The Research On Reconstruction Method Of Missing Seismic Data Based On Compressed Sensing Theory

In recent years,with the further development of geological exploration,the targets of exploration have become more and more complicated and diversified.The seismic data collected have also exhibited irregularities and incompleteness,which has brought troubles about the processing of seismic data and will ultimately affect the determination of the exploration results,so we have to rebuild these incomplete seismic data.The traditional reconstruction method relies on a higher sampling rate and does not work well when reconstructing seismic data with a lower sampling rate.The data reconstruction method based on compressed sensing theory is not limited by the Nyquist sampling theorem.It shows that as long as the data reconstructed is sparse in itself,or is sparse in a transform domain,it can reconstruct the seismic data well even at a low sampling rate.The compressed sensing theory closely integrates the measurement matrix of the data acquisition phase and the reconstruction algorithm of the data processing phase in the seismic exploration.Not only obtaining a more effective processing result,but also the sampling rate can be reduced,thus saving exploration costs.Forward modeling in seismic exploration is the foundation.Many methods cannot be separated from forward modeling.This paper does some research on the forward modeling of seismic waves,and simulates the lack of seismic data acquisition by forward modeling.The boundary conditions are perfectly matched layer boundary conditions,and the flux correction technique is used to eliminate the dispersion problem in the forward simulation.The reconstruction of seismic data under compressive sensing theory consists of three parts: sparse transformation,measurement matrix,and reconstruction algorithm.With the rapid development and gradual improvement of Compressive Sensing theory in the field of signal processing,it is also possible to obtain good reconstruction results when reconstructing data far below the frequency required by the Nyquist sampling theorem using a reconstruction algorithm.In this paper,the reconstruction algorithm is studied in depth.According to the selected seismic data,the wavelet transform is used to sparsely represent the seismic data,and different measurement matrixes are used to delete the seismic data.Finally,Matching Pursuit(MP)algorithm,Fixed Point Continuation(FPC)algorithm and Fast Fixed Point Continuation(FFPC)are used to reconstruct the missing seismic data.The principle and structure of various reconstruction algorithms are studied in depth,and on the basis of multiple experiments,the Fast fixed point continuous algorithm is compared with some previous reconstruction algorithms,it has obvious advantages both in the accuracy of reconstruction and time consuming.