The Curvelet Tyansform And Its Application To Information Extraction For Potential Data

A new series of mathematical transforms have emerged and been used for more effectiverepresentation and processing of high dimensional singularity data based on the wavelet transform,collectively referred to as"muti-scale geometric analysis". Not only do they have thecharacteristics of muti-resolution, time-frequency localized, muti-directional and anisotropic, butovercome the existing limitations of the wavelet transform representation of singularities such asedge and the outline of contour. Curvelet transform has become a hot topic as one theory ofmuti-scale geometric analysis.The first generation of the curvelet transform is derived from the ridgelet theory, which hasthe decomposition on all possible scales(s≥0) . The curvelet transform, like the wavelet transform,is a multiscale transform, with frame elements indexed by scale and location parameters. Unlikethe wavelet transform, it has directional parameters, and the curvelet pyramid contains elementswith a very high degree of directional septicity. In addition, the curvelet transform is based on acertain anisotropic scaling principle which is quite different from the isotropic scaling of wavelets.The elements obey a special scaling law, where the length of the support of a frame elements andthe width of the support are linked by the relation width~length2. The second generation of thecurvelet transform does not use ridgelet transform, and give the basic form of curvelets infrequency domain. Two new fast discrete curvelet transform namely USFFT and Wrapping havebeen developed which are simpler, faster, and less redundant than existing proposals.The thesis has developed the first application of the second generation of the curvelettransform to muti-scale and muti-directional data processing for gravity and magnetic data, andobtained the following conclusions:To begin with, the curvelet analysis is performed on the synthetic gravity data sets of simpleand complex models. The difference between the curvelet transform and wavelet transform is thefact that the curvelet transform adds a direction parameter. So you can accurately capture thecharacteristics of any direction of the curves. Also, the curvelet transform has very strong localfeatures. It is notable that the decomposition scale number of the curvelet transform is closelyrelated to the data the number of data sets. The sampling rate of data sets will affect the results ofthe curvelet transform to a certain extent. In addition, the gravity and magnetic field data sets needto expand the edge before using the curvelet transform in general.Secondly, the curvelet transform is used in the gravity and magnetic data sets of North ChinaCraton, and the different layers of corresponding scales and all directions are obtained. The resultsabove are compared and analyzed with those of the wavelet transform, pointing out that thecurvelet transform has better resolution to reflect the details of geological bodies and obtaining thepreliminary results for the geological knowledge.Finally, the curvelet transform is conducted in the satellite Bouguer gravity anomaly data ofthe Chinese mainland and adjacent areas. Based on the decomposition results of different scalesand directions, the characteristics of regional gravity field and tectonic division are analyzed andthe preliminary geological interpretations are given.