Distributed Acoustic Sensing (DAS) is a highly appealing technology for seismology, prized for its flexibility, durability, and high sensitivity to vibrations and strain field changes. However, despite these advantages, optical fibers are susceptible to external interference, which introduces incoherent noise during measurements. Recognizing that this noise in raw DAS data is unstructured and has a zero mean, we propose ZSN2N-DAS, a self-supervised learning method that achieves zero-shot Noise2Noise denoising for ground-based DAS data. The effectiveness of ZSN2N-DAS is underpinned by a mathematically proven equivalence. Results demonstrate its ability to effectively suppress incoherent noise and significantly enhance the Signal-to-Noise Ratio (SNR) of microseismic events, as validated using datasets from a DAS array on the Rutford Ice Stream in Antarctica. Furthermore, compared to the current leading deep learning model, N2N-DAS, ZSN2N-DAS achieves a 54% reduction in network parameters while simultaneously improving the SNR of seismic signals by approximately 20% and mitigating the issue of signal leakage. Consequently, in arrival time picking, ZSN2N-DAS enhances picking quality and increases the average number of effectively picked arrivals by roughly 28%. The denoised data produced by ZSN2N-DAS can benefit downstream seismological analyses like magnitude estimation, hypocenter location, and focal mechanism inversion.

Migration is the core link in reflection seismic exploration. Seismic images are often extended into angle domain for interpretations. However, affected by limited acquisition aperture and complex overburden, the generated images are far from ideal. The illumination is unbalanced, causing unreliable amplitude variation in angle gathers. Band-limited seismic data and wavelet stretch in large angles, lead to low-resolution angle gathers. Image-domain least-squares migration (IDLSM) implemented by point spread function (PSF) deconvolution is a promising solution. Extending the concept of IDLSM to the angle domain, we develop a new method to construct angle-dependent PSFs and optimize angle gathers. The essential element to construct PSFs is the Green’s function. The proposed method reconstructs Green’s functions using a bidirectional long short-term memory (LSTM) network. We use a ray tracing method to efficiently obtain wave propagation directions (travel-time gradients). And wave-equation forward modeling is used to accurately calculate wavefront amplitudes. The LSTM network is trained by labels composed of travel-time gradients and amplitudes to surrogate the solver of Green’s functions. Angle-dependent PSFs are constructed according to the mathematical model of the angular local Hessian. And inversions with PSFs are performed to optimize angle gathers. Numerical tests on a 3-D synthetic model demonstrate that the proposed method is able to improve the image quality of prestack angle gathers and poststack seismic images. The proposed method compensates illumination and improves the resolution of angle-dependent seismic images. Both vertical and lateral resolution are enhanced. Amplitude versus angle (AVA) responses can be corrected for further analysis and interpretations.

Seismic interpretation and reservoir characterization require the seismic data having faithful amplitudes that relate to subsurface physical parameters. Nowadays, the amplitude fidelity of seismic imaging becomes more important than ever. Although reverse time migration (RTM) adopts the full wave equation as true amplitude seismic wave propagator, it is still not sufficient for true amplitude seismic imaging since migration is only the adjoint operator corresponding to the forward modeling process. The complex overburden and limited migration aperture lead to unbalanced illumination of subsurface structures. Least-squares migration was proposed to correct amplitudes of seismic images, but it is computationally expensive and sometimes unstable. The illumination compensation is an available alternative which only considers the amplitude correction regardless of the resolution issue. In this article, we propose a true amplitude seismic imaging method with illumination compensation performed on both RTM stacked images and angle gathers. We derive the angle-dependent illumination intensity from the Hessian of least-squares migration in which Green’s functions are essential components. We propose a new method to estimate the Green’s function and its corresponding wave propagation direction based on wavefields excitation amplitudes and Poynting vectors at excitation times. Then, the illumination intensity is constructed as a function of dip and reflection angles to correct both angle gathers and stacked images. The proposed method is tested using two synthetic models and a real marine dataset. Numerical results demonstrate that the proposed method can effectively correct amplitudes of seismic images. Deep events beneath complex structures are enhanced with more balance illumination.

Seismic facies classification involves assigning geological meaning to seismic amplitudes based on distinct sedimentary facies responses. Various deep learning approaches have been developed for seismic facies classification. Currently, most deep neural networks applied for this task are manually engineered based on domain expertise. However, these human-designed architectures may not be optimal for seismic facies classification. To address this, we introduce differentiable architecture search with partial channel connections (PC-DARTS), enabling automated architecture search instead of manual design. We modify the PC-DARTS search space and propose PC-DARTS for seismic facies classification (PC-DARTS-SFC) to determine architectures tailored for this problem. We apply PC-DARTS-SFC on the Netherlands F3 seismic volume. The results demonstrate the superiority of the architecture discovered by PC-DARTS-SFC over original PC-DARTS, conventional networks, and a previous method. This confirms the potential of leveraging network architecture search (NAS) to find specialized networks surpassing human design for seismic facies classification.

The precise decomposition of P/S-waves in multi-component seismic data is critical for seismic imaging. Inaccuracies in this decomposition can result in migration images with biased amplitudes and undesirable crosstalk artifacts. Although vector-decomposition (VD) methods are effective, they rely on the availability of elastic parameters at the acquisition surface. Therefore, we propose a data-driven deep-learning (DL)-P/SVD(DL-PSVD) method that eliminates the need for prior elastic parameter information. We used publicly available elastic models to generate training datasets by simulating multi-component data and their amplitude-preserving P/S-wave components using the decoupled elastic wave equation. Our analysis explores the impact of the loss function type, output channel quantity, and direct wave removal on the generalization ability of DL-PSVD. The critical insights from the numerical experiments include the superior generalization ability of DL-PSVD using two channels when the P/S-wave energy distribution is highly unbalanced. Moreover, DL-PSVD exhibits improved generalization ability using four channels for observed data with removed direct waves. Finally, the L1 loss function is more effective for DL-PSVD’s generalization ability than the L2 loss function. Overall, the proposed DL-PSVD is a promising method for automatic P/S-wave VD without requiring prior elastic parameter information.

Studying the statistical characteristics of primary reflection coefficients is crucial for gaining a deeper understanding of the structure of the Earth’s rock layers. In this study, we collected 686 logging data from scientific ocean drilling sites worldwide, and after careful data cleaning, 328 logging data remained. Using a data-driven approach, we constructed an overall score index to measure the quality of the fit for various distribution models. This index comprised metrics, including the residual sum of squares (RSSs), Kolmogorov–Smirnov (KS) statistics, Wasserstein distance, and energy distance. From 80 distribution models, top 5 with the best overall fitting performance were the Johnson SU (Johnsonsu),$T$, Tukey lambda, generalized normal, and double Weibull distributions. Further comparison of goodness-of-fit metrics that revealed the Johnsonsu distribution demonstrated the optimal fit for the primary probability distribution of reflection coefficients. In addition, logging data from three onshore wells in China’s Dongying Shengli Oilfield provided validation support for the Johnsonsu distribution. Our results illustrated the advantages of the Johnsonsu distribution for simulating primary reflection coefficients and provided approximate parameter ranges for fitting the distribution.

The data-driven approach has become significant in various scientific fields, such as climate modeling and weather forecasting, where a mechanistic description of physics and chemistry is either unavailable or insufficient for the desired purpose. However, the prominent nonstationarity poses a significant challenge to the accurate prediction of recent global average temperature (GAT) using conventional methods. To address this challenge, we draw inspiration from signal analysis’s moving-window approach, wherein we split the GAT into shorter segments to alleviate nonstationarity. These segments are transformed into a time-symmetric graph (TSG) structure in the non-Euclidean domain. Consequently, we introduce the GlobalTempNet model, which incorporates a graph convolutional network (GCN) embedded with a residual neural network (NN) and a long short-term memory (LSTM) network. In addition, we propose the entire graph node training (EGNT) process, optimizing parameters by treating each sample as a graph node for feature aggregation and information updating. Validation using the HadCRUT5 dataset demonstrates that GlobalTempNet outperforms nine established models, showcasing higher prediction accuracy. Furthermore, long-term estimation and future prediction analyses reveal GlobalTempNet’s capability to predict the climate change trend in the coming years. The model’s applicability is confirmed across ten different temperature datasets. Consequently, the proposed GlobalTempNet, coupled with the EGNT process, emerges as a robust, reliable, and open-source method for global temperature prediction, offering promising potential as a tool for univariate time series analysis using graph NNs (GNNs).

The acquisition and reconstruction of seismic data are fundamental to seismic exploration. The balancing data quality and acquisition cost is essential. To address this challenge, we propose Seis-PDDN, a novel framework that integrates edge-preserving piecewise undersampling design with diffusion null-space iteration, optimizing both survey design and data reconstruction. Seis-PDDN uses the prior distribution of seismic reflectivity to design a linear missing mask operator, guiding the undersampling process. Reconstruction is achieved through a diffusion null-space iteration, combining range-null space decomposition with a pretrained diffusion model, ensuring both consistency and fidelity in the reconstructed data. Extensive experiments on synthetic and public seismic shot gathers demonstrate that Seis-PDDN outperforms traditional random, jittered, and uniform sampling schemes. Further comparisons with other deep learning reconstruction methods confirm that Seis-PDDN achieves higher metrics in seismic reconstruction, especially with a spatial sampling rate as low as 10%. Overall, Seis-PDDN holds significant potential for advancing flexible, economical acquisition and accurate reconstruction in seismic exploration.

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.

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.

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.

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.

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

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 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.

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.

One important application of time-frequency analysis (TFA) is seismic spectral decomposition for reservoir characterization. However, traditional seismic TFA techniques are usually limited by diffused TF distribution, which can result in unreliable seismic interpretations. Synchrosqueezing transform (SST) is an effective TFA method that improves the concentration of the TF representation (TFR) of nonstationary signals. However, for the signal with a rapidly varying instantaneous frequency, the SST method suffers from a blurred TFR. In this letter, we propose a novel TFA method called time-synchroextracting transform (TSET) that provides highly concentrated TFR for transient signals where the TF curve is nearly parallel to the frequency axis. We applied the proposed TSET to synthetic signals and field seismic data to verify its validity of time localization and effective delineation of subsurface geological information.

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.

Seismic records are often contaminated with various kinds of noise, which makes it very difficult to distinguish the expected geological features. In this paper, we introduce a novel adaptive variable time fractional-order anisotropic diffusion equation for seismic data noise removal and strongly oriented structure enhancement. Since the time fractional-order differential equation interpolates a parabolic equation and a hyperbolic equation, the solution benefits both of these approaches. The presented differential equation can be written as a Volterra integral equation, and its well-posedness can be guaranteed for all time. We employ a structure tensor to analyze the flow-like texture characteristic which is typical in seismic data. Then, the diffusion process is guided reasonably by a diffusion tensor based on the structure tensor analysis which allows real anisotropic behavior comparing to the classical scalar diffusion approach. In reference to the numerical implementation, we utilize the predictor-corrector algorithm to solve the Volterra integral equation which provides high-order numerical precision jointly with good stability property. Finally, numerical experiments involved with synthetic and prestacked real seismic data are presented. The obtained results demonstrate that the noise is effectively removed, and the coherent seismic events that express some important geological structures are not only preserved but significantly enhanced.

Time-frequency analysis can provide useful information in seismic data processing and interpretation. An accurate time-frequency representation is important in highlighting subtle geologic structures and in detecting anomalies associated with hydrocarbon reservoirs. The popular methods, like short-time Fourier transform and wavelet analysis, have limitations in dealing with fast varying instantaneous frequencies, which is often the characteristic of seismic data. The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation. We apply the SST to seismic data and show its potential to seismic signal processing applications.