Research On Sparse Representation Method Of Seismic Data Based On AMDL

Seismic exploration,as the most important means of oil and gas survey,is developing toward large scale and high precision,while the complexity of the field environment and the limitation of construction cost make it difficult to improve the efficiency of seismic data acquisition through hardware enhancement.Therefore,the compressive sensing theory guides a new research direction for seismic exploration,by using sparse representation methods to sparsely represent the original seismic data within the acquisition nodes,followed by using observation matrices to observe the seismic data after sparse representation,and finally using reconstruction algorithms to recover the original seismic data.According to the theory of compressive sensing,it is known that the stronger the sparsity of seismic data,the higher the accuracy of its reconstruction,and the sparsity of the same seismic data differs after sparse representation by different methods.Therefore,it is necessary to study the sparse representation method for stronger fitting ability.The sparse representation of seismic data can be divided into two types of sparse representation methods based on fixed-base dictionaries and learning dictionaries according to the dictionaries.The former uses a set formula to calculate and generate the dictionary,and the process of constructing the dictionary is simple and fast,but the fixed base cannot be changed after it is determined,so it is difficult to achieve high quality fitting for seismic data;while the latter can learn the sparse transform domain adaptive according to the characteristics of different seismic data,and can obtain higher reconstruction accuracy compared with the fixed base dictionary.However,the constraints of the widely used MOD,K-SVD and other sparse representation methods based on learned dictionaries are too strict,and they have the shortcomings of weak adaptive capability and limited degrees of freedom for extracting features.To address the shortcomings of the existing methods,this paper adopts the adaptive multilayered dictionary learning(AMDL)method for sparse representation of seismic data,and proves through numerical experiments that the method is superior in sparse representation of seismic data compared with the K-SVD algorithm.The thesis research is as follows:(1)The theory related to the sparse representation of seismic data is studied and analyzed.The Nyquist sampling theory is studied.The framework and process of compressive perception theory are studied,and the three important components of compressive perception theory are investigated together with formulas;finally,the definition of sparse representation is studied and the process of sparse representation of signals is analyzed,and several common optimization models for solving sparse representation problems are summarized.(2)The sparsity and sparse representation of seismic data are studied.The sparsity of seismic data is analyzed by seismic wave field theory and matrix theory,respectively,and its sparsity is proved.The sparse representation methods based on fixed-base dictionaries are studied,and the principles,expressions,advantages and disadvantages of several commonly used methods are studied in detail;the sparse representation methods based on learning dictionaries are studied,and the K-SVD method,which is widely used in many fields,is analyzed in detail,and its shortcomings in the sparse representation of seismic data are summarized.(3)The adaptive multilayered dictionary learning(AMDL)method is investigated and a sparse representation of seismic data is performed.The K-SVD method is improved by adopting a multilayered dictionary learning scheme,dividing the dictionary into several sub-dictionaries in the sparse representation process,and designing four termination conditions to make it adaptive determine the number of atoms selected,and finally designing the steps of the adaptive multilayered dictionary learning(AMDL)method for the sparse representation of seismic data.(4)The sparse representation performance of different methods is investigated by combining two kinds of simulated and measured seismic data,and the sparse representation results are analyzed in detail.Firstly,two metrics,reconstruction signal-to-noise ratio and reconstruction error,are chosen to evaluate the sparse representation effects of different sparse representation methods on seismic data.Secondly,simulated seismic data are designed using ricker wave,and then two sets of measured seismic data with different geographical locations are selected.Finally,the K-SVD and AMDL algorithms are used to perform the sparse representation of the simulated and measured seismic data respectively,and their sparse representation performance is compared and studied according to the reconstruction indexes,and the sparse representation effect is summarized in detail.In summary,this paper improves the K-SVD method to address the shortcomings of the K-SVD method,and adopts the adaptive multilayered dictionary learning(AMDL)method for the sparse representation of seismic data,using a multilayered dictionary learning scheme so that it can acquire more features of the original seismic data during the dictionary learning process;and adopts four termination conditions so that it can adaptive determine for different original seismic data during the sparse coding process atomic number.The dictionaries obtained by the K-SVD algorithm and the adaptive multilayered dictionary learning(AMDL)method are tested and evaluated.Under the premise of processing the same seismic data and using the same reconstruction algorithm,the reconstruction signal-to-noise ratio of the seismic data is higher and the reconstruction error is smaller after the sparse representation of the AMDL method.