaries, as signals of interest, can be used to image the subsurface geology. Surface-related multiple elimination (SRME), one important class of multiple attenuation algorithms, operates in two stages, multiple prediction and subtraction. Due to the phase and amplitude errors in the predicted multiples, adaptive multiple subtraction (AMS) is the key step of SRME. The main challenge of this technique resides in removing multiples without distorting primaries. The curvelet-based AMS methods, which exploit the sparsity of primary and multiple in curvelet domain and the misfit between the original and estimated signals in data domain, have shown outstanding performances in real seismic data processing. These methods are realized by using the iterative curvelet thresholding (ICT), which has heavy computation burden since it includes two forward/inverse curvelet transform (CuT) pairs in each iteration. To ameliorate the computational cost, we propose an accelerating ICT method by exploiting the misfit between the original and estimated signals in curvelet domain directly. Since the proposed method only needs do one forward/inverse CuT pair, it is faster than the traditional ICT method. Considering that the error of the predicted multiple is frequency-dependent, we furthermore introduce the joint constraints within different frequency bands to stabilize and improve the multiple attenuation. Synthetic and field examples demonstrate that the proposed method outperforms the traditional ICT method. In addition, the proposed method has shown to be suitable for refining other AMS methods' results, yielding a SNR improvement of 0.5-2.8 dB.

For e-commerce platforms such as Taobao and Amazon, advertisers play an important role in the entire digital ecosystem: their behaviors explicitly influence users' browsing and shopping experience; more importantly, advertiser's expenditure on advertising constitutes a primary source of platform revenue. Therefore, providing better services for advertisers is essential for the long-term prosperity for e-commerce platforms. To achieve this goal, the ad platform needs to have an in-depth understanding of advertisers in terms of both their marketing intents and satisfaction over the advertising performance, based on which further optimization could be carried out to service the advertisers in the correct direction. In this paper, we propose a novel Deep Satisfaction Prediction Network (DSPN), which models advertiser intent and satisfaction simultaneously. It employs a two-stage network structure where advertiser intent vector and satisfaction are jointly learned by considering the features of advertiser's action information and advertising performance indicators. Experiments on an Alibaba advertisement dataset and online evaluations show that our proposed DSPN outperforms state-of-the-art baselines and has stable performance in terms of AUC in the online environment. Further analyses show that DSPN not only predicts advertisers' satisfaction accurately but also learns an explainable advertiser intent, revealing the opportunities to optimize the advertising performance further.

Ground-roll is a common coherent noise in land seismic records. It has a low frequency, low velocity, and, yet, strong energy, which often conceals important information about reflections. Various approaches were proposed to suppress or remove ground-roll from reflections. The main difficulty of this task is the accurate separation of the ground-roll and reflections without damaging the morphological structure and frequency characteristics of both waves. In this article, we directly aim at the separation in the low-frequency band, where ground-roll and reflections are overlapped, and the recovery of low-frequency reflections deteriorated by ground-roll noise. First, we explore the morphological self-similarity of different frequency bands in seismic data and then utilize this similarity to synthesize pseudolow-band reflections from higher frequency band reflections that contain no ground-roll contamination. After the pseudolow-band reflections are generated, the pattern coding method is then applied to learn patterns from pseudolow-band reflections. The learned pattern dictionary is used to reconstruct the low-band reflections from the mixture of ground-roll and low-band reflections. After the whole scheme, recovered low-band reflections and clean reflections in other frequency bands are combined to form the recovered reflections. Detailed analysis is conducted to illustrate the validity of the scheme, and experiments on both synthetic data and real-land records show promising results.

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.

The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots' reconstruction. The spatial reciprocity of Green's function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization.

In the field of exploration geophysics, vibroseis system is one of the widely used seismic sources to acquire seismic data. “Ringing effect” is a common phenomenon in vibroseis data due to the limited frequency bandwidth of the vibroseis system, which degrades the performance of automatic first-break picking. In this letter, we proposed a deringing method for vibroseis data using a deep convolutional neural network (CNN). In this method, we use end-to-end network structure to obtain the deringed data directly and skip connections to improve model training performance and preserve the details of vibroseis data. For real vibroseis data processing, train data set is first generated from the data to be processed. We extract seismic wavelet and pseudoreflectivity series from real vibroseis data and use them to synthesize training data, which resembles real data. Pseudoreflectivity series with a broader frequency range is used as a training label. Experiments are conducted both on synthetic and real vibroseis data. The experiment results show that deep CNN-based method can attenuate the ringing effect effectively and expand the bandwidth of vibroseis data. The short-time average/long-time average ratio method for first-break picking also shows improvement on deringed vibroseis data.

The Radon transform (RT) has been widely used as a powerful tool, especially in exploration geophysics fields, such as multiple removal, interpolation, and velocity analysis. However, the existing strong outlier effects can seriously decrease the accuracy of the traditional RT. Therefore, a robust time-invariant RT (TIRT) is proposed in the mixed time-frequency domain to attenuate the outlier effects by using double L1-norm sparse constraints performed on the data misfit and the Radon model in the time domain. For the TIRT, the forward RT and its adjoint can be implemented in the frequency domain efficiently. Only one matrix inversion for each frequency component is involved in all iterations to speed up the iterations. Then, the 1-D alternating split Bregman (ASB) algorithm is introduced and improved for 2-D Radon model updating efficiently. It involves matrix-vector multiplication operators and two proximity operators. These two proximity operators can guarantee the robustness and sparseness of the proposed method. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of the proposed method. The proposed method is also used for interpolation to decrease the trace interval. After interpolation, seismic data are more continuous with less serrations along the spatial direction and the frequency-wavenumber spectrum is more focused. The interpolated data have wider potential applications in improving the accuracy of the following seismic processing. It should be noted that the proposed robust and efficient RT can also be used in remote sensing and computerized tomography fields instead of the traditional RT.

Marine seismic data may be contaminated by external source interference noise (ESIN) in some cases. These ESINs can be suppressed automatically, provided we can localize these external sources correctly. In this paper, we propose an automatic method to localize the external sources using a density-based clustering method and then suppress the ESINs according to the sources. In a shot gather, the time delays between three randomly selected seismic traces are used to calculate the location of one potential external source directly. Since there are many seismic traces in one shot gather, we can get a lot of estimates of the external source locations. In general, some of these locations are falsely detected sources. Assuming that the location of the external source is fixed or slowly changes during one seismic shot acquisition, multiple true estimates of an external source location, which are obtained from different trace groups, should focus together. In contrast, the false locations are arbitrarily distributed. Therefore, a density-based clustering method is applied to obtain the final source location estimate. Since each potential source corresponds to one cluster, we find out the strongest ESIN corresponding to the cluster with maximum sample number to ensure the accuracy. After that, the detected ESIN is flattened and then extracted by singular value decomposition. This method is an iterative method, and in each iteration, one ESIN is suppressed. And the high-pass filter is optional to detect the weak ESINs and protect the valid signals. The synthetic data example and real field marine data example prove that the proposed method can localize the external sources accurately and suppress multiple ESINs effectively.

Deghosting is a critical step to improve the resolution of marine seismic data. For the frequency wavenumber (f-k) spectra of the original seismic data with ghosts, there always exist some low-SNR frequency components around the centers of the frequency notch bands, which are caused by the ghosts. In general, the traditional inverse filtering-based deghosting methods lack the ability to recover these low-SNR frequency components without amplifying the additive noise. In this letter, we propose a postprocessing method to enhance the deghosted seismic data by reconstructing these low-SNR frequency components. The proposed method includes two key steps. First, the low-SNR frequency components of the deghosted seismic data in the f-k domain are located adaptively by using both the original seismic data and its deghosted result. Second, the projection onto convex sets algorithm is introduced to reconstruct these low-SNR frequency components located in the previous step. To illustrate this, we use the proposed method to improve the deghosted results obtained by the non-Gaussianity maximization based f-k deghosting method. Applications on synthetic and real field marine data sets demonstrate the validity of the proposed method which can enhance the deghosted results significantly.

The time-frequency analysis tools, which are very useful for anomaly identification, reservoir characterization, seismic data processing, and interpretation, are widely used in discrete signal analysis. Among these methods, the generalized S transform (GST) is more flexible, because its analytical window can be self-adjusted according to the local frequency components of the selected discrete signal, besides there exist another two adjustable parameters to make it superior to the S transform (ST). But the amplitude-preserving ability is a little poor near the boundary because the analytical windows do not satisfy the partition of unity, which is a sufficient condition for amplitude-preserving time-frequency transforms. In order to make the GST with the amplitude-preserving ability, we first design a new analytical window, and then propose an amplitude-preserving GST (APGST), but with a higher computational cost. To accelerate the APGST, we provide two strategies: the 3$\sigma$ criterion in the probability theory is introduced to accelerate the analytical windows summation and a convolution operator is derived to accelerate the time integral or summation, which generates an efficient APGST (EAPGST). Finally, the proposed EAPGST is used for seismic data attenuation compensation to improve the vertical resolution. Detailed numerical examples are used to demonstrate the validity of the proposed EAPGST in amplitude preserving and high efficiency. Field data attenuation compensation result further proves its successful application in improving the vertical resolution. Besides, the proposed EAPGST can be easily extended into other applications in discrete signal analysis, and remote-sensing and seismology fields.

Random noise in seismic data can affect the performance of reservoir characterization and interpretation, which makes denoising become an essential procedure. This letter focuses on suppressing random noise in poststack seismic data while preserving the edges of desired signals. Due to the lateral continuity of seismic data, polynomial fitting (PF) method can be a good alternative in attenuating random noise. However, discontinuities exist widely in poststack seismic data, which might be damaged by the PF filter. By contrast, principle component analysis (PCA)-based filters have better performance in edge preserving, but there appear artifacts in the denoised results using the PCA-based filters. Thus, we propose an edge-preserving polynomial PCA filter which combines advantages of the PF and PCA methods by optimizing a PCA problem with a weighted polynomial constraint. The weight coefficient is determined adaptively according to the signal-to-noise ratio estimation and the energy proportion in the selected analysis window, which can help distinguish the horizontal continuous events and the edges effectively. To deal with the complicated slopes which make the local linear hypothesis invalid, we introduce a robust local slope estimation method and apply the slope estimation-based event tracing strategy to horizontally align the data set. Synthetic and field data examples show that the proposed method has a better performance in noise attenuation and edge preserving, compared with the edge-preserving PF method. In addition, the denoised results are free from artifacts.

Multiple removal is one of the key steps in seismic data processing. In the surface-related multiple elimination method, the adaptive multiple subtraction technique is of great importance. In this paper, we propose a new pattern-based adaptive multiple subtraction method using the sparse coding technique (AMS-SC). By assuming that the multiples consist of different patterns from those of the primaries in the time-space domain, the proposed method first obtains some basis vectors, which represent the patterns of the multiples compactly, from the predicted multiples by sparse coding, and then estimates the multiples contained in the recorded seismic data using these basis vectors obtained in the previous step. Different from the traditional matching filter methods, which estimate the multiples by fitting the predicted multiples to the recorded seismic data directly, AMS-SC obtains the multiple estimations by reconstructing the recorded seismic data with the basis vectors obtained from the predicted multiples. Benefitting from sparse coding, AMS-SC is robust to the differences between the predicted and the true multiples, and preserves the primaries well. Applications on several data sets give some promising results of AMS-SC.

Classification of hyperspectral images usually suffers from high dimensionality and few reference data, which limits the performance of the pixelwise classifiers. The spectral-spatial classifiers, which integrate the spectral data and the spatial information during the classification, perform impressively in terms of the high classification accuracy and the homogeneous appearance of the classification map. In this paper, we propose a new probabilistic framework for spectral-spatial classification (PFSSC), which integrates the spectral data and the spatial information from the probabilistic point of view. Both the spectral data and the spatial information are used to estimate the per-pixel probability, which gives the likelihood that one pixel belongs to one class, respectively. The classification map can then be directly derived from the joint probability. In the proposed framework, a pixelwise probabilistic classifier can be extended as a spectral-spatial one since it can integrate spatial information easily. Furthermore, these spectral-spatial classifiers in the proposed framework are realized in an iterative way to avoid the problem caused by the limited reference data to some extent. In each iterative step, some unassigned pixels are classified by considering the pixels assigned in previous iterative steps. In this iterative process, pixels are assigned to specific labels step by step gradually. In the proposed framework, the probabilistic support vector machine (SVM) and random forest (RF) are extended to be two spectral-spatial classifiers. In short, we denote them as SVM-PFSSC and RF-PFSSC, respectively. The experimental results show that SVM-PFSSC and RF-PFSSC outperform some pixelwise and spectral-spatial classifiers.

The L1linear estimator which is used to solve the linear problem by minimizing the L1norm in the data-fitting term does better than traditional least square (LS) methods in applications where the residual vector is super-Gaussian or contains outliers. We propose a fast L1linear estimation algorithm by first translating the L1norm data-fitting problem into a L1norm regularized L2norm data-fitting problem and then solving the equivalent problem by fast iterative shrinkage-thresholding algorithm (FISTA). The method of the equivalence is carefully chosen and designed to achieve sufficiently low computational complexity of each FISTA iteration. The commonly used iterative reweighted least square (IRLS) algorithm is used as a benchmark in this letter. In comparison with IRLS, our numerical experiments show that the proposed algorithm is 5-11 times faster when achieving the same estimation accuracy. To demonstrate the performance of the proposed algorithm, we apply it on seismic predictive deconvolution. Both synthetic and real field data examples show that our method outperforms the IRLS-based and the traditional LS-based seismic predictive deconvolution method.

An iterative algorithm is presented for blind channel estimation of a nonminimum phase system using the zero-lag slice (ZS) of its third-order moment (TOM) only. The proposed method has simple computations because it is performed by using simple one-dimensional (1-D) operations with fast convergency and needs calculation of the ZS only. Furthermore, our method achieves good results since the ZS estimate obtained from the received signal exhibits high reliability. Simulations verify the good performance of our method in relatively lower signal-to-noise ratios (SNRs) and when there is a channel length mismatch.

Singular value decomposition (SVD) is an efficient tool for separation of signal and noise subspace. When it is used to process seismic image, SVD can enhance the signal-to-noise ratio (SNR) of horizontal events effectively. An adaptive SVD filter is proposed to enhance the non-horizontal events by detecting seismic image texture direction and then adjusting the input matrix of SVD. The features derived from the co-occurrence matrix are used to detect the texture direction. The parameter of the SVD filter is designed by the ratio of the stacking energy along the detected direction and the energy of the whole image adaptively. The coherent noise events are recognized by their direction difference from the signal events and attenuated by high-rank approximation firstly. Then the signal events are enhanced by low-rank approximation.

A novel localized two-dimensional (2-D) filter is proposed. The proposed filter derived from the frequency-wavenumber filter and Radon transform filter, with the filtering operation applied at the stage of Fourier projection, has good local property and less filtering distortion. An example of the proposed method to attenuate linear coherent noise in a seismic image is given. Comparisons of the results between our method and the conventional 2-D filters (including frequency-wavenumber filter and Radon transform filter) show that the new method outperforms both frequency-wavenumber method and Radon transform method.