Research On Seismic Data Denoising Method Based On Matrix Completion And Optimization Theory

With the development of exploration technology and exploration work,the focus areas of seismic exploration in China have moved toward more and more complex deserts,lakes,and remote mountainous areas.The complex geological conditions in these areas often cannot be arranged according to the theoretical assumptions of geophone acquisition data,and the data acquisition is difficult and the data S/N ratio is low,therefore,an effective seismic data denoising method is needed to cope with the current massive low S/N ratio data.Multi-channel singular spectrum analysis(MSSA)is a well-known class of seismic signal denoising methods based on matrix completion theory,which recovers noise-free seismic data by arranging the seismic frequency domain data into block Hankel matrices to satisfy the assumption of uniform sampling.Then,based on the assumption of linear homogeneous axis,each frequency domain slice is transformed into a block Hankel matrix and the singular value decomposition is performed.The number of singular values is estimated for each block of data.The existing algorithms assume that the number of truncated singular values is known,and although they have good results,it is difficult to industrialize them because the number of singular values that should be determined for each block is different,and the traditional methods rely on manual determination,so it is crucial to study a method that can automatically determine the number of singular values retained for data blocks for such algorithms as MSSA.In this paper,we propose an adaptive multi-channel singular spectrum analysis denoising algorithm by analyzing the distribution of singular values,and an Akaike information criterion to automatically distinguish the singular values corresponding to valid signals from the noise related singular values,thus overcoming the problem of needing to manually select the number of singular values,and the method is beneficial to realize large-scale seismic data denoising.To verify the effectiveness of the method in this paper,an empirical estimation method is also given to determine the number of effective singular values,which is statistically and empirically estimated to determine the number of reliable singular values.The numerical implementation shows that the adaptive method in this paper can estimate the reliable number of singular values,thus realizing high-precision automatic denoising and avoiding the arbitrariness of manual selection of the number of singular values,which is more suitable for large-scale industrial production.