Self‐Supervised Seismic Data Reconstruction With Blind‐Trace Mask Mapper and Attention

Seismic data are often undersampled owing to physical or financial limitations. However, complete and regularly sampled data are becoming increasingly critical in seismic processing. In this paper, we present an efficient two-dimensional (2D) seismic data reconstruction method that works on texture-based patches. It performs completion on a patch tensor, which folds texture-based patches into a tensor. Reconstruction is performed by reducing the rank using tensor completion algorithms. This approach differs from past methods, which proceed by unfolding matrices into columns and then applying common matrix completion approaches to deal with 2D seismic data reconstruction. Here, we first re-arrange the seismic data matrix into a third-order patch tensor, by stacking texture-based patches that are divided from seismic data. Then, the seismic data reconstruction problem is formulated into a low-rank tensor completion problem. This formulation avoids destroying the spatial structure, and better extracts the underlying useful information. The proposed method is efficient and gives an improved performance compared with traditional approaches. The effectiveness of our patch tensor-based framework is validated using two classical tensor completion algorithms, low-rank tensor completion (LRTC), and the parallel matrix factorization algorithm (TMac), on both synthetic and field data experiments.

Data acquired through seismic surveys suffers from information loss for various reasons. Among these, shallow gas affects signals beneath it and causes distortion of seismic wave signals. These distorted signals often cause difficulties in interpreting seismic data. Various preceding research has been conducted to mitigate this issue, and this study presents an interpolation method using self-supervised machine learning. The dataset we use consists of small-scale marine seismic survey data acquired from Youngil Bay near eastern continental margin of the Korean Peninsula. 2D planes are randomly extracted from 3D seismic data to generate training data of various sizes, which are then used to create an artificial neural network model. This study utilizes the U-Net++ architecture with an attention module to overcome the limitations associated with U-Net and to focus and emphasize repetitive patterns. In the training process, both the L1 loss function and the structural similarity index (SSIM) loss function are used as hybrid loss function. This enables the network to recognize both the overall patterns of the data and the key patterns to focus on. The neural network model created through this study shows successful performance in detecting patterns in the original data and interpolating missing values of seismic data. The output data generated through the proposed network improves stratigraphic continuity by interpolating the missing values of the original data and restoring the lost structure.

The 3-D seismic data reconstruction can be understood as an underdetermined inverse problem, and thus, some additional constraints need to be provided to achieve reasonable results. A prevalent scheme in 3-D seismic data reconstruction is to compute the best low-rank approximation of a formulated Hankel matrix by rank-reduction methods with a rank constraint. However, the predefined Hankel structure is easily damaged by the low-rank approximation, which leads to harming its recovery performance. In this article, we present a structured tensor completion (STC) framework to simultaneously exploit both the Hankel structure and the low-tubal-rank constraint to further enhance the performance. Unfortunately, under the assumption of elementwise sampling used by existing methods, STC is intractable to be solved since Hankel constraints cannot be expressed as linear tensor equations. Instead, tubal sampling is proposed to describe the missing trace behavior more accurately and further build a bridge between tensor and matrix completion (MC) to overcome the solving issue in two aspects: through the bridge from tensor to MC, STC can be solved efficiently using MC from random samplings of each frontal slice in the Fourier domain. Through the bridge from matrix to tensor completion, various tensor models within the framework can be developed from noise-specific MC to meet the need for data reconstruction in changeable noise environments. Moreover, alternating-minimization and alternating-direction methods of multipliers are developed to solve the proposed STC. The superior performance of STC is demonstrated in both synthetic and field seismic data.

Seismic impedance inversion is a geophysical technique that transforms seismic data into quantitative subsurface properties, primarily acoustic impedance. This process enables the identification of rock boundaries, hydrocarbon reservoirs, and lithological variations, thus supporting informed drilling decisions and reducing exploration risks. However, conventional inversion methods face limitations such as noise sensitivity, low resolution, and reduced effectiveness in geologically complex areas, often resulting in oversimplified subsurface models. This study addresses these challenges by employing deep learning approaches, specifically LeNet, AlexNet, and conventional CNN architectures, to improve seismic resolution and synthetic seismogram generation. The methodology involves preprocessing seismic and well-log data, calculating acoustic impedance and reflection coefficients, and applying Continuous Wavelet Transform (CWT) for feature extraction. The models are trained using synthetic seismograms and validated against real seismic data. Among the models evaluated, AlexNet demonstrates superior performance in seismic data reconstruction, achieving the lowest MSE (0.0031), RMSE (0.0557), and MAE (0.052), along with the highest R2 score (0.993). The proposed technique demonstrates superior predictive accuracy, refined subsurface characterization, and reduced geological risk, thereby establishing a robust benchmark for advanced geophysical data analysis.

Due to limitations such as geographic, physical, or economic factors, collected seismic data often contain missing traces. Traditional reconstruction methods require extensive empirical parameter tuning and perform poorly on large contiguous sections of missing traces. Recent advances in deep learning have led to diffusion models with strong reconstruction capabilities. However, UNet-based diffusion models are computationally intensive and struggle to learn correlations between different traces. To address these challenges, we proposed SeisRDT — a latent diffusion transformer (DiT) based on representation learning for seismic data reconstruction. This uses a new architecture that we proposed, the representation diffusion transformer (RDT) architecture, which incorporates a relative positional bias that is added when calculating attention. It also uses a mask modeling scheme based on representation learning to enhance reconstructed data amplitude distribution consistency. The combination of these features enables the method to have global information awareness of the seismic data set, which is especially beneficial when there are large contiguous gaps in the data. Despite having these advantages that improve the quality of results, the proposed method has smaller computational resource requirements than most of the alternative approaches we compared it against. This is in part achieved due to its use of a pre-trained data compression model that compresses data into a latent space. Experiments on field and synthetic data sets show that our method achieves higher reconstruction accuracy than some existing methods and can handle various complex missing data scenarios. However, as the SeisRDT learns the probability distribution of the training data, it may not generalize well to data sets with significantly different distributions.

Deep learning methods for high-precision seismic data reconstruction are typically constrained by the reliance on high-quality labeled datasets and the inherent limitations of time-domain loss functions in capturing frequency features. This study introduces a self-supervised multi-layer wavelet convolutional neural network (MWCNN) enhanced with the coordinate attention (CA) module, termed as CMWCNN, for high-precision seismic data reconstruction. The self-supervised mechanism is incorporated through dynamic random masking, which generates pseudo input-label pairs from incomplete seismic data to diversify the training datasets. The CA module, which extracts spatial location details via global pooling in horizontal and vertical directions, is integrated to guide CMWCNN to accurately capture spatial features within regions of missing traces. Multi-level discrete wavelet transform (DWT) is employed to preserve multi-scale frequency features, enhancing the network’s ability to reconstruct fine details. Furthermore, a novel time-frequency hybrid loss function is proposed for CMWCNN training, referred to as TF‑CMWCNN. This loss function simultaneously constrains multi-scale frequency features and time-domain characteristics to effectively enhance the network’s robustness. Experimental results demonstrate that the proposed CMWCNN achieves superior reconstruction accuracy and computational efficiency compared to ResNet, U-Net++, and MWCNN. Additionally, compared to conventional time loss functions, the proposed hybrid loss improves CMWCNN performance by approximately 12 dB in signal-to-noise ratio (SNR) and peak signal-to-noise ratio (PSNR).

ABSTRACTLow‐rank reconstruction methods assume that noiseless and complete seismic data can be represented as low‐rank matrices or tensors. Therefore, denoising and recovery of missing traces require a reduced‐rank approximation of the data matrix/tensor. To calculate such approximation, we explore the CUR matrix decompositions, which use actual columns and rows of the data matrix, instead of the costly singular vectors derived from singular value decomposition. By allowing oversampling columns and rows, CUR decompositions obviate the need for the exact rank. We evaluate three different procedures for randomly selecting columns and rows to obtain the CUR. Once the low‐rank approximation is estimated, data reconstruction is achieved by an iterative optimization scheme. To demonstrate the effectiveness of CUR matrix decompositions for multidimensional seismic data recovery, we present examples of 3D and 4D synthetic and field data. Results derived by CUR compare well to conventional eigenimage‐family methods.

Seismic data reconstruction plays an important role in the whole seismic data processing and imaging workflow, especially for those data that are acquired from severe field environment and are missing a large portion of the reflection signals. The rank-reduction method is considered to be a very effective method for interpolating data that are of small curvature, e.g. the post-stack data. However, when the data are more complicated, the rank-reduction method may fail to achieve acceptable performance. A useful strategy is to use local windows to process the data so that the data in each local window satisfy the plane-wave assumption of the rank-reduction method. However, the rank in each window requires a careful selection. Traditional methods select a global rank for all windows. We have proposed an automatic algorithm to select the rank in each processing window. The energy ratio between two consecutive singular values is chosen as the criterion to define the optimal rank. We apply this strategy to seismic data interpolation and use both synthetic and field data examples to demonstrate its potential in practical applications.

The collection of a range of different seismic data types has greatly improved our understanding of the crustal architecture of Australia's Archaean Yilgarn Craton over the last few years. These seismic data include broadband seismic studies, seismic receiver functions, wide-angle recordings and mine-scale to deep seismic reflection transects. Each data set provides information on the three-dimensional (3D) tectonic model of the Yilgarn Craton from the craton scale through to the mine scale. This paper demonstrates that the integration and rationalisation of these different seismic data sets into a multi-scale 3D geological/seismic model, that can be visualised at once in a single software package, and incorporating all available data sets, significantly enhances this understanding. This enhanced understanding occurred because the integrated 3D model allowed easy and accurate comparison of one result against another, and facilitated the integrated questioning and interrogation across scales and seismic method. As a result, there are feedback questions regarding understanding of the individual seismic data sets themselves, as well as the Yilgarn Craton as a whole. The methodology used, including all the data sets in the model range, had to allow for the wide range of data sets, frequencies and seismic modes. At the craton scale, P-wave, S-wave and surface wave variations constrained the 3D lithospheric velocity model, revealing noticeable large-scale velocity variations within and across the craton. An interesting feature of the data, easily identified in 3D, is the presence of a fast S-wave velocity anomaly (> 4.8 km s − 1 ) within the upper mantle. This velocity anomaly dips east and has a series of step-down offsets that coincide approximately with province and terrane boundaries of the Yilgarn Craton. One-dimensional receiver function profiles show variations in their crustal velocity across the craton. These crustal velocity variations are consistent with the larger-scale geological subdivision of the craton, and provide characteristic profiles for provinces and terranes. The receiver function results and the deep seismic reflection data both agree on the depth to the Moho, and both indicate an increase in Moho depth to the east. The 2D seismic refraction results in the south-west of the craton provide crustal thickness information, an indication of middle and lower crustal compositions, and information regarding the broad-scale architectural framework. At the province- and terrane-scale, the deep seismic reflection data and the mine-scale seismic data provide geometric constraints on crustal architecture, in particular the orientation of the region's fault systems as well as variations in the thickness of the granite–greenstone succession. Integration of the results from wide-angle seismic refraction data coincident with the deep seismic reflection data provided additional constraints on likely upper crustal lithologies. The integrated 3D seismic model implies the dominant geodynamic process involved the development of an orogenic belt that developed with a series of contractional (folding and thrusting) events, separated by equally important extensional events. The seismic reflection data in particular suggests that extensional movement on many shear zones was more common than previously thought. The seismic reflection data suggest that the dominant mineral systems involved deeply sourced fluid flowing up crustal-penetrating shear zones. These deeply sourced fluids were further focussed into sites located above fault-breached domal regions in the upper crust.

The efficiency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets (POCS) algorithm, we propose an inversely proportional threshold model that defines the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coefficient section and slower than in the exponential threshold in the small-coefficient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak reflections. To improve the flexibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and field data. The results suggest that the inversely proportional threshold model improves the computational efficiency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.

Seismic reflection amplitude data are increasingly used in reservoir modeling to provide information on changes in earth properties away from well locations. In geostatistical reservoir modeling, the most common application is to use seismic data as background data in some form of comodeling. Seismic data image reflectors and not earth layer properties. Therefore, prior to use in comodeling, seismic data must first be transformed into an earth layer property. Typically, the transform is to acoustic impedance using an appropriate seismic inversion method. Seismic inversion methods generate results that are generally band limited in nature, resulting in limits to vertical resolution. The vertical resolution achieved can be an order of magnitude below the vertical model resolution required from geostatistical reservoir modeling, which is in the order of well-log resolution. Hence, in using seismic data, geostatistical modelers encounter a problem of downscaling, not the more commonly encountered upscaling problem. This difference in scale introduces scatter between the primary data with well-log order resolution and the secondary seismically derived rock property data used in the comodeling. As a result, to preserve vertical heterogeneity, only limited use of the secondary data can be made in comodeling procedures. This results in models that only partially fit the seismic data, i.e., only limited use is made of the seismic information. If the secondary data are more strongly imposed, the fit to the seismic data improves, but the required vertical heterogeneity is not preserved. The inability to overcome this difference in scale issue, therefore, limits the value of the application of comodeling methods to integrate seismic data into reservoir models. One class of geostatistical methods that overcomes this limitation relies on iterative geostatistical modeling. In these methods, referred to as geostatistical seismic inversion, the iterative modeling process is conditioned such that the final models generated closely match the seismic data while maintaining the required vertical heterogeneity. The application of these methods is computationally expensive relative to comodeling methods but is now practical for large models on today's desktop hardware. Relative to comodeling, geostatistical seismic inversion methods make full use of the information carried in the seismic data, resulting in a significant reduction in model uncertainty away from well control.

Seismic data suffer from under-sampling along spatial dimensions due to physical and economic limitations during acquisition, which can adversely impact subsequent imaging processes. Various approaches have been proposed to address this issue, including rank-reduction, transform, and deep learning (DL) methods for reconstructing missing traces in observed seismic data. While many DL-based reconstruction methods employ convolutional neural networks (CNNs) as their core components in supervised or unsupervised settings, the accuracy of CNN-based DL reconstruction methods can still be enhanced due to the inherent localization of convolutional operators. In this study, we present an innovative method, termed Attentive CNN (ACNet), that incorporates a transformer model with a multi-head self-attention mechanism into the CNN framework for unsupervised seismic data reconstruction. ACNet consists of an encoder built with the transformer model and a CNN decoder, enabling an iterative reconstruction process within the proposed unsupervised DL-based approach. We compare the performance of our method with that of the damped rank-reduction (DRR) method using synthetic and field data examples. The results demonstrate that our proposed method exhibits superior signal reconstruction and random noise suppression capabilities compared to the DRR method.

Seismic data reconstruction is an inverse problem in the geophysical community. Deep learning-based methods directly learn the projection between undersampled and complete data from large training datasets. However, when the feature difference between the test and training datasets increases, the recovery performance is degraded. Fine-tuning the pretrained network on the undersampled test field data has been introduced to adapt the trained network to new data. However, the pseudo-labels of the fine-tuning process need to be obtained by some traditional method in advance. In this paper, we explore a strategy for interpolating regularly sampled aliased seismic data by incorporating deep external and internal learning, i.e. by combing external pretraining with internal unsupervised fine-tuning. The pretrained network is obtained from an external synthetic dataset. Then, the pretrained network is fine-tuned on the internal dataset to obtain the final trained network adapting the test data. The inputs and labels of the internal dataset are generated solely from the currently regularly undersampled test data. As such, the fine-tuning process is totally unsupervised. Finally, the interpolated result is acquired by feeding the test data into the trained network. The proposed algorithm learns the external priors from large external datasets and it learns the internal features from undersampled test data. Thus, the network has an enhanced capacity to adapt to new data. Poststack and prestack field data are provided to verify the performance of the proposed algorithm.

Preserving amplitude information when imaging 3‐D multichannel seismic data is a challenging task. The imaging process can be described as seeking the inverse for a large matrix that relates the data to a reflectivity model. Due to irregular coverage at the surface and uneven illumination of the subsurface, the matrix is often ill‐conditioned and its coefficients are badly scaled. We present a new approach for regularizing the coverage of 3‐D surveys by partial imaging before migration. After regularization, 3‐D data become better suited for prestack migration using either “true amplitude” Kirchhoff methods or wave extrapolation techniques.Posing partial stacking before migration as an inverse problem, we develop a new optimization technique named “inversion to common offset” (ICO) that solves for optimal partial stacks from multifold 3‐D data. The inversion approach takes advantage of the redundancy of information present in multichannel recording to recover densely and regularly sampled common‐offset common‐azimuth volumes. The reconstruction of each of these volumes combines data from multiple incomplete experiments over a common earth model to simulate the ideal data that would have been recorded from a single common‐offset common‐azimuth experiment. The method is based on the inversion of a partial prestack migration operator that maps seismic data from a given acquisition geometry to an arbitrary one. This data mapping operator is the azimuth moveout operator (AMO). The main advantage of ICO is that the AMO operator is compact and consequently cheaper to apply than other imaging operators, such as full 3‐D prestack migration.We present a cost‐effective implementation of ICO based on a log‐stretch transformation of the time axis. After this transformation, AMO becomes time invariant, so the inversion can be performed in the Fourier domain on each temporal‐frequency slice independently. To accelerate the convergence of the iterative solution, we precondition the system of linear equations by two diagonal transformations that scale the rows and columns of the modeling operator. A stable solution is achieved by adding a penalty function that constrains the spatial variability of the model.Results of applying ICO to a field 3‐D land survey show that we can recover the high‐frequency features of the reflectivity function from a severely undersampled data set obtained by decimating a densely sampled prestack data set. The images produced by prestack migration after regularization are superior to those produced by direct migration of the decimated data.

Onshore non-repeatable time-lapse (TL) seismic exploration is a challenging yet convenient technique for enhancing production in mature oil and gas fields. Data repeatability across two or more acquisition phases is fundamental for reliable TL analysis. However, differences in acquisition geometries – from variations in geological targets, acquisition technologies, and acquisition parameters – can cause significant inconsistencies between two data vintages. Drawing on survey design parameters, this study proposes a dual-constraint method for data reconstruction and quality control, integrating common midpoint (CMP) similarity with the sum of shot-receiver geometric distances. Unlike conventional techniques, the proposed approach simultaneously controls shot and receiver position errors through a dynamic threshold, indirectly preserving offset and azimuth consistency. Compared with typical methods, it avoids cross-domain transformations and multi-parameter adjustments, offering high applicability. Applied to conventional (2004) and high-density (2008) datasets from a Chinese onshore oilfield, the method achieved data utilization rates of 77.5% and 39.8%, respectively. The reconstructed data demonstrated higher offset distribution uniformity and improved CMP fold consistency compared with the CMP-constrained receiver deviation method. This study provides a practical reference for TL studies in onshore mature oilfields.