Research On Sparse Representation Method Of Seismic Data Bsed On BDLF

The demand for oil in China has been increasing year by year,but the production of oil cannot meet the growing demand,which has led to a continuous increase in oil imports.Seismic exploration is an important means to increase oil production.With the development of "two widths and one height" seismic exploration technology,the scale of seismic data acquisition in China has been further improved,and a million level seismic data acquisition system will become the development direction of future seismic exploration.However,increasing the scale of data collection means a significant increase in the amount of seismic data collected,a significant increase in data storage pressure,and real-time data transmission becoming more difficult.The compressed sensing theory provides solutions to these problems.Applying compressed sensing theory to seismic exploration can reduce the amount of seismic data acquisition,reduce the burden of data transmission,and improve the efficiency of seismic data acquisition.The theory of compressed sensing consists of three parts,namely sparse representation,measurement matrix and reconstruction algorithm.This paper focuses on the research of sparse representation.The learning dictionary based sparse representation method updates the dictionary by learning the features of seismic data,generating a dictionary that matches the seismic data better.It has high research value,among which the K-SVD algorithm is the most typical algorithm in the learning dictionary based sparse representation method.However,the K-SVD algorithm has the drawback of difficult to fully learn the features of seismic data during use.In response to its shortcomings,this paper studies the Boosted Dictionary Learning Frame(BDLF)and sets the learning dictionary within the framework as the K-SVD dictionary.At the same time,in order to further improve the sparse representation effect of BDLF algorithm,the core dictionary learning(CDL)method is studied to replace the K-SVD dictionary in BDLF in view of the defect that the K-SVD dictionary has strong coherence between atoms.The results show that under the same conditions,sparse representation of the same seismic data can be achieved using the BDLF algorithm,which outperforms the K-SVD algorithm.At the same time,using the CDL dictionary can further improve the sparse representation performance of the BDLF algorithm.The main research content of this article includes:(1)Studied the relevant theories of sparse representation.By deriving the mathematical expression of wave equation,it is proved that the seismic signal meets the precondition of compressed sensing theory and has sparsity;Studied the relevant theories of sparse representation and introduced four norm minimization algorithms to solve sparse representation problems;Three properties that measurement matrices must satisfy were studied,and several common measurement matrices were also introduced.(2)We have studied various sparse representation methods.Introduce the theory,formulas,and advantages and disadvantages of fixed transformation domain and learning dictionary based sparse representation methods,and analyze the shortcomings of each algorithm in sparse representation of seismic data based on the research content of this article.(3)Studied the BDLF algorithm.Design a multi-layer frame structure,with three links for learning the characteristics of seismic data on each layer except for the first layer.The operating mechanism and judgment criteria of each link were studied,and the steps of sparse representation of seismic data using the BDLF algorithm were described in detail.At the same time,in view of the defect that K-SVD algorithm dictionary has strong coherence between atoms,the CDL algorithm is studied,and the algorithm flow of the CDL algorithm and the steps of sparse representation of seismic data are introduced in detail.(4)Test the BDLF algorithm.After sparse representation of seismic data,algorithms that can achieve higher signal-to-noise ratio and lower relative error are considered better sparse representation methods;Test the sparse representation performance of K-SVD algorithm,BDLF algorithm,and BDLF algorithm using CDL dictionary using simulated and measured seismic data,respectively.The results show that compared to K-SVD algorithm,BDLF algorithm has stronger sparse representation ability,and it also proves that using CDL algorithm can further improve the sparse representation performance of BDLF algorithm.In summary,this article investigates the Boosted Dictionary Learning Framework(BDLF)based on the limitation that a single K-SVD algorithm is difficult to fully learn the features of seismic data.The BDLF algorithm utilizes a multi-layer structure to introduce new seismic data into the dictionary learning process of each layer.By learning the features in the new seismic data,it generates a dictionary set that better matches the seismic data.At the same time,in order to further improve the sparse representation effect of BDLF algorithm,CDL algorithm is studied to replace the K-SVD dictionary in BDLF and improve the sparse representation effect of BDLF algorithm in view of the strong coherence of the K-SVD dictionary.