Signal And Noise Separation In Sparse Transform Domain

Removing random noise in seismic data is one key problem of seismic dataprocessing. With the requirement of high quality for seismic data, denoising methodsbecome more and more important. Scholars coming from different areas have putforward a number of different methods to remove random noise, such as the classicwavelet transform, median filter, but these methods have their limitations. On theother hand, multiple is common information in seismic data processing. Thevariability of its distribution, period and frequency has brought great difficulties inseismic data processing (especially offshore seismic data processing). Typically,processors always treat multiple as noise. With the further research, some scholarstake advantage of multiple, which has wider range of ray illumination as informationfor complex structure imaging. Thus, with the target of separation of signal and noisein seismic data, this thesis tries to find a method to protect effective signal whendenoising. Starting from the theory of sparse representation, this thesis develops asignal and noise separation method based on seismic data sparse representation tosolve corresponding key technical issues. The thesis focuses on developing aneffective sparse domain method to separate reflection wave and random noise,primaries and multiples.Firstly, this thesis reviews the theory of Fourier transform, wavelet transform andseislet transform. Using the characteristics of seismic data’s coefficients in sparsetransform domain and conventional hard threshold method, the proposed methodextracts the big value coefficient that denotes valid signal and suppresses small valuecoefficient that denotes noise, so that the inverse problems of signal and random noiseseparation is established. When one uses thresholding method in sparse transformdomain to deal with discontinuous data (thresholding algorithm can also causediscontinuities), it may cause pseudo-Gibbs artifact, therefore, this thesis introducesthe total variation regularization term, which can weaken the pseudo-Gibbs artifact,into sparse inverse problem. The advantage of total variation function is protecting theinherent discontinuity of data, it means that the method can protect discontinuityinformation such as border when one separates signal and noise. By converting signaland noise separation problem into functional extremum problem, this thesis usesvariation method to derive a set of partial differential equations with boundary conditions. Optimal solution corresponds to the useful information after signal andnoise separation by numerical method. After that, one can archive the reflected waveand random noise separation method in sparse transform domain based on totalvariation regularization. After compared with the conventional sparse transformthresholding method in synthetic and field data tests, the proposed method shows thecorrectness and effectiveness.Seislet transform is a wavelet-like transform, which combines lifting schemewith seismic local slope. Based on hyperbolic time-distance relationship, this thesisproposes a velocity-dependent (VD) method for reflected wave and pegleg multiplesto estimate their corresponding local slopes. By improving the prediction operator andupdate operator in seislet transform, the thesis develops a VD-seislet transform torepresent primaries and pegleg multiples with different orders, and proposes aVD-seislet frame. By converting primaries and pegleg multiples separation to sparseoptimization inverse problem, signal and noise separation can be achieved by usingiterative algorithm. The synthetic and field data tests show that the algorithm in thisthesis can effectively separate primaries and pegleg multiples of different orders,which can provide different for seismic wave field image.