Reconstruction Of Seismic Data Based On Optimized Poisson Disk Sampling

With the deepening of oil and gas exploration,the complex and variable exploration target area has intensified the incompleteness and irregularity of seismic data,affected the processing and interpretation of subsequent seismic data,and ultimately affected the judgment of oil and gas resources.Therefore,we have to reconstruct these incomplete data.Limited by the Nyquist sampling theorem,the traditional seismic data reconstruction method has higher requirements on sampling rate and higher exploration cost.It is the great significance to find a better compression reconstruction method and compress and reconstruct missing seismic data.In view of the above problems,this paper introduces Compressed Sensing theory to solve the problem of missing seismic data reconstruction.By using the sparse feature of seismic data in the dictionary transformation domain,the appropriate measurement matrix and reconstruction algorithm are designed to reconstruct the missing seismic data,and the ideal processing results are obtained.The details are as follows:(1)The reconstruction principle of traditional seismic data reconstruction methods is summarized,and their respective advantages and disadvantages are compared and analyzed.It is concluded that the traditional reconstruction methods have strong dependence on sampling frequency.When reconstructing seismic data with low sampling rate,the reconstruction effect is poor,which affects the subsequent interpretation of seismic data.Therefore,the research content of this paper is introduced,and the missing seismic data are reconstructed by using compressed sensing theory.(2)In view of the problem that the sparse representation method in compressed sensing can not be adaptively adjusted according to the characteristics of the data itself once it is selected,this paper explores the use of learning overcomplete dictionary to sparse representation of seismic data.According to the characteristics of seismic data,sparse transform bases are constructed adaptively,which has stronger sparse representation ability.(3)In order to improve the inadequacy of the simple random sampling algorithm in compressed sensing that can not control the sampling interval,the Poisson disk sampling is introduced.Based on the Poisson disk sampling,the sampling region is divided by the grid index,and the candidate is randomly selected in the mesh region.Whether the candidate points meet the minimum interval limit.Improved Poisson disk sampling ensures sampling randomness while improving sampling efficiency while controlling sampling interval.(4)In the selection of reconstruction algorithm,it is found that the Orthogonal Matching Pursuit(OMP)algorithm selects one of the optimal atoms into the support set every iteration,which results in slower iteration and low reconstruction precision.In this paper,the Stagewise Orthogonal Matching Pursuit(StOMP)reconstruction algorithm is introduced into the missing seismic reconstruction.The algorithm selects multiple atoms into the support set each time,which avoids the atomic non-optimal deficiency of the OMP algorithm.Both accuracy and timeliness have significant advantages.The experimental results show that the proposed method of seismic data reconstruction based on compressed sensing and Poisson disk sampling algorithm can effectively reconstruct missing seismic data and improve reconstruction efficiency and reconstruction accuracy.