Research On Seismic Data Denoising Method Based On Non-local Self-similarity And Low-rank Approximation Theory

With the continuous exploitation of oil and gas resources,oil and gas seismic exploration targets gradually turn to complex,hidden,deep and unconventional oil and gas reservoirs,which has higher requirements for the quality of seismic data.Affected by the complex natural environment and other factors,the seismic data collected in the field will inevitably be disturbed by noise,which affects the imaging of underground structures and the interpretation of seismic data.Therefore,suppressing the noise in seismic data and improving the signal-to-noise ratio of seismic data are of great significance in the field of seismic data processing.In recent years,low-rank approximation theory has played an important role in the field of seismic data processing because of its powerful ability to analyze and process redundant information in seismic data.However,limited by the assumptions of the low-rank model,traditional low-rank approximate denoising algorithms are generally suitable for processing seismic data with low noise levels or simple structures.In fact,seismic data has a large number of non-local self-similar structures.With the help of the non-local self-similarity of seismic data,the original seismic data can be divided into blocks,and the similar seismic data blocks can be formed into low-rank block-group matrix.The block-group matrix is more in line with the hypothesis of the low-rank model,which is helpful for low-rank approximation algorithm to accurately recover the low-rank structure hidden in seismic data and enhance the denoising effect of for complex seismic data.To this end,this paper focuses on the in-depth analysis of the noise suppression problem of seismic data with complex structure or low signal-to-noise ratio,and carries out seismic data noise suppression mathematical optimization algorithm and its application research with the help of non-local self-similarity prior information and low-rank approximation theory.The main research contents and achievements of this paper are as follows:(1)This paper proposed a seismic data denoising method based on the smooth patch ordering-based nonlocal means.This method introduces the idea of "patch order" into the non-local mean method,divides the noise-contaminated seismic profile into overlapping small data patches,and reorders the data patches according to the similarity between the data patches;then,for each data patch,the weighted average value of the center point of its neighborhood patches after permutation is used as the estimated value of the center point of the block,which reduces the negative effect on the denoising performance caused by the non-similar patches participating in the calculation of weight;at the same time,patch classification strategy and iterative strategy are designed to enhance the ability of the algorithm to suppress strong random noise.The experimental results show that,for the seismic data with less complex structure,the method can effectively suppress random noise and protect the effective structure of seismic data.Even if the random noise is strong,it can achieve good results without introducing pseudo Gibbs artifacts.(2)This paper proposed a seismic data denoising method based on total variation and low rank regularization.This method integrates total variation and low-rank regularization into a unified framework.Through the block matching step,the nonlocal similar seismic data blocks are formed into an approximate low-rank block-group matrix.The nonlocal low rank regularization constraint based on nuclear norm is adopted to effectively denoise and preserve the structural information in the block group matrix of seismic data.Meanwhile,with the help of total variation regularization constraint,the artifacts caused by stack of seismic data blocks are reduced.Furthermore,the local singular value decomposition operator is introduced to update the basis function to enhance the low rank property of the block group matrix of seismic data.The experimental results show that for the seismic data with low signal-to-noise ratio and weak seismic features,this method can effectively suppress the random noise,retain the weak featuresof the seismic data,and will not cause the pseudo-Gibbs phenomenon.(3)This paper proposed a seismic data denoising method based on truncated nuclear norm minimization.This method uses the non-local self-similar priors of seismic data to transform the original seismic data denoising problem into a series of low-rank approximation problems of the block-group matrix by constructing a low-rank block-group matrix.In low rank approximation problems,nuclear norm is usually used as a convex replacement of rank function.However,nuclear norm minimization will shrink the components of different ranks equally,which will lead to a biased solution in practice.This paper proposes to use truncated nuclear norm to better approximate the rank of the matrix,and constructs a low-rank approximation model based on truncated nuclear norm minimization.A two-step iterative optimization strategy is designed to approximately solve the nonconvex objective function,and the randomized singular value decomposition is used to replace the singular value decomposition to reduce the computational cost of the algorithm.Finally,the denoised block-group matrices are embedded into the residual-based iterative framework to further improve the denoising result,so as to estimate the potential low rank structure of the block group matrix more accurately while suppressing the noise.The experimental results show that this method is superior to the traditional low rank approximation algorithm based on nuclear norm minimization for seismic data with complex structure.(4)This paper proposed a seismic data denoising method based on double non-convex non-smooth rank minimization.The denoising process of this method is the same as that of(3),except that in the rank approximation stage,a more flexible and accurate double nonconvex nonsmooth rank minimization model is used to the denoise low-rank block-group matrix.Thanks to the iterative weighting strategy and the super-gradient properties of non-convex functions,the weighted non-convex non-smooth rank approximation function can adaptively assign weights to different singular values,avoid the unbalanced shrinkage of different rank components,provide a more flexible and accurate rank than the traditional convex rank approximation and non-convex rank approximation function,and improve the effect of potential low-rank structure restoration of seismic data.In addition,this paper designs a solution combining generalized singular value contraction operator and fixed point iterative algorithm to complete the optimization of non-convex objective function.Experimental results show that compared with weighted nuclear norm minimization denoising method,this method achieves better noise suppression and useful signal protection effects.