Amplitude variation with angle (AVA) prestack seismic inversion plays a critical role in oil and gas exploration and mineral resource assessment. Recently, deep learning methods, particularly convolutional neural networks (CNNs), have been widely adopted for seismic inversion. However, many of these methods, especially supervised learning, struggle with poor generalization and noise resistance. Seismic data contains rich texture information that can be used as prior to constrain the convolutional kernels of the network. Gabor functions have long been used for seismic data representation, and learnable Gabor filters improve upon this by dynamically extracting latent seismic data information via adaptively updating Gabor filter parameters. In this letter, we propose a multitask AVA inversion method using learnable Gabor filters within a 2-D multitask attention U-Net. We equip the network’s first layer with learnable Gabor filters for latent seismic data feature extraction to enhance both generalization and noise resistance. An adaptive weight update method (AWUM) is employed to balance multitask learning efficiency and generalization performance. By creating a training dataset that combines synthetic and field seismic data with corresponding labels, we integrate field samples into the network training. Experiments for both synthetic and field datasets demonstrate that the proposed method exhibits superior generalization and stability compared to several existing approaches.

Seismic data denoising is essential for subsequent inversion and interpretation tasks. However, most existing methods rely on loss functions that assume seismic noise follows an independent and identically distributed (i.i.d.) Gaussian distribution, which does not align with the characteristics of actual seismic noise. In this paper, we first analyze the principle of the L2norm loss function in suppressing i.i.d. Gaussian noise from the maximum a posteriori (MAP) perspective, and then introduce the Mixture of Gaussians (MoG) model to handle non-i.i.d. noise suppression. Additionally, we optimize the MoG model using the Expectation-Maximization (EM) algorithm for improved performance. We propose a novel approach, DIP-MoG, which integrates the Deep Image Prior (DIP) with the MoG model for enhanced denoising. To validate the performance of DIP-MoG, we conduct experiments on two synthetic datasets contaminated with a mixture of Gaussian noise and field noise, as well as a field seismic dataset. The results from both synthetic and field data demonstrate the superior denoising performance of DIP-MoG.

In seismic data interpretation, accurate delineation of faults is crucial for subsurface hydrocarbon resource exploration and production. Traditional manual interpretation is time-consuming, labor-intensive and subjective. Deep learning has been widely studied for automatic fault detection in recent years. U-Net and its variants dominate the network structures for the excellent performance in terms of accuracy and generalizability, however, often require significant computational resources and memory usage. For conventional U-Nets, they usually need large channel number at each layer for diverse feature extraction. As multiple channels may capture similar features, this may lead to feature redundancy and a waste for memory and computing resource. To mitigate this problem, we propose a lightweight 3D fault detection neural network, LightUNetFault3D, which contains Global Spatial Convolution Module (GSCM) and Semantic Difference Module (SDM), which dramatically decreases channel number at both encoding and decoding side of U-Net. In the encoding stage, GSCM is used to improve the ability to capture long-range features by introducing additional global spatial information. In the decoding stage, SDM containing difference and fusion operations is used instead of original skip connection. Difference is conducive to extracting boundary features in seismic data, which are closely related to fault detection. Fusion performs weighted summation of differential features from encoder and decoder instead of concatenation. These two modules greatly improve the efficacy of feature extraction for the task of fault detection and a small number of channels is used in LightUNetFault3D. Consequently, the capacity and Floating-Point Operations Per Second (FLOPs) of LightUNetFault3D are only 15% and 9% of the baseline FaultSeg3D model. Meanwhile, LightUNetFault3D still achieves continuous fine fault structures on field dataset tests.

Coherent noise suppression in Common Reflection Point (CRP) gather is a crucial task in seismic data processing. The valid signals in CRP gathers are horizontally aligned which can be represented effectively by low-rank approaches but not the coherent noise. Leveraging this characteristic, we propose a neural network low rank approximation method for CRP gather coherent noise suppression. Specifically, to increase the self-similarity between adjacent traces in CRP gather, we first use plane-wave structural prediction operator to flatten seismic events within a local neighboring window. Subsequently, a fully connected neural network with low rank regularization is used to approximate the locally flattened seismic data. Moreover, a transfer learning strategy is employed to improve the efficiency of multiple seismic gather processing.blueOn two field CRP gathers, the proposed method achieves the lowest local similarity (LS) values of 0.0328 and 0.0629, compared with both state-of-the-art (SOTA) and traditional methods. The denoising results on both synthetic and field data demonstrate the effectiveness of the proposed method both in attenuating coherent noise and protecting valid signals.

Full waveform inversion (FWI) is pivotal for exploring subsurface structures and physical parameters. However, classical FWI methods often experience challenges like cycle skipping and non-linearity, necessitating accurate initial velocity models. Pure data-driven approaches based on deep learning are constrained by limited real labeled data and inadequate generalization, hindering practical applications. To address these issues, we propose an unsupervised physics-informed machine learning FWI with low-rank implicit neural representation (termed LR-IFWI), which utilizes a low-rank matrix factorization parameterized by coordinate-based neural networks, continuously and compactly representing the velocity model by implicitly encoding low-rank properties and smoothness. Our method has three crucial advantages: (i) LR-IFWI considerably improves inversion accuracy and shows steadier inversion convergence behavior; (ii) LR-IFWI can reduce the number of iterations for comparable inversion accuracy, improving efficiency attributed to the compact low-rank representation; (iii) LR-IFWI has better robustness, alleviating the dependence on the initial models and improving noise resistance due to the physical constraints and low-rank neural representation. Numerical tests on the two-dimensional Marmousi model demonstrate that LR-IFWI achieves efficient and accurate inversion with fewer iterations and greater precision when utilizing smooth, linear, and random initial velocity models. Further experiments with noisy seismic data, missing low-frequency components, and more challenging velocity models, such as 2D SEG/EAGE Salt and Overthrust models, highlight its robustness and generalization.

Seismic data inevitably suffers from random noise due to environmental contributors, which seriously affects subsequent processing and analysis. Deep learning has been a successful tool for seismic data random noise attenuation. Due to the scarcity of clean labels in real scenarios, researchers have attached more attention to self-supervised methods without paired training data. However, most self-supervised methods are costly in computations and thus are inefficient for practical large data volume implementation. In this paper, we propose a novel self-supervised method for seismic random noise attenuation by designing a Kolmogorov-Arnold network (KAN)-empowered neural low-rank representation (NLRR) method. Specifically, the proposed method adopts a compact tensor factorization parameterized by implicit neural representations to efficiently encode both low-rank and smooth priors of seismic data into the model. Moreover, we introduce generalized KANs by using multiple sinusoidal activation functions with different frequencies, serving as factor functions of NLRR to empower its representation ability. Extensive experiments on synthetic and field seismic data demonstrate the clear superiority of our method in terms of efficiency and efficacy over several traditional and deep learning-based methods for random noise attenuation. Specifically, our method reduces over 90% execution time against existing self-supervised methods while still achieving evidently better denoising results.

Seismic inversion is crucial for oil and gas exploration. Recently, the development of deep learning (DL) provides new means for the continuous improvement of seismic inversion. However, field seismic data exhibits non-stationarity and multi-scale features due to wavelet attenuation and dominant frequency variations. Although atrous spatial pyramid pooling (ASPP) module concatenated of dilated convolution greatly facilitates the multi-scale feature learning ability of network, the adjustment of dilation rate, which is a hyperparameter, requires ample ablation experiments, and is a tedious and time-consuming process. To alleviate these issues, the stacked multiple deformable convolution (DConv) layers are employed as the feature extraction module to adaptively capture the multi-scale correspondence between seismic data and elastic parameters in multitask seismic inversion. The sampling grids of DConv can automatically be modulated by adding an learnable offset. Thus DConv can provides flexible and effective receptive field, which is conducive to aggregating pivotal information of seismic data and improving the inversion accuracy. To further enhance the reliability and stability, the proposed method incorporates multi-trace to single-trace (M2S) strategy and the closed-loop wasserstein generative adversarial network with gradient penalty (WGAN-GP) framework. Experiments show that the application of DConv to the inversion of P-wave velocity (Vp) and density (ρ) yield superior transverse continuity and vertical resolution. Compared with ASPP, the MSE of the predicted profiles and the true models in synthetic Marmousi2 experiment is degraded by 36% and 32% respectively, and the MSE of the reconstructed seismic data and the real data is reduced by an order of magnitude for the field test.

Seismic wavefield simulation is crucial for acquisition design, inversion, and interpretation in seismic exploration. The essence of seismic wavefield simulation is to solve wave equations. A physics-informed neural network (PINN) provides an alternative approach to solving partial differential equations and shows great potential for various geophysical problems. However, the accuracy of PINN-based seismic wavefield simulation is unsatisfactory due to spectral bias. Multiscale Fourier feature mapping (MFFM) has been shown to be effective in enhancing the accuracy of simulation results. This letter proposes a modified MFFM PINN for solving the Helmholtz wave equation to further improve the accuracy of seismic wavefield simulation. An auxiliary network is used to determine the initial hyperparameter value for the multiscale feature range in MFFM using the velocity model as input. The hyperparameter is fine-tuned by allowing it to be learnable during the subsequent training process of the neural network. In addition, activation functions with learnable frequencies are proposed for use in all hidden layers. Experiment results demonstrate that the proposed method automatically determines the optimal hyperparameter for accurate wavefield simulation efficiently.

Prestack seismic data amplitude variation with angle (AVA) inversion is critical in identifying oil and gas reservoirs. Recently, deep learning (DL) has gained significant popularity in AVA multi-parameter inversion, often employing one-dimensional (1-D) network on a trace-by-trace basis. However, the limited availability of well log data (label) and the inability of 1-D network to capture spatial features result in predictions with inadequate lateral stablity and structural consistency. At the same time, the adoption of multiple single task learning strategy leads to weak efficiency and generalization in multi-parameter inversion. To address these challenges, we propose InverMulT-STP, a 2-D multitask closed-loop Transformer with synthetic data style transfer pretraining for prestack AVA inversion. The proposed semi-supervised learning paradigm combines multitask learning and transfer learning strategies to improve prestack AVA inversion. Specifically, the multitask closed-loop Transformer (InverMulT) utilizes a Transformer-based encoder-decoder architecture to extract comprehensive spatial structure information from angle gathers, enabling simultaneous and accurate multi-parameter inversion. We enhance the cycle consistency loss and introduce Learned Perceptual Image Patch Similarity (LPIPS) as the criterion to achieve more detailed structures in the inversion results. To make balance on the inversion of different parameters, an adaptive weight update method (AWUM) is introduced for the weighting of each task in loss functions. To improve generalization on field data, neural style transfer (NST) is employed to generate the realistic synthetic dataset for network pretraining. From both synthetic and field data experiments, the inversion results show that the proposed method outperforms several existing DL inversion methods and commercial software.

Seismic inversion is crucial in estimating subsurface properties in the oil and gas industry. However, the limited well-log data obtained in production is primarily one-dimensional (1D) data, leading to the dominant of 1D trace-to-trace inversion methods. Inherently, these algorithms do not take seismic data spatial correlation into consideration, resulting in unstable results with poor lateral continuity. Obtaining high-precision multi-parameter inversion results simultaneously for prestack inversion remains a challenge. To address these issues, this work proposes a 2D Multi-task Full Attention U-Net for prestack three-parameter inversion. The proposed network captures geological structural features through shared information and allows each task to learn task-specific attention weights in separate branches. The full attention mechanism fuses shared and internal features of each task and pays attention to both channels and feature maps. A joint hybrid loss function based on mean squared error and structural similarity is used to enhance the continuity and resolution of inversion results. To obtain sufficient training samples, we generate small sample patches by sliding windows both laterally and vertically around the wells. We also incorporate initial models and feed them into the network together with seismic data as input to achieve stable inversion results. Experiments on field data demonstrate that the proposed approach can simultaneously obtain high-resolution and transversely continuous three-parameter inversion results.

In recent years, deep learning methods have made great achievements in seismic impedance inversion, and Convolutional Neural Networks (CNNs) become one of dominating framework relying on extracting local features effectively. In fact, the elastic parameters temporal correlation consists of local and global dependencies, with the latter as a general trend in the vertical direction due to gravity and diagenesis. Therefore, considering the excellent performance in capturing global dependencies by Self-attention of Transformer, we propose a Transformer and CNN hybrid neural network (Trans-CNN) to combine convolution and Self-attention for diverse feature extraction. Then, a combination of self-supervised and supervised learning is adapted under multi-task framework to train the network. We first perform experiments on the synthetic model, which show Trans-CNN has better inversion than comparable networks. We then test on a field data and demonstrate that the proposed network can obtain stable inversion results with better horizontal continuity and vertical resolution.

Noise suppression is crucial for seismic data processing and interpretation. Both the supervised and self-supervised methods need to construct training data pairs, which is challenging for practical implementations. In this research, we propose an unsupervised denoising framework based on improved blind spot strategy, which operates directly on single noisy seismic data. Firstly, a global masker is introduced to mask the noisy data to obtain two masked data and input them into the denoising network, and then utilize the mask mapper to integrate all blind spots onto the same channel. Secondly, original noisy data is incorporated into the network training process to avoid information loss. Finally, a hybrid loss function with orthogonal convolution regularization constraint is adopted to further improve the performance of the network. Synthetic and field seismic data experiments show that the proposed method can make good balance between noise suppression and valid signals preservation.

Due to various reasons, seismic data are often inevitably affected by noise. Therefore, random noise suppression of seismic data is a key step for seismic data processing workflow. Recently, deep learning method has performed well in seismic data denoising. In this study, we propose a self-supervised deep learning seismic data noise attenuation method. We introduced an effective Blind2Unblind (B2U) denoising framework, which can complete denoising using only a single noisy seismic data. Use a mask mapper with global awareness, which can sample all pixels at the blind spots on noisy data and map them to a same channel. At the same time, a re-visible loss function is used to train the network, which can optimize all blind spots, mitigating the information loss and retaining more details of geological structure. The denoising experiments on synthetic and field data show that our method has achieved superior results compared with previous work.

Seismic elastic parameter inversion enables the transformation of seismic data into subsurface structures and physical parameters of formations. However, due to the intricate geological structure, deep learning methods have been discovered to produce more precise inversion results than traditional methods. Nevertheless, inverting multiple elastic parameters individually is both time-consuming and prone to causing significant errors for the ignorance of interconnections among the parameters. Therefore, multi-task learning is employed in this work. To further improve the inversion accuracy, a hybrid network leveraging the advantages of Fully Convolutional Residual Network (FCRN) and Gated Recurrent Unit Network (GRU) is proposed for the simultaneous inversion of the velocity of P-wave and density, named Multi-task FCRN and GRU (MFG). FCRN is responsible for the efficient extraction of local information from the seismic data, while GRU captures the global dependencies in the data along time. To be mentioned, an auxiliary task of seismic data reconstruction has been added as a regularization technique to enhance the stability of network training. The experimental results obtained using both synthetic model and field data indicate that MFG significantly enhances the inversion accuracy, lateral continuity, and vertical resolution.

Tumor classification based on microarray gene expression data is easy to fall into overfitting because such data are composed of many irrelevant, redundant, and noisy genes. Traditional gene selection methods cannot achieve satisfactory classification results. In this study, we propose a novel multi-target hybrid gene selection method named RMOGA (ReliefF Multi-Objective Genetic Algorithm), which aims to select a few genes and obtain good tumor recognition accuracy. RMOGA consists of two phases. Firstly, ReliefF is used to select the top 5% subset of genes from the original datasets. Secondly, a multi-objective genetic algorithm searches for the optimal gene subset from the gene subset obtained by the ReliefF method. To verify the validity of RMOGA, we conducted extensive experiments on 11 available microarray datasets and compared the proposed method with other previous methods. Two classical classifiers including Naive Bayes and Support Vector Machine were used to measure the classification performance of all comparison methods. Experimental results show that the RMOGA algorithm can yield significantly better results than previous state-of-the-art methods in terms of classification accuracy and the number of selected genes.

Deep learning has been widely used in seismic inversion. Since the label data obtained in production is actually a small amount of one-dimensional (1D) well-log data, most deep learning based seismic inversion is 1D trace-to-trace method based on poststack seismic data. However, the 1D algorithm does not take seismic data spatial correlation into consideration and the results lack of stability with good lateral continuity. Meanwhile, it is still a challenge to obtain high-precision multi-parameter inversion results simultaneously for prestack inversion. To mitigate the above issues, we propose a 2D Multi-task Full Attention U-Net for prestack three-parameter inversion. The proposed network can capture geological structural features in shared information and allow each task to automatically learn task-specific attention weights in a separate branch. The full attention mechanism fuses the shared features and the internal features of each task in stages, and pays attention in both channels and feature maps. Moreover, a joint hybrid loss function based on mean squared error and structural similarity is used to further enhance the continuity and resolution of inversion results. To obtain sufficient training samples, we generate a large number of small sample patches by sliding window both laterally and vertically with equidistant around the wells. In order to obtain stable inversion results, we incorporate the initial models and feed them into the network together with seismic data as input. Experiments on synthetic and field data show that our proposed method can simultaneously obtain three-parameter inversion results with high vertical resolution and transverse continuity.

Seismic fault interpretation is of extraordinary significant for hydrocarbon reservoir characterization and drilling hazard mitigation. In recent years, deep learning-based seismic fault detection methods have been conducted actively. Considering efficiency and fault prediction consistency, the most appealing way is to train a 3D segmentation network using synthetic seismic data with ground truth fault structure. However, the differences in signal-to-noise ratio, resolution, and fault strike distribution between synthetic and real data, can lead to inconsistent and unreliable prediction results. In this paper, we propose a multi-task deep learning-based seismic fault detection method, which takes seismic fault detection as the main task and 3D seismic data reconstruction as the auxiliary task, named MTL-FaultNet. The auxiliary branch can provide suggestive information to the main branch thereby improving its performance. We also designed two levels of multi-scale modules and embedded attention mechanisms in the network, so as to improve the network’s ability to focus on multi-scale fault features and learn stable fault structures. Different weights are assigned to the loss for different tasks, with large and small weights on the main and the auxiliary branch respectively. We apply the proposed method to Netherlands offshore F3 seismic data and a land field seismic data collected from Tarim Basin with mainly strike-slip faults, and Poseidon 3D seismic data. The proposed fault detection method is experimentally demonstrated on the improved network generalization and achieves reliable fault interpretation on field seismic data.

Seismic data often undergoes severe noise due to environmental factors, which seriously affects subsequent applications. Traditional hand-crafted denoisers such as filters and regularizations utilize interpretable domain knowledge to design generalizable denoising techniques, while their representation capacities may be inferior to deep learning denoisers, which can learn complex and representative denoising mappings from abundant training pairs. However, due to the scarcity of high-quality training pairs, deep learning denoisers may sustain some generalization issues over various scenarios. In this work, we propose a self-supervised method that combines the capacities of deep denoiser and the generalization abilities of hand-crafted regularization for seismic data random noise attenuation. Specifically, we leverage the Self2Self (S2S) learning framework with a trace-wise masking strategy for seismic data denoising by solely using the observed noisy data. Parallelly, we suggest the weighted total variation (WTV) to further capture the horizontal local smooth structure of seismic data. Our method, dubbed as S2S-WTV, enjoys both high representation abilities brought from the self-supervised deep network and good generalization abilities of the hand-crafted WTV regularizer and the self-supervised nature. Therefore, our method can more effectively and stably remove the random noise and preserve the details and edges of the clean signal. To tackle the S2S-WTV optimization model, we introduce an alternating direction multiplier method (ADMM)-based algorithm. Extensive experiments on synthetic and field noisy seismic data demonstrate the effectiveness of our method as compared with state-of-the-art traditional and deep learning-based seismic data denoising methods.

Noise suppression for seismic data can meliorate the quality of many subsequent geophysical tasks. In this work, we propose a novel self-supervised learning method, the deep nonlocal regularizer (DNLR), for 3D seismic denoising. Our DNLR fully exploits the nonlocal self-similarity of seismic data under a self-supervised learning framework for noise attenuation. It can be flexibly combined with different hand-crafted regularizers, e.g., total variation, nuclear norm, and correlated total variation, by performing the regularizer on nonlocal self-similar patches, which more effectively characterizes the intrinsic structures underlying seismic data. Our DNLR can be easily plugged into existing self-supervised denoising methods, e.g., deep image prior and Self2Self, and consistently improve their performance. To make the optimization model tractable, an algorithm based on the alternating direction multiplier method is introduced to solve the DNLR-based seismic denoising problem. Extensive seismic denoising experiments on synthetic and field data validate the superior performances of our DNLR as compared with state-of-the-art model-based and deep learning seismic denoising methods. Code is available at https://github.com/XuZitai/DNLR.

Missing trace reconstruction is a basic step in seismic data processing workflow. Recently, many deep learning based seismic data reconstruction methods have been proposed. However, lack of label data can impair the performance for practical applications due to domain gaps on seismic data prior. In this research, we propose a “Missing-As-Complete” (MAC) strategy for training networks to solve the problem of missing labels in practical situation. Specially, the missing seismic data is directly taken as the “complete” target. While the input is seismic data consisted of missing trace and a second missing trace mask. A hybrid loss function FFL+SSIM +L1based on the focal frequency loss (FFL), structural similarity (SSIM) and L1norm is used to further improve the reconstruction performance. Experiments on synthetic data demonstrate that the network can reconstruct reasonable results by the proposed method.

Deep learning has achieved promising results in predicting impedance inversion from seismic data. The volume of seismic data, especially 3D seismic data, is very large. Therefore, it is particularly important to improve the accuracy while ensuring the model efficiency for practicability and follow-up research. In this paper, we present Residual Attention Net (ResANet), a CNN with residual modules and two attention mechanisms: channel-wise attention and feature-map attention, for seismic impedance inversion. The proposed network can fuse multi-scale channel information and recalibrate channel-wise feature responses as well as receptive fields adaptively. At the same time, we adopt grouped convolution to improve the computation. Marmousi2 model test results show that our network outperforms several state-of-the-art neural network models in accuracy and stability with superior efficiency for seismic data impedance inversion.

Seismic inversion is a process to obtain the spatial structure and physical properties of underground rock formations by using surface acquired seismic data, constrained by known geological laws, drilling and logging data. The principle of seismic inversion based on deep learning is to learn the mapping between seismic data and rock properties by training a neural network using logging data as labels. However, due to high cost, the number of logging curves are often limited, leading to a trained model with poor generalization. Multi-task learning (MTL) provides an effective way to mitigate this problem. Learning multiple related tasks at the same time can improve the generalization ability of the model, thereby improving the performance of the main task on the same amount of labeled data. However, the performance of multi-task learning is highly dependent on the relative weights for the loss of each task, and manual tuning of the weights is often time-consuming and laborious. In this paper, a method based on homoscedastic uncertainty of the Bayesian model is used to balance the weights of the loss function for multiple tasks, and a Fully convolutional residual network (FCRN) is used to achieve seismic impedance inversion and seismic data reconstruction simultaneously. The test results on the synthetic dataset of Marmousi2 model show that the proposed method can automatically determine the approximate optimal weight of the two tasks, and predicts impedance with higher accuracy than single-task FCRN model.

Due to the constraints of natural environments, acquired prestack seismic data is usually not complete, which seriously affects subsequent seismic data processing. With the progress of deep learning, many neural networks with different structures have been applied to missing seismic data interpolation. Among them, U-net can efficiently interpolate the regularly and irregularly missing seismic traces with small gap. While for consecutively missing seismic traces with big gap, the interpolation results for low amplitude missing components need to be further improved. In this letter, we analyze the variation of interpolation results for consecutively missing seismic traces during the traditional U-net training process, and find that U-net tends to only interpolate the high amplitude missing components. Meanwhile, due to the distribution difference between low and high amplitude seismic data, one U-net model is insufficient to interpolate both high and low amplitude missing components with a wide amplitude range. To improve the interpolation results of single U-net, we propose a multistage training process to train multiple U-net models. Each U-net model focuses on interpolating different missing components with a small amplitude range. In this way, more accurate interpolation results for low amplitude missing components can be obtained. Comparison experiments conducted on synthetic and field seismic data show that, under the same number of training epochs, the proposed training process can produce more accurate interpolation results comparing with traditional single U-net.

Missing traces interpolation is a basic step in the seismic data processing workflow. Recently, many seismic data interpolation methods based on different neural networks have been proposed. The existing research shows that when the seismic data are consecutively missing, the larger gap for missing traces, the more difficult task of interpolation, due to convolution operation in the neural network can only capture local relations. In this letter, we incorporate the coordinate attention block to the Unet for 2-D successive missing traces interpolation. The hybrid loss function combined with structural similarity (SSIM) and$\text {L}_{ {1}}$norm is used as the loss function to further improve the interpolation performance of the designed network. Comparison experiments on 2-D synthetic and field seismic data show that the interpolation results obtained by the proposed method are more accurate and reasonable compared with Unet and Unets equipped state-of-the-art similar modules.

Deep-learning methods, such as convolutional neural networks (CNNs), have been successfully applied to seismic impedance inversion in recent years. Compared with traditional geophysical inversion, deep-learning inversion can give inversion results with higher resolution. In this letter, we further improve the performance of deep-learning inversion and propose a seismic impedance inversion method based on conditional generative adversarial network (cGAN). In the proposed method, a generator learns to predict seismic impedance from seismic data, and a discriminator learns to distinguish between fake and real impedance. We mix the cGAN objective with mean square error (MSE) loss to bring in more information for model training. Besides, a CNN-based seismic forward model is trained to introduce the constraint of unlabeled data in the training of cGAN. Tests on Marmousi2 model and overthrust model show that the proposed method can obtain more accurate impedance and have better robustness against random noise than CNN method.

Denoising is an indispensable step in seismic data processing. Deep-learning-based seismic data denoising has been recently attracting attentions due to its outstanding performance. In this letter, we investigate the architecture of deep Convolutional Networks (ConvNets) for seismic data denoising. The untrained ConvNets are served as a generative network to a single seismic data profile with Gaussian noise. Starting with random initialized parameters, the generative networks with various handcrafted architectures have different ability to map the seismic data at iterations and can separate the Gaussian noise as residuals. For the purpose of exploring the ability of Gaussian noise separation, the depth, width, and skip connection as the main components of generative network are assembled as various architectures to fit Gaussian noise, clean, and noisy seismic data, respectively. Then, the favorable network architecture with high and low impedance (an ability to hinder data reconstruction) to noise and seismic data is adopted as prior model to seismic data denoising task. Furthermore, a stopping criterion is designed for the data fitting process to obtain the latent clean seismic data automatically. The proposed method does not need data sets for training and it makes use of network architecture as prior. Extensive experiments both on synthetic and field data demonstrate the effectiveness of the selected ConvNet and the advantages are evaluated by comparing the denoising results with f-x multi-channel singular spectrum analysis (MSSA) and state-of-the-art unsupervised neural network (NN)-based method.

Fault detection is a crucial task in seismic structure interpretation. Convolutional neural network (CNN)-based methods, in general, require large amount of labeled data for network training. One way to build the labeled data is to create synthetic seismic images with corresponding fault labels. However, it is hard to ensure that the synthetic data have the same fault feature distributions as the field data, which may lead to inaccurate and unreliable prediction results. Another way is to manually label the faults, which is time-consuming and subjective. In this letter, we propose that using knowledge distillation (KD) to improve the performance of fault detection by integrating the features from large number of synthetic samples and a small number of field samples. We distill knowledge from an ensemble of two teacher CNNs to train a student CNN (applied to final target) for seismic fault detection. In our work, one segmentation teacher CNN is trained on synthetic samples with known ground truth fault labels and another classification teacher CNN is trained on field samples with manually picked labels. Then, a classification student network is trained on samples generated by voting the results from two teacher models. The student CNN learns not only the general fault characteristics in the synthetic data but also the specific fault features of the target field data. Test on the field data shows that the student CNN highlights seismic fault more accurately with higher resolution than the teacher CNNs.

Deep learning has achieved promising results for impedance inversion via seismic data. Generally, these networks, composed of convolution layers and residual blocks, tend to deliver good results with deep architectures. Nevertheless, deep networks accompany a large number of parameters and longer training time. The volume of seismic data, especially 3D scenarios, is very large. Therefore, it is particularly important to improve the accuracy while ensuring the model efficiency for practical implementation. With the flourishing new modules and techniques, deep learning has set the state-of-the-art in many applications across wide range of scientific and engineering disciplines. In this paper, we present Residual Attention Network (ResANet), a CNN incorporating with residual modules and two attention mechanisms: channel-wise attention and feature-map attention, for seismic impedance inversion. The proposed network can fuse multi-scale channel information and recalibrate channel-wise feature responses as well as receptive fields adaptively. At the same time, ResANet adopts grouped convolution, dilated convolution and dropout techniques to improve the computation efficiency and stability. Marmousi2 synthetic model and field data test results show that the proposed network outperforms several comparable neural networks in accuracy and generalization ability while ensuring efficiency for seismic data impedance inversion. For the field data test, transfer learning is also evoked to further improve the performance. ResANet tends to predict impedance with high resolution and strong lateral continuity compare with three closely related networks. The accuracy of ResANet is improved by 1 to 2 orders of magnitude on the 6 well logs provided in field dataset tests compare with commercial software (InverTrace Plus module in Jason) using Constrained Sparse Spike Inversion (CSSI) method.

Missing trace reconstruction is an essential step in the seismic data processing. Various interpolation methods have been proposed for handling this issue. In recent years, deep learning-based interpolation techniques, especially convolutional neural networks (CNNs), have been widely studied. Typically, these studies target regularly/randomly missing cases, leaving consecutively missing situations not handled properly. In this article, we propose a hybrid loss function$\text {SSIM}+L_{1}$, based on structural similarity (SSIM) and$L_{1}$norm, for network training and attention mechanism as a network component that explicitly utilizes global information. We further design a CNN equipped with the hybrid loss and attention mechanism for successively missing trace reconstruction. Experiments on synthetic and field data demonstrate that our network can reconstruct more reasonable results than networks without attention mechanism in large gap situation and$\text {SSIM}+L_{1}$loss promotes interpolation results. We also discuss the setup of key hyperparameters of the network by a thorough ablation study.

Semblance velocity analysis plays an indispensable role in seismic data processing. In order to avoid the huge time-cost when performed manually, some deep learning methods are proposed for automatic velocity picking from semblance. However, the application of existing deep learning methods is still restricted by the shortage of labels in practice. To solve this problem, we take semblance velocity analysis as a point-to-point regression problem at each time sample. A time window on semblance which can extract the block corresponding to a time-velocity (t-v) pair and the reference velocity curve (RVC) which can transform semblance randomly are employed together to augment the labeled data. We divide the development of data augmentation strategy into three progressive modes. The datasets from three modes are prepared for training designed attention neural network. The field experiments show that the attention neural network can produce reasonable results and the data augmentation strategy can effectively improve the velocity picking accuracy.

The numerical solution of wave equation is the computational engine of many high-precision imaging and inversion methods in seismic exploration. Conventional methods generally use uniform gird to discrete medium. The discretization sampling method based on the minimum model velocity is easy to bring over-sampling in high speed region. We propose a frequency-domain trapezoid grid finite difference method to improve the efficiency of acoustical wavefield modeling. Numerical tests on Marmousi model show that compared with regular grid average-derivative 9-point frequency domain finite difference scheme, our method can achieve almost 5 times faster computation with comparable accuracy. Dispersion analysis is also given for further optimization of difference coefficients.

Landslide susceptibility mapping is a practical approach for identifying landslide-prone areas. In this letter, we apply a semisupervised learning method, positive unlabeled-bagging (PU-bagging) to generate a landslide susceptibility map over a study area from the Loess Plateau in North-Central China. PU-bagging deals with the lack of negative samples in a training set and uses only positive and unlabeled samples. We prove the effectiveness of our approach by comparing the PU-bagging decision tree (DT) generated landslide susceptibility map with the ground truth (known landslide locations), as well as by comparing its performance with three widely used models (logistic regression, support vector machine, and artificial neural network). The promising results and the fact that the method is general urge us to believe that the PU-bagging should be able to perform in other landslide-prone areas where only positive samples are provided.

Deep learning methods have been successfully applied to solve seismic inversion problems in recent years. Though deep learning inversion can obtain results with much higher resolution compared to geophysical inversion, its performance often suffers from the limitation of the well logs which are main source of labels in training data. To overcome this problem, we propose a semi-supervised deep learning workflow based on Generative Adversarial Network (GAN) for seismic impedance inversion. The workflow contains three networks: a generator, a discriminator, and a forward model. The training of the generator and discriminator are guided by well logs and constrained by unlabeled data via the forward model. Test on Marmousi2 model shows that, by making use of both labeled and unlabeled data, the proposed method predicts impedance with better consistency than conventional deep learning inversion.

To better reveal time-varying spectral components of nonstationary seismic signals, time-frequency analysis (TFA) has been widely applied in seismic processing and analysis. In this letter, we propose an advanced seismic TFA method based on an optimal spectral mode separation and an adaptive wavelet bank design. The proposed adaptive mode separation-based wavelet transform (AMSWT) generates a superior time-frequency resolution. In addition, because the wavelet bank is adaptively built on the intrinsic spectral modes, the ability to accurately characterize geophysical structures has been significantly improved. To demonstrate the effectiveness of the proposed AMSWT method, we apply it on both synthetic and field data. Compared with the results from continuous wavelet transform (CWT), empirical mode decomposition (EMD), variational mode decomposition (VMD), and empirical wavelet transform (EWT), AMSWT provides a higher resolution and offers potentials in precisely highlighting stratigraphy boundaries.

In[1], the grant number in the first footnote for the National Postdoctoral Program for Innovative Talents should be BX20190279.

In this letter, we use a fully convolutional residual network (FCRN) for seismic impedance inversion. After training with appropriate data, the FCRN can effectively predict impedance with high accuracy, and have good robustness against noise and phase difference. However, it cannot give acceptable results in training and predicting models with different geological features. Transfer learning is later introduced to ease this problem. Marmousi2 and Overthrust models are used to verify the effectiveness of the proposed method. Tests show that after fine-tuned by five traces of Overthrust model, the FCRN trained on the Marmousi2 model can give a comparable result similarly predicted by the FCRN trained purely on the Overthrust model.

Traffic noise is often coupled with seismic signals when seismic data are acquired close to the road. The traffic noise usually exhibits high amplitudes in the recorded seismic profile, and it is a challenging task to remove it. In this article, we propose a workflow to attenuate seismic traffic noise using the${l}_{p}$-norm robust principal component analysis (RPCA). This method is implemented in the frequency domain, where the${l}_{p}$-norm RPCA is applied to each frequency slice and results in a low-rank approximation of seismic reflections. The alternating direction method of multipliers (ADMM) algorithm is included in the implementation for efficiency. The proposed workflow is demonstrated on a 3-D field shot gather contaminated by complex traffic noise. The performance indicates that our method can remove strong traffic noise effectively and, in turn, accentuate the seismic reflections with balanced amplitudes.

To deal with the rigid template matching problem in real-world scenarios, we propose a novel iterative feature-pair updating framework which is also robust to high levels of outliers, such as background changing, complex nonrigid deformation and partial occlusion. Given a pair of template image and target image, we first extract a set of corresponding feature-pairs as candidates. Then, we propose a robust objective function under the iterative framework for discriminatively updating these candidates, where the space distance, appearance distance, and the overlapping percentage of feature pairs are integrated simultaneously. Finally, a hierarchical matching strategy is provided with the parameter discussion. Experimental results compared with the-state-of-art methods on public data sets demonstrate the effectiveness of the proposed method.