Research On Low-Rank Representation And Reconstruction Method Of Seismic Data

As a new method of big data analysis,sparse representation is widely used in image processing,seismic exploration,computer vision and other fields.As a high-dimensional generalization of sparse representation,low rank matrix restoration theory takes advantage of the low rank property of big data matrix and adopts appropriate optimization algorithm to restore the original low rank data matrix from the observation matrix with large-scale error,data pollution,damage and other phenomena.Based on the theory of low rank matrix restoration,this paper deeply studies the methods of suppressing nonstationary random noise,reconstructing missing seismic data and inversion of reflection coefficient,and obtains obvious application effect.The details are as follows:(1)In order to overcome the disadvantage that conventional random noise suppression methods can not deal with non-stationary random noise,this paper proposes a non-stationary random noise suppression method based on low rank matrix decomposition.Firstly,the seismic data is rearranged into second-order Hankel matrix,and the second-order Hankel matrix is decomposed into low rank effective signal and sparse random noise by using sparse Bayesian learning algorithm.Then,the low rank effective signal is transformed into time-domain seismic signal to suppress the non-stationary random noise.Compared with the conventional median filter,the non-stationary random noise suppression method based on low rank matrix factorization can make full use of the low rank property of seismic data,maintain the effective signal to the greatest extent,improve the continuity of seismic reflection,and has stronger nonstationary random noise suppression ability.(2)When using conventional rank reduction methods to reconstruct seismic data,it is often necessary to adjust the rank of the matrix artificially to achieve high-precision seismic data reconstruction.However,this adjustment requires repeated experiments,which leads to low computational efficiency.To solve this problem,this paper uses the adaptive low rank matrix fitting algorithm to complete the low rank matrix.Firstly,the sparse norm constraint is used to automatically estimate the rank of the matrix,and then the estimated rank is used as the initial value to fit the large data matrix rearranged by frequency domain seismic data with low rank.Under the low rank matrix completion model,the missing seismic data reconstruction is realized.Numerical experiments show that compared with the conventional multi-channel singular spectrum analysis method,the reconstruction method based on low rank matrix completion proposed in this paper can make full use of the frequency domain correlation of seismic data,achieve higher accuracy and efficiency of seismic data reconstruction,and further improve the quality of seismic data.(3)Since the sedimentary strata have local lateral continuity,the local continuity of the strata is shown in the reflection coefficient matrix,which can be considered as low rank.In this paper,the low rank characteristic of the reflection coefficient matrix is used to add the nuclear norm regularization term to the conventional frequency domain reflection coefficient inversion objective function,and the frequency domain multi-channel reflection coefficient inversion objective function is constructed.The low rank matrix representation model is used to eliminate the influence of seismic wavelet in seismic records,and then the original low rank and sparse reflection coefficient is restored.The application of the model and actual data shows that the inversion reflection coefficient can break through the limit of seismic resolution,enhance the resolution of thin layer,thin interbed and smal-scale geological body,and fundamentally improve the resolution of seismic data.