2026-02-10 2026, Volume 35 Issue 1

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  • research-article
    Frank O. Ofowena, Akhmal Sidek, Yasir Bashir, Mingtao Nie

    Three-dimensional (3D) seismic parameter optimization has become an essential component of subsurface imaging, especially in oil fields where space, safety, and environmental restrictions limit conventional survey design. This study critically reviews and synthesizes 87 English-language publications on 3D seismic parameter optimization retrieved from the Scopus database. The analysis combined a systematic literature review with bibliometric mapping, using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines and Biblioshiny software to identify thematic patterns, research clusters, and methodological gaps. The results show that global research on 3D seismic optimization has grown steadily from 2003 to 2025, reflecting an increasing emphasis on survey efficiency and sustainable exploration. Early studies focused on geometric configuration and fold distribution, whereas recent works integrate environmental safety, vibration control, and cost efficiency. Three major thematic clusters were identified: Geometric and operational optimization, congestion and environmental management, and the integration of emerging sensing and modeling technologies. Despite this progress, most studies lack standardized congestion metrics, quantitative vibration thresholds, and comprehensive economic evaluations. The review concludes that 3D seismic optimization has evolved into a multidisciplinary framework that connects geometry, environmental protection, and operational safety. Future research should adopt measurable congestion indices, integrate distributed acoustic sensing technologies, and strengthen academic-industry collaboration to promote reproducible, cost-effective, and environmentally responsible seismic survey design.

  • research-article
    Mingliao Wu, Juan Wu, Min Bai, Haiyu Li, Zhixian Gui, Guangtan Huang

    Enhancing seismic image resolution while effectively suppressing noise remains a critical challenge in accurately characterizing subsurface geological structures for oil and gas exploration. Traditional methods often fail to balance the recovery of fine details with robustness to noise, particularly in complex geological settings or under high-noise conditions. This study proposes a deep learning-based joint model, U-Net Shifted Window (Swin) Transformer-based dense residual network (U-STDRNet). The model integrates the global modeling capability of the Swin Transformer, the hierarchical feature reuse mechanism of the residual dense network, and an attention-guided strategy to jointly perform seismic image super-resolution and denoising. Built upon the U-Net encoder-decoder architecture, the model embeds Swin Transformer-based convolutional residual blocks. These blocks employ both a feature fusion block with the Swin Transformer and a feature fusion block with a convolutional neural network to effectively capture stratigraphic continuity and enhance detailed features such as fault edges. Residual dense blocks further improve weak signal recovery (e.g., thin-layer interfaces) through dense residual connections. Furthermore, the convolutional block attention module is integrated into skip connections, employing a dual-channel spatial weighting mechanism to suppress noise and emphasize key geological regions. Experimental results and field-data experiments demonstrate that U-STDRNet achieves a higher peak signal-to-noise ratio than the traditional U-Net. In addition, the model successfully restores fault and fold continuity details while exhibiting superior noise suppression compared to existing methods.

  • research-article
    Hui Qi, Jing Ba, Wenhao Xu, Yuanyuan Huo, Jishun Pan, Qingchun Jiang, Congsheng Bian

    Oil-sand reservoirs saturated with heavy oil are subject to complex physical and chemical changes under high-temperature conditions. These changes can be quantified using the thermal damage factor, which we evaluated based on Young’s modulus and the velocities of P- and S-waves. For the quasi-solid phase of heavy oil-bearing rocks, this method effectively characterizes the degree of rock damage. As temperature increases, heavy oil transitions into a fluid state, reducing rock stiffness. In addition, the thermal expansion of heavy oil weakens the rock matrix and influences the extent of rock damage. We combined an extended Gassmann equation with the Maxwell model for heavy oil to estimate the thermal damage factor. The model was validated using ultrasonic experimental data from rock samples, enabling a quantitative description of the relationship between dry and wet rocks at different temperatures of thermal damage in oil sand. We found that in these rock samples, the temperature-dependent trend of the thermal damage factors can be separated into two stages based on the fluid-viscosity threshold (the liquid point). The porosity of rock samples has no significant influence on this threshold, whereas the viscosities of different fluids affect the threshold value of the thermal damage factor in oil sands. The proposed model provides a theoretical basis for improving the accuracy of reservoir prediction, evaluation, and adjustment, and for optimizing heavy-oil thermal recovery. Furthermore, it offers practical applicability for thermal-recovery monitoring and numerical simulation, enabling more reliable interpretations of temperature-dependent elastic responses.

  • research-article
    Yiru Du, Guoqing Chen, Cong Pang, Tianwen Zhao

    To address the challenges of fracture-vuggy parameter prediction in carbonate reservoirs, such as strong multi-scale heterogeneity and a lack of physical constraints, this study proposed a Transformer-Graph Neural Operator (GNO)-Physics-Informed Neural Network (PINN) joint prediction framework, which achieves a bidirectional coupling between multi-source data fusion and physical laws. First, a Transformer module with a multi-scale attention mechanism and spherical coordinate effectively captures cross-scale spatiotemporal features in three-dimensional geological space (reducing error by 12.3%). Second, a dynamic GNO based on physical similarity adaptively tracks the evolution of fracture-vuggy connectivity (achieving a topology update accuracy of 93.5%). Finally, a PINN module embedded in the seepage-mechanical coupling equations constrains the physical residual loss to the order of 0.42×10⁻3, reducing the conservation error from 3.17% to 0.48%. In an empirical study of Ordovician fracture-vuggy reservoirs in the Tarim Basin, this framework achieved a mean absolute error of 3.57% and an R2 of 0.90 for fracture-vuggy volume fraction (Vf). In high-pressure gradient regions (>5 MPa/m), the relative error was reduced by 18%, significantly outperforming traditional methods(reducing Kriging error by 40.7%) and single-module models (PINN error reduction of 15.3%). Experimental results showed that dynamic graph construction increased the spatial autocorrelation index (Moran’s I) to 0.71; the introduction of physical constraints reduced extreme error samples by 63%; and the multimodal collaborative training strategy resulted in a 19.7% improvement in overall performance. This research provides a new paradigm for high-precision and physically interpretable digital twin modeling of carbonate reservoirs.

  • research-article
    Peidong Huang, Jun Lu, Chun Yang, Zhe Yang, Wei Yang

    Since transmission losses, internal multiples, and mode conversions are not considered, conventional inversion methods based on the Zoeppritz equations and related approximations have limited capability in high-resolution inversion of thin interbeds. Reflectivity methods, which account for these wave propagation effects, are more suitable for inverting thin interbeds; however, most related studies approximate thin interbeds as several isotropic thin beds, which are inadequate for complex thin interbeds containing thin vertical transverse isotropy (VTI) beds. In this study, thin VTI beds with the characteristics of short-term cycles are regarded as the fundamental compositional units of thin interbeds. We propose a joint PP- and PS-wave amplitude variation with angle inversion method for thin interbeds containing thin VTI beds. The method uses second-order approximations to the Kennett equations for thin interbeds containing thin VTI beds as the forward operator. The inversion objective function is established using the Levenberg-Marquardt algorithm, incorporating sparse constraints to improve the stability and resolution of the five-parameter inversion. Inversion results from model tests and field data demonstrate that the proposed method more accurately extracts elastic parameters and anisotropic information from thin interbeds compared to conventional methods based on the exact Zoeppritz equations, effectively improving inversion accuracy and offering a technical advancement for fine prestack inversion of complex thinly interbedded reservoirs.

  • research-article
    Qingling Du, Qian Xu, Nan Guo, Shuai Liu, Shijie Liu, Denghui Gao

    The precise identification of adverse geological bodies, such as goafs, karst cavities, and faults, is crucial for engineering safety and economic viability. However, conventional drilling methods suffer from high costs, limited coverage, and the risk of overlooking anomalies. While existing geophysical techniques can address drilling’s limitations, they are often constrained by non-uniqueness and insufficient resolution. To address these challenges, this paper proposes a novel technique for stratigraphic evaluation based on the polarization analysis of microtremor surface waves, aiming to improve the accuracy and efficiency of identifying dynamic site parameters in complex geological settings. We systematically validated the feasibility of using the elliptical polarization ratio of Rayleigh waves for subsurface characterization through theoretical analysis and field data. Numerical simulations confirmed that the method can clearly identify localized geological anomalies under noise-free conditions. For field data processing, we developed a workflow to extract Rayleigh waves with a high signal-to-noise ratio from microtremors. This workflow isolates valid wave components using principal frequency filtering and directional discrimination, while mitigating noise impact on dispersion estimation. The final polarization ratio profile strongly correlated with magnetotelluric resistivity data, successfully imaging goafs, fractured zones, and bedrock interfaces. Stacking codirectional wave events further enhanced deep structural resolution and resulted in consistency. In conclusion, this study demonstrates that the polarization-based method is a feasible, flexible, and promising tool for engineering applications, offering a reliable foundation for fine-scale site characterization.

  • research-article
    Xu Song, Guanghong Ju, Jun Shen

    The eastern section of the Northern Margin Fault of the Hami Basin is located in the easternmost part of the active tectonic belt of the Tianshan Mountains, and is an important active fault in the region. Since major projects need to consider avoiding or adopting anti-fracture measures, it is necessary to determine the exact location of the fracture, three-dimensional (3D) orientation, and other anti-fracture-related parameters. To obtain the accurate location and 3D geometric parameters of the rupture, we carried out a systematic study in three typical sites based on remote sensing interpretation and geomorphological survey, and the comprehensive use of microdynamic detection and trench verification. The results show that the fracture section is spreading in east-west direction, with a total length of about 35 km, and is dominated by retrograde movement, which is geomorphologically manifested as a fault steep canyon on the pre-hill flood fan, with the height of steep canyon up to 11-13 m. The microdynamic profiles reveal the deep production of the fracture, with the width of the fracture zone ranging from 60 to 100 m, and the dipping angle ranging from 60° to 70°; and the trench validation reveals that the dipping angle of the faults is slowing down to 35°-45° at the surface, showing a “deep and steep” pattern, and the “deep and steep dipping angle” is also shown. The geometrical structure of the fault is characterized as “deep, steep, and shallow.” As an emerging geophysical detection method, the micro-motion detection technique used in the study showed good recognition ability in complex terrain and thick cover conditions, improving the detection accuracy of fracture location. The results of the study not only enrich the understanding of the active features of the Northern Margin Fault of the Hami Basin, but also provide the fault resistance parameters for the evaluation of regional seismic hazard and the selection of sites for major projects, and expand the scope of application of the micro-motion detection method in the study of active faults, providing an important reference for the regional tectonic evolution and seismic resistance of the project.

  • research-article
    Yunhao Cui, Yuhua Chen, Chao Xu, Yaping Huang, Qiang Guo, Zhiqiang Lu, Zhanpeng Chen, Yuwen Qian

    Identifying and characterizing fractured cavities is essential for exploring carbonate reservoirs. However, characterizing the development and distribution of fractured cavities through post-stack seismic attribute analysis remains challenging. Recently, convolutional neural networks (CNNs), such as UNet and its enhanced versions, have enabled the quantitative identification of fractured cavities. Despite these advancements, the local receptive field and weight-sharing mechanisms of these CNNs limit their capability to capture long-range features within strike-slip fault systems. In addition, neural networks are inherently affected by data uncertainty. To address these challenges, a two-step methodology is proposed. The first step utilizes a Swin-UNet transformer (UNETR) model, enhanced with an attention gate, to interpret fractured cavities. The transformer in Swin-UNETR improves the detection of fractured cavities in strike-slip fault zones, whereas the attention gate enhances the recognition of small fractured cavities by increasing their response in the feature maps. This enhanced Swin-UNETR model overcomes the limitations in modeling long-range features. In the second step, the fractured-cavity identification results are combined with seismic attributes from conventional analysis. Principal component analysis is employed both to increase the relative weight of the neural network recognition results in the attribute fusion and to reduce the uncertainty associated with any single identification method. The methodology was validated in the Shunbei area, yielding horizontal segmentation and vertical zonation of fractured cavities, as well as their characterization through fixed-grid modeling. By combining deep learning-based feature extraction with seismic attributes, this approach improves the accuracy of fractured cavity identification and characterization in carbonate reservoirs.

  • research-article
    Wei Liu, Yi Liao, Jie Cui, Ning Zhang, Guo Dong Zhang, Zi Jing Gong, Rong Li, Lian Lian Liu, Miaoyang Yuan

    In deepwater fields, drilling costs are extremely high, and the “one sand, one well” situation is common, in which a single well must control an overly large area of the gas field. Structural accuracy decreases in areas distant from the well locations, making gas reservoir prediction and sand body delineation challenging due to the limited resolution of seismic data. To address these challenges, this study applied high-precision full-waveform inversion (FWI) velocity modeling and broadband imaging technology in a deepwater exploration of the South China Sea. In the preprocessing stage, based on the geological challenges and features of the acquired seismic data, we selected appropriate signal-processing methods and optimized the algorithms and parameter sets, successfully developing a customized broadband processing workflow specifically tailored for deepwater applications. The entire broadband processing sequence effectively supported subsequent FWI modeling. During the imaging stage, FWI was successfully applied for the 1st time in the deepwater of the South China Sea. Together with Q pre-stack depth migration, this integrated approach effectively addressed challenges in structural depth prediction and significantly improved imaging resolution. This study provided real-time support for gas field development and optimized the well placement for deepwater development.

  • research-article
    Cong Pang, Tianwen Zhao, Guoqing Chen, Sirui Liu, Xingxing Li, Ya Xiang, Piyapatr Busababodhin

    The precise determination of microseismic source locations is one of the core components of theoretical research in microseismic monitoring technology. Multi-objective intelligent optimization is an effective approach for microseismic source positioning, but it faces challenges such as unclear rationality of model combinations, susceptibility to local optima, and significant variability in positioning results. To address these issues, four distinct mathematical models for microseismic source positioning were designed based on the arrival time difference model and the arrival time difference quotient model. These models were then combined in pairs to form six different microseismic source positioning model combinations, which were used as the optimization objective functions for the multi-objective computational algorithm. A set of microseismic source forward modeling experiments based on three-dimensional polyhedral array shapes, two sets of engineering microseismic data validation experiments, and one set of multi-objective computational method comparison experiments were designed. the multi-objective grasshopper optimization algorithm (MOGOA) was introduced to solve the six model combinations and employed in four sets of microseismic source positioning experiments. Multiple statistical metrics were applied to evaluate the performance of each model combination. The experimental results indicate that the microseismic inversion mathematical model combination (TDA, TDA-P1), combined with the MOGOA algorithm’s multi-objective optimization positioning strategy, can achieve high microseismic source positioning accuracy under relatively reliable microseismic event data, and the model calculations are relatively robust. Under microseismic blasting data, the average positioning error over 100 rounds reached 27.6035 m, with standard deviation and interquartile range averages of only 3.2114 m and 5.5896 m, respectively, outperforming other inversion model combinations and similar multi-objective positioning methods. For microseismic event data with significant systematic errors, the microseismic inversion mathematical model combination (TDA-P1, TDQA-P1) demonstrates superior positioning performance, with an average positioning error of 151.1915 m over 100 iterations, significantly outperforming other model combinations. These model combination positioning performance studies hold practical application value in the field of microseismic monitoring.

  • research-article
    Mingtao Nie, Zhouhong Wei, Tao Fang, Xiaolong Jiang, Yongan Xu, Yang Liu, Yongfei Qi

    Seismic vibrators are the primary sources for land seismic acquisition, featuring controllable bandwidth and energy, low environmental impact, safety, and high efficiency. With the widespread application of “2W&H” technology, wide-frequency seismic data, particularly low-frequency components, have attracted increasing attention. However, the ground force output of a vibrator is severely constrained at low frequencies, primarily due to limitations in its mechanical and hydraulic systems. Among these, hydraulic system limitations are often associated with oil flow, which is largely constrained by the pump’s maximum capacity; however, oil flow is not measured during vibrator sweeps. The system complexity prevents the installation of flow sensors on vibrators, making the performance of the vibrator oil flow unmonitored. Since the oil flow directly determines the quality of the vibrator ground force output, it is essential to understand the behavior of vibrator oil flow. In this study, a detailed analysis of the working mechanism of a seismic vibrator was conducted, as well as its low-frequency force-output limitations. Then, we proposed a method for estimating vibrator oil flow. Both theoretical analyses and field-testing data were used to validate the proposed estimation method. The estimated data demonstrated strong consistency with the direct flow measurement using flow sensors. Moreover, the results confirm the feasibility of the proposed estimation method. This method provides a real-time quality control indicator for the vibrator oil flow performance during vibrator sweeps, thereby enabling complete monitoring of the vibrator performance quality at low frequencies. In addition, this method holds promising potential for broad application in land vibroseis exploration.

  • research-article
    Jianhua Wang, Cong Niu, Yandong Wang, Yun Ling, Di Wang, Xiuping Jiang, Chenshuo Yuan

    Fault identification is a critical step in seismic data interpretation. Traditional fault identification methods rely heavily on manual interpretation, which is inefficient and significantly influenced by subjective factors. This paper proposes a fault identification algorithm based on a Residual U-Net-curvelet hybrid framework. By introducing residual learning strategies and applying batch normalization and skip connection techniques, the generalization ability and convergence speed of the network are enhanced, thereby improving the accuracy and efficiency of fault identification. Results from field data processing demonstrate that this method achieves high identification accuracy under complex geological structures and low signal-to-noise ratio conditions, providing reliable fault identification results for efficient seismic data interpretation.

  • research-article
    Meng Yuan, Zhiwei Miao, Lei Pan, Jianlong Su, Chang Sun

    Tight sandstone channel systems occur in the second member of the Lianggaoshan Formation in the Sichuan Basin. These channels predominantly exhibit single bright-spot reflections on seismic sections. Due to the limited resolution of post-stack data and the constraints of attribute dimensionality, drilling results reveal complex internal lithological assemblages and pronounced lateral heterogeneity within these channels. Traditional post-stack methods struggle to effectively characterize internal channel details, thereby hindering subsequent exploration planning and reserve evaluation. To address these challenges, this study develops a pre-stack seismic inversion workflow based on generalized Gaussian distribution (GGD) prior constraints, aiming to enhance the identification and prediction of complex channel sand bodies. First, pre-stack amplitude versus offset (AVO) response analysis was conducted using typical wells to determine the effective incident angle range. By integrating optimal angle stacked data and AVO attribute extraction, the accuracy of characterizing the lateral distribution of channels was improved. Subsequently, a low-frequency facies-controlled model was constructed by integrating AVO attributes with elastic parameters. GGD prior constraints were incorporated into the pre-stack elastic parameter inversion, enabling detailed prediction of internal channel architecture. This technique yielded promising results in the Fuxing Block and was successfully validated in the Bazhong Block. It effectively enhanced the accuracy of identifying and predicting complex channels, providing technical support for the exploration, deployment, and resource evaluation of Jurassic tight sandstone channels in the Sichuan Basin.

  • research-article
    Daling Hou, Jixiang Xu, Meng Li

    In mountainous seismic exploration, complex near-surface environments cause strong wave scattering, reducing the signal-to-noise ratio and complicating data processing. Therefore, suppressing scattered waves is crucial. To address this issue, this study proposes a convolutional autoencoder constrained by local scattered wave characteristics to suppress near-surface scattered waves (NSWs) in full-wavefield seismic data. This method uses the scattered waves predicted by seismic interferometry as the network input, and the original seismic records containing true scattered waves as the label. Since there are differences in amplitude and phase between the predicted scattered waves and the true scattered waves, the network introduces local wavefield features of the scattered waves for constraint, and adds a smoothness regularization term in the loss function to ensure the continuity of the output waveform. After training, the network maps the energy of predicted scattered waves into the actual seismic records, thereby accurately extracting scattered waves. Finally, by subtracting the network output from the original records, clean data with scattered waves removed can be obtained. This method is a self-supervised learning strategy and does not require additional clean signal samples. During training, the weights of each item in the loss function can be dynamically adjusted to guide the network to focus on local scattered-wave features, avoid learning effective wave information, and ensure that only scattered-wave components are retained in the output. Practical application results show that this method can effectively suppress NSWs and improve the signal-to-noise ratio of seismic data.

  • research-article
    Wenlong Jiao, Naihao Liu, Yongxiang Jiang, Jun Yang, Wei Zhao

    Seismic attenuation estimation is an important tool for hydrocarbon identification and reservoir characterization. Conventional time-frequency (TF) methods, particularly the S-transform (ST), are widely applied but suffer from a systematic dominant-frequency shift and fixed TF resolution, which may reduce the accuracy of attenuation analysis. To address these limitations, we introduce the unscaled generalized ST (UGST) and apply it to field seismic data from the Ordos Basin in Northwest China to qualitatively estimate attenuation. The UGST corrects the frequency shift inherent in the standard ST and introduces two tunable parameters that enable flexible adjustment of TF resolution to better match local seismic responses. Application to a three-dimensional seismic dataset demonstrates that the UGST produces TF spectra with improved readability and accurate frequency localization, resulting in a reduction of approximately 10 Hz in dominant frequency error compared to ST. The attenuation attributes derived from UGST show strong correspondence with known gas-bearing intervals, as verified by well-log data. The derived attenuation attributes show strong correspondence with gas-bearing intervals, with anomaly overlap rates exceeding 85% relative to well-log fluid indicators. These results indicate that the UGST provides a robust and effective approach for delineating seismic attenuation, offering practical value for reservoir characterization in exploration geophysics.

  • research-article
    Shunhao Hu, Shulin Pan, Ziyu Qin, Yinghe Wu, Yaojie Chen

    The conventional iterative shrinkage-thresholding algorithm (ISTA) faces several limitations, such as dependence on manual parameter tuning and limited ability to recover weak reflections. Hence, this study proposes a sparse spike deconvolution method based on an adaptive learned ISTA (Ada-LISTA) and a self-supervised physics-driven objective function to overcome these challenges. First, using Ada-LISTA as the backbone, the threshold and step size in the iterative process were dynamically adjusted through its adaptive parameter learning, and the seismic wavelet dictionary was used as the model input to enhance the adaptability to different complex geological scenarios. Then, a self-supervised physics-driven objective function was introduced to jointly optimize the residual of seismic records and the sparsity of reflection coefficients, further improving the interpretability of the model. Finally, comparative experiments were carried out using theoretical simulation data and actual seismic data from the Bohai Bay Basin, China, to evaluate the inversion performance of the proposed method. The experimental results indicate that, compared to the traditional ISTA algorithm, the proposed method achieved marked enhancements in reflection coefficient inversion accuracy, seismic resolution, and robustness against noise. Overall, the proposed method offers an efficient and reliable technical solution for high-resolution seismic inversion and effective recovery of weak reflection signals, providing practical support for interpreting complex subsurface geological structures.

  • research-article
    Yunbo Niu, Yingming Qu, Zhenchun Li

    Full-waveform inversion (FWI) is highly sensitive to the initial model and low-frequency content, and it often suffers from cycle skipping and degraded resolution in complex media. We propose a physics-constrained autoencoder-based FWI with axial self-attention (AxPCAE-FWI). In a unified encoder-decoder architecture, a differentiable acoustic wave-equation solver is explicitly embedded, and the data-domain waveform misfit is used as the primary objective, so that training is consistently governed by wave physics and does not rely on paired seismic-velocity labels. The encoder extracts inversion-relevant, low-dimensional features, while the decoder reconstructs physically admissible velocity models. To capture long-range spatiotemporal dependencies in the time-offset plane, axial multi-head self-attention is introduced in the encoder, where global attention is computed separately along the time and receiver axes; two one-dimensional global attentions approximate a single two-dimensional (2D) global attention, reducing the computational complexity relative to full 2D attention while preserving global context. This design improves the representation of complex wavefield phenomena, including multiples, converted waves, and far-offset reflections, thereby alleviating cycle skipping when low-frequency information is limited. Numerical experiments on the Marmousi2 and Society of Exploration Geophysicists salt-dome models demonstrate stable convergence and high structural similarity with improved geological plausibility. Compared to conventional physics-informed adaptive extended FWI under the same iteration budget, AxPCAE-FWI yields clearer salt-body boundaries and better imaging of structurally complex regions, with improved robustness to noise.

  • research-article
    Jianlei Zhang, Bo Yang, Min Bai, Xilin Qin, Baobin Wang, Zhen Zou, Boyuan Lv

    The dictionary learning approach has proven effective in seismic data denoising and interpolation. Its core advantage lies in the ability to continuously update the initial dictionary, thereby adapting to the complex structural characteristics of seismic data. However, many existing implementations rely on predefined transforms (e.g., discrete cosine transform) for dictionary initialization. These fixed, data-agnostic bases often fail to fully capture the unique features of seismic signals, which may compromise the sparsity and fidelity of signal representation. Such a limitation can significantly degrade the performance of tasks requiring high-precision reconstruction or noise attenuation. To address this issue, we propose an innovative dictionary learning framework based on a variational sparse representation model. Specifically, this framework first extracts small data patches from arbitrary locations in seismic data, and then constructs a pre-training dataset using a windowing algorithm to preserve fine-grained data features. This process yields an initial dictionary that inherently encodes the intrinsic characteristics of the input seismic data. Subsequently, the initial dictionary is separately refined and updated through the K-singular value decomposition (K-SVD) and sequential generalization of K-means (SGK) algorithms, resulting in an optimized dictionary with more accurate and data-adaptive features. In addition, we integrate a multi-iteration projections onto convex sets algorithm to compensate for missing data features, ultimately achieving high-precision seismic data interpolation and noise attenuation. Numerical experiments demonstrate that the proposed methods(variational SGK and variational K-SVD) outperform the conventional K-SVD and SGK algorithms in both interpolation accuracy and denoising performance.