Fourier Reconstruction Algorithm Of Two-dimensionalnon-uniformly Sampled Seismic Signal

Seismic signal reconstruction is quite significance in seismic signal processing.Essentially,seismic signal reconstruction is part of multidimensional non-uniform sampled signal reconstruction.Fourier reconstruction algorithm of seismic signal has been paid much attention in recent years.Some of classical algorithms are Fourier reconstruction with minimum norm(FRMN)and Fourier reconstruction with sparse inversion(FRSI).The algorithms have advantages of intuitive,pure principle of data,assumption conditions.But there are also shortcomings of slow computation speed and low reconstruction accuracy.In this paper,on the basis of FRMN and FRSI,two-dimensional non-uniformly sampled seismic signal reconstruction was researched deeply.Specific research work as follows:(1)Partition methods for FRSI(P-FRSI)FRSI algorithm has problems of slow calculation speed and time-consuming.The algorithm of Partition methods for FRSI(P-FRSI)was constructed.The basic idea of P-FRSI was that seismic signal including large amount of data was partitioned and the adjacent blocks were overlap in order to avoid the boundary effect.Then the blocks of seismic signal were reconstructed on the basic of FRSI.Finally,the blocks of seismic signal were overlapped and formed the whole seismic signal.There were three experiments of two-dimensional seismic signal reconstruction for verifying the feasibility and effectiveness of P-FRSI.Theoretical analysis and the results of experiments show that comparing with the traditional FRSI,parameter selection of P-FRSI is more flexible,the reconstruction speed is improved significantly especially for large amount of data of seismic signal,the reconstruction accuracy is improved in a certain extent,and the reconstruction effect is better.(2)Fourier Reconstruction with Landweber Iteration(FRLI)The reconstruction accuracy of FRMN algorithm is poor.The reconstruction accuracy of FRSI algorithm is good but its reconstruction speed is low.The algorithm of Fourier Reconstruction with Landweber Iteration(FRLI)was constructed.The basic idea of FRLI was that fast Landweber iteration solved the Fourier coefficients for inverse Fourier transform based on FRMN.Then seismic signal was reconstructed through the inverse Fourier transform.There were experiments of a one-dimensional seismic signal reconstruction three two-dimensional seismic signal reconstruction for verifying the feasibility and effectiveness of FRLI.The results of experiments show that comparing with the traditional FRMN,FRLI can effectively improve reconstruction speed,reconstruction accuracy and reconstruction effect.By comparison with FRSI,the reconstruction accuracy of FRLI is about the same,however,FRLI saved the approximately half of time.Therefore,FRLI ensures the accuracy and fast reconstruction speed is its obvious advantage.