The Research Of Seismic Data Reconstruction Via Sparse Representation

Seismic exploration as a geophysical exploration means plays an important role in oil and gas exploration.Seismic exploration includes three parts: acquisition,processing and interpretation,as seismic data processing is a link between acquisition and interpretation,previous researchers have done a lot of research in this field and made a lot of progress.However,at that time,restricted by the science and technology,seismic data processing technology developed slowly in a period of time.As time goes by,the emergence of digital computers has brought seismic data processing into the digital era,and various processing methods have made the ability of seismic exploration to find and interpret geological phenomena develop greatly.In recent years,due to the increasing difficulty of exploration,the complex geological conditions in exploration area,the influence of exploration instruments and environment,and the restriction of economic factors during exploration,the seismic data collected are irregular and incomplete,which is very unfavorable to the processing and interpretation of seismic data.Therefore,it is necessary to reconstruct the incomplete data.The reconstruction of seismic data includes three methods: filter-based method,wave equation-based interpolation method and transformation method.The first two methods have the disadvantages of large computation and unstable results.Traditional methods based on transformation have been studied since 1980 s.However,this method is restricted by Nyquist sampling theorem and requires a higher sampling rate to complete reconstruction,which limits the efficiency of data processing.Compressive sensing theory breaks the limitation of Nyquist sampling theorem and provides theoretical support for seismic data reconstruction with lower sampling rate.According to the theory of compressive sensing,when the signal is sparse or can be sparsely represented in a transform domain,the signal is projected from high dimension to low dimension through an observation matrix which is not related to the sparse transform basis,and then the data is reconstructed with high probability by solving the optimization problem by sparse promotion algorithm.The application of compressive sensing theory framework in seismic exploration improves the efficiency and accuracy of reconstruction,and has broad prospects for development in seismic exploration.Seismic data reconstruction method based on compressive sensing theory includes three parts: measurement matrix,sparse transformation and reconstruction algorithms.For different seismic data,three parts affect the efficiency and accuracy of reconstruction in varying degrees.Because the scale of seismic data obtained in seismic exploration is different,the size of the scale affects the application of different sparse transformation and reconstruction algorithms to a certain extent.By comparing the effect of sparse transformation and reconstruction algorithms on reconstructing simulated and actual data in different scales,this paper studies a seismic data reconstruction method suitable for large-scale data.This method uses L1 Norm Spectral Projection Gradient algorithm to reconstruct the missing sparse coefficients in contourlet transform domain to complete the reconstruction of seismic data.The synthetic data and the actual data show that: compared with Orthogonal Matching Pursuit(OMP)and Gradient Projection for Sparse Reconstruction(GPSR),L1 Norm Spectral Projection Gradient(SPGL1)has higher reconstruction accuracy and can meet the requirements of reconstruction efficiency when processing large-scale data on the same sparse transformation.