Trace Interpolation Research Articles

Seismic trace interpolation based on the principle of reciprocity using a conditional Generative Adversarial Network (cGAN)

Seismic trace interpolation based on the principle of reciprocity using a conditional Generative Adversarial Network (cGAN)

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization

Understanding the orientation of geologic structures is crucial for analyzing the complexity of the earths’ subsurface. For instance, information about geologic structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that uses the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in 2D and 3D inverse problems. Specifically, our approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method’s performance. Our algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results indicate that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that our anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

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

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

Multichannel seismic attenuation compensation and interpolation with curvelet sparse constraint of frequency-wavenumber spectrum

Abstract High-resolution exploration is hampered by seismic attenuation, caused by the viscosity and heterogeneity of underground media. Conventional single-channel attenuation compensation methods can increase the corresponding vertical resolution partially. However, the lateral continuity of compensated seismic data is always ignored and the noise resistance can be improved. Therefore, multichannel attenuation compensation methods were proposed, including the algorithm with sparse curvelet coefficient constraint of the time-space (t–x) data. However, nonstationary seismic data may be affected by irregular missing traces in field cases, which severely degrades its lateral continuity and negatively affects the performance of multichannel attenuation compensation. Therefore, we concentrate on simultaneous multichannel attenuation compensation and missing trace interpolation in a unified framework. Based on the inversion framework of sparsity promotion, we propose an approach for simultaneous multichannel compensation and interpolation, utilizing sparse curvelet coefficient constraint of the recovered principal frequency-wavenumber (f–k) spectrum. The size of the principal f–k spectrum is reduced by at least half compared with that of the corresponding t–x band-limited data. It significantly reduces the computational expense of curvelet transform-based processing. Synthetic and field data experiments validate the effectiveness of the proposed method in efficiency improvement with consistent performance when compared to the multichannel method with sparse curvelet coefficient constraint of the t–x data in improving the vertical resolution and lateral continuity. Furthermore, we have discussed a potential acceleration strategy based on random sampling in the normal compensation issue.

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.

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

Depthwise separable convolution Unet for 3D seismic data interpolation

In seismic exploration, dense and evenly spatial sampled seismic traces are crucial for successful implementation of most seismic data processing and interpretation algorithms. Recently, numerous seismic data reconstruction approaches based on deep learning have been presented. High dimension-based methods have the benefit of making full use of seismic signal at different perspectives. However, with the transformation of data dimension from low to high, the parameter capacity and computation cost of training deep neural network increase significantly. In this paper, we introduce depthwise separable convolution instead of standard convolution to reduce the operation cost of Unet for 3D seismic data missing trace interpolation. The structural similarity (SSIM), L1 hybrid loss function, and switchable normalization further improve the reconstruction performance of the network. The comparative experiments on the synthetic and field seismic data show that depthwise separable convolution can effectively reduce the number of network parameters and computation intensity with the interpolation results comparable to the standard convolution results.

Improvement of Spectrum Suppression-Based Deep Learning Interpolation Technique

Seismic data are often coarsely or inconsistently sampled along the acquisition geometry due to the inherent limitations in survey equipment or insufficient survey budgets. Recently, machine learning techniques have been utilized to acquire compactly sampled seismic data. Among them, the self-supervised learning-based techniques that do not require labels are actively being used, and the interpolation technique based on the blind trace network (BTN) and spectrum suppression using suppression masks through line detection has shown high accuracy. However, the interpolation technique using BTN and the suppression masks through line detection suffers from instability caused by the reconstruction loss and inaccuracy of the suppression masks. To mitigate those problems, we propose suppression masks using generalized frequency-wavenumber ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f-k</i> ) trace interpolation (GFKI), patch-based learning, masked UNet, and equalized learning rate. The suppression masks using GFKI are generated by correlating the zero-padded data with the data obtained by regularly removing traces from the zero-padded data in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f-k</i> domain. Additionally, we divide data into patches to enhance the accuracy of the suppression masks. Masked UNet is used to constrain the output to contain the input signals at the designated positions using the binary mask in the space–time domain. Furthermore, we normalize each layer in the network so that the learning speeds for each layer can be commensurate with each other. The synthetic and field data experiments show that the proposed interpolation technique effectively suppresses aliasing of signals and enables the training process to stably converge.

High‐efficiency and high‐precision seismic trace interpolation for irregularly spatial sampled data by combining an extreme gradient boosting decision tree and principal component analysis

AbstractIn seismic data acquisition, because of several factors, such as surface barriers, receiver failure, noise contamination and budget control, seismic records often exhibit irregular sampling in the space domain. As corrupted seismic records have a negative effect on seismic migration, inversion and interpretation, seismic trace interpolation is a key step in seismic data pre‐processing. In this paper, we propose a high‐efficiency and high‐precision seismic trace interpolation method for irregularly spatially sampled data by combining an extreme gradient boosting decision tree and principal component analysis in a semi‐supervised learning method. The adjacent trace number, sampling number and amplitudes of the effective seismic data were taken as features to build the training data set for the extreme gradient boosting decision tree. Principal component analysis is applied to remove redundant information and accelerate the training speed. This is different from the traditional trace interpolation method in that the proposed method is data‐driven; therefore, it does not require any assumptions. Compared with other deep learning‐based trace interpolation methods, the proposed method has fewer control parameters and learning labels and a smaller training cost. Experiments using synthetic and field data demonstrated the validity and flexibility of this trace interpolation method.

Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data

We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ([Formula: see text]) waveform misfit of one is achieved, and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.

Increasing the Lateral Resolution of 3D-GPR Datasets through 2D-FFT Interpolation with Application to a Case Study of the Roman Villa of Horta da Torre (Fronteira, Portugal)

The approach presented in this work uses an interpolation methodology to densify 3D-GPR datasets to sharpen the results obtained in GPR surveys carried out in an archaeological environment. It allows the estimation of missing data from the combined use of mathematical transforms, such as the Fourier and curvelet transforms, and predictive filters. This technique makes it possible to calculate the missing signal simply by meeting two requirements: the data in the frequency domain must be limited in a range of values and must be able to be represented by a distribution of Fourier coefficients (verified conditions). The INT-FFT algorithm uses an open-access routine (Suinterp, Seismic Unix) to interpolate the GPR B-scans based on seismic trace interpolation. This process uses automatic event identification routines by calculating spatial derivatives to identify discontinuities in space by detecting very subtle changes in the signal, thus allowing for more efficient interpolation without artifacts or signal deterioration. We successfully tested the approach using GPR datasets from the Roman villa of Horta da Torre (Fronteira, Portugal). The results showed an increase in the geometric sharpness of the GPR reflectors and did not produce any numerical artifacts. The tests performed to apply the methodology to GPR-3D data allowed for assessing the interpolation efficiency, the level of estimation of missing data, and the level of information lost when we chose to increase the distance between B-scans in the acquisition stage.

Robust local slope estimation by deep learning

ABSTRACTIn the seismic community, the local slope is essential for various applications, including structure prediction, seislet transform, trace interpolation and denoising. The most popular method to calculate slope is the plane‐wave destruction, which assumes that the seismic data can be represented by local plane waves. However, the plane‐wave destruction method fails when the seismic data become very noisy. Taking random noise into consideration, we adopt the deep learning method to calculate the local slope. In the deep learning architecture, the input is noisy data and the target is an accurate slope estimated from the clean data using plane‐wave destruction. The deep learning architecture includes a convolutional layer, deconvolutional layer, normalization layer and activation layer which are suitable to suppress noise and learn the nonlinear relationship between the input and the target. After training, the network is applied to other test examples to calculate local slopes. In addition, we implement the seislet transform and structure prediction applications based on the estimated slope. Both the estimated slope and the related applications indicate that the proposed method can robustly obtain the local slope from noisy seismic data, compared with the plane‐wave destruction method.

Cuspate-lobate folding in glacial sediments revealed by a small-scale 3-D seismic survey

We carried out a small-scale 3-D seismic survey (120 × 120 m2, bin size 1.5 m) in advance of a research borehole. The target consists of 150 m of Quaternary sediments in a glacially overdeepened valley. We used a wheelbarrow-mounted electrodynamic vibrator as seismic source and chose a simple orthogonal layout. During one week of acquisition, we fired 1024 shots into 384 vertical geophones.The key processing step was the interpolation and regularization of traces, realized by common reflection surface (CRS) processing. This enhances data quality in low fold regions at small offsets. Despite the small source, the entire Quaternary fill and the base of the valley is imaged well.At a depth of 20–50 m, glaciotectonic deformation, in the form of cuspate-lobate folds, is visible, which was not recognized previously in a 2-D seismic profile that runs along the edge of the 3-D area. The folding indicates that compressional glacial stresses acted on layers of stiff till and less competent clastics. We interpret that the varying fold axes' directions indicate varying stress fields during the Last Glacial Maximum. Cuspate-lobate folding has hitherto not been used to describe the deformation of glacial sediments.

Research on Seismic Signal Enhancement Method Based on Deep Learning

At present, human beings are increasingly dependent on oil and gas energy. Due to the influence of a series of factors such as exploration technology and natural environment, in the process of actual oil and gas exploration technology, the collected seismic data usually has the problem of low sampling rate. The lower sampling rate of seismic data may cause spatial aliasing in migration imaging, resulting in inaccurate exploration. Therefore, in order to carry out more accurate oil and gas exploration, the seismic signal enhancement method also puts forward higher requirements. In this paper, the seismic signal enhancement will be realized by seismic data channel interpolation. A seismic trace interpolation method based on generative adversarial network is proposed to realize it. The traditional seismic trace interpolation is generally carried out based on complex mathematical transformation or certain assumptions, in order to solve the problems existing in the traditional seismic trace interpolation method. This paper will use the generative adversarial network model in deep learning to combine the generative adversarial network with the residual network, and the loss function is the sum of the Wasserstein distance and the content loss. The optimized generative adversarial network can better realize the interpolation of seismic traces, and the spatial aliasing frequency has been suppressed. Therefore, the enhancement of seismic signals can be better achieved, and theoretical support for accurate exploration can be provided.

Seismic Data Consecutively Missing Trace Interpolation Based on Multistage Neural Network Training Process

Due to the constraints of natural environments, acquired prestack seismic data is usually not complete, which seriously affects subsequent seismic data processing. With the progress of deep learning, many neural networks with different structures have been applied to missing seismic data interpolation. Among them, U-net can efficiently interpolate the regularly and irregularly missing seismic traces with small gap. While for consecutively missing seismic traces with big gap, the interpolation results for low amplitude missing components need to be further improved. In this letter, we analyze the variation of interpolation results for consecutively missing seismic traces during the traditional U-net training process, and find that U-net tends to only interpolate the high amplitude missing components. Meanwhile, due to the distribution difference between low and high amplitude seismic data, one U-net model is insufficient to interpolate both high and low amplitude missing components with a wide amplitude range. To improve the interpolation results of single U-net, we propose a multistage training process to train multiple U-net models. Each U-net model focuses on interpolating different missing components with a small amplitude range. In this way, more accurate interpolation results for low amplitude missing components can be obtained. Comparison experiments conducted on synthetic and field seismic data show that, under the same number of training epochs, the proposed training process can produce more accurate interpolation results comparing with traditional single U-net.

Coarse-Refine Network With Upsampling Techniques and Fourier Loss for the Reconstruction of Missing Seismic Data

Seismic data are often irregularly or insufficiently sampled along the spatial direction due to malfunctioning of receivers and limited survey budgets. Recently, machine learning techniques have begun to be used to effectively reconstruct missing traces and obtain densely sampled seismic gathers. One of the most widely used machine learning techniques for seismic trace interpolation is UNet with the mean-squared error (MSE). However, seismic trace interpolation with the UNet architecture suffers from aliasing, and the MSE used as a loss function causes an oversmoothing problem. To mitigate those problems in seismic trace interpolation, we propose a new strategy of using coarse-refine UNet (CFunet) and the Fourier loss. CFunet consists of two UNets and an upsampling process between them. The upsampling process is done by padding zeroes in the Fourier domain. We design the new loss function by combining the MSE and the Fourier loss. Unlike the MSE, the Fourier loss is not a pixelwise loss but plays a role in capturing relations between pixels. Synthetic and field data experiments show that the proposed method reduces aliased features and precisely reconstructs missing traces while accelerating the convergence of the network. By applying our strategy to realistic cases, we show that our strategy can be applied to obtain more densely sampled data from acquired data.

A Consensus Equilibrium Approach for 3-D Land Seismic Shots Recovery

Physical and budget constraints often result in inadequate sampling for accurate subsurface imaging. Preprocessing approaches, such as missing trace interpolation, are typically employed to enhance seismic data in such cases. The compressed sensing (CS) framework has been applied for modeling missing seismic data, which is estimated by sparsity-based computational algorithms. While existing work mainly focuses on recovering missing traces resulting from receiver subsampling, source subsampling has greater economical advantages, as sources are more expensive than receivers. Moreover, stronger image models different from sparsity have not been explored for source recovery. This work presents a consensus equilibrium (CE) approach to recover missing seismic shots, which enables to incorporate various regularization operators modeling different data priors. Simulation results from a real 3-D land seismic dataset demonstrate that the CE approach provides more accurate estimations of the linear and hyperbolic events in the recovered shots, compared with pure sparsity-based reconstructions.

Seismic data interpolation using deep learning with generative adversarial networks

ABSTRACTWe propose an algorithm for seismic trace interpolation using generative adversarial networks, a type of deep neural network. The method extracts feature vectors from the training data using self‐learning and does not require any pre‐processing to create the training labels. The algorithm also does not make any prior explicit assumptions about linearity of seismic events or sparsity of the data, which are often required in the traditional interpolation methods. We create the training labels by removing traces from different receiver indices of the original datasets to simulate the effect of missing traces. We adopt the framework of the generative adversarial networks to train the network and add additional loss functions to regularize the model. Numerical examples using land and marine field datasets demonstrate the validity and effectiveness of the proposed approach. With minimal computational burden and proper training, the proposed method can be applied to three‐dimensional seismic datasets to achieve accurate interpolation results.

Research on Seismic Data Interpolation and Reconstruction

The seismic record samples are frequently larger than appropriate and the record data is often lost in survey, so we need to perform interpolation and reconstruct of seismic data. In this thesis, generalized F-K seismic trace interpolation method is applied to resolve the problem of the serious insufficiency of spatial sampling. τ-p transformation is applied to reconstruct seismic data technique to resume lost seismic data. Finally, models of theoretic data and practical seismic data can verify that the interpolation and reconstruction methods described in this thesis own high applicability and efficiency.

Seismic Data Reconstruction Using Deep Bidirectional Long Short-Term Memory With Skip Connections

Due to environmental and economic constraints on their acquisition, seismic data are always irregularly sampled and include bad or missing traces, which can cause problems for seismic data processing. Recently, many researchers have attempted to improve seismic data reconstruction using machine learning (ML) techniques, such as convolutional neural networks, which are inspired by computer vision and imaging processing. In this letter, we propose a novel approach for reconstructing missing traces in seismic data using ML techniques, especially recurrent neural network (RNN) algorithms. Instead of processing seismic data as an image, the proposed approach performs seismic trace interpolation using traces that are sequences of time-series data. More specifically, we adopt deep bidirectional long short-term memory (LSTM) for seismic trace interpolation and test models with and without skip connections. Field seismic data are used to demonstrate the effectiveness of the proposed approaches, and the deep bidirectional LSTM (DBiLSTM) with skip connections shows the best performance compared to cubic interpolation, minimum weighted norm interpolation (MWNI), and DBiLSTM without skip connection.