Seismic Data Reconstruction Based On Multichannel Singular Spectrum Analysis Method

With the deepening of China’s and gas exploration in recent years, geologicaland tectonic environment exploration areas have become more complex, the objectiveexistence of these environmental factors exacerbated the imperfection andirregularities seismic data. Irregular seismic data come from the stage of seismic datacollecting and preprocessing stage. From seismic exploration process, the irregularseismic data generated from two main aspects: First, seismic data acquisition phase,seismic data along the spatial direction is non-regular sampling; Second, the seismicdata processing stage, due to the exclusion of waste guns, waste channel and channelloss and other factors make the irregular distribution of seismic data in the spatialdirection. Irregular seismic data not only causes subsequent processing of seismicnoise, but also processing adversely affect multi-channel seismic proper runningtechnique.In this paper, the problem of lack of seismic trace will be discussed, and the lackof irregular seismic data reconstruction comes down to a high rank matrix singularproblem. In the frequency domain, using MSSA (multichannel singular spectrumanalysis) method to the data for each frequency slice to construct complex Toeplitzmatrix and the matrix rank reduction to achieve the restoration and reconstruction ofmissing data. During the implementation of complex Toeplitz matrix rank reduction,using Lanczos double diagonal fast decomposition algorithm to replace the traditionaltruncated SVD (Singular value decomposition) algorithm to improve the computingspeed descending rank process. It should be noted, the rank reduction of Toeplitzmatrix use FFT algorithm with matrix and vector multiplication directly, therefore,this paper constructed Toeplitz matrix directly to replace Hankel matrix.The conditions of a linear or quasi-linear are the basis of multichannel singularspectrum analysis of seismic data reconstruction method. So nonlinear phase axisbending is required to select the appropriate length of the window, as far as possible so that each seismic trace data within a small window to be linear or quasi-linearconditions, then make the original seismic data within each respective window forrank reduction and reconstruction.In addition, the current multichannel SVD method does not exist anti-aliasingdefects. The singular values and singular vectors of aliasing information, singularvalues and singular vectors of seismic data valid signal superimposed on each otherand make it impossible to distinguish them in rank reduction, so there is no effect tothe regular missing data interpolation. This article introduce Spitz’s single-stepprediction filter interpolation thought to have known Lanczos vector data indescending rank low frequencies as the missing channel data interpolation constraintsof high frequency components, so as to realize the anti-aliasing singular spectrumanalysis based on multi-channel theory fast frequency seismic data reconstructionmethod. Finally, the theoretical and practical data processing results show theeffectiveness of this method.