Seismic Wave Field Data Reconstruction Based On Compressed Sensing

Along with the exploration of constraint for acquisition conditions and get rid of residual seismic trace, which makes the seismic wave field data incomplete inevitably. These situations influence on the subsequent processing of seismic data, so it is necessary to carry out seismic wave field data reconstruction. However, due to the limit of Nyquist sampling theory, most traditional reconstruction techniques require high-rate samples.Compressed sensing theory mainly includes the sparsity of signal processing, the structure of the measurement matrix and reconstruction algorithm. Reconstruction algorithm is the core content of CS theory, that is, through the low dimensional sparse signal recovers the original signal accurately. This thesis based on the theory of CS. to study further on reconstruction algorithm. We select Orthogonal Matching Pursuit algorithm as a reconstruction algorithm.Then do the specific research for the implementation principle, the structure of the algorithm of OMP and make the signal simulation at the same time. In view of the OMP algorithm reconstruction speed is slow and the problems need to be a given number of iterations, which developed an improved scheme. We combine the optimized OMP algorithm of constraint the optimal matching of atom selection strategy, the backwards gradient projection ideas of adaptive variance step gradient projection method and the original algorithm to improve it. Simulation experiments show that improved OMP algorithm is superior to traditional OMP algorithm of improvement in the reconstruction time and effect under the same condition.Aimed at rebuilding the mixed with random noise in seismic wave field data, this thesis selects curvelet threshold to denoising.Then we introduce the blocking idea and secondary curvelet transform to curvelet threshold to improve the original denoising method when dealing with a large amount of data. Combined with CS theory can reconstruct the seismic signal at the same time. Through the simulation experiments show that improved curvelet threshold method is superior to original curvelet reshold method in the reconstruction quality under the same condition.Finally, to summarize research work of this thesis and we can show the method is effective and practical hrough the establishment of simulation model.