Seismic Data Reconstruction Research Articles

Unsupervised 3D seismic data reconstruction using a weighted-attentive deep-learning framework

The physical and cost limitations of seismic data acquisition often result in the spatial undersampling of data, which has a detrimental impact on subsequent data processing. Seismic data reconstruction plays a crucial role in recovering missing traces arising from the acquisition process. In recent years, deep learning (DL) has emerged as an intelligent solution for this purpose. We introduce an innovative approach called the weighted-attentive DL framework for unsupervised 3D seismic data reconstruction, which combines an attentive transformer network (ATNet) with a conventional projection onto convex sets (POCS) algorithm. Our framework follows the plug-and-play concept, requiring only the original subsampled data to achieve robust performance. It accomplishes this by iteratively updating ATNet parameters, wherein ATNet serves as the reconstruction operator during the DL process. This approach allows us to simultaneously recover missing traces and filter out random noise, with a key feature being its enhanced attention to the observed signal compared with convolutional neural networks. In addition, we incorporate the POCS algorithm into our framework to introduce a linear decay weight for the aliasing space containing noise and signal during the reconstruction process. We rigorously evaluate our method against four existing approaches: adaptive POCS, fast dictionary learning sequential generalized K-means, optimally damped rank-reduction, and DenseNet methods. Our comparative experiments, conducted on synthetic and field data examples, clearly demonstrate the substantial improvements achieved by our method in terms of reconstruction and denoising when compared with the four benchmarked methods.

3D Seismic Data Reconstruction based on Weighted Fast Iterative Shrinkage Thresholding algorithm

3D Seismic Data Reconstruction based on Weighted Fast Iterative Shrinkage Thresholding algorithm

Removing random noise and improving the resolution of seismic data using deep‐learning transformers

AbstractPost‐stack data are susceptible to noise interference and have low resolution, which impacts the accuracy and efficiency of subsequent seismic data interpretation. To address this issue, we propose a deep learning approach called Seis‐SUnet, which achieves simultaneous random noise suppression and super‐resolution reconstruction of seismic data. First, the Conv‐Swin‐Block is designed to utilize ordinary convolution and Swin transformer to capture the long‐distance dependencies in the spatial location of seismic data, enabling the network to comprehensively comprehend the overall structure of seismic data. Second, to address the problem of weakening the effective signal during network mapping, we use a hybrid training strategy of L1 loss, edge loss and multi‐scale structural similarity loss. The edge loss function directs the network training to focus more on the high‐frequency information at the edges of seismic data by amplifying the weight. Additionally, the verification of synthetic and field seismic datasets confirms that Seis‐SUnet can effectively improve the signal‐to‐noise ratio and resolution of seismic data. By comparing it with traditional methods and two deep learning reconstruction methods, experimental results demonstrate that Seis‐SUnet excels in removing random noise, preserving the continuity of rock layers and maintaining faults as well as being strong robustness.

Self representation based methods for tensor completion problem

Tensor, the higher-order data array, naturally arises in many fields, such as information sciences, seismic data reconstruction, physics, video inpainting and so on. In this paper, we intend to provide a new model to recover a tensor, based on self-representation, for the all-mode unfoldings of the desired tensor, regardless of the tensor rank. The suggested idea generalizes self-representation to tensor and recovers an incomplete tensor by reconstructing one fiber by others in such a way that they all belong to the same subspace. We design least-square and low-rank self-representation algorithms based on the Linearized Alternating Direction Method utilizing this concept. We show that the proposed algorithms converge to the rank-minimization of the incomplete tensor.

NeRSI: Neural Implicit Representations for 5D Seismic Data Interpolation

Due to challenging field operations and resource constraints, seismic data acquisition often requires coping with missing traces. Interpolation algorithms are crucial for reconstructing these missing traces to enable improved subsurface analysis and interpretation. While deep learning has made exciting advances in seismic reconstruction, its focus has predominantly been on 2D and 3D datasets with relatively low rates of missing data. Five-dimensional (5D) seismic data reconstruction entails considering simultaneous sources and receivers deployed in areal arrays to solve the reconstruction problem. The latter offers greater data redundancy, which can be leveraged to enhance interpolation quality. Traditional 5D deep learning interpolation methods rely heavily on synthetic training pairs, posing challenges when applied to real-world data. This necessitates transfer learning techniques, which can be cumbersome. Addressing this, we introduce a self-supervised, coordinate-based deep interpolation algorithm that obviates the need for labeled data. Employing a multi-layer perceptron (MLP) network can effectively encode the continuous seismic wavefield inherent in 5D data. Once trained, the MLP can infer missing trace amplitudes from their coordinates. We contribute to boosting the MLP, enabling it to generate seismic profiles rather than single-point predictions. This enhancement significantly strengthens the model’s performance and efficiency. Moreover, we apply nuclear norm regularization to the output profiles, improving the reconstruction quality. The effectiveness of our algorithm is supported by both synthetic and field data experiments, demonstrating its superior reconstruction capabilities.

Robust unsupervised 5D seismic data reconstruction on regular and irregular grids

Seismic data reconstruction has become a central focus in seismic data processing, addressing challenges posed by sparse sampling due to physical and budgetary constraints. The advent of 5D acquisition methodologies marks a significant advancement in the quality and completeness of seismic data sets. Most traditional 5D reconstruction methods commonly use the fast Fourier transform (FFT), requiring regular grids and preliminary 4D binning before 5D interpolation. Discrete Fourier transform and nonequidistant FFT can honor the original irregular coordinates. However, when using exact locations, these methods become computationally expensive. We introduce an unsupervised deep-learning methodology to learn a continuous function across the sampling points in seismic data, facilitating reconstruction on regular and irregular grids. The network comprises a multilayer perceptron with linear layers and element-wise periodic activation functions. It excels at mapping the input coordinates to the corresponding seismic data amplitudes without relying on external training sets. The network’s intrinsic low-frequency bias is crucial in prioritizing acquiring self-similar features over high-frequency and incoherent ones during training. This characteristic mitigates incoherent noise in seismic data, such as random and erratic components. To assess the robustness of the unsupervised reconstruction technique, we conduct comprehensive evaluations using synthetic data examples sampled regularly and irregularly, as well as field-data examples with and without binning. The findings demonstrate the efficacy of our deep-learning framework in achieving resilient and accurate seismic data reconstruction across diverse sampling scenarios.

A self-supervised missing trace interpolation framework for seismic data reconstruction

A self-supervised missing trace interpolation framework for seismic data reconstruction

Evaluating machine learning predicted subsurface properties via seismic data reconstruction

In recent years, machine learning (ML) approaches have gained significant attention in seismic-based subsurface property estimation problems. However, because of the purely data-driven nature, it is challenging to evaluate the quality of the estimated properties in regions without ground truth data. In this article, we discuss evaluating the quality of ML predicted subsurface properties through ML-based seismic data reconstruction. We use a deep learning workflow to reconstruct the poststack seismic data, then use the misfit between the measured data and the reconstructed data as a proxy for the quality of ML predicted subsurface properties. We also use self-supervised learning to improve the model generalization when training the deep learning model for reconstruction. This proposed method is particularly valuable for subsurface properties without direct physical relation to seismic data. We provide both synthetic and field data examples to demonstrate the consistency of the proposed method.

Reconstruction and denoising of high-dimensional seismic data via Frobenius-nuclear mixed norm constraints

Abstract The seismic data acquisition design with ‘two-wide and one-high’ geometry effectively improves the imaging quality of seismic records. However, when data are acquired in the field, complex near surface conditions and environmental factors can introduce a variety of noises and gaps in seismic data, impacting the accuracy of seismic imaging. Currently, the method of low-rank matrix/tensor completion is commonly employed for data reconstruction after normal moveout (NMO). In a complex subsurface medium, common midpoint data processed with NMO may not satisfy the linear or quasi-linear assumptions within local data windows. Therefore, this paper exploits the inherent low-rank structure of high-dimensional data to propose a high-dimensional tensor completion method under the Frobenius-nuclear mixed norm constraint (FN-TC). This method unfolds the 4D data tensor into the frequency-space domain along its modes (m, n) and subsequently imposes a non-convex Frobenius-nuclear mixed norm constraint on the unfolded approximate matrices. This approach closely approximates the rank function of the factor matrices, thereby enhancing the accuracy of data modeling. Theoretical and practical studies demonstrate that the novel FN-TC approach can effectively reconstruct high-dimensional seismic data and suppress noise, thereby providing data support for subsequent high-precision seismic imaging.

Seismic data extrapolation based on multi-scale dynamic time warping

Seismic data reconstruction can provide high-density sampling and regular input data for inversion and imaging, playing a crucial role in seismic data processing. In seismic data reconstruction, a common scenario involves a significant distance between the source and the first receiver, which makes it unattainable to acquire near-offset data. A new workflow for seismic data extrapolation is proposed to address this issue, which is based on a multi-scale dynamic time warping (MS-DTW) algorithm. MS-DTW can accurately calculate the time-shift between two time series and is a robust method for predicting time-offset (t−x) domain data. Using the time-shift calculated by the MS-DTW as the basic input, predict the two-way traveltime (TWT) of other traces based on the TWT of the reference trace. Perform autoregressive polynomial fitting on TWT and extrapolate TWT based on the fitted polynomial coefficients. Extract amplitude information from the TWT curve, fit the amplitude curve, and extrapolate the amplitude using polynomial coefficients. The proposed workflow does not necessitate data conversion to other domains and does not require prior knowledge of underground geological information. It applies to both isotropic and anisotropic media. The effectiveness of the workflow was verified through synthetic data and field data. The results show that compared with the method of predictive painting based on local slope, this approach can accurately predict missing near-offset seismic signals and demonstrates good robustness to noise.

Low-frequency marine seismic data reconstruction based on the far-field signature using a modified U-Net

Preserving low-frequency components in seismic data is challenging due to data acquisition restrictions and the processing of low-cut filtering after surveys. If seismic data lack low frequencies, their resolution deteriorates, leading to inaccurate seismic interpretations. To resolve this problem, we developed a low-frequency reconstruction that employs a modified U-Net neural network. To improve the training of the neural network, we generated training data analogous to unseen data, based on the far-field signature as the wavelet source to retain the spectral characteristics of field data. We addressed potential overfitting by generating a large amount of various synthetic data through wave equation-based modelling using a variety of velocity and density models. After synthesising the seismic data, we implemented a filtering method to produce input data with insufficient low frequencies and label data with sufficient low frequencies. The far-field signature plays an important role in the successful reconstruction of low frequencies due to its intrinsic field data features and greater low-frequency information compared to field data alone. We tested the generalisation of the network using unseen synthetic and field data not used in the training stage, and analyzed the results in the time and frequency domains. Although the input data did not retain frequencies below 10 Hz, the trained network predicted low frequencies that were similar to the desired data. We also produced post-stack sections via simple processing to evaluate low-frequency reconstructions produced by our trained network. The low-frequency reconstruction scheme led to a better understanding of subsurface media.

Seismic data reconstruction method using generative adversarial network based on moment reconstruction error constraint.

The seismic data acquired are usually spatially undersampled due to the constraints of the field acquisition environment. However, the removal of multiple waves, offsets, and inversions requires high regularity and integrity of seismic data. Therefore, reasonable data reconstruction methods are usually applied to the missing data in the indoor processing stage to recover regular seismic data. The traditional reconstruction methods for seismic data reconstruction are generally based on some assumptions (e.g., assuming that the data satisfies linearity or sparsity, etc.) and have some limitations of use. To overcome the applicability problem of traditional seismic data reconstruction methods, this article proposes a generative adversarial network (GAN) seismic data reconstruction method based on moment reconstruction error constraints. The method can extract the deep features of the data nonlinearly without any assumptions. First, the error function in the GAN is improved, and the commonly used joint error function of adversarial loss plus L1/L2 amplitude reconstruction loss is improved to a new error function consisting of adversarial loss and moment reconstruction loss weighting. Then, an adversarial network data reconstruction generation method based on the moment reconstruction error constraint is given. Next, an experimental analysis of different types of data missing was carried out using theoretical model data, and the study method was analyzed by interpolation errors. Finally, actual seismic data is used to further validate the effect of the research method. The experimental results show that the improved algorithm performs superiorly in dealing with the data reconstruction problem. Compared with the error function of conventional GAN optimization, the reconstruction results of GAN based on the moment reconstruction error constraint have better amplitude preservation.

A comparative study over improved fast iterative shrinkage-thresholding algorithms: an application to seismic data reconstruction

A comparative study over improved fast iterative shrinkage-thresholding algorithms: an application to seismic data reconstruction

Seismic data reconstruction based on a multicascade self-guided network

Due to inherent limitations in data acquisition, seismic data reconstruction is an important procedure to recover missing data or improve observation density. Many conventional methods exist to solve the reconstruction task. Reconstruction is challenging, especially in the case of complex seismic data. Recently, convolutional neural networks (CNN) have been applied in seismic data processing. In most cases, the architectures of these CNN-based methods are relatively simple, without sufficient feature interaction, limiting their performance. To improve reconstruction results, a multicascade self-guided network (MSG-Net) is presented. In general, MSG-Net is inspired by the self-guided scheme, and a multicascade architecture is designed to extract informative features within the analyzed seismic data at different resolutions. Following this, a parallel spatial attention module is used to further refine and enhance the primary features, thereby improving reconstruction accuracy. To test and verify the new approach, a training data set is generated, based on the synthetic records obtained by forward modeling methods. Experimental results demonstrate that MSG-Net is a promising approach for performing seismic data interpolation.

Sparse Regularization Based on Orthogonal Tensor Dictionary Learning for Inverse Problems

In seismic data processing, data recovery including reconstruction of the missing trace and removal of noise from the recorded data are the key steps in improving the signal-to-noise ratio (SNR). The reconstruction of seismic data and removal of noise becomes a sparse optimization problem that can be solved by using sparse regularization. Sparse regularization is a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed inverses feasible. It deals with ill-posedness by replacing an ill-posed inverse problem with a well-posed problem that has a solution close to the true solution. In the last 2 decades, interest has shifted from linear toward nonlinear regularization methods even for linear inverse problems. In inverse problems, regularizations serve as stabilizing the solution of ill-posed inverse problems and give a solution that adequately fits measurements without producing unjustifiably complex artifacts. In this paper, we present a novel sparse regularization based on a tensor-based dictionary method for inverse problems (seismic data interpolation and denoising). This regularization avoids the vectorization step for sparse representation of seismic data during the reconstruction process. The key step in sparsifying signals is the choice of sparsity-promoting dictionary learning. The learning-based approach can adaptively sparsify datasets but has high computational complexity and involves no prior-constraint pattern information for the dataset. Many existing dictionary learning methods would be computationally infeasible for the high dimensional seismic data processing. These methods also destroy the essential information as well as it reduces the discriminability and expressibility of the signal, since they deal with vectorization. In this paper, the orthogonal tensor dictionary learning that learns a dictionary from the input data by employing orthogonality and separability is proposed as sparse regularization for the inverse problems. The performance of the proposed method was validated in seismic data interpolation and denoising individually as well as simultaneously. Numerical examples of synthetic and real seismic datasets demonstrate the validity of the proposed method. The SNR of the recovered data confirms that the proposed method is the most effective method than K-singular value decomposition and orthogonal dictionary learning methods.

MLPCC-MLMAE-Based Early Stopping Strategy for Unsupervised 3-D Seismic Data Reconstruction

MLPCC-MLMAE-Based Early Stopping Strategy for Unsupervised 3-D Seismic Data Reconstruction

Accurate Reconstruction of Short-Duration Passive Seismic Data With Transformer Integrating Multiscale Dense Network

Accurate Reconstruction of Short-Duration Passive Seismic Data With Transformer Integrating Multiscale Dense Network

STUGAN: An Integrated Swin Transformer-Based Generative Adversarial Networks for Seismic Data Reconstruction and Denoising

STUGAN: An Integrated Swin Transformer-Based Generative Adversarial Networks for Seismic Data Reconstruction and Denoising

GAN Supervised Seismic Data Reconstruction: An Enhanced Learning for Improved Generalization

GAN Supervised Seismic Data Reconstruction: An Enhanced Learning for Improved Generalization

Ensemble Deep Learning for Enhanced Seismic Data Reconstruction

Ensemble Deep Learning for Enhanced Seismic Data Reconstruction