Research On High Resolution Methods Based On Sparse Representation

High resolution processing is of great significance for reducing the risk of exploration and development.The processing methods of improving resolution include deconvolution,inverse Q filtering and absorption attenuation compensation based on time-frequency analysis.However,these methods have many limitations in practical applications.In order to improve the resolution of seismic data more effectively,this paper attempts to improve the resolution by using the theory of sparse representation.Through the analysis of the compressed sensing theory,this paper improve the resolution through compressed sensing in the frequency domain.In specific implementation,noise is taken into the sampling matrix,which makes the sampling matrix larger probability to meet the RIP criterion,and effectively improves the original compressed sensing algorithm in frequency domain.In the further research on the reconstruction algorithm of sparse representation and the compressed sensing theory,the characteristics of Matching Pursuit and Basis Pursuit are discussed.In the high resolution algorithm based on compressed sensing,when dealing with the dominant frequency band,the wavelet matrix will suffer rank loss.Therefore,this paper studies the reconstruction accuracy and convergence speed of two algorithms of two algorithms at different sampling rates through numerical simulation by numerical simulation.Through the experiment,we obtained when the sparsity remains constant,the result of signal reconstruction decreases with the sampling rate.Subspace matching Pursuit algorithm has the same reconstruction performance as the Basis Pursuit algorithm,and it can be better used for data reconstruction.Finally,the algorithm experiments are carried out by using the minimum phase and the mixed phase wavelet to synthesize the seismic records.Experiments show that the improved algorithm is not limited by phase and has good anti noise ability.But by derivation,it is also realized that the algorithm can achieve good results only when wavelet is invariant.In order to solve the problem of time-varying wavelet,this paper studies the high resolution processing method based on the wavelet attenuation atom library,and improves the construction method of wave dictionary.Through the analysis of the problems in the Ricker wavelet dictionary,the idea of extracting wavelet from the actual data and using the Q value for the absorption and attenuation of the subwave to obtain the subset of the wavelet is proposed.In the experiment,this paper compared this method with the common Ricker wavelet dictionary,and proved that the algorithm greatly improves the speed and precision of the inversion.Because the high resolution processing method of sparse representation and compressed sensing theory needs the information of wavelet,the quality of wavelet extraction will directly affect the final result.Therefore,the wavelet extraction method is studied in this paper.By comparing and analyzing the shortcomings of the common methods,the three order cumulants algorithm is selected to solve the problem of the extraction of different phase wavelet.At the end of this paper,the theoretical data of different phase and different signal to noise ratio are tested,it shows that the improved algorithm has good noise resistance,can adapt to time variable wavelet,is able to adapt to seismic data of different phases and it is an excellent resolution algorithm to improve the resolution.Finally,the method is applied to the actual data processing,and a good result is obtained.