The Research Of Seismic Data Denoising Methods Based On Sparse Representation

In recent years, seismic exploration has gradually turned to complex, deep and unconventional underground environment. This increasingly complex field acquisition environment makes the collected seismic data often contaminated by noise seriously, which brings great obstacles for subsequent seismic data interpretation and affected the judgment accuracy of underground mineral resources. Therefore, it is the most important work of seismic data processing to improve the signal to noise ratio of seismic data.Sparse representation is a hot research spot in the field of signal processing, and signal can be simply represented in an effective way by sparse representation. In consideration of the superiority of sparse representation, and taking the fact that seismic data has complex morphology and large amount of data in spatio-temporal domain into account, this thesis mainly studied signal sparse representation theory and its application in random noise attenuation of seismic data. The main research contents and innovations points of this thesis are summarized as below:(1) First, we introduced the related basic knowledge of signal sparse representation theory, studied the common sparse decomposition algorithm and the classical dictionary learning algorithm, and analyzed the advantages and disadvantages of various algorithms. We also introduced the Fourier transform, wavelet transform and curvelet transform, which are commonly used in signal analysis, and then applied them to the denoising of seismic data.(2) Based on sparse representation theory, we built the seismic data denoising model, and combined with the dictionary learning ideas, researched the denoising principle of seismic data over learning-type sparse dictionaries. On the basis of classical K-SVD (K-Singular Value Decomposition) dictionary learning method, we delved into the multi-scale dictionary learning method in the wavelet domain, and denoised seismic data based on sparse representation over this multi-scale learning-type dictionary. The signal-to-noise ratio (SNR) of seismic data was improved effectively.(3) Group sparsity of signal sparse representation reveals the correlation between the coefficients, and can better express the structural characteristics of the signal. Based on this, we researched the mathematical model and algorithm of structured dictionary learning method. Then we applied it to the seismic data denoising and obtained a seismic data denoising method based on sparse representation over learning-type group-structured dictionary and verified the correctness and superiority of the method by experiments.