Seismic Data Interpolation Research Articles

Seismic data interpolation with recurrent inference mechanism

Abstract Seismic data interpolation is a significant procedure in seismic data processing as the highly complete data is extremely useful for the subsequent imaging and interpretation workflows. Recently, numerous deep learning based techniques have been utilized to help improve the reconstruction quality. Supervised learning approaches are able to predict the results in a second, but they depend heavily on the training data, which therefore limits the generalized applications. In contrast, unsupervised learning methods are applicable to any data, but they need much more computational time and prior knowledge to be implemented. Especially, the recovery of aliased and consecutively missing data is incredibly challenging. To solve this problem, we propose a novel framework for Seismic Interpolation using Recurrent Inference Mechanism(SIRIM). Integrating the advantages of supervised and unsupervised learning paradigms, we build a specific convolutional recurrent inference network such that it is able to learn the dynamic priors when plugged in the physics-informed iterative algorithm, as well as directly reconstruct various types of incomplete data. We validate SIRIM in comparison with some traditional and learning-based methods. The performance on synthetic and field data illustrates the effectiveness and robustness of our proposed approach which outperforms baseline methods in terms of aliased and consecutively missing data.

Dealiased seismic data interpolation by dynamic matching

Interpolation is a critical step in seismic data processing. Gaps in seismic traces can lead to severe spatial aliasing phenomena in the corresponding f- k spectra. The aliasing caused by regularly spaced gaps has similar f- k spectra as those of the actual data. Existing dealiasing interpolation algorithms generally assume that seismic events are linear and cannot handle nonstationary events. To address this shortcoming, we develop a novel dealiased seismic data interpolation approach using dynamic matching. First, we match two adjacent seismic traces using the local affine regional dynamic time-warping algorithm. Subsequently, we calculate the local slope between two seismic traces. Finally, we perform linear interpolation on the regularly missing seismic data using local slope information. Our approach is tested on synthetic and field seismic data sets. The interpolation results indicate that our approach has a better antialiasing ability and computational efficiency than the traditional Spitz and seislet-based approaches. In addition, this method can be applied to interpolate irregularly sampled seismic data and for simultaneous seismic data interpolation and denoising.

A Comparison of U-Net with Conditional Generative Adversarial Networks and Cycle-Consistent Adversarial Networks for real seismic data interpolation: Tupi Field

Deep learning models have been used to improve seismic trace interpolation in recent years. Encode-Decode models, such as U-Net, have been implemented to solve interpolation problems. The success of U-Net in seismic interpolation has inspired us to test the U-net also as an image generator for further Generative Adversarial Network (GAN) interpolation models. The objective of the present paper is to compare the performance of U-Net inside the GAN models for seismic interpolation: the U-Net alone and two GAN models, the conditional GAN (cGAN) and the Cycle Consistent GAN (CycleGAN), both using the U-Net as a generator inside their workflow. We test the methodologies for two scenarios: regular and irregular interpolation. All tests were performed in a real dataset from the Tupi Field which belongs to the Brazilian pre-salt region. A comparison of the statistical metrics shows that cGAN performs better than CycleGAN and the U-Net alone in most cases. The computational training time of the cGAN model, for all interpolation scenarios, is better than the CycleGAN. Finally, the cGAN training time is comparable to the training of the U-Net alone.

PINNslope: Seismic data interpolation and local slope estimation with physics informed neural networks

Interpolation of aliased seismic data constitutes a key step in a seismic processing workflow to obtain high-quality velocity models and seismic images. Building on the idea of describing seismic wavefields as a superposition of local plane waves, we propose to interpolate seismic data by using a physics informed neural network (PINN). In the proposed framework, two feed-forward neural networks are jointly trained using the local plane wave differential equation as well as the available data as two terms in the objective function: a primary network assisted by positional encoding is tasked with reconstructing the seismic data, whereas an auxiliary, smaller network estimates the associated local slopes. Results on synthetic and field data validate the effectiveness of the proposed method in handling aliased (coarsely sampled) data and data with large gaps. Our method compares favorably against a classic least-squares inversion approach regularized by the local plane-wave equation as well as a PINN-based approach with a single network and precomputed local slopes. We find that introducing a second network to estimate the local slopes, whereas at the same time interpolating the aliased data enhances the overall reconstruction capabilities and convergence behavior of the primary network. Moreover, an additional positional encoding layer embedded as the first layer of the wavefield network confers to the network the ability to converge faster, improving the accuracy of the data term.

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.

Generative interpolation via a diffusion probabilistic model

Seismic data interpolation is essential in a seismic data processing workflow, recovering data from sparse sampling. Traditional and deep-learning-based methods have been widely used in the seismic data interpolation field and have achieved remarkable results. In this paper, we develop a seismic data interpolation method through the novel application of diffusion probabilistic models (DPMs). DPM transforms the complex end-to-end mapping problem into a progressive denoising problem, enhancing the ability to reconstruct complex situations of missing data, such as large proportions and large-gap missing data. The interpolation process begins with a standard Gaussian distribution and seismic data with missing traces and then removes noise iteratively with a UNet trained for different noise levels. Our DPM-based interpolation method allows interpolation for various missing cases, including regularly missing, irregularly missing, consecutively missing, noisy missing, and different ratios of missing cases. The ability to generalize to different seismic data sets is also discussed in this paper. Numerical results of synthetic and field data indicate satisfactory interpolation performance of the DPM-based interpolation method in comparison with the f- x prediction filtering method, the curvelet transform method, the low-dimensional manifold method (LDMM), and the coordinate attention-based UNet method, particularly in cases with large proportions and large-gap missing data. Diffusion is all we need for seismic data interpolation.

FUDLInter: Frequency-Space-Dependent Unsupervised Deep Learning Framework for 3-D and 5-D Seismic Data Interpolation

FUDLInter: Frequency-Space-Dependent Unsupervised Deep Learning Framework for 3-D and 5-D Seismic Data Interpolation

5-D Seismic Data Interpolation by Continuous Representation

5-D Seismic Data Interpolation by Continuous Representation

Dip-Informed Neural Network for Self-Supervised Anti-Aliasing Seismic Data Interpolation

Dip-Informed Neural Network for Self-Supervised Anti-Aliasing Seismic Data Interpolation

Self-supervised transfer learning POCS-Net for Seismic Data Interpolation

Self-supervised transfer learning POCS-Net for Seismic Data Interpolation

Swin Transformer for simultaneous denoising and interpolation of seismic data

Seismic data are often characterized by low quality due to noise contamination or missing traces. Convolutional neural networks are popular in dealing with denoising and interpolation. However, fixed-size convolution kernels have limited feature extraction range, and popular networks aim at either denoising or interpolating. In this paper, we propose a Swin Transformer convolutional residual network (SCRN) for simultaneous denoising and interpolation. We step-by-step show on synthetic datasets that SCRN can effectively denoise, interpolate, or denoise and interpolate simultaneously. Following this, the trained simultaneous denoising and interpolation model is directly used to handle multi-tasks on the field datasets. We assess the reconstruction effect of SCRN based on synthetic and field datasets. Comparison methods include both supervised ones (DnCNN, Unet and RIDNet) and unsupervised ones (DDUL, MultiResUNet and DL-POCS). Experimental results show that SCRN outperforms the counterparts in terms of (1) quantitative evaluation indices, (2) event continuity and weak signal retention, (3) generalization seismic data ability to suppress various noise levels and interpolate different sampling rates, and (4) preservation of first-arriving edge signals. These results indicate that SCRN can effectively reconstruct seismic data.

Sparse prior-net: A sparse prior-based deep network for seismic data interpolation

Seismic data interpolation plays a crucial role in obtaining dense and regularly sampled data, contributing to improving the quality of seismic data in seismic exploration. Sparsity-promoting methods use a two-step iteration to gradually recover missing traces, by exploiting the sparsity representation of seismic data in transform domains, such as Fourier, wavelet, and curvelet transform, within the framework of the projection onto convex sets (POCS). In the first step, the missing traces are restored by applying the thresholding shrinkage to the transform coefficients. In the second step, the observed data are inserted into the updated result. However, this method relies on a preselected transform and lacks the capability to adaptively capture sparse representations. In addition, determining the optimal threshold parameters can pose difficulties. These limitations yield unsatisfactory reconstruction results. To address this issue, we propose a novel approach called sparse prior-based seismic interpolation network (SP-net) that combines the sparsity-promoting method with a deep neural network. Unlike traditional end-to-end networks, our proposed neural network integrates the widely used POCS method into its architecture, enabling automatic learning of the sparse transform, and threshold parameters from the training data set. By combining the merits of the sparsity-promoting techniques and data-driven deep-learning approaches, SP-net achieves enhanced adaptability and more accurate interpolation results. Through experiments conducted on synthetic and field seismic data, we demonstrate the effectiveness of our proposed method.

Seismic data interpolation via Unet with non-local blocks

Due to the constraints of the exploration environment, acquired seismic data are commonly irregular or incomplete, which seriously affects the quality of subsequent seismic data processing and interpretation. Convolutional neural network (CNN)- based seismic data interpolation methods have been receiving increased attention owing to better efficiency and interpolation performance. UNet is a commonly used encoder-decoder network that uses skip connection, which can extract seismic data features using convolution filters. However, convolution filters are local operations that process a local neighbourhood and extract local features, but experience difficulty capturing global representations. Although an increase in network depth can expand the receptive field, the local operator still limits the precision of the recovered result. To address this limitation, we propose an improved UNet with a non-local block (NL-UNet), wherein non-local blocks are added to the classic UNet network. Owing to the addition of non-local blocks, NL-UNet can capture both local and non-local features of seismic data, which is conducive to improving its reconstruction performance. The applicability and effectiveness of NL-UNet were demonstrated through experiments on both synthetic and field datasets.

Seismic Data Interpolation via Improved cGAN Network

The seismic data are always spatially undersampled during filed acquisition, limited by the natural environment and economic conditions. Irregularly missing seismic traces can affect the subsequent processing of seismic data, ultimately impacting the imaging and inversion results. Therefore, seismic data regularisation and interpolation are particularly necessary and have become an important step for data pre-processing. This abstract presents an improved GC algorithm with partial convolution layers and spectral normalization and applies it on 2D seismic data reconstruction. Compared with the traditional cGAN reconstruction method, The proposed method can effectively enhance the generative capability of the cGAN algorithm. Both synthetic and field data experiments demonstrate that the reconstruction performance of the improved cGAN method is better than the conventional cGAN method.

Relative Amplitude Preservation Analysis on Interpolation Methods of The Unaliased F-K Trace Interpolation and Regularized Nonstationary Autoregression

The seismic data interpolation method has been widely used to increase the fold coverage in seismic data processing. This technique can be applied to convert multi-2D lines into pseudo-3D, which is an alternative to obtaining 3D seismic volume data due to the relatively high acquisition cost. However, the quality of the seismic interpolation results is not the same as the real 3D seismic data acquisition results. This study carefully analyzed these differences to understand how accurate the results were. There are two methods used for data interpolation, namely Unaliased f-k trace interpolation (UFKI) and Regularized Interpolation Nonstationary Autoregression (RNA) methods, which are applied to 2D pre-stack data to increase the fold coverage and 3D data to convert multi-2D lines into pseudo-3D. Then, the interpolation results on the pre-stack data are evaluated on the 2D and 3D data, and an amplitude change is analyzed. It is done to test whether the amplitude of the seismic data from the interpolation results is still relatively preserved based on the evaluation results of the changes in the AVO response. The results show that the interpolation process in the receiver and shot gather domain (UFKI and RNA) could increase the fold coverage and maintain the relative amplitude preservation and AVO response

CCNet-5D: 5D convolutional neural network for seismic data interpolation

Convolutional neural network (CNN)-based seismic interpolation methods recover missing traces by feeding corrupted data to a trained neural network, whose parameters are obtained by training pairs of corrupted data and their complete labels. Compared with traditional reconstruction approaches, these methods require less human-computer interaction and computation time; therefore, CNN approaches have been popular for 2D/3D seismic interpolation. Five-dimensional seismic data interpolation methods recover missing traces simultaneously in five dimensions, considering all the physical coordinates with high accuracy. Unfortunately, existing deep-learning frameworks (such as TensorFlow and PyTorch) only provide low-dimensional convolution operators (no more than three dimensions), which makes it difficult to generalize to 5D seismic reconstruction directly. To this end, we develop an effective 5D-CNN by cascading low-dimensional convolution to deal with 5D seismic interpolation, referred to as the CCNet-5D. First, based on the definition of convolution and the theory of tensor decomposition, the 5D convolution operator is approximated by the sum of multiple cascading of low-dimensional convolution operators. Then, we determine the CNN architecture for the 5D convolutional operators by cascading the 3D and 2D convolutional layers, called the CC-3D2D module. The final CCNet-5D is constructed by stacking the four resulting CC-3D2D modules. In our setup, 5D-CNN outperforms the existing 5D traditional method and 3D CNN-based method.

Interpolation of irregularly sampled seismic data via non-convex regularization

Seismic data interpolation is necessary for high-resolution imaging when the field data are not adequate or when some traces are missing. Sparse inversion is an important interpolation method for seismic data, which requires sparse transformation to build an inversion model. Most existing sparsity-promoting interpolation methods are generally based on convex function regularization, especially the L1 norm. Some studies suggest that non-convex regularization with non-convex functions can achieve better sparsity than L1 norm, and produce faster and better results. But this approach is only suitable for noise-free data interpolation, as it is less stable than convex regularization. To overcome the noisy data interpolation problem and improve the stability of non-convex regularization, we propose a novel non-convex function, called arc-tangent function, to construct the inversion model. We also present a gradient-based prediction-projection method to solve the proposed models. We used a prediction-projection method to solve the proposed models. In each iteration, we first obtained a predictive solution by gradient update algorithm and then projected it onto a convex set to update the iterative solution, and the predictive solution instead of the projection solution was output as the final results. Tests on synthetic and field data demonstrated that our non-convex regularization method performed well for both noise-free and noisy data interpolation.

Orthogonal dictionary learning based on l 4-Norm maximisation for seismic data interpolation

Due to geological conditions, acquisition environment, and economic restrictions, acquired seismic data are often incomplete and irregularly distributed, and this affects subsequent migration imaging and inversion. Sparse constraint-based methods are widely used for seismic data interpolation, including fixed-base transform and dictionary learning. Fixed-base transform methods are fast and simple to implement, but the basis function needs to be pre-selected. The dictionary learning method is more adaptive, and provides a means of learning the sparse representation from corrupted data. K-singular value decomposition (K-SVD) is a classical dictionary learning method that combines sparse coding and dictionary updating iteratively. However, the dictionary atoms are updated column-by-column, leading to high computational complexity due to long SVD calculation times. In this study, we evaluated the dictionary learning method via l 4-norm maximisation using an orthogonal dictionary, which is different from the traditional l 0-norm or l 1-norm minimisation, and interpolated the missing traces in the projection onto convex sets (POCS) framework. The optimal objection function is convex, but can be solved using a simple and efficient Matching, Stretching and Projection (MSP) algorithm, which greatly reduces the dictionary learning time. Numerical experiments using synthetic and field data demonstrate the effectiveness of the proposed method.

A projection-onto-convex-sets network for 3D seismic data interpolation

Seismic data interpolation is an essential procedure in seismic data processing. However, conventional interpolation methods may generate inaccurate results due to the simplicity of assumptions, such as linear events or sparsity. In contrast, deep learning trains a deep neural network with a large data set without relying on predefined assumptions. However, the lack of physical priors in the traditional pure data-driven deep learning frameworks may cause low generalization for different sampling patterns. Inspired by the framework of projection onto convex sets (POCS), a new neural network is proposed for seismic interpolation, called POCS-Net. The forward Fourier transform, the inverse Fourier transform, and the threshold parameter in POCS are replaced by neural networks that are independent in different iterations. The threshold is trainable in POCS-Net rather than manually set. A nonnegative constraint is imposed on the threshold to make it consistent with traditional POCS. POCS-Net is essentially an end-to-end neural network with priors of a sampling pattern and a predefined iterative framework. Numerical results on 3D synthetic and field seismic data sets demonstrate the superiority of the reconstruction accuracy of the proposed method compared with the traditional and natural image-learned POCS methods.