Seismic fault detection is one of the key steps for seismic structure interpretation, potential reservoir prediction, and geological hazard forecasting. Currently, the most prevalent methods involve training deep learning (DL) models to accelerate seismic fault detection. Although many DL-based fault detection methods have been proposed, most rely solely on seismic amplitude to train convolutional neural networks (CNNs). Consequently, they often struggle to accurately interpret faults in regions with low data quality or complicated structures. We propose the Dip integrated Spatial-Spectral UFormer (DSSUF) with the Auxiliary Semi-DSSUF Module (ASM) to improve the fault detection performance by integrating seismic reflector dip as an extra input. The proposed DSSUF is embedded with the Spatial-Spectral Augmentation Transformer (SSAT) block, the pixel shuffle and unshuffle, and a Dual-Dimension Reduction Module (DRM). By integrating DSSUF with ASM, our model can effectively extract features from seismic data and dip. The proposed method fuses features extracted from two input data by defining the hybrid loss function containing a supervised constraint and a feature constraint. We then evaluate the proposed DSSUF with ASM by applying it to synthetic blind test data and two 3-D field data. Quantitative and qualitative comparisons between baseline methods and our method indicate that the DSSUF with ASM provides accurate and continuous fault detection results. Applications on two field data also illustrate the excellent generalization performance of the proposed method.

Deep learning (DL) has been widely used to enhance the efficiency and accuracy of seismic facies classification. However, most DL-based seismic facies classification methods rely only on seismic amplitudes and require substantial labeled training data. We propose the Unconformity-enhanced Hierarchical Context Fusion Network (UHCFNet), which uses seismic unconformity attribute to increase the accuracy of seismic facies classification and reduce the amount of data required for model training. We first calculate the seismic unconformity attribute to highlight potential seismic facies boundaries. We then propose the UHCFNet by combining the Hierarchical Context Fusion Network (HCFNet) with an unconformity guiding branch to integrate the unconformity attribute as an additional constraint. The unconformity guiding branch incorporates the unconformity-aware Transformer block (UTB) to extract unconformity features. Next, we validate the performance of our proposed UHCFNet by applying it and two baseline DL models to the Netherlands F3 field data. Quantitative and qualitative comparisons illustrate that our proposed model provides more accurate seismic facies classification results than baseline DL models, especially for regions with complicated structures and minority facies with fewer seismic samples. Moreover, to further demonstrate the robustness of our UHCFNet, we train the proposed model and baseline DL models using only 5% of the original training dataset. Comparisons between different models indicate that our proposed UHCFNet has a lower dependency on large datasets, as the UHCFNet still provides accurate seismic facies classifications for regions with complicated structures with limited training data.

Seismic fault delineation and parameter prediction, including fault dip and strike, are vital for subsurface structure modeling, hazard assessment, and resource exploration. Although numerous deep learning-based methods have been developed for fault interpretation, there are few methods designed for fault parameter interpretation. The main reason is that extracting accurate fault parameter labels from the fault location label is a difficult task, especially for conjugate faults and dense fault systems. To address this issue, we propose a workflow for automatically generating 3-D synthetic seismic datasets with fault location, dip, and strike labels by using seismic reflection features from field data to enhance the realism of synthetic data. Afterward, we build the Dual U-shape Domain Fusion-Net (DUDF-Net), which is embedded with a multi-scale feature fusion block that integrates Haar wavelet transform and 3-D axial convolution to effectively fuse voxel and frequency-domain features, overcoming the limitations of spatial-domain-only approaches. Finally, we train the DUDF-Net using the generated synthetic dataset, and apply the well-trained model to the blind test synthetic dataset and two field seismic surveys. Both quantitative and qualitative comparisons between our method and baseline models illustrate that the DUDF-Net generates more accurate and robust results for fault delineation and parameter interpretation, especially for conjugate faults and dense fault systems.

Seismic horizon picking is vital in seismic interpretation, forming the foundation for reservoir exploration and seismic inversion. Traditional horizon picking methods heavily depend on geologists’ experience, making the process time-consuming, labor-intensive, and prone to subjective interpretation. The emergence of deep learning (DL) offers new solutions for horizon picking. However, conventional DL models often struggle to segment seismic horizons accurately when faced with limited training samples and low-quality labels. To address these issues, we suggest a geological simulation modeling approach to generate synthetic data sets with field features for model training. Afterward, we suggest an adaptive weighted feature fusion multi-task LSTM (AWFF-MT-LSTM) network, which treats horizon picking as two tasks, i.e., stratigraphic boundary segmentation and target waveform detection. Moreover, we propose the AWFF layer that balances the relationship between two tasks and shares feature information across two tasks to enhance model convergence speed. Finally, we apply our methods to field data to validate their feasibility.

The stratigraphic sequence correlation of well logs is a crucial step for reservoir investigation. The manual interpretation is a commonly used method, and the experience of geophysicists influences it. Recently, deep learning (DL) has been introduced for automated stratigraphic correlation of well logs. However, building a complete training dataset with high-quality labels is challenging and time-consuming. In this study, we propose an automated stratigraphic sequence correlation method called OMP-KANFormer, which integrates the Kolmogorov-Arnold network with the transformer (KANFormer) model with orthogonal matching pursuit (OMP)-based data augmentation. To solve the problem of training dataset generation, we first propose a data augmentation algorithm based on OMP to simulate waveform features and generate a large number of synthetic well logs as training data. We suggest combining the KANFormer to accurately segment the stratigraphic. The KAN effectively models complex nonlinear relationships, while the transformer excels at capturing long-range dependencies in the features of well logs. Finally, we apply the proposed data augmentation method and KANFormer to a well-log dataset, demonstrating their validity and effectiveness via a comprehensive ablation study and comparisons with widely used SegNet and U-Net.

Seismic facies classification is crucial in interpreting subsurface geological structures for oil and gas exploration. Traditional methods for seismic facies classification usually rely on handcrafted features and heuristic rules, limiting their ability to capture complex geological patterns. We suggest a label-integrated and VMD-augmented transformer (LIVAT) to address these issues, which refers to transformers’ embedding stage infused with seismic facies labels and uses variational mode decomposition (VMD) to augment training data. Four advanced time-series transformer models are selected to verify the effectiveness of our proposed label-integrated embedding and VMD-augmentation on F3 Netherlands and New Zealand Parihaka datasets. Moreover, we evaluate the performance of LIVAT by comparing it with convolutional neural networks (CNNs) and bidirectional long short-term networks (BiLSTM) in few-shot learning. Experimental results demonstrate that LIVAT achieves superior classification accuracy and outperforms existing deep learning methods, showcasing its potential as a powerful tool for automatic seismic facies interpretation.

Horizon picking is of paramount importance in seismic interpretation because it has a significant impact on subsequent interpretation and inversion. Although manual and various automatic interpretation methods have been widely used for horizon picking, they still have several problems, such as being time-consuming and highly dependent on human experience. Recently, deep-learning (DL) methods have been implemented to solve these problems. However, traditional convolutional neural networks (CNNs) have a shortage of capturing global features, and vision transformers, recently proposed, aim to address this. To segment the seismic horizon accurately, we suggest a dense inception transformer (DIFormer) by combining the dense extreme inception network (DexiNet) and the inception transformer network. When implementing model training with the patch technique, the DIFormer can retrieve more information and interpret horizons smoothly. Furthermore, we utilize multiple attributes computed from seismic data to train basic DIFormer models and then adopt ensemble learning to obtain the fusion model, that is the ensemble DIFormer (EDIFormer). We implement qualitative and quantitative analyses to verify the effectiveness of the suggested model and compare it with the state-of-the-art (SOTA) SegFormer and basic DIFormer trained with a single attribute in trace- and patch-based modes.

With the rise of deep learning (DL), there are kinds of DL-based models proposed for addressing seismic data reconstruction, especially convolutional neural network (CNN)-based methods. However, most of these models are supervised, which require a large amount of training data and ground-truth labels that are difficult to obtain in real applications. We propose the polarity-constrained dual-cycle generative adversarial networks (PCDC-GANs) for reconstructing the irregularly sampled seismic data. We first adopt a traditional generative adversarial networks (GANs) framework as the base model, integrating with a dual-cycle mechanism. Instead of the conventional generator network, we suggest a self-prior generator that uses the prior information extracted by the generator in the first stage to enhance the reconstruction performance, i.e., the mask data of the irregularly sampled seismic data. In addition, we introduce polarity constraints to promote the recovery of sampled seismic traces, amplifying the model’s sensitivity to the locations of missing traces. Furthermore, our model incorporates various loss functions to promote its convergence. Numerical experiments on synthetic and field data show that our PCDC-GANs can reconstruct irregularly sampled seismic data more accurately than the SuperstarGAN and CycleGANs, and achieve comparable performance to the supervised U-Net.

Suppressing random noise is an effective way to improve the signal-to-noise ratio (SNR) of seismic data. Supervised deep learning methods have recently been widely applied to seismic image denoising. However, these methods require a large amount of noise-free data to train the network, which is unavailable in practical applications. Moreover, most of these denoising methods focus on removing random noise, assuming that the noise is zero-mean and independent of seismic signals. In field applications, real seismic noise often exhibits band-limited and spatial correlations. We propose an unsupervised learning method to train a denoising network using only noisy images, termed Pixel-shuffle Down-sampling and Visible Blind-Spots (PD-VBS). First, we propose to utilize Pixel-shuffle Down-sampling (PD) to destroy the spatial correlation of real seismic noise, followed by feeding the data into the blind-spots network. Next, we introduce additional input derived from the input data with a finer stride PD to compensate for the information loss induced by both the blind-spots network and PD mechanisms. Experimental results on both synthetic and field data show that our proposed PD-VBS can effectively remove noise while preserving valid signals, compared with traditional denoising methods and state-of-the-art deep learning models.

S-transform (ST) and its generalized versions are commonly used for seismic data processing and interpretation. Nevertheless, these transforms have several unavoidable drawbacks, including parameter selection and the Heisenberg uncertainty principle’s restriction. To overcome these drawbacks, we suggest a cycle-consistent generalized ST network (CGSTN), inspired by sparse-based transforms. The CGSTN contains four main modules, i.e., two generators and two discriminators. The forward generator is trained to convert a seismic trace into a 2-D high-resolution time–frequency (TF) spectrum, while the inverse generator is trained to reconstruct the seismic trace based on the generated TF spectrum provided by the forward generator. Similarly, one discriminator is trained to distinguish whether the TF spectrum generated by the forward generator is a true TF spectrum or not, while the other is utilized to distinguish the seismic trace generated by the inverse generator. After model training, we apply the well-trained CGSTN to a 3-D field data volume acquired in the Ordos Basin, Northwest China. The results show that the CGSTN can obtain the TF spectrum with higher resolution than the contrastive methods, benefiting further reservoir delineation.

Seismic fault interpretation is a crucial task for hydrocarbon reservoir characterization, CO2geological storage, and geothermal energy evaluation. Deep learning (DL)-based methods have been conducted to accelerate seismic fault interpretation and studies have shown that the most practicable way is to train neural networks using synthetic data with ground truth labels. However, synthetic and field data are different in local seismic structures, seismic reflection characteristics, and seismic fault features. These differences would lead to the poor generalization of DL-based methods and unreliable fault predictions. We propose an automatic fault interpretation method with the aid of the Data-, Physics-, and Math-assisted synthetic data generation, including the Data-assisted module, the Physics-assisted module, and the Math-assisted module. The Data-assisted module provides structural features and reflection characteristics of seismic events. The Physics-assisted module provides seismic fault features from physical experiments. The Math-assisted module generates realistic synthetic data and ground truth fault labels based on the extracted features. We then propose the Multi-scale Attention-based Convolutional Neural Network (MSACNN), by combining a simplified deeplab module and attention mechanism. Finally, we train the MSACNN using the generated synthetic dataset. To illustrate the validity and generalization of the proposed model, we apply it to synthetic data and two 3D real seismic volumes. The superiority of the proposed method is experimentally demonstrated with the qualitative and quantitative comparisons of fault interpretation results using different methods.

Deep learning (DL) has been widely used for various geological tasks but not much for seismic unconformity estimation because of the limited labeled training data. We propose the physical knowledge constrained synthetic data generation workflow for building the synthetic training dataset, which mainly contains the Data-assisted module, the Physics-assisted module, and the Math-assisted module. The Data-assisted module is used to extract geometry and reflection features of seismic events from field data. The Physics-assisted module is used to provide geological knowledge related to seismic unconformity and define the unconformity geometry criteria for simulating unconformities in synthetic seismic images. The Math-assisted module is used to modify extracted features, create synthetic seismic images, and generate unconformity labels with the aid of the Data- and Physics-assisted modules. Therefore, incorporating these three modules makes the synthetic seismic datasets closely resemble field data. The synthetic datasets are used to train the DL model that we proposed, named ECA-UNet++, which integrates the UNet++ with the Transformer block and efficient channel attention (ECA). To validate the performance of our proposed method, we apply it to synthetic data and two 3-D field data. The results demonstrate the effectiveness of our proposed method for accurate and efficient seismic unconformity estimation, even when trained exclusively on synthetic data. Furthermore, we integrate the estimated unconformity results into seismic facies analysis, indicating that our method benefits other seismic interpretation tasks.

Sparse coding (SC) has been proven effective in various geological tasks, such as seismic time-frequency (TF) analysis and seismic reflection inversion. Nevertheless, it inevitably has several drawbacks, e.g., low computational efficiency and difficulty in parameter selection. Recently, self-supervised learning (SSL) has emerged as a promising alternative to mitigate these issues, offering high computational effectiveness and requiring fewer labels. We suggest a generalized physically driven workflow for geophysical inversion based on SSL and SC, named the physically driven SSL network (PDSSLNet). This generalized PDSSLNet model comprises two main modules. One is the inverse model, generated by convolutional neural networks (CNNs), which can benefit from their high computational effectiveness and strong nonlinear fitting ability. The other one is the forward model based on the SC theory, ensuring the physical meaning of the geophysical applications with high accuracy. Afterward, we provide two typical geological inversion cases to demonstrate the validity and effectiveness of the suggested PDSSLNet, including sparse TF analysis and seismic reflectivity inversion. Three-dimensional (3D) field data volume applications confirm that the proposed inversion workflow may efficiently circumvent the drawbacks of the conventional SC-based approach while maintaining excellent computing efficiency.

Seismic attenuation, parameterized as quality factor Q, holds great significance in enhancing seismic resolution and reservoir characterization. Most methods for estimating Q values are performed in the frequency domain, however, the frequency spectrum of the seismic data may usually be influenced by the closely adjacent reflections and the seismic noise, leading to an unreliable Q estimation. To address this challenge, we propose a kernel-based regression method for Q estimation on manifolds. This supervised learning model computes the kernel function on the tangent space of the manifold. We apply this method to Euclidean space, Spherical manifold, and Wasserstein spaces, and provide a detailed comparison of their performance. Our experimental results using synthetic data demonstrate a significant improvement in both robustness and accuracy compared to conventional methods. Furthermore, the validation of our methodology using real data confirms its effectiveness and superiority. Notably, our method on Wasserstein space consistently outperforms others in all experiments.

Seismic frequency attributes are commonly used for describing geological structures and characterizing complex reservoirs. Although there are different kinds of machine learning based methods proposed, how to select appropriate attributes and how to map them to reservoir thickness is still an open issue. In this study, we suggest an adaptive multi-frequency attribute analysis (AMFAA)-based workflow to address these issues. We first utilize a generalized S-transform to extract multi-frequency attributes, which can describe local time-frequency features of seismic data. Then, we propose a sensitive attribute analysis method to reduce frequency attribute redundancy with the aid of hierarchical clustering and correlation analysis. Afterward, based on the selected sensitive attributes, we propose to adopt the potential of heat diffusion for affinity-based transition embedding (PHATE) for multi-frequency attribute analysis, which can map seismic multi-frequency attributes to reservoir thickness. To test the validity and effectiveness of our method, we first apply it to a synthetic wedge model and then post-stack field data in the Ordos Basin, Northwest China.

Object part parsing involves segmenting objects into semantic parts, which has drawn great attention recently. The current methods ignore the specific hierarchical structure of the object, which can be used as strong prior knowledge. To address this, we propose the Hierarchical Dual Transformer (HDTR) to explore the contribution of the typical structural priors of the object parts. HDTR first generates the pyramid multi-granularity pixel representations under the supervision of the object part parsing maps at different semantic levels and then assigns each region an initial part embedding. Moreover, HDTR generates an edge pixel representation to extend the capability of the network to capture detailed information. Afterward, we design a Hierarchical Part Transformer to upgrade the part embeddings to their hierarchical counterparts with the assistance of the multi-granularity pixel representations. Next, we propose a Hierarchical Pixel Transformer to infer the hierarchical information from the part embeddings to enrich the pixel representations. Note that both transformer decoders rely on the structural relations between object parts, i.e., dependency, composition, and decomposition relations. The experiments on five large-scale datasets, i.e., LaPa, CelebAMask-HQ, CIHP, LIP and Pascal Animal, demonstrate that our method sets a new state-of-the-art performance for object part parsing.

Multifrequency attribute analysis is an effective tool to delineate sand bodies with different thicknesses. Conventionally, red–green–blue (RGB) blending technique is often used to fuse three frequency components for depicting reservoir thicknesses, that is, the low-, medium-, and high-frequency components. However, the seismic signal is a typically broadband signal, while RGB blending can only fuse three frequency components. Moreover, how to select these three specific frequency components is also a difficult and unsolved task. In this study, we suggest a multifrequency attribute analysis workflow for delineating sand bodies. First, we introduce the S-transform (ST) to extract multifrequency components of the analyzed seismic data. Then, the t-distributed stochastic neighbor embedding (t-SNE)-based workflow for fusing multifrequency components is proposed, which is used to capture the local structural features of the analyzed high-dimensional data and reveal the global structures simultaneously. Afterward, we adopt a synthetic trace and a 3-D field data volume to test the effectiveness of the proposed workflow. Compared with the contrastive methods, our workflow performs better in delineating the spatial distribution and thicknesses of sand bodies, which benefits further well deployment.

The bilinear based method is one of the commonly used tools in time-frequency analysis (TFA) fields. However, it suffers from the trade-off of high resolution and cross-term interference. We propose WVDNet, a semi-supervised learning model for time-frequency analysis based on the Wigner-Ville distribution (WVD), to reduce the cross-term existing in WVD and relax the requirements of the training data set. The proposed WVDNet is based on the Mean-Teacher model to enable the task model to exploit the unlabeled training data. We first build a synthetic data set for model training, that contains different kinds of amplitude-modulated and frequency-modulated (AM-FM) signals. Next, a task model of WVDNet is designed and the consistency regularization based method is utilized to promote model training. Finally, experiments are conducted on both synthetic and real-world data, showing the effectiveness of suppressing cross-term and strong generalization ability.

Time-frequency analysis (TFA) is widely used to describe local time-frequency (TF) features of seismic data. Among the commonly used TFA tools, sparse TFA (STFA) is an excellent one, which can obtain a TF spectrum with good readability. However, many STFA algorithms suffer from expensive calculation time and unavoidable prior knowledge, such as the iterative shrinkage-thresholding algorithm (ISTA) and the sparse reconstruction by separable approximation (SpaRSA). Inspired by the unrolled algorithm and its successful applications in signal processing, we propose a deep learning-based ISTA unrolled algorithm, which is named the sparse time-frequency analysis network (STFANet). The STFANet contains two parts, i.e., the sparse time-frequency spectrum generator and the reconstruction module. The former learns how to transform a one-dimensional (1D) seismic signal from a large amount of unlabelled data into a two-dimensional (2D) sparse time-frequency spectrum, which is implemented based on the proposed unrolled iterative dynamic shrinkage-thresholding (UIDST) algorithm. Note that the UIDST algorithm is carried out by using a simplified deep learning network. The latter serves as a physical constraint of model training to ensure that our generator obtains an accurate TF spectrum, which is actually an inverse time-frequency transform. In this study, the traditional inverse short-time Fourier transform (STFT) is utilized in the reconstruction module. To test the effectiveness of the proposed model, we apply it to 3D post-stack field data. The results show that, compared with the traditional TFA tools, the STFANet can availably compute time-frequency spectrum with better readability, which benefits seismic attenuation delineation.

The stratigraphic correlation of well logs is crucial for characterizing subsurface reservoirs. However, due to the complexity of well logs and the huge amount of well data, manual correlation is time- and resource-intensive. Hence, various computerized stratigraphic correlation methods have been developed, especially regarding convolutional neural networks (CNNs). Recently, Transformer, a self-attention system that evolved from Natural Language Processing (NLP), has attained state-of-the-art performance over CNNs in a variety of domains because of its ability to perceive global features. We propose the Axial and Sliding window based attention with High-resolution Transformer (ASHFormer), combining the High-Resolution Network (HRNet) with an Axial and Sliding window self-attention Block (ASBlock) intended for stratigraphic correlation of well logs. ASBlock includes three different forms of Multi-Head Self-Attentions (MHSA), including sliding-window attention, horizontal-axis attention, and vertical-axis attention, therefore, it is possible to retrieve well logs’ long-range and local information. The experiments show that ASHFormer predicts more accurate stratigraphic correlation results than HRNet and CMT (a Transformer combining CNN and self-attention). The usefulness of the Transformer for well log feature extraction and automatic stratigraphic correlation is demonstrated by ASHFormer’s 9.74% improvement in correlation accuracy over HRNet with the same architecture.

Random noise attenuation is a crucial task in seismic data processing, which can not only improve the signal-to-noise ratio (SNR) of seismic data, but also facilitate accurate geological interpretation. Recently, deep learning (DL) has emerged as a powerful technique for seismic data noise suppression. However, most of the related works are based on supervised learning. To reduce the cost and complexity of constructing noise-free seismic data as training labels, this study focuses on a self-supervised deep learning method with the dropout strategy. By considering the Bayesian deep network, our proposed approach trains a denoising network with random weights, which predicts the noise-free seismic data from noisy seismic data. The experimental results of synthetic and field data illustrate the superiority and robustness of the self-supervised Bayesian Neural Network (BNN) model for seismic data denoising. Compared with the traditional denoising schemes and several state-of-the-art DL models, our method can effectively enhance the lateral continuity of seismic events and preserve the geological structure information while improving the SNR. We believe that this provides a solid foundation for the subsequent seismic data processing and interpretation.

Random noise attenuation is an essential procedure of seismic data processing, which is crucial to improve the signal-to-noise ratio (SNR) of seismic data. Recently, deep learning (DL) has emerged as a promising tool for seismic data denoising. Although the DL-based method has excellent learning and representation capabilities, it lacks the interpretability of the traditional hand-crafted denoisers. Furthermore, supervised learning involved in most of the previous work is usually not feasible to construct a great amount of noisy/noise-free training data pairs for real applications. We develop a total variation (TV) regularized self-supervised Bayesian deep learning model, dubbed as TVRBNN, which combines the advantages of Bayesian deep neural network (BNN) and TV regularization techniques for seismic random noise suppression. The significant characteristic of the proposed model is that it does not rely on the ground-truth seismic data as training labels and solely utilizes the observed noisy data to train TVRBNN. Synthetic and field experiments are implemented to verify the effectiveness of the TVRBNN model in seismic data denoising. Compared with the classical non-learning denoising approaches and the state-of-the-art self-supervised DL model, TVRBNN can effectively enhance the lateral continuity of seismic events and preserve the geological structure information while effectively removing random noise.

Seismic facies classification plays an important role in oil and gas reservoir interpretation. In the past few years, convolution neural network (CNN)-based models have been widely used in supervised seismic facies classification. However, to improve some inherent limitations of CNNs, it is significant to explore alternative architectures, such as the Transformer with the self-attention mechanism. In this study, based on the Segformer, a cutting-edge semantic segmentation Transformer, we propose a U-shaped model of joint the Segformer and the Hypercolumn representation for seismic facies classification, named U-Segformer-Hyper. As the emerging lightweight variant of the Transformer for seismic facies segmentation, the proposed U-Segformer-Hyper consists of a specific encoder–decoder–hypercolumns scheme, which can extract various features in different layers and fuse the output features of different layers with different scales. In the application of the public F3 seismic data, compared with the CNN Benchmark model, the U-Segformer-Hyper model has fewer parameters, fewer floating-point operations per second (FLOPS), and higher accuracy of classification in both the section-based and patch-based training modes. Moreover, the proposed U-Segformer-Hyper is open source, which benefits to further explore alternative deep models in seismic interpretation.

High-resolution seismic data allows us to better characterize the reservoir and detect the hydrocarbon. To improve the resolution of seismic data, in this article, we extend the conventional S transform to Hyperbolic spaces, and propose a hyperbolic spaces S transform (HS transform) and its deformed reconstruction. By considering the seismic signal as an element of hyperbolic spaces, the HS transform performs the time–frequency (TF) decomposition of the data in Hyperbolic space and the reconstruction in Euclidean space. The whole process from the TF decomposition to the reconstruction gives a natural nonlinear transformation to the spectrum of the original signal. By investigating the analytical relationship between the spectra of the original signal and its deformed reconstruction, we then propose the frequency-dependent curvature HS transform, which allows a desired change in the spectrum of the seismic data. By performing such decomposition and reconstructing iteratively, the final deformed reconstruction of the seismic data will have a broad and whitened band, and the resolution of the seismic data can be enhanced. The effectiveness of our proposed method is demonstrated through the comparison with the Wiener filter in the synthetic and field data examples. The significant advantage of our method is that it is nondeconvolutional, and requires no information about the seismic wavelet.

Time–frequency analysis (TFA) technology plays a significant role in seismic signal processing. The time–frequency representation (TFR) calculated using the TFA method is helpful for the localization of time-varying frequencies within the signal. Nevertheless, limited by the Heisenberg uncertainty principle, traditional linear TFA methods always provide blurred TFRs, which makes them difficult to distinguish details of time–frequency structures. Recently, the synchrosqueezing transform (SST) was designed to improve the concentration of the TFR. The SST can provide a much concentrated TFR for the weakly frequency-modulated (FM) signal, but it is not effective for the interpretation of strongly FM signals, such as the thin interbed in seismic exploration. In this work, we propose a new tool by introducing the multi-synchrosqueezing operator to the frame of wavelet transform (WT). Employing an iterative operator to correct the frequency estimation of the original SST step-by-step, it thus can calculate a TFR with better concentration and robustness. Synthetic signals and a field seismic data are employed to verify the performance of the proposed method for characterizing the time-varying frequency features.

We propose a novel seismic signal processing approach to efficiently and effectively attenuate seismic random noises. The proposed approach is a generalized seismic noise attenuation solution that can be applied to typical denoising operators. Our work has two main contributions. First, conventional filtering operators “regularize” the denoised results through the operator design. However, as seismic data have strong nonstationarity, it is inevitable to remove certain signal components. The resampling mechanism alleviates the signal loss. Second, the resampling operation does not require a lot of parameter tuning, which improves the denoising efficiency. Using the proposed approach, compared with existing denoising operators, the intrinsic seismic signal components are better recovered since random noise has been suppressed. Synthetic example and field data applications quantitatively and qualitatively demonstrate excellent performances of the proposed approach.

Microseismic event picking is one of the key steps in seismic processing and imaging. Manually picking is a widely used way to pick the microseismic events, which is time-consuming. The standard short-term average/long-term average (STA/LTA) is a traditional method to pick the microseismic first arrivals, which would lead to inaccurate first-arrival picks in case of low signal-to-noise ratio (SNR). We developed a workflow to automatically pick the microseismic first arrivals by using the feature pyramid networks (FPNs). To train the proposed model, we first randomly select part of the microseismic traces and manually pick the time index of the first arrivals. Next, we segment every selected trace into two parts based on the time index of the manual picking and then assign each part a label. Afterward, we train the proposed fine-tuning FPN model by using the training data and the corresponding labels. It should be noticed that we proposed a loss function, named the point-aware loss, for solving the microseismic first-arrival picking issue. Finally, we predict the microseismic first arrivals by using the well-trained fine-tuning FPN model. The numerical examples demonstrate that our proposed model successfully identifies the microseismic first arrivals. The microseismic first arrivals predicted by using our proposed model are more robust and more accurate than those obtained by using the STA/LTA and the encoder–decoder network.

Multi-frequency analysis is an effective tool for seismic data interpretation, such as fluvial channel characterization and sand bodies interpretation. Due to the broadband and non-stationary properties of seismic data, time-frequency transform is widely used for extracting multi-frequency components, e.g., S-transform and wavelet transform. However, how to fuse these extracted band-limited multi-frequency components for complex reservoir characterization is still a hot topic in exploration geophysics. In this study, we propose a multi-frequency analysis workflow for complex reservoir delineation based on the local tangent space alignment (LTSA). First, we utilize the generalized S-transform (GST) for extracting multi-frequency components, which is easy to implement and also a valid time-frequency analysis tool. Afterward, we adopt LTSA for blending the decomposed multi-frequency components. Finally, we apply the proposed workflow on a 3D post-stack field data for delineating complex carbonate reservoir. The results prove that the proposed workflow can effectively delineate carbonate reservoir, which is superior to the individual seismic attribute analysis and the contrastive blending method.

Seismic instantaneous frequency (IF), as one of the instantaneous attributes, is widely used for seismic interpretation and stratigraphy analysis. The Hilbert transform (HT)-based complex analysis approaches are commonly used to extract seismic IF, which are sensitive to kinds of noise contained in field data. Although the normalized HT (NHT) improves the antinoise property of HT by normalizing the original trace, the HT-based methods are a global operator that is not suitable for the local analysis. For example, IF calculated by using the HT-based method is unstable when meeting strong seismic events. In this letter, we propose a workflow to extract local IF (LIF) and then apply it to describe superposed sands. Note that the proposed workflow extracts a stable IF result even when processing a seismic trace with strong events. To demonstrate the effectiveness of the proposed workflow, we apply it to both synthetic and field data. Compared with results from HT and NHT, the proposed workflow provides a stable IF extraction and offers potentials in precisely highlighting superposed sands.

Seismic attenuation estimation is a significant task for characterizing reservoirs and improving the resolution of seismic data. The logarithmic spectral ratio (LSR) is one of the widely used tools for seismic attenuation estimation. However, how to select a suitable frequency bandwidth for the LSR is a difficult task, especially for field data. Moreover, field data are often contained kinds of noises, which makes seismic attenuation estimation difficult and unstable. We proposed an enhanced LSR (ELSR) workflow to estimate seismic attenuation. First, we built a sparse S-transform (SST) to obtain a sparse time-frequency (TF) spectrum of the analyzed seismic trace. Then, based on the SST spectrum, we introduced an ELSR workflow to estimate seismic attenuation. It should be noticed that we provided an adaptive frequency band selection for the LSR. To demonstrate the effectiveness of the proposed workflow, we apply it on both synthetic and field data. Compared with the results from several traditional attenuation estimation methods, the proposed ELSR provides a more stable and more accurate attenuation estimation result and offers the potentials in improving the resolution of post-stacked seismic data.

Geologic structure characterization is a key step for seismic structure interpretation, such as fluvial channels, faults, and fractures. The coherence attribute is a widely used tool for describing seismic discontinuities, which is usually calculated based on the similarity and dissimilarity of the adjacent seismic traces. However, accurately extracting coherence attribute is a difficult task in field data applications because seismic signal is one of the typical nonstationary, non-Gaussian, and wideband signals. To describe seismic discontinuities at different scales, we propose a workflow to extract the multiscale coherence (MSC) attribute. We first decompose seismic data into several band-limited intrinsic mode functions (IMFs) with different dominant frequencies via the multichannel variational mode decomposition (MVMD). Afterward, we develop a Cauchy kernel correlation-based coherence algorithm to extract the coherence attributes at different scales based on the decomposed IMFs. Finally, we can compute the MSC attribute by utilizing the calculated coherence attributes. Field data applications demonstrate that the proposed MSC attribute characterizes seismic discontinuities, such as faults and fluvial channels, more accurately and more clearly than the traditional coherence attribute and the 1-D variational mode decomposition (VMD)-based coherence attribute.

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.

In this letter, we concern the acoustic impedance (AI) inversion from the known reflectivity based on the increasingly mature deconvolution techniques. For seismic data with the complicated geological structures, we first construct the regularization model for the AI inversion with the proposed regularizer consisting of the total variation (TV) seminorm and the Frobenius norm of the Hessian. Second, we develop the split Bregman (SB) iterative algorithm in the frequency domain for solving the proposed model. Finally, we verify the effectiveness of our proposed method via synthetic and field data. Experimental results demonstrate that our proposed method can not only preserve the lateral continuity and the impedance interfaces of the inverted AI section well, but also provide a higher resolution impedance section than the other related methods.

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.

The time-frequency (TF) analysis method plays a significant role in the detection of natural gas hydrates. As a data-driven method, compressed sensing (CS) has been widely used in the TF methods due to the sparsity of the TF representation. This study proposes a data-driven TF method based on the CS theory and a non-convex regularization. In the implementation, a continuous wavelet transform (CWT) with a generalized beta wavelet (GBW) is formulated as an inverse problem based on the CS theory. The selection of appropriate parameters enables the GBW to match the seismic wavelets better than the widely used Morlet wavelet. The GBW can constitute a tight frame to reduce calculation time, particularly for large-scale field data processing. Additionally, the proposed TF method introduces the generalized minimax concave (GMC) penalty function as a non-convex regularization term. Compared with the classical sparse approximation method with$\ell _{1} $regularization, the GMC regularization term can enhance the sparsity in sparse inverse problems and ensure the convexity of sparse inversions. This article also presents an exponentially decreasing threshold scheme to adaptively select the regularization parameters. Three synthetic examples are investigated to demonstrate the performance of the proposed sparse TF representation with GMC regularization. Finally, the proposed TF method’s performance in detecting free gas of gas hydrates is validated using field seismic data obtained from the Blake Ridge.

Delineating seismic faults is one of the main steps in seismic structure interpretation. Recently, deep learning (DL) models are used to automatic seismic fault interpretation. For the DL-based models, there are two widely used techniques, which can enhance the model performance, that is, data augmentation (DA) and ensemble learning (EL). Qualitatively and quantificationally analyzing the performances of these two techniques is a rarely studied domain. In this study, we make detailed comparisons between the DL models using DA and EL. For the DL model with DA, we first build a holistically nested Unet (HUnet) model by adopting the holistically nested module to the widely used Unet model. Then, we train a HUnet model by using the original and its augmented synthetic datasets (HUnet-D model for short). Besides, we train a Unet model in the same way as a comparison (Unet-D model for short). On the other hand, for the DL model with EL, we first obtain several individual HUnet models separately trained by only using a type of the augmented datasets for each time. Next, we propose a data-driven EL model to integrate these HUnet models. Specially, we propose an adjoint-net module for the EL model to extract the multi-scale features from seismic data, which benefits for checking and fine-tuning the fusing results. Finally, we qualitatively and quantificationally evaluate these DL models (Unet-D, HUnet-D, and EL-HUnet) using the synthetic validation dataset. Moreover, we apply these models to 3-D field data volumes for automatic fault interpretation. Compared with the coherence attribute, Unet-D and HUnet-D models, we find that the EL-HUnet model achieves the comparable model performance for effectively enhancing the precision and continuity of the detected faults.

Traditional optimization algorithms are usually applied to estimate the elastic parameters of the subsurface by using field seismic data. However, these optimization algorithms highly depend on prior knowledge (e.g., the initial model setup and sparsity), leading to serious inversion uncertainties. Nowadays, with the rapid development of neural networks, convolutional neural networks (CNNs) have been widely imposed on estimating elastic parameters from field data. However, the deficiency of labeled seismic data impedes the CNNs application in seismic inversion. Moreover, both the size and diversity of labeled datasets are also critical factors influencing the accuracy and resolution of predicted parameters when using the CNNs-based inversion techniques. In this work, taking the unconventional tight sandstone formation as an example, we develop a geological and geophysical model driven CNNs (GGCNNs), named as GGCNNs. The proposed GGCNNs allow us to take advantage of both the prior geological information and basic geophysical model from the generated synthetic labeled prestack seismic datasets, representing essential characteristics of the subsurface. Moreover, under the consideration of data diversity, the GGCNNs model enables us to make a tradeoff between the inversion accuracy and labeled data size. Applications on both synthetic and field data clearly demonstrate the effectiveness of the proposed GGCNNs model for predicting elastic parameters by using prestack seismic data, i.e., its predicted results are with high accuracy in the vertical profile and continuity and smooth in the horizon slice.

Accurate estimation of petrophysical properties (e.g., porosity, clay volume) of subsurface rock from seismic data/elastic properties is significant to reservoir characterization. Conventional model-driven inversion strategies for estimating petrophysical parameters confront with the deficiency of prior knowledge. In contrast, machine learning-based approaches are adapted to account for reservoir parameter estimation through developing nonlinear mapping and quantifying uncertainty. However, most of the current researches mainly concentrates on the single parameter prediction with different neural network architectures, which, in turn, conflicts with the truth of coupling multiple reservoir properties. To quantify the sensitivity of input-output parameters and the effects of network architecture on the accuracy of petrophysical parameter inversion, we propose a CNN-based network strategy to estimate multiple reservoir parameters simultaneously. The results from both synthetic labeled data and field data and uncertainty analysis strongly demonstrate that SopenCNN, abbreviated from multiple input and single output openCNN, exhibits the highest prediction accuracy, while the cycleCNN with multiple input and multiple output, referred to as McycleCNN, is superior to the MopenCNN, which means that an openCNN contains multiple input and multiple output. It means that, for similar network architecture, the number of input and output parameters makes a significant impact on prediction accuracy. Moreover, for similar multiple inputs and outputs, the fine-tuning McycleCNN, parallelly updated in each intermediate closed-loop step, behaves much better accordingly. The application of the three workflows with varying architecture on field tight sandstone reservoirs demonstrates that network based inversion strategy could establish a mapping function to characterize spatially varying reservoir parameters.

Lithology interpretation is important for understanding subsurface properties. Yet, the common manual well log interpretation is usually with low efficiency and bad consistency. Therefore, the automatic well log interpretation tools based on machine learning and deep learning have been developed. Although the state-of-the-art sophisticated models can show fine interpretation performance with acceptable accuracies, “blind” tests do not always exhibit satisfactory results because of the complexity of lithology interpretation with respect to subsurface rock properties and the data-labeling quality. To solve this generalization challenge, we propose to leverage the parameterized quantum circuits in the deep-learning model. The quantum computing takes advantages of the superposition and entanglement quantum systems, which could potentially endow the generalization power or capability to the deep-learning model. Using the proposed quantum-enhanced deep-learning (QEDL) model, we have tested the model performance on field well log data from different wells. Compared with the classic fine convolutional neural network (CNN) model and the long short-term memory (LSTM) model, the proposed QEDL model achieves comparable model performance with a clearly improved generalization power for interpreting both thin and thick lithology layers. In addition, because of the quantum circuit structure, the QEDL model needs much fewer model parameters than LSTM and CNN models, i.e., the QEDL parameter number in our study can be approximately 75% less than that of LSTM and 89% less than that of CNN.

Ground roll, a source-generated surface wave, is a main type of coherent noise in a land seismic survey. Low-frequency and high-amplitude ground roll often overlays valid reflection events, resulting in obscuring seismic reflections. Ground-roll attenuation is an essential step for seismic data processing, which is based on the accurate separation of the ground roll and reflections without damaging their morphological characteristics. In this study, we effectively separate and suppress ground roll in shot gathers through a proposed workflow. We first identify the major components of the ground roll adopting the multichannel variational mode decomposition (MVMD), which shows significant improvements compared to the conventional single-channel VMD. Ground roll can be identified on the decomposed band-limited intrinsic mode functions (IMFs). Moreover, we propose an adaptive criterion to determine the number of decomposed IMFs. Due to the narrowly concentrated frequency components with the multichannel continuity constraint from MVMD, ground roll is mainly contained in low-frequency IMFs, which benefits the accurate ground-roll suppression. Next, we separate ground roll and reflections on the selected low-frequency IMFs through a curvelet based block-coordinate relaxation method. Afterward, we can obtain a filtered gather by removing the separated ground roll from the original shot gather. Finally, we apply the proposed workflow to synthetic and field gathers to testify its validity and effectiveness for simultaneously attenuating ground roll and preserving valid seismic reflector information.

Seismic image denoising is essential to enhance signal-to-noise ratio (SNR) of seismic images and facilitate seismic processing and geological structure interpretation. With the development of deep learning (DL), several DL based models have been proposed for seismic image denoising. However, the commonly used supervised DL based denoising models require noise-free data as training labels, yet noise-free data is often difficult to be obtained in field application scenarios. By considering the similarity of seismic images, we propose a similarity informed self-learning (SISL) to address seismic image denoising in the absence of noise-free seismic images. To accurately preserve valid seismic signals when constructing training pairs, we develop a specialized workflow, termed the similar image sampler. In this way, we can fully use the self-similarity of noisy seismic images to build training pairs and then train a denoising model. Moreover, to effectively attenuate random noise, we propose a hybrid loss function with a regularization constraint to availably retain valid seismic events. After comparing with traditional denoising methods and several state-of-the-art unsupervised DL models, the experiment results from synthetic and field data quantitatively and qualitatively demonstrate the effectiveness and the stability of the proposed SISL model for seismic image denoising.

Attenuation of incoherent noise is an effective way to improve signal-to-noise ratio (SNR) of seismic data. Recently, supervised deep learning based methods have been widely utilized for seismic image denoising, which often need plenty of noise-free data as training labels. However, noise-free seismic data are often unavailable in field applications. We propose an unsupervised learning method (NS2NS) to train a denoising network by using single noisy seismic data. The proposed model is based on two basic truths of seismic data: (1) High self-similarity of seismic data; (2) Spatially independence of incoherent noise in seismic data. To implement the proposed method, we first build a sampling workflow to generate paired noisy images based on single noisy seismic image. Moreover, we create similar noisy images that are similar but different with the original noisy image by using the proposed self-similar sampler. The original noisy images and generated similar noisy images are then fused by using a suggested Bernoulli sampler to create new paired noisy images. These new paired noisy images are used as the input and target of the denoising model, respectively. Next, an end-to-end convolutional neural network (CNN) is built for seismic image denoising, which aims to learn features of valid signals and suppress unpredictable random noise. Finally, we apply the proposed NS2NS method to both synthetic and field data. The results show that our proposed method can effectively suppress incoherent noise while preserving valid signals.

Time-frequency (TF) representations achieve better TF localization properties compared with Fourier transform (FT) and perform well for Q estimation via methods such as spectral ratio (SR), centroid frequency shift (CFS), and peak frequency shift (PFS). However, these attenuation estimation methods all require a given frequency band or certain source wavelet assumptions, also heavily interfered by noise. In addition, the resolution and accuracy of TF spectrum also determine whether the extracted spectrum can accurately characterize the frequency properties of seismic wavelets, thus affecting the accuracy of seismic estimation results. In this study, we propose an unscaled generalized S-transform (UGST), which achieves better TF localization while avoiding the dominant frequency shift of S-transform (ST). Next, we build a Q estimation method based on the weighted Kullback-Leibler (WKL) divergence and then give an estimation workflow combined with the proposed UGST. Note that the proposed workflow does not need to make specific wavelet assumptions or consider the frequency band selection, which is also proved to be not sensitive to noise. Finally, to demonstrate the effectiveness of the proposed workflow, we apply it to synthetic and field data. Compared with the contrastive methods, our proposed workflow can achieve more accurate estimation results and show better noise immunity, which can benefit delineating seismic hydrocarbon reservoirs.

Seismic data reconstruction is one of the essential steps in the seismic data processing. Recently, the deep learning (DL) models have attracted huge attention in seismic exploration, which has been applied to seismic data reconstruction, especially the convolutional neural network (CNN)-based methods. However, the general CNN-based models only consider seismic features in the time domain and do not take into account the frequency features. Moreover, there are detailed features lost due to the downsampling scheme. We propose a wavelet-based residual DL (WRDL) network to reconstruct the incomplete seismic data. By selecting the U-Net as the backbone, we introduce the discrete wavelet transform (DWT) to replace the pooling operations, whose invertibility property benefits reserving the detailed features. Furthermore, the inverse wavelet transform (IWT) with the expansion convolutional layer is introduced to restore the feature maps. In addition, we adopt the residual blocks into the proposed model to promote the training accuracy and avoid the overfitting issue. To accurately and effectively reconstruct the missing seismic data, we propose a hybrid loss function based on the structural similarity (SSIM) loss and the Huber loss. Numerical experiments on synthetic data and field data show that the WRDL model reconstructs the missing seismic data more accurately than the U-Net and MWCNN models, including the irregularly missing seismic data and the consecutively missing seismic data with a big gap. Furthermore, the qualitative and quantitative results demonstrate the advantages of the proposed hybrid loss function over the commonly used traditional loss for seismic data reconstruction.

Time-frequency analysis (TFA) is a powerful tool for describing time-frequency (TF) features of seismic data, such as short-time Fourier transform and S-transform. Recently, sparse time-frequency analysis (STFA) is proposed for enhancing TF readability of commonly used TFA tools. However, STFA is often solved via an optimal inverse problem with a prior regularization term, which is difficult to set in practice, where the key regularization parameters are sensitive to noise. Moreover, it often takes expensive calculation time, especially for 3D field data application. We build a deep learning based workflow for implementing STFA to obtain sparse time-frequency (STF) spectra, termed the sparse time-frequency network with transfer learning (STFNTL). We first adopt a Marmousi II reflectivity model and Ricker wavelets with different dominant frequencies to generate synthetic training data set. Then, we adopt a simplified STFA method with optimized parameters to generate synthetic training labels, i.e., sparse TF spectra. Afterward, we propose the sparse time-frequency network (STFN) based on a simplified Unet model, which is trained using synthetic training data and corresponding STF labels. Moreover, to enhance the generalization of STFN, we introduce an adaptive transfer learning strategy based on small samples of field data and their corresponding STF labels. Finally, synthetic and field data are utilized to illustrate the effectiveness and generalization ability of our proposed model.

Although there are plenty of approaches proposed for addressing seismic volumetric dip estimation, it still suffers from several limitations, for example, the expensive computation cost, the perturbations from sequence stratigraphic anomalies, and the difficulty for handling the complicated geologic structures. Recently, deep learning (DL) based models have been proposed for seismic dip estimation, which utilize seismic dips calculated by using the traditional methods as the training labels. Apparently, these DL based models can effectively improve the computational efficiency, however, it still subjects to the limitations of the traditional algorithms. We propose a multi-channel deep learning (MCDL) model for implementing seismic volumetric dip estimation, mainly including share module (SM), particular module (PM), and fused module (FM). First, we calculate seismic dips by using several traditional methods based on 3D real seismic data as the training labels, which are used to pre-train SM and PM. Then, we propose a workflow to create synthetic seismic data and ground truth dip labels, which are utilized to fine-tune SM/PM and train FM. In this way, we can obtain a DL model by considering both the features of synthetic ground truth dips and the calculated dips from real data. Moreover, we can effectively enhance the generalization ability of the MCDL by pre-training with the estimated dip volumes from real data. To demonstrate its validity and availability, we apply the MCDL to synthetic data and two 3D real seismic volumes. The qualitative and quantitative comparisons illustrate the superiority of the proposed model over the traditional methods.

The time-frequency (TF) analysis is an effective tool in seismic signal processing. The sparsity-based TF transforms have been widely used to obtain high localized TF representations in recent past years. These TF transforms formulate a sparse TF representation as an inverse optimization problem using simple mathematical models, which are typically based on a hand-crafted prior knowledge. Unlike the traditional sparsity-based TF transforms, the supervised deep learning (DL)-based sparse TF representations don’t require this prior knowledge and instead use a large amount of labeled data set, which is difficult to label for seismic data. In this study, to bridge the gap between the traditional sparsity-based transforms and the supervised DL-based transforms, we propose a DL-based sparse TF analysis approach based on a physically informed autoencoder model, named the SparseTFNet. The proposed SparseTFNet includes two modules: a convolutional neural networks (CNN)-based encoder and a traditional inverse TF representation-based decoder. The CNN-based encoder is implemented by training the inverse optimization problem in the absence of the “ground-truth" TF representation, which can be trained with only seismic traces. The traditional inverse short time Fourier transform (STFT) is utilized as the decoder module in this study, which is used as a physical constraint to ensure the high accuracy of the calculated TF representation. Finally, after training and validating the proposed model using the noise-free and noisy synthetic seismic traces, the model is applied to three-dimensional (3D) offshore seismic data. The results show that the proposed SparseTFNet model has good performance in the delineation of the depositional fluvial channels.

Seismic attenuation is one of the crucial attributes for seismic resolution enhancement and reservoir characterization, which is often described by quality factor Q. Among the commonly used methods for Q estimation, the frequency based method is demonstrated for effectively estimating Q factor, mainly including the frequency shift (FS) based, and the spectral correlation (SC), and the logarithm spectral ratio (LSR) based methods. However, the frequency spectrum of the received wave may be affected by the closely adjacent reflections, which may result in an unreliable Q estimation. To handle this limitation, the error modeling based discriminative approach in machine learning is proposed in this study. We utilize the seismic wave first received to construct the classifier based on the reproducing kernel Hilbert spaces representer theorem, then give an effect Q estimation by applying the classifier to the wave second received. Furthermore, to improve the robustness of the estimation results, the error models of the classifier are introduced. The loss functions are proposed to correspond to the distributions of the error models, from which two different implementations of Q estimation are derived. When applying to the synthetic data, the corresponding results show that the proposed method greatly improves the robustness and accuracy of the conventional methods. Field data test is also provided and demonstrates the effectiveness of our proposed method.

Seismic noise separation and attenuation is a fundamental topic in the seismic signal processing and geological interpretation. Several kinds of algorithms are proposed for separating and attenuating seismic random noises. However, the conventional methods often handle a seismic volume trace by trace, which ignores the lateral continuity of seismic data. Moreover, seismic signal is a typical broadband signal, which makes it difficult to separate and attenuate random noises contained in the whole frequency bands of the raw seismic data. Additionally, the tuning parameters for the denoising methods are also a difficult task to filter a broadband seismic signal. In this study, we propose a multi-channel scheme which is referred as the multi-channel variational mode decomposition (MVMD) based on multi-channel singular spectrum analysis (MSSA), to efficiently and effectively separate and attenuate seismic random noises. The proposed workflow first adopts the MVMD to decompose a 2-D seismic data into several band-limited intrinsic mode functions (IMFs) with different center frequencies and different bandwidths. Then, we leverage the MSSA for each decomposed IMF to separate and attenuate random noises. It is worth to be noted that we can select the tuning MSSA parameters for each IMF based on their different center frequencies and bandwidths. Finally, we restore the valid seismic data by summing all filtered IMFs. Through detailed comparisons with the traditional denoising methods, the results from the synthetic examples and field data quantitatively and qualitatively demonstrate the effectiveness and accuracy of the proposed workflow for separating and attenuating seismic random noises.

Lithology classification in well logging plays a significant role in evaluating the quality of oil and gas reservoirs. Conventionally, the manual interpretation method is of much more limited use, partly because it is time-consuming, but mainly because it is subjective. This is due primarily to the massive volume of logging data and the dependence of the experience of geophysical practitioners. By considering the features that logging data are typically sequential and long short-term memory (LSTM) network is well-suited to process a sequential signal, an LSTM-based architecture is proposed to identify rock facies based on borehole data automatically in the study area. The tests based on data from one well of the tight gas sandstone reservoir demonstrate that, when the sample size and the number of hidden layer neurons are appropriately set, the trained LSTM-based Adam optimizer can precisely recognize the rock facies boundaries than that based on Sgdm and Rmsprop optimizers. Additionally, results on another eight wells in the same study area statistically show a good generalization of the trained LSTM. Moreover, another complex reservoir with similar lithology interbedding also demonstrates the usefulness of the LSTM-based network.

Continuous wavelet transform (CWT) is an effective tool for seismic time-frequency (TF) analysis. Selecting a matched wavelet to the analyzed seismic wavelet is a key issue for accurately characterizing TF features of seismic data. The three-parameter wavelet (TPW) can match different seismic wavelets by adjusting the three parameters. However, it is difficult to select appropriate parameters for matching TPW to seismic wavelets in real applications. In this letter, we propose a basic wavelet construction method by using the TPW and the deep learning network. The proposed workflow first builds a mapping relationship between seismic wavelet and seismic data by using the alternating iterative deep neural network (AIDNN). Based on this relationship, we then estimate a seismic wavelet. Using the estimated seismic wavelet, we can finally construct an analytical basic wavelet by matching the TPW to the extracted wavelet. Note that we named the TPW with optimal parameters as the optimal basic wavelet (OBW), and its wavelet transform is OBWT. To demonstrate the validity and effectiveness of the proposed approach, we apply it to synthetic traces and field data for characterizing their TF features. The results show that OBWT preserves the amplitude better and has a higher resolution than the CWT with mismatched basic wavelets to the seismic wavelet, which is helpful for seismic data analysis in the future.

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.

Seismic inversion problems often involve strong nonlinear relationships between model and data so that their misfit functions usually have many local minima. Global optimization methods are well known to be able to find the global minimum without requiring an accurate initial model. However, when the dimensionality of model space becomes large, global optimization methods will converge slow, which seriously hinders their applications in large-dimensional seismic inversion problems. In this article, we propose a new method for large-dimensional seismic inversion based on global optimization and a machine learning technique called autoencoder. Benefiting from the dimensionality reduction characteristics of autoencoder, the proposed method converts the original large-dimensional seismic inversion problem into a low-dimensional one that can be effectively and efficiently solved by global optimization. We apply the proposed method to seismic impedance inversion problems to test its performance. We use a trace-by-trace inversion strategy, and regularization is used to guarantee the lateral continuity of the inverted model. Well-log data with accurate velocity and density are the prerequisite of the inversion strategy to work effectively. Numerical results of both synthetic and field data examples clearly demonstrate that the proposed method can converge faster and yield better inversion results compared with common methods.

Noise attenuation is a very important step in seismic data processing, which facilitates accurate geologic interpretation. Random noise is one of the main factors that lead to reductions in the signal-to-noise ratio (SNR) of seismic data. It is necessary for seismic data, including complex geological structures, to develop a number of new noise attenuation technologies. In this article, we concern with a new variational regularization method for random noise attenuation of seismic data. Considering that seismic reflection events often have spatially varying directions, we first employ the gradient structure tensor (GST) to estimate the spatially varying dips point by point and propose the structure-oriented directional total generalized variation (DTGV) (SODTGV) functional. Then, we employ the SODTGV as a regularizer to establish an ℓ2-SODTGV model and develop the primal-dual algorithm for solving this model. Next, the choice of the model parameters is discussed. Finally, the proposed model is applied to restore noisy synthetic and field data to verify the effectiveness of the proposed workflow. For contrastive methods, we select the structure adaptive median filtering (SAMF), anisotropic total variation (ATV), total generalized variation (TGV), DTGV, median filtering, KL transform, SVD transform, and curvelet transform. The synthetic and real seismic data examples indicate that our proposed method can preferably improve the vertical resolution of seismic profiles, enhance the lateral continuity of reflection events, and preserve local geologic features while improving the SNR. Moreover, the proposed regularization method can also be applied to other inverse problems, such as image processing, medical imaging, and remote sensing.

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.

Time-frequency (TF) analysis algorithms are widely used to process seismic data. Unfortunately, most TF analysis algorithms cannot process 2-D seismic data, which contain more information than 1-D data. In fact, 2-D x-t domain seismic data should be analyzed in the multi-dimensional phase space (MDPS). In this letter, we develop and explain an MDPS analysis method for 2-D seismic data. In order to map the 2-D seismic data into MDPS, the synchrosqueezed curvelet transform (SSCT) is extended from the x-y domain to the x-t domain. By comparing the 2-D synchrosqueezing transform (SST) with the 1-D SST, we explain how the 2-D SST makes the connection between the 4-D curvelet domain and the 4-D space-time-wavenumberfrequency domain (xt-kf domain). This new analytical method can help us to obtain the angle, scale, frequency, and wavenumber information, which are useful to separate the overlapped seismic data. The numerical example and real data example illustrate the effectiveness of this method.

To better describe features of nonstationary seismic signals, mode decomposition-based approaches are widely used for seismic processing and analysis, such as empirical mode decomposition (EMD) and empirical wavelet transform (EWT). EWT builds an adaptive filter bank and then decomposes a nonstationary seismic trace into several intrinsic mode functions (IMFs), which has been applied for analyzing the nonstationary seismic signal. In this letter, we propose an enhanced EWT (EEWT) using Hankel transform (HT), which is an integral transform whose kernels are Bessel functions. Compared with sinusoidal functions of Fourier transform (FT), Bessel functions are more effective for describing features of nonstationary signals. Moreover, HT obtains a more compact spectrum than FT for wideband and nonstationary signal analysis, which contributes to the detection of spectral segmentation. To demonstrate the effectiveness of the proposed algorithm, we apply it to both synthetic and field data. Compared with the results provided by EWT, EEWT provides a time-frequency spectrum with higher resolution and offers potentials in precisely highlighting reservoirs.

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

Time-frequency (TF) analysis is a powerful tool in seismic data processing and interpretation, and it characterizes the frequency response of subsurface rocks and hydrocarbon reservoirs effectively. In this letter, we proposed a new method called the second-order synchrosqueezing wave packet transform (SSWPT2) for seismic TF analysis. The proposed approach introduces two posttransform, i.e., reassignment method (RM) and synchrosqueezing transform (SST), into the wave packet transform. Such a technique achieves a highly concentrated TF representation by using a second-order local estimate of the instantaneous frequency (IF). We validate the proposed approach with a synthetic example and compare the result with the existing methods, and field data examples also illustrate its effectiveness in delineating more distinct channels in the horizon slices.

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.

Synchrosqueezing transform (SST) is an effective time-frequency analysis (TFA) approach for the processing of nonstationary signals. The SST shows a satisfactory ability of the TF localization of the nonlinear signal with a slowly time-varying instantaneous frequency (IF). However, for the signal of which ridge curves in the TF domain are fast varying, or even almost parallel to the frequency axis, the SST will provide a blurred TF representation (TFR). To solve this issue, the transient-extracting transform (TET) was recently put forward. The TET can effectively characterize and extract transient features in the much concentrated TFR for the strongly frequency-modulated (FM) signal, especially the impulse-like signal. However, contrary to the SST, it is not suitable for weak FM modes. In this study, we propose a TFA method called the time-synchroextracting general chirplet transform (TEGCT). The TEGCT can achieve a highly concentrated TFR for strong FM signals as well as weak FM ones. Quantized indicators, the concentration measurement and the peak signal-to-noise ratio, are used to analyze the performances of the proposed method compared with those of other methods. The comparisons show that the TEGCT can provide a result with better TF localization. Then, the proposed method was applied to the spectrum analysis of the seismic data for oil reservoir characteristics. The horizontal slices of the offshore 3-D seismic data show that the TEGCT delineates more distinct and continuous subsurface channels in a fluvial-delta deposition system. All the results illustrate that our proposed method is a good potential tool for seismic processing and interpretation in the geoscience.

We proposed a multitrace semiblind nonstationary deconvolution method. The proposed method estimates reflectivity and source wavelet simultaneously for pursuing high-resolution seismic processing. The mathematical framework is derived based on convolution exchange law and Fourier transform property. In this framework, seismic records are treated as the convolution of a time-varying wavelet and nonattenuated reflectivity or the convolution of a constant wavelet and attenuated reflectivity. Using these two equivalence relations, we devise an objective function containing two variables, the reflectivity and wavelet. In addition, we add the 2-D total variation constraint to the cost function, which preserves lateral and vertical continuity of the estimated reflectivity. The cost function is solved by alternating iteration and proximal splitting methods, under the assumptions of a known attenuation model and sparse reflectivity. In addition, the mathematical framework is extended to implement semiblind deconvolution in an approximate layered earth model. To demonstrate the effectiveness of the proposed method, we apply the proposed method to synthetic data and field data and confirm that the proposed method can achieve better reflectivity and source wavelet.

By building an adaptive filter bank, the empirical wavelet transform (EWT) decomposes an analyzed signal into several intrinsic mode functions (IMFs). Although some applications have certified the effectiveness of the EWT, the effectiveness of the EWT is affected obviously when analyzing nonstationary signals (e.g., seismic data). In this letter, we propose an improved EWT (IEWT) to decompose a nonstationary seismic signal into several IMFs and describe its frequency features. After computing the Fourier spectrum of the seismic signal, the scale-space representation (SSR) is used to extract the slowly varying component of the Fourier spectrum. Then, the frequency components contained in the seismic signal and the boundaries can be obtained using the central frequency information. Finally, we obtain an adaptive spectrum segmentation using detected boundaries based on the SSR. Afterward, the proposed algorithm obtains accurate and stable IMFs in decomposing the nonstationary seismic signal. To demonstrate the effectiveness of the proposed IEWT, we apply it to synthetic seismic signal and field data.

Coherence algorithm is widely used to describe geological discontinuity and subtle features of seismic data. Traditional coherence algorithms often use the linear correlation measurement to measure the relationship between two seismic traces. It does not work well because seismic data do not obey the normal distribution. To describe the coherence measurement of seismic data, we propose an improved coherence algorithm by combining the mutual information (MI) and third-generation coherence (C3) algorithm. The MI is a measurement of the general dependence and used to describe nonlinear relationships between two variables. Note that, the MI does not require that variables obey specific distribution (e.g., the normal distribution). Note that, we calculate precise MI values using the copula function. In addition, we introduce the information divergence to save calculation time by replacing the eigenvalue decomposition of the C3 algorithm. To demonstrate the effectiveness of the proposed algorithm, we apply it to field data. Field data experiments demonstrate the effectiveness of the proposed algorithm to describe geological discontinuity and heterogeneity, such as channels with different thicknesses.

Achieving a proper time-frequency (TF) resolution is the key to extract information from seismic data using TF algorithms and characterize reservoir properties using decomposed frequency components. The generalized S-transform (GST) is one of the most widely used TF algorithms. However, it is difficult to choose an optimized parameter set for the whole seismic data set. In this paper, we propose to set the parameters of the GST adaptively using the instantaneous frequency (IF) of seismic traces. Our workflow begins with building a relationship between the parameter set of the GST and IF using a synthetic wedge model. We use the IF as an indicator for the time thickness of each trace in the wedge model. We then compute the TF spectrum of each trace using the GST with different parameter sets and compare the similarity between the computed TF spectrum and theory TF spectrum. The parameter set with the largest similarity is regarded as the best parameter set for each trace in the wedge model. In this manner, we build a relationship between the parameter set and IF value. We can finally choose the optimum parameter set for the GST according to the IF values of seismic traces. We name the proposed workflow as the self-adaptive GST (SAGST). To demonstrate the validity and effectiveness of the proposed SAGST, we apply it to synthetic seismic traces and field data. Both synthetic and real data examples illustrate that the SAGST can obtain a TF representation with a high TF resolution.

The S transform (ST) is one of the most commonly used time-frequency (TF) analysis algorithms and is commonly used in assisting reservoir characterization and hydrocarbon detection. Unfortunately, the TF spectrum obtained by the ST has a low temporal resolution at low frequencies, which lowers its ability in thin beds and channels detection. In this letter, we propose a three parameters ST (TPST) to optimize the TF resolution flexibly. To demonstrate the validity and effectiveness of the TPST, we first apply it to a synthetic data and a synthetic seismic trace and then to a filed data. Synthetic data examples show that this TPST achieves an optimized TF resolution, compared with the standard ST and modified ST with two parameters. Field data experiments illustrate that the TPST is superior to the ST in highlighting the channel edges. The lateral continuity of the frequency slice produced by the TPST is more continuous than that of the ST.

In this letter, a new method is introduced for a seismic time-frequency (TF) analysis. The proposed method is called synchrosqueezing generalized S-transform (SSGST), which belongs to a postprocessing procedure of the GST. The frequency-dependent Gaussian window used in the standard S-transform may be not suitable for real applications. In order to overcome this limitation, the frequency-dependent Gaussian window is replaced by a parameterized function containing three parameters. These three parameters result in flexibility in the variation of TF resolution. Then, the synchrosqueezing transform is employed to squeeze the TF coefficients of the GST to achieve an energy-concentrated TF representation. Synthetic examples and field data show that the SSGST achieves a high resolution and has the potential in highlighting geological structures with high precision.

Time-frequency (TF) analysis can reveal local variations in seismic data processing and interpretation, where seismic signals are nonstationary and time varying. High-quality TF representation (TFR) is important for revealing the local information about these nonstationary seismic signals and describing geological structures. Due to the Heisenberg uncertainty principle, traditional TF methods (e.g., short time Fourier transform and continuous wavelet transform) cannot get the finest time resolution and the best frequency resolution at the same time, which leads to ambiguous TFR with a negative effect on the seismic signal analysis. Concentration in frequency and time is proposed to distinguish the different TF contents of time-dependent signals with time-varying amplitude and instantaneous frequencies. We introduce this promising TF analysis tool to seismic data processing. Experiments on synthetic signals and seismic data show its validity and effectiveness, which is helpful for seismic data interpretation in the future.