Study On The Applications Of Curvelet Transform In Seismic Data Processing

The proposing and developing of wavelet transform has brought a revolution tosignal processing, following the wavelet analysis, researchers have proposed a series ofmulti-scale geometric analysis methods, to overcome its lack of directionality andsparsity in image processing. Curvelet transform is among such methods, which canprovide optimum sparse representation for image signals that have piecewise smoothcurved edges, and it has the advantages of multi-scale, multi-direction and localizationfeatures as well. Fortunately, this mathematical tool is also applicable to many geophysicsproblems, and we can achieve good results in some applications with it. Especially in thefield of seismic exploration, researchers have carried on more study from differentaspects.In this thesis, the author discussed some applications of Curvelet transform inseismic data processing, For the contents of the following three aspects: Curvelet-basedrandom noise suppression, data interpolation, and sparsity-constrained deconvolution, theauthor first introduced the corresponding theories, then completed some of the pertinentprogramming in MATLAB environment, and analyzed the effects using model examplesand real data. At the end, the author summarized the results and conclusions.At the beginning of this thesis, the author first introduced the concepts of sparserepresentation, compressed sensing, and then, showed the excellent characteristics ofcurvelet transform, and its broad application prospects as well. On the basis of seismicdata sparse representation utilizing curvelet transform, the author discussed three parts ofcontents respectively: curvelet threshold methods for seismic data random noisesuppression, seismic data interpolation based on sparsity promotion inversion in curveletdomain (CRSI), and sparsity constrained deconvolution based on curvelet transform. Theauthor also showed the effects and characteristics of such methods through both modelexamples and real data processing, and pointed out some problems as well. Boththeoretical analysis and actual results show that, with the help of such a powerful mathematical tool, we can improve the quality of seismic data effectively, that is, we canimprove the signal-to-noise ratio, regularity, and resolution of seismic data by introducingcurvelet transform into some processing flows, which would help to facilitate furtherprocessing and analysis.