Video anomaly detection (VAD) aims at locating the abnormal events in videos. Recently, the Weakly Supervised VAD has made great progress, which only requires video-level annotations when training. In practical applications, different institutions may have different types of abnormal videos. However, the abnormal videos cannot be circulated on the internet due to privacy protection. To train a more generalized anomaly detector that can identify various anomalies, it is reasonable to introduce federated learning into WSVAD. In this paper, we propose Global and Local Context-driven Federated Learning, a new paradigm for privacy protected weakly supervised video anomaly detection. Specifically, we utilize the vision-language association of CLIP to detect whether the video frame is abnormal. Instead of leveraging handcrafted text prompts for CLIP, we propose a text prompt generator. The generated prompt is simultaneously influenced by text and visual. On the one hand, the text provides global context related to anomaly, which improves the model's ability of generalization. On the other hand, the visual provides personalized local context because different clients may have videos with different types of anomalies or scenes. The generated prompt ensures global generalization while processing personalized data from different clients. Extensive experiments show that the proposed method achieves remarkable performance.

Recent advancements in reasoning capability of Multimodal Large Language Models (MLLMs) demonstrate its effectiveness in tackling complex visual tasks. However, existing MLLM-based Video Anomaly Detection (VAD) methods remain limited to shallow anomaly descriptions without deep reasoning. In this paper, we propose a new task named Video Anomaly Reasoning (VAR), which aims to enable deep analysis and understanding of anomalies in the video by requiring MLLMs to think explicitly before answering. To this end, we propose Vad-R1, an end-to-end MLLM-based framework for VAR. Specifically, we design a Perception-to-Cognition Chain-of-Thought (P2C-CoT) that simulates the human process of recognizing anomalies, guiding the MLLMs to reason about anomalies step-by-step. Based on the structured P2C-CoT, we construct Vad-Reasoning, a dedicated dataset for VAR. Furthermore, we propose an improved reinforcement learning algorithm AVA-GRPO, which explicitly incentivizes the anomaly reasoning capability of MLLMs through a self-verification mechanism with limited annotations. Experimental results demonstrate that Vad-R1 achieves superior performance, outperforming both open-source and proprietary models on VAD and VAR tasks.

Deep learning methods have gained widespread popularity for effectively suppressing random noise in seismic data. The recent progress in techniques based on supervised learning for attenuating seismic random noise underscores their potential, particularly when an abundant set of training examples is accessible. Unfortunately, collecting an adequate amount of representative training samples is not always feasible. DIP aims to capture a lot of low-level statistical information by using rich implicit prior knowledge inherent in the structure of the generation network itself. Therefore, it is not essential to provide a training database or uncontaminated data as a truth label, whereas only requires a noisy seismic image. In order to boost the performance, we add an explicit prior, weighted total variation, to the standard DIP, which leverages sparsity-promoting priors and restricts the solutions of DIP to satisfy a prior inherent in the seismic data. The proposed method is tested on synthetic seismic data with random noise that follows different distributions, then is applied to field pre- and post-stack seismic data. Furthermore, a comparison is drawn between the new method and the traditional DIP-based denoising method in terms of signal to noise ratio and local similarity. Our method shows more promising results because prior information from both the structure of the network and the seismic data is considered in the denoising processing.

The enhancement of seismic migration and inversion processes critically depends on the precise interpolation of seismic data. In recent years, the rapid advancements in deep learning have led to the widespread adoption of convolutional neural networks (CNNs) in seismic interpolation applications. Nonetheless, the inherent limitations of traditional CNNs, due to the fixed structure of their convolution kernels, impede the extraction of high-level features of seismic data. The accuracy of CNN-based seismic data characterization and interpolation is open to improvement. Therefore, we introduce deformable convolution kernels and design a novel deformable residual U-Net (DRU-Net) for a more nuanced characterization and interpolation of seismic data. The proposed DRU-Net allows a deformable convolution kernel with adaptive shape adjustments for the receptive field by using learnable offsets to effectively extract advanced features from the training data. In conjunction with a residual learning approach, the DRU-Net significantly refines the network’s learning process and boosts interpolation precision. Through numerical experiments on synthetic and field data with irregular traces missing, the proposed DRU-Net achieves superior precision in seismic data interpolation compared to traditional U-Net and U-Net with the squeeze and excitation block.

Acoustic impedance (AI) is an important parameter for seismic reservoir characterization. Traditional algorithms can obtain AI whereas the resolution is open to improvement. Single-channel supervised algorithms can characterize seismic data accurately to achieve high-resolution AI at the cost of a large volume of labels. In the case of limited labels, the single-channel closed-loop (SCCL) algorithm based on linear convolution forward modeling can provide some help while the horizontal continuity can be enhanced. To further improve the horizontal continuity, we propose a multichannel closed-loop (MCCL) AI estimation algorithm for seismic data with limited single-channel labels. By masking multichannel output with ones at the well locations and zeros at nonwell locations, we properly use available single-channel labels for network training. A patching strategy is also used to enlarge labeled data. Besides, the used linear convolution operator cannot fully characterize complicated features in post-stack profiles, so we design a nonlinear correction procedure to capture refined features. Nonstationary examples of the Marmousi-II model with five single-channel labels quantitatively demonstrate the effectiveness of the proposed MCCL algorithm with nonlinear correction. It achieves superiority in terms of the recovered signal-to-noise ratio (S/N) when compared to SCCL with/without nonlinear correction and MCCL. The obtained AI profile of field data using the MCCL algorithm with nonlinear correction is of high resolution and horizontal continuity visually. Quantitative assessments at the well locations underscore the proposed algorithm’s ability to improve AI estimation performance.

Traditional inverse Q filtering methods for post-stack seismic data attenuation compensation (AC) have the drawback of instability or under-compensation. Besides, the quality factor (Q) should be known as a prerequisite, which is commonly estimated using the attribute difference between the reference and observed wavelets of pre-stack vertical seismic profile (VSP) data. The alternating iterative AC and Q estimation method is also researched for post-stack data, while the instability or huge computation becomes a defect. In this letter, we propose a simultaneous AC and Q estimation method for nonstationary post-stack seismic data based on semi-supervised learning. Specifically, we choose the long short-term memory algorithm which is sensitive to time series and can characterize seismic signal nonlinearly with high accuracy. The proposed AC and Q estimation method employs the Q information from well-logs and the compensated high-resolution data for supervised learning, and uses nonstationary seismic data beyond wells for self-supervised learning, without the wavelet extraction procedure. The synthetic data analysis and field data applications prove the feasibility of the designed semi-supervised method in improving the vertical resolution and Q estimation. The field data impedance inversion after AC further demonstrates its effectiveness.

Antialiasing seismic data interpolation algorithms can reconstruct sparse seismic data into dense data, which helps obtaining high-precision migration images and accurately locate reservoirs. Nonlinear seismic interpolation techniques based on deep learning (DL) have become popular in recent years. The majority of supervised techniques, however, depend on large volumes of labeled datasets, which are rarely available for field data interpolation. To overcome the limitations of the labeled data requirement in supervised learning, some unsupervised interpolation techniques, such as the well-known deep image prior (DIP), have been developed. However, these unsupervised techniques often have poor generalization. In order to avoid the complete labeled data requirement and achieve an accurate interpolation result efficiently, we propose a novel self-supervised interpolation via frequency extrapolation (SIFE) algorithm for regularly missing seismic data. The proposed SIFE mainly contains two steps: aliasing-free low-frequency complete data reconstruction via the Nyquist sampling theorem and high-frequency data recovery via self-supervised frequency extrapolation. In the first step, a low-frequency filter is adopted to obtain aliasing-free sparse data, which can be interpolated into dense low-frequency data via the Nyquist sampling theorem. In the second step, the low-frequency filtered observation data is mapped to its original full-band observed data via self-supervised learning for frequency extrapolation. After the training convergence, we can obtain an optimized network that can map the reconstructed low-frequency data at the missing locations to the corresponding full-band seismic data via frequency extrapolation, i.e., reconstructing the missing seismic traces. Numerical examples with synthetic and field data show the superiority of the proposed SIFE when compared with DIP.

Blended acquisition can improve the efficiency of seismic data acquisition sharply, thus decreasing the acquisition costs. However, there may exist irregularity in blended data, which poses challenges for traditional seismic data processing. Thus, the deblending or interpolation should be done as a prerequisite. Because the deblending and interpolation can affect each other, we propose a unified 3-D joint deblending and interpolation method with a sparsifying transform and a sparsity promotion strategy in the blending fold of 4. To overcome the huge computational cost of 3-D curvelet transform (CT), we implement iterative thresholding in each principal frequency slice efficiently with 2-D CT. With decades of iterations, we can obtain an estimate of the regularized and deblended data. The core idea is that unblended signal can be characterized sparsely, and the blending noise and sampling irregularity have low-amplitude values in the CT domain. If blending was not used during acquisition, the proposed method becomes a pure interpolation algorithm. Similarly, if no sampling irregularity is present in the recorded data, the proposed method turns into a traditional deblending method. Numerical examples on the 3-D synthetic and field artificially blended data demonstrate the validity of the proposed method in simultaneously removing the blending noise and sampling irregularity. The regularized, deblended data can be beneficial for subsequent seismic data inversion and migration procedures.

In recent years, simultaneous source seismic data acquisition attracts much attenuation because of its higher efficiency and lower cost. However, the presence of blending noise reduces the accuracy of subsequent traditional seismic data processing steps, necessitating the separation of simultaneous source data. Conventional separation methods assume that seismic data is distributed on uniform grids, but in field cases, firing shots are always distributed on non-uniform grids. The binning strategy assigns a non-uniform sample onto its nearest uniform sample, introducing unavoidable errors and lowering the separation accuracy of simultaneous source data. As a result, irregularity influences must be taken into account during simultaneous source separation. To separate non-uniform simultaneous source data, a robust and sparse Radon transform (RSRT) is introduced because the Radon transform can deal with non-uniform grids along the space adaptively. The effectiveness of the proposed method in attenuating blending noise and reconstructing seismic data to uniform grids is demonstrated by synthetic and field data analysis.

High-density seismic data is critical for enhancing the accuracy of subsequent processing. Deep learning is useful in seismic interpolation due to its powerful nonlinear mapping capability based on the extracted high-level features. Most supervised methods, however, rely on a large labeled training set, which is always unavailable due to limited resources and complex acquisition environment. Furthermore, the optimized model with a small training set is prone to poor accuracy and generalization. We pre-train a designed U-net with an adaptive aliasing-free low-frequency dataset, then fine-tune the pre-trained U-net with a tiny original labeled dataset. The low-frequency pre-trained model effectively improves the interpolation accuracy when using a limited labeled training set. We use the aliasing-free low-frequency parts of original regularly sampled sparse data to construct dense low-frequency data based on the Nyquist sampling theorem in the frequency-wavenumber domain, resulting in an adaptive pre-training dataset. Second, we use the adaptively constructed pre-training dataset to pre-train a designed U-net for interpolation, with similar sampling patterns as the original seismic data. Third, based on transfer learning, we use the original small-volume training set to fine-tune the pre-trained U-net, which has captured the macro features of the original data during the pre-training stage. Finally, the fine-tuned U-net is applied to the remaining regularly sampled data for interpolation. The proposed adaptive low-frequency pre-trained model can significantly improve the generalization ability and the interpolation accuracy using the fine-tuned model. Numerical experiments of synthetic and field data validate the superiority of our method in terms of improving interpolation accuracy.

Due to the special petrophysical properties of tight reservoirs, such as poor connectivity and low porosity, conventional rock physics models show limitations. Based on an inclusion-based method, a new formula containing fluid pressure is derived without an equilibration assumption of fluid pressures in the inclusions. Then, the formula is simplified with an equivalent pore structure to yield a new fluid identification parameter, the inclusion-based effective fluid modulus (IEFM). By analysis, this fluid identification factor is quite sensitive to water saturation for different pore connectivity. A well-logging data test shows the superiority of the proposed model in identifying tight gas-bearing zones. Seismic data application also demonstrates the validity of the proposed model and the predicted results match well with the well-logging data. In fluid identification, two probabilistic estimation methods are used: Bayes posterior prediction framework is a combination of Bayes’ theory and a deterministic rock physics model; Bayes discriminant method is a statistical rock physics method. The proposed IEFM is a novel identification parameter for tight gas-bearing reservoirs, which can have many applications in the exploration of tight reservoirs.

Blended acquisition improves the efficiency of seismic data acquisition sharply and deblending algorithms are still open to prepare separated data. Most deblending methods are suitable for on-the-grid blended data. However, blended data in field cases is always at off-the-grid samples which poses great challenges in providing accurate deblended results. A binning strategy can assign an off-the-grid sample at its nearest on-the-grid sample approximately with the amplitude and phase bias caused by the existing distance between them. However, the subsequent deblending accuracy is low, especially when the amplitude and phase biases are large. With true off-the-grid data constraints, we introduce a Kaiser window tapered sinc interpolator to link off-the-grid samples and on-the-grid samples during the procedure of compressive sensing-based functional construction. Full expressions of the interpolator and its adjoint operator are provided to generate an iterative thresholding algorithm for off-the-grid blended data deblending. Separated on-the-grid data can be obtained accurately in an iterative manner. The deblending performance of artificially off-the-grid blended data demonstrates the validity of the proposed method quantitatively no matter the amplitude and phase biases are large or small. Field examples of off-the-grid blended data further prove the effectiveness of the proposed method to provide accurate on-the-grid separated data.

Marine seismic data with towered streamers have played an important role in marine exploration. However, the distance between adjacent sources and the distance between adjacent receivers/channels are inconsistent (i.e., like regularly missing shots) and near-offset information is unrecorded, which can decrease the performances of surface-related multiple elimination (SRME) and seismic migration. Traditional algorithms to provide prestack seismic data with consistent trace interval and to recover near-offset data have some drawbacks, including low efficiency of computation and super-parameter selection by trial and error. Thus, we propose a novel self-supervised deep learning (DL) algorithm to reconstruct regularly missing shots and recover near-offset information with an improved U-net by combining U-net and residual learning of ResNet. Via the spatial reciprocity of Green’s function, common shot gathers (CSGs) have similar features as common receiver gathers (CRGs). The reconstruction performances of regularly missing shots in CRGs can be guaranteed by using the network that is trained and validated by adaptively extracted CSGs. To reconstruct near-offset information of CSGs, we first construct pseudo-seismic data with the dip approaching 0 at near-offset parts by a rotation-truncation strategy. Pseudo-seismic data can be regarded as seismic data with approximate near-offset information to train and validate the designed network, which is later used to reconstruct near-offset information for CSGs. Finally, field marine seismic data with towered streamers is used to demonstrate the validity and effectiveness of the proposed self-supervised algorithm in reconstructing regularly missing shots and recovering near-offset information, which are beneficial for subsequent processing of seismic data.

Blended acquisition can improve the acquisition efficiency, and thereby reduce the acquisition costs. It becomes an important acquisition method in seismic exploration. However, the blending noise imposes challenges for subsequent traditional seismic data processing procedures, and thus deblending algorithms are necessary to obtain deblended seismic data. Based on the assumption that the signal is coherent and the blending noise is randomized in a specific domain, traditional deblending methods using the$L_{2}$-norm measuring the data misfit can obtain separated gathers. However, the$L_{2}$-norm is improper when the appearing seismic noise bias the normal distribution, that is, abnormal noise appears. To attenuate the abnormal noise effects during iterative deblending, we proposed an accurate deblending algorithm based on a robust sparse Radon transform (RSRT). For the RSRT, the alternating split Bregman (ASB) algorithm is used for robust 2-D Radon model updating with an$L_{1}$-norm to measure data misfit in the mixed time–frequency domain and the sparsity constraint to the time-domain Radon model. Using the RSRT iteratively, the Radon model and the corresponding deblended data can be estimated robustly, accurately, and efficiently. Blended synthetic data with different levels of abnormal noise and with different trace intervals demonstrate the validity and flexibility of the proposed robust deblending method quantitatively with a high recovered SNR. Numerically blended field data further prove the effectiveness of the proposed method in attenuating the abnormal and blending noise.

Prestack amplitude variation with offset (AVO) inversion can provide abundant reservoir information underground, which is always implemented trace-by-trace. However, it cannot guarantee the lateral accuracy of the inversion results. To utilize the lateral difference of the angle gathers and improve the lateral resolution, the difference angle gathers are introduced. Based on the Bayes inversion framework, the objective function considering the difference angle gathers is first constructed. Then, the effect of difference angle gathers on inversion results is analyzed, which is essential to improve the accuracy of the inversion results. To further figure out the applicable conditions of difference angle gathers, different forward operators are analyzed including a nonlinear operator and a linear operator. The used nonlinear operator is the exact Zoeppritz’s equation. The linear operator is a linear perturbation equation based on the elastic inverse-scattering theory. Due to the difference of angle gathers in adjacent traces, the linear forward operator may cause a deviation of the updated parameters. By comparison, the exact Zoeppritz’s equation as the nonlinear forward operator has better applicability and precision. Based on the proposed method, the elastic parameters are obtained from seismic data. Numerical examples show that the inverted elastic parameters of the proposed method have a higher horizontal resolution, and the details in the inversion profile can be better highlighted.

The time–frequency analysis is very useful for attenuation compensation, quality factor Q estimation, anomaly detection, and so on. Among plenty of time–frequency analysis methods, the S transform (ST) and its extensions are widely used because of their self-adjustable flexibility, compared with the short-time Fourier transform and Gabor transform. However, the traditional ST has a poor amplitude-preserving property near the boundary while being implemented in the time domain, because the partition of unity cannot be guaranteed. Besides, the frequency distribution biases the actual Fourier spectrum because of the linear-frequency-dependent term in the analytical window, which can decrease the accuracy of attenuation estimation. To preserve the amplitude and frequency, a new analytical window is designed, and the corresponding comprehensive window is derived in the time domain. The frequency-domain formulae are derived in detail for an efficient implementation, in which the time-domain convolution is achieved through multiplication. Numerical examples on the synthetic layered model and pseudorandom time series demonstrate the validity of the proposed method in amplitude- and frequency-preserving quantitatively. Examples at a well location of field data further demonstrate its frequency-preserving property qualitatively. Furthermore, the proposed method can have wide applications in exploration geophysics, seismology, or signal analysis fields, combining with the synchrosqueezing transform.

External source interference noise (ESIN) is a common kind of noise in marine seismic data acquisition. According to the noise-to-signal ratio (NSR), a shot gather can be divided into a low NSR part and a high NSR part. The existing ESIN attenuation methods work well in high NSR parts of shot gathers. However, because the signals in low NSR parts are much stronger than ESINs, these methods cannot suppress the ESINs in low NSR parts, and they usually damage the signals. In this letter, we propose a deep-learning method to suppress the ESINs in low NSR parts based on a convolutional neural network (CNN). The end-to-end fully convolutional network needs labeled training samples; however, the real data are unlabeled, i.e., the ESINs in low NSR parts are unknown. To obtain the labeled training data, we propose a sample generation method based on real data. The ESINs in high NSR parts extracted by the traditional methods and the signals of the clean shot gathers are added together to synthesize training samples. We then use the synthesized data and its ESINs to train the network. The experiments prove that the proposed method can suppress the ESINs in low NSR parts properly and protect the signals as well.

Full waveform inversion (FWI) is a powerful tool to understand the real complicated earth model. As FWI is a highly nonlinear problem and depends strongly on the initial model, how to effectively retrieve the large-scale background model is critical for the success of FWI. For elastic FWI (EFWI), the inversion challenge increases because the P-wave and S-wave are coupled together if no mode separation technologies are applied. In this article, we develop a new EFWI strategy, where we simultaneously implement the angle decomposition and mode separation for the wavefield. Based on the analysis of radiation patterns of different parameters and the fact that small scattering angles correspond to large-scale model perturbations, we can retrieve the large-scale background model of the P-wave velocity with pure small scattering angle P-P mode wavefield. On the other hand, the pure small scattering angle S-S, S-P, and P-S mode wavefields are used to estimate the large-scale background model of the S-wave velocity. The correctly retrieved large-scale background models further guarantee the success of subsequent fine structure retrieving for the P- and S-wave velocity models by using different wave modes. The proposed method is able to reduce the cycle-skipping problem and the multiparameter crosstalk problem simultaneously. Numerical examples show that the proposed method provides much improved inversion results than the conventional EFWI, which demonstrates the validity of the proposed method.

The blended acquisition allows multiple sources to be simulated simultaneously in a narrow time interval, which can improve the acquisition efficiency and reduce the acquisition cost tremendously. However, the overlapped information from multiple sources poses challenges for traditional seismic data migration or inversion algorithms. Thus, accurate and efficient deblending should be implemented as a pre-requisite. Traditional inversion-based deblending algorithms can provide deblended data with a high computational burden, especially for a large volume of seismic data. As a deep learning strategy can match seismic data accurately in a nonlinear way through supervised learning, we propose a U-net-based accurate deblending algorithm, which incorporates transfer learning and an iterative strategy. A set of labeled synthetic data with a blending fold of 2 are classified into the training and validation data for U-net training and validation. Field data are regarded as the test data to assess the performance of the trained U-net. To guarantee the deblending performance of the field data to some extent, parts of field data with labels are used to fine-tune the trained U-net based on transfer learning. The fine-tuning procedure is relatively fast within several minutes. To further improve the deblending performance, we incorporate an iterative strategy with the fine-tuned U-net. The deblending performance is promising in the quality and computational efficiency compared with the curvelet-thresholding-based deblending method, which demonstrates the validity of the proposed intelligent deblending method.

The blended acquisition can help improve the seismic data quality or enhance the acquisition efficiency. However, the blended seismic data should first be separated for subsequent traditional seismic data processing steps. The signal is coherent in the common receiver domain, and the blending noise shows randomness when the blending operator is constructed using a random time delay series. The seismic data can be characterized sparsely by the curvelet transform which can be used for deblending. However, it has a high computational cost, especially for large-volume seismic data. The spectrum of the seismic data is band-limited with the conjugate symmetry property, and thus the principal frequency components can characterize the signal accurately. The size of the principal frequency components is at least halved. Thus, we propose to implement the curvelet transform on the principal frequency wavenumber (PFK) domain data instead of the time-space (TX) domain data. The size of the PFK domain data is at least halved compared with the TX domain data, which can improve the deblending efficiency reasonably. The related formulae are fully derived and the efficiency enhancement analysis is provided in detail. One synthetic and two field artificially blended data are provided to demonstrate the validity and flexibility of the proposed method in the efficiency improvement and the deblending performance. The separated gathers can be beneficial for subsequent traditional seismic data processing procedures.

The trace interval in the common shot and receiver gathers is always inconsistent. The inconsistency affects the final performance of seismic data processing, and the reconstruction methods can enhance the consistency. Unfortunately, most interpolation algorithms are suitable in randomly missing cases, and the difficulty increases sharply in regularly missing cases, especially with big gaps. As deep learning (DL) has a strong self-learning ability in nonlinear characterizations to avoid linear events, sparsity, and low rank assumptions, we introduce DL into missing shots' reconstruction. The spatial reciprocity of Green's function is used to provide reasonable training data sets. First, the residual learning networks (ResNets) and the interpolation issue are briefly illustrated. Then, the spatial reciprocity is reviewed and illustrated qualitatively using the common shot and receiver gathers. The similar features in the common shot and receiver gathers guarantee the reasonability to regard the common shot gathers as the training sets and to regard the common receiver gathers as the test sets. The common shot gathers are divided into the training sets to train ResNets and the validation sets to verify the performance of the trained ResNets. Finally, the trained ResNets are used to reconstruct missing shots intelligently in the common receiver gather. Three different data sets are used to prove the validity of the proposed strategy. After reconstruction, the events are more continuous with less serrations and serious frequency wavenumber (FK) aliasing is attenuated effectively. The reconstructed data with a better consistency can improve the accuracy of migration and the final reservoir characterization.

The Radon transform (RT) has been widely used as a powerful tool, especially in exploration geophysics fields, such as multiple removal, interpolation, and velocity analysis. However, the existing strong outlier effects can seriously decrease the accuracy of the traditional RT. Therefore, a robust time-invariant RT (TIRT) is proposed in the mixed time-frequency domain to attenuate the outlier effects by using double L1-norm sparse constraints performed on the data misfit and the Radon model in the time domain. For the TIRT, the forward RT and its adjoint can be implemented in the frequency domain efficiently. Only one matrix inversion for each frequency component is involved in all iterations to speed up the iterations. Then, the 1-D alternating split Bregman (ASB) algorithm is introduced and improved for 2-D Radon model updating efficiently. It involves matrix-vector multiplication operators and two proximity operators. These two proximity operators can guarantee the robustness and sparseness of the proposed method. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of the proposed method. The proposed method is also used for interpolation to decrease the trace interval. After interpolation, seismic data are more continuous with less serrations along the spatial direction and the frequency-wavenumber spectrum is more focused. The interpolated data have wider potential applications in improving the accuracy of the following seismic processing. It should be noted that the proposed robust and efficient RT can also be used in remote sensing and computerized tomography fields instead of the traditional RT.

Marine seismic data may be contaminated by external source interference noise (ESIN) in some cases. These ESINs can be suppressed automatically, provided we can localize these external sources correctly. In this paper, we propose an automatic method to localize the external sources using a density-based clustering method and then suppress the ESINs according to the sources. In a shot gather, the time delays between three randomly selected seismic traces are used to calculate the location of one potential external source directly. Since there are many seismic traces in one shot gather, we can get a lot of estimates of the external source locations. In general, some of these locations are falsely detected sources. Assuming that the location of the external source is fixed or slowly changes during one seismic shot acquisition, multiple true estimates of an external source location, which are obtained from different trace groups, should focus together. In contrast, the false locations are arbitrarily distributed. Therefore, a density-based clustering method is applied to obtain the final source location estimate. Since each potential source corresponds to one cluster, we find out the strongest ESIN corresponding to the cluster with maximum sample number to ensure the accuracy. After that, the detected ESIN is flattened and then extracted by singular value decomposition. This method is an iterative method, and in each iteration, one ESIN is suppressed. And the high-pass filter is optional to detect the weak ESINs and protect the valid signals. The synthetic data example and real field marine data example prove that the proposed method can localize the external sources accurately and suppress multiple ESINs effectively.

Deghosting is a critical step to improve the resolution of marine seismic data. For the frequency wavenumber (f-k) spectra of the original seismic data with ghosts, there always exist some low-SNR frequency components around the centers of the frequency notch bands, which are caused by the ghosts. In general, the traditional inverse filtering-based deghosting methods lack the ability to recover these low-SNR frequency components without amplifying the additive noise. In this letter, we propose a postprocessing method to enhance the deghosted seismic data by reconstructing these low-SNR frequency components. The proposed method includes two key steps. First, the low-SNR frequency components of the deghosted seismic data in the f-k domain are located adaptively by using both the original seismic data and its deghosted result. Second, the projection onto convex sets algorithm is introduced to reconstruct these low-SNR frequency components located in the previous step. To illustrate this, we use the proposed method to improve the deghosted results obtained by the non-Gaussianity maximization based f-k deghosting method. Applications on synthetic and real field marine data sets demonstrate the validity of the proposed method which can enhance the deghosted results significantly.

The time-frequency analysis tools, which are very useful for anomaly identification, reservoir characterization, seismic data processing, and interpretation, are widely used in discrete signal analysis. Among these methods, the generalized S transform (GST) is more flexible, because its analytical window can be self-adjusted according to the local frequency components of the selected discrete signal, besides there exist another two adjustable parameters to make it superior to the S transform (ST). But the amplitude-preserving ability is a little poor near the boundary because the analytical windows do not satisfy the partition of unity, which is a sufficient condition for amplitude-preserving time-frequency transforms. In order to make the GST with the amplitude-preserving ability, we first design a new analytical window, and then propose an amplitude-preserving GST (APGST), but with a higher computational cost. To accelerate the APGST, we provide two strategies: the 3$\sigma$ criterion in the probability theory is introduced to accelerate the analytical windows summation and a convolution operator is derived to accelerate the time integral or summation, which generates an efficient APGST (EAPGST). Finally, the proposed EAPGST is used for seismic data attenuation compensation to improve the vertical resolution. Detailed numerical examples are used to demonstrate the validity of the proposed EAPGST in amplitude preserving and high efficiency. Field data attenuation compensation result further proves its successful application in improving the vertical resolution. Besides, the proposed EAPGST can be easily extended into other applications in discrete signal analysis, and remote-sensing and seismology fields.

Random noise in seismic data can affect the performance of reservoir characterization and interpretation, which makes denoising become an essential procedure. This letter focuses on suppressing random noise in poststack seismic data while preserving the edges of desired signals. Due to the lateral continuity of seismic data, polynomial fitting (PF) method can be a good alternative in attenuating random noise. However, discontinuities exist widely in poststack seismic data, which might be damaged by the PF filter. By contrast, principle component analysis (PCA)-based filters have better performance in edge preserving, but there appear artifacts in the denoised results using the PCA-based filters. Thus, we propose an edge-preserving polynomial PCA filter which combines advantages of the PF and PCA methods by optimizing a PCA problem with a weighted polynomial constraint. The weight coefficient is determined adaptively according to the signal-to-noise ratio estimation and the energy proportion in the selected analysis window, which can help distinguish the horizontal continuous events and the edges effectively. To deal with the complicated slopes which make the local linear hypothesis invalid, we introduce a robust local slope estimation method and apply the slope estimation-based event tracing strategy to horizontally align the data set. Synthetic and field data examples show that the proposed method has a better performance in noise attenuation and edge preserving, compared with the edge-preserving PF method. In addition, the denoised results are free from artifacts.

Sampling irregularity in observed seismic data may cause a significant complexity increase in subsequent processing. Seismic data interpolation helps in removing this sampling irregularity, for which purpose complex-valued curvelet transform is used, but it is time-consuming because of the huge size of observed data. In order to improve efficiency as well as keep interpolation accuracy, I first extract principal frequency components using forward Fourier transform. The size of the principal frequency-space domain data is at least halved compared with that of the original time-space domain data because the complex-valued components of the representation of a real-valued signal (i.e., a complex-valued signal with zero as its imaginary component) exhibit conjugate symmetry in the frequency domain. Then, the projection onto convex projection (POCS) method is used to interpolate frequency-space data based on complex-valued curvelet transform. Finally, interpolated seismic data in the time-space domain can be obtained using inverse Fourier transform. Synthetic data and field data examples show that the efficiency can be improved more than two times and the performance is slightly better in the frequency-space domain compared with the POCS method directly performed in the time-space domain, which demonstrates the validity of the proposed method.

The S-transform (ST), as a time-frequency analysis tool, has been widely used, but the amplitude preserving property is a little poor near the boundary of the selected discrete signal. The reason lies that the summation of the product between the analytical window and the comprehensive window over the sliding step deviates from unity near the boundary in the discrete cases. In order to hold the amplitude preserving property for the discrete signal recovery analysis, an amplitude preserving S-transform (APST) is proposed based on a novel analytical window selection. First, lots of numerical tests are used to analyze the shortcomings of the ST near the boundary for the selected discrete signal and demonstrate the effectiveness and the validity of the proposed APST using the novel analytical window. After that, the proposed APST is used for seismic data attenuation compensation, during which the attenuation function is estimated based on the minimum phase assumption using a statistical variable-step hyperbolic smoothing method. Numerical examples on synthetic and field data demonstrate the validity of the proposed method using the seismogram and time-frequency spectrum comparisons. Besides, the proposed APST can be easily extended into a generalized ST which is more flexible compared with the ST, and it can also be used in seismology, remote sensing, and other related discrete signal analysis fields.