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978-3-8439-1588-5, Reihe Mathematik
Decorrelation of Gravimetric Data
132 Seiten, Dissertation Technische Universität Kaiserslautern (2014), Softcover, A5
Up to now, the exploration of the Earth's interior is a difficult task that is identified with a large number of applications as, for example, the exploration of geological structures or the geothermal energy exploration. Especially in this regard, it is of dremendous importance to have detailed knowledge about the underlying structures in a geological interesting region. In this work we penetrate particular space techniques to decompose signal information of gravimetric data by use of locally supported wavelet functions to decorrelate data sets in order to filter out detail-information, that are not detectable in the original data base.
Beside the theory of singular integrals the regularization of the singular character of the Newton potential motivates certain techniques to simultaneously decompose the signal information of the gravitational potential and the density, however, under the (usually only for certain local geothermal purposes realistic) assumption that the data are discretely known to some extend in the interior of the region under consideration. Both approaches facilitate the opportunity to construct a geothermally motivated multiscale postprocessing of gravitational and density data in terms of locally supported wavelets in order to filter out available detail-information of both quantities by “zooming-in” into geothermal relevant regions. The resulting detailed knowledge about the underlying geological structures exhibit the interpretation of the data in local regions.
Within the postprocessing procedure of decorrelating gravitational and density signals the knowledge of a discrete data set of both quantities inside a local part of the Earth is required. Since, usually, the amount of observed data available from borehole measurements is less, a spline interpolation method by use of discrete gravitational as well as oblique derivative data is proposed to improve the gravitational data situation inside the domain under consideration. The regularization techniques derived from the regularization of the Newton potential enables the continuation of the spline interpolation to a regularized variant by use of internal data. In any case, if a spline (regularized) approximation for the gravitational potential is available from discrete data, the corresponding density approximation can be deduced by “Laplace differentiation” according to the fact that the Newton potential satisfies the Poisson equation in the interior of the reference domain.