Irregular seismic data reconstruction based on exponential threshold model of POCS method

Irregular seismic data causes problems with multi-trace processing algorithms and degrades processing quality. We introduce the Projection onto Convex Sets （POCS） based image restoration method into the seismic data reconstruction field to interpolate irregularly missing traces. For entire dead traces, we transfer the POCS iteration reconstruction process from the time to frequency domain to save computational cost because forward and reverse Fourier time transforms are not needed. In each iteration, the selection threshold parameter is important for reconstruction efficiency. In this paper, we designed two types of threshold models to reconstruct irregularly missing seismic data. The experimental results show that an exponential threshold can greatly reduce iterations and improve reconstruction efficiency compared to a linear threshold for the same reconstruction result. We also analyze the anti- noise and anti-alias ability of the POCS reconstruction method. Finally, theoretical model tests and real data examples indicate that the proposed method is efficient and applicable.

Efficient seismic data reconstruction based on Geman function minimization

Seismic data typically contain random missing traces because of obstacles and economic restrictions,influencing subsequent processing and interpretation.Seismic data recovery can be expressed as a low-rank matrix approximation problem by assuming a low-rank structure for the complete seismic data in the frequency–space(f–x)domain.The nuclear norm minimization(NNM)(sum of singular values)approach treats singular values equally,yielding a solution deviating from the optimal.Further,the log-sum majorization–minimization(LSMM)approach uses the nonconvex log-sum function as a rank substitution for seismic data interpolation,which is highly accurate but time-consuming.Therefore,this study proposes an efficient nonconvex reconstruction model based on the nonconvex Geman function(the nonconvex Geman low-rank(NCGL)model),involving a tighter approximation of the original rank function.Without introducing additional parameters,the nonconvex problem is solved using the Karush–Kuhn–Tucker condition theory.Experiments using synthetic and field data demonstrate that the proposed NCGL approach achieves a higher signal-to-noise ratio than the singular value thresholding method based on NNM and the projection onto convex sets method based on the data-driven threshold model.The proposed approach achieves higher reconstruction efficiency than the singular value thresholding and LSMM methods.

Seismic data reconstruction based on low dimensional manifold model

Seismic data reconstruction is an essential and yet fundamental step in seismic data processing workflow,which is of profound significance to improve migration imaging quality,multiple suppression effect,and seismic inversion accuracy.Regularization methods play a central role in solving the underdetermined inverse problem of seismic data reconstruction.In this paper,a novel regularization approach is proposed,the low dimensional manifold model(LDMM),for reconstructing the missing seismic data.Our work relies on the fact that seismic patches always occupy a low dimensional manifold.Specifically,we exploit the dimension of the seismic patches manifold as a regularization term in the reconstruction problem,and reconstruct the missing seismic data by enforcing low dimensionality on this manifold.The crucial procedure of the proposed method is to solve the dimension of the patches manifold.Toward this,we adopt an efficient dimensionality calculation method based on low-rank approximation,which provides a reliable safeguard to enforce the constraints in the reconstruction process.Numerical experiments performed on synthetic and field seismic data demonstrate that,compared with the curvelet-based sparsity-promoting L1-norm minimization method and the multichannel singular spectrum analysis method,the proposed method obtains state-of-the-art reconstruction results.

Seismic data reconstruction based on iterative linear expansion of thresholds

Based on the compressive sensing,a novel algorithm is proposed to solve reconstruction problem under sparsity assumptions.Instead of estimating the reconstructed data through minimizing the objective function,the authors parameterize the problem as a linear combination of few elementary thresholding functions,which can be solved by calculating the linear weighting coefficients.It is to update the thresholding functions during the process of iteration.The advantage of this method is that the optimization problem only needs to be solved by calculating linear coefficients for each time.With the elementary thresholding functions satisfying certain constraints,a global convergence of the iterative algorithm is guaranteed.The synthetic and the field data results prove the effectiveness of the proposed algorithm.

Sparse Seismic Data Reconstruction Based on a Convolutional Neural Network Algorithm

At present,the acquisition of seismic data is developing toward high-precision and high-density methods.However,complex natural environments and cultural factors in many exploration areas cause difficulties in achieving uniform and intensive acquisition,which makes complete seismic data collection impossible.Therefore,data reconstruction is required in the processing link to ensure imaging accuracy.Deep learning,as a new field in rapid development,presents clear advantages in feature extraction and modeling.In this study,the convolutional neural network deep learning algorithm is applied to seismic data reconstruction.Based on the convolutional neural network algorithm and combined with the characteristics of seismic data acquisition,two training strategies of supervised and unsupervised learning are designed to reconstruct sparse acquisition seismic records.First,a supervised learning strategy is proposed for labeled data,wherein the complete seismic data are segmented as the input of the training set and are randomly sampled before each training,thereby increasing the number of samples and the richness of features.Second,an unsupervised learning strategy based on large samples is proposed for unlabeled data,and the rolling segmentation method is used to update(pseudo)labels and training parameters in the training process.Through the reconstruction test of simulated and actual data,the deep learning algorithm based on a convolutional neural network shows better reconstruction quality and higher accuracy than compressed sensing based on Curvelet transform.

Reconstruction method of irregular seismic data with adaptive thresholds based on different sparse transform bases

Oil and gas seismic exploration have to adopt irregular seismic acquisition due to the increasingly complex exploration conditions to adapt to complex geological conditions and environments.However,the irregular seismic acquisition is accompanied by the lack of acquisition data,which requires high-precision regularization.The sparse signal feature in the transform domain in compressed sensing theory is used in this paper to recover the missing signal,involving sparse transform base optimization and threshold modeling.First,this paper analyzes and compares the effects of six sparse transformation bases on the reconstruction accuracy and efficiency of irregular seismic data and establishes the quantitative relationship between sparse transformation and reconstruction accuracy and efficiency.Second,an adaptive threshold modeling method based on sparse coefficient is provided to improve the reconstruction accuracy.Test results show that the method has good adaptability to different seismic data and sparse transform bases.The f-x domain reconstruction method of effective frequency samples is studied to address the problem of low computational efficiency.The parallel computing strategy of curvelet transform combined with OpenMP is further proposed,which substantially improves the computational efficiency under the premise of ensuring the reconstruction accuracy.Finally,the actual acquisition data are used to verify the proposed method.The results indicate that the proposed method strategy can solve the regularization problem of irregular seismic data in production and improve the imaging quality of the target layer economically and efficiently.

Irregularly sampled seismic data interpolation via wavelet-based convolutional block attention deep learning

Seismic data interpolation,especially irregularly sampled data interpolation,is a critical task for seismic processing and subsequent interpretation.Recently,with the development of machine learning and deep learning,convolutional neural networks(CNNs)are applied for interpolating irregularly sampled seismic data.CNN based approaches can address the apparent defects of traditional interpolation methods,such as the low computational efficiency and the difficulty on parameters selection.However,current CNN based methods only consider the temporal and spatial features of irregularly sampled seismic data,which fail to consider the frequency features of seismic data,i.e.,the multi-scale features.To overcome these drawbacks,we propose a wavelet-based convolutional block attention deep learning(W-CBADL)network for irregularly sampled seismic data reconstruction.We firstly introduce the discrete wavelet transform(DWT)and the inverse wavelet transform(IWT)to the commonly used U-Net by considering the multi-scale features of irregularly sampled seismic data.Moreover,we propose to adopt the convolutional block attention module(CBAM)to precisely restore sampled seismic traces,which could apply the attention to both channel and spatial dimensions.Finally,we adopt the proposed W-CBADL model to synthetic and pre-stack field data to evaluate its validity and effectiveness.The results demonstrate that the proposed W-CBADL model could reconstruct irregularly sampled seismic data more effectively and more efficiently than the state-of-the-art contrastive CNN based models.