A Study On Seismic Multi-wavelet Decomposition And Reconstruction Based On Matching Pursuit Algorithm

The seismic signal is the compound harmonic wavelet which is obtained by the superposition of seismic wavelet with different energy and different shapes. The effective signal separation of describing the geological structure and lithology information in the acquisition of seismic signal, is a key step to directly determine the correctness for the interpretation of seismic data. Currently, due to the seismic wavelet form is single, the common conventional seismic model cannot meet the need of actual seismic signal processing well. And multi-wavelet seismic trace model can satisfy the practical application better due to its rich wavelet form and the characteristics of simulating the seismic wave propagation process well. Multi-wavelet decomposition and reconstruction technique can decompose the signal into a set of wavelet series, according to the characteristics of the frequency, amplitude, energy and other properties, and then rebuild the wavelets according to certain rules. The research of the multi-wavelet decomposition and reconstruction technique has important practical significance and application value. It is mainly studied that the seismic multi-wavelet decomposition and reconstruction technique based on the matching pursuit algorithm in this paper.It is introduced in this paper the basic thought of the multi-wavelet seismic trace model and multi-wavelet decomposition and reconstruction, and then the basic principle of the signal sparse representation, and mainly introduces the principle and the implementation steps of the matching pursuit algorithm.Although the matching pursuit algorithm can adaptively decompose by the seismic signal according to the characteristics of its own, its huge amount of computation is still a weakness difficult to avoid. Aiming at solving this problem, it is proposed that a Matching Pursuit Algorithm based on Improved Particle Swarm Optimization, used to search the optimal matching atom of the seismic signal sparse decomposition fast. The improved content is divided into two aspects: one is to introduce a polynomial mutation operator in the particle swarm optimization algorithm, effectively avoid the excessive concentration of searching for the optimal solution; the other is to identify the parameters searching area in the energy concentration part of the Gaussian function during the iterative process, to avoid the searching process from being "greedy". This can effectively reduce the complexity of the sparse decomposition. Using Gabor wavelet to construct the atom dictionary, to decompose and reconstruct the actual seismic signal by multi-wavelet, the effect is significantly enhanced.Ricker wavelet is a kind of common seismic wavelet, and the degree of correlation to the seismic signal is higher than Gabor wavelet. Using Ricker wavelet to construct the time-frequency atom dictionary by the four parameter coding form similar to the Gabor wavelet, the multi-wavelet decomposition and reconstruction algorithm based on Ricker wavelet time-frequency atom dictionary can be put into use. In the experiment part, put the actual seismic signal into decompose and reconstruct by the multi-wavelet. The experimental results show that, these two algorithms make the computation efficiency improve greatly while keeping the matching pursuit decomposition accuracy basis. The effect of the algorithm based on Ricker wavelet time-frequency atom dictionary is more prominent.