Research On Seismic Data Reconstruction Method Based On Sparse Representation And Compressed Sensing

When collecting seismic data in the field,due to economic cost constraints and unpredictable factors such as complex geological environments,the actual collected seismic data is often irregular and incomplete,seriously affecting subsequent data processing and interpretation.Therefore,regularization of missing seismic data is an indispensable key step.Traditional signal acquisition is limited by Nyquist sampling theorem.In recent years,compressed sensing theory provides a new idea,which breaks through the limitation of sampling theorem.Even if the sampling frequency is lower than twice the maximum frequency,the complete signal can be recovered.Based on the theoretical framework of Compressed sensing,this paper firstly compares the sparse representation methods such as Fourier transform,discrete cosine transform,wavelet transform,Curvelet and K-SVD dictionary,and selects greedy algorithm for reconstruction experiment analysis;Secondly,the OMP orthogonal Matching pursuit algorithm and the St OMP piecewise orthogonal Matching pursuit algorithm are compared.The results show that the St OMP algorithm is more efficient;At the same time,the projection algorithm of convex set is deeply studied,and the seismic data reconstruction effect under different threshold functions and sampling methods is analyzed.The results show that the combination of new soft and hard compromise threshold functions and Jitter sampling method can achieve better reconstruction effect;Then,the reconstruction effects of different algorithms,such as the FISTA fast iterative soft threshold algorithm,Bregman iterative algorithm,and FPOCS fast convex set projection algorithm,were compared.Through comparative experiments between Pluto model data and actual seismic data,it was shown that the FPOCS algorithm has higher reconstruction accuracy,relatively faster computational efficiency,and good practicality;Finally,for the missing seismic data with random noise,this paper introduces the weighting factor on the basis of FPOCS algorithm and proposes a weighted fast POCS algorithm.Combined with Curvelet,this algorithm can remove random noise while reconstructing seismic data.The effectiveness of this method is proved through numerical simulation tests.