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.

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.

Reconstructing missing seismic data is crucial for seismic processing and interpretation. Recent methods struggle when seismic traces are regularly missing, such as near offset data. We proposed a classifier-guided conditional seismic denoising diffusion probabilistic model (CCSeis-DDPM) to enable consistent reconstructions. The CCSeis-DDPM adopts the Markov model architecture of denoising diffusion probabilistic models to generate high-quality results. The model involves classifier-guided training and tailored inference. During training, we employ a U-Net with embedded timestep and three class labels for noise prediction, utilizing classifier guidance to enhance reconstruction accuracy. In the inference phase, the model selectively samples unmasked regions using available seismic data. Our experiments on synthetic and field shot gathers with regularly missing near, mid and far offsets show the proposed CCSeis-DDPM reconstructs regularly missing traces more accurately than current state-of-the-art methods, demonstrated qualitatively and quantitatively. This successful integration of diffusion probabilistic models with classification guidance and conditioning underscores the immense potential of this approach for enhancing seismic data reconstruction processes.

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 lithology interpretation based on seismic data is an important task to delineate oil and gas reservoirs. However, this is an extremely unstable work when only utilizing seismic data, which would result in multiple solutions. We suggest a multiattribute integrated deep learning (MAIDL) workflow for automatic seismic lithology interpretation. To implement the proposed model, we first propose to apply the wavelet scattering transform (WST) to seismic data for multiscale features extraction. Note that the WST has local deformation stability and translation invariance for analyzing seismic data, which would be proven to promote seismic lithology interpretation. Next, the MAIDL model is suggested to combine the multiscale features extracted by the WST and seismic data simultaneously, which can improve the accuracy of automatic seismic lithology prediction. Afterward, the Res-UNet, which incorporates residual blocks into the UNet, is introduced to avoid the over-fitting and the degradation problem of the proposed MAIDL model. Finally, a 2-D synthetic data and a 2-D post-stack field data are adopted to test the effectiveness of the suggested MAIDL model for automatic seismic lithology interpretation.

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.

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.

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.

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.

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.

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.

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.

Time-frequency (TF) analysis is an available tool to estimate seismic absorption qualitatively. The high TF concentration is a key factor for the seismic attenuation qualitative estimation. To obtain a more concentrated TF representation, we propose a sparse TF method based on sparse representation (SR) and sparse Group-Lasso (GL) penalty function. Based on the SR theory, TF representation can be regarded as an inverse problem, and thus, sparse GL penalty function can be added in this inverse problem to enhance the TF concentration. Sparse GL penalty function, includingl1penalty andl2,1penalty, can provide group-wise and within-group sparsity for TF coefficients. Using the proposed sparse GL-based TF (GLTF) method, we develop a workflow to characterize seismic attenuation qualitatively. Finally, a synthetic data of viscoacoustic model and a 2-D field data are applied to test the validity and effectiveness of the proposed workflow for indicating the gas and oil reservoirs.

We proposed a multichannel deconvolution method. The method uses a mixed norm to promote structured forms of sparsity. To solve this deconvolution problem, we develop a new algorithm called the Hadamard product parametrization (HPP) sparse-group (HPPSG) algorithm. We define each layer of seismic profile as a group, and perform$L_{p}$-norm for all elements within each group to preserve the lateral continuity. Based on the assumption that the reflectivity is sparse,$L_{q}$-norm is applied among groups along the time direction. Then, we construct an$L_{p,q}$optimization problem. After that, we solve this problem using the proposed HPPSG algorithm. The HPPSG algorithm is formed by converting the$L_{p,q}$optimization function into the$L_{1}$optimization function which is solved with the help of the HPP algorithm. The proposed algorithm is simple and applicable for an arbitrary$L_{p,q}$-norm inverse problem. Synthetic and real data examples demonstrate the effectiveness of the proposed method in improving the lateral continuity of seismic profiles.

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.

Quality factor$Q$can be used for hydrocarbon detection and reservoir characterization. The commonly used methods for$Q$estimation include the logarithm spectral ratio (LSR) method, the centroid frequency shift (CFS) method, and the peak frequency shift (PFS) method. However, all these methods are existing limitations respectively. The LSR method is sensitive to random noise. The CFS and PFS methods are lack of applicability owing to their assumptions of the source wavelet type. To overcome these limitations, we derived a new formula without any wavelet assumption. This formula establishes a relationship between the$Q$factor and the spectral centroid downshift concisely through the Jeffery divergence. The proposed method is named the generalized centroid frequency shift (GCFS) method. Compared with the conventional methods, the proposed method can achieve higher accuracy and better antinoise performance. In addition, the proposed method is suitable for various source wavelet types. Synthetic and field examples demonstrate the effectiveness and potential of the proposed method.