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.

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 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.

Brain functional connectivity has been widely explored to reveal the functional interaction dynamics between the brain regions. However, conventional connectivity measures rely on deterministic models demanding application-specific empirical analysis, while deep learning approaches focus on finding discriminative features for state classification, having limited capability to capture the interpretable connectivity characteristics. To address the challenges, this study proposes a self-supervised triplet network with depth-wise attention (TripletNet-DA) to generate the functional connectivity: 1) TripletNet-DA firstly utilizes channel-wise transformations for temporal data augmentation, where the correlated & uncorrelated sample pairs are constructed for self-supervised training, 2) Channel encoder is designed with a convolution network to extract the deep features, while similarity estimator is employed to generate the similarity pairs and the functional connectivity representations, 3) TripletNet-DA applies Triplet loss with anchor-negative similarity penalty for model training, where the similarities of uncorrelated sample pairs are minimized to enhance model's learning capability. Experimental results on pathological EEG datasets (Autism Spectrum Disorder, Major Depressive Disorder) indicate that 1) TripletNet-DA demonstrates superiority in both ASD discrimination and MDD classification than the state-of-the-art counterparts, where the connectivity features in beta & gamma bands have respectively achieved the accuracy of 97.05%, 98.32% for ASD discrimination, 89.88%, 91.80% for MDD classification in the eyes-closed condition and 90.90%, 92.26% in the eyes-open condition, 2) TripletNet-DA enables to uncover significant differences of functional connectivity between ASD EEG and TD ones, and the prominent connectivity links are in accordance with the empirical findings, thus providing potential biomarkers for clinical ASD analysis.

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.

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.

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.

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.