Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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DMV Tagung 2011 - Köln, 19. - 22. September Doreen Fischer University of Siegen Sparse Regularization of an Inversion of Gravitational Data and Normal Mode Anomalies To recover the density of the Earth we invert Newton’s gravitational potential which is an ill-posed problem. Thus, we need to develop a regularization method to solve it appropriately. We apply the idea of a Matching Pursuit to recover a solution stepwise. At step n + 1, the expansion function dn+1 and the weight αn+1 are selected to best match the data structure. However, all kinds of different functions may be taken into account to improve the solution stepwise. Moreover, this new approach generates models with a resolution that is adapted to the data density as well as the detail density of the solution. For the area of South America, we present an extensive case study to investigate the performance and behavior of the new algorithm. Furthermore, we research the mass transport in the area of the Amazon where the proposed method shows great potential for further ecological studies, i.e. to reconstruct the mass loss of Greenland or Antarctica. However, from gravitational data alone it is only possible to recover the harmonic part of the density. To get information about the anharmonic part as well, we need to be able to include other data types, e.g. seismic data in the form of normal mode anomalies. We present a new model of the density distribution of the whole Earth as the result of such an inversion. Literatur Berkel, P., Fischer, D. and Michel, V. (2011). Spline multiresolution and numerical results for joint gravitation and normal mode inversion with an outlook on sparse regularisation. GEM, 1, 167 - 204. Fischer, D. and Michel, V. (2011). Sparse regularization of inverse gravimetry — case study: spatial and temporal mass variations in South America. Preprint. Willi Freeden TU Kaiserslautern Spherical Discrepancies Of practical importance in geomathematics is the problem of generating equidistributed point sets on the sphere. In this respect, the concept of spherical discrepancy, which involves the Laplace-Beltrami operator to give a quantifying criterion for equidistributed point sets, is of great interest. In this lecture, an explicit formula in terms of elementary functions is developed for the spherical discrepancy. Several promising ways are considered to generate point sets on the sphere such that the discrepancy becomes small. 154
Christian Gerhards TU Kaiserslautern Multiscale Methods in Geomagnetic Modeling DMV Tagung 2011 - Köln, 19. - 22. September With the upcome of high quality satellite magnetic field data from past missions like MAGSAT, Ørsted, CHAMP and future missions like Swarm, it becomes of more and more interest to have adequate mathematical tools at hand for geomagnetic modeling. We present multiscale methods for the modeling of different aspects of the Earth’s magnetic field. A special focus is set to the construction of locally supported wavelets for the treated problems, e.g., the reconstruction of radial current densities and the separation of the magnetic field with respect to the sources. Furthermore, some applications to real data sets are presented. Kamil S. Kazimierski Universität Bremen Efficiency of iterative regularization methods using Banach space norms In this talk we want do discuss several, recently developed methods for iterative regularization with sparsity constraints. In particular: Landweber-regularization of linear and non-linear operators (with sparsity constraints); conjugate gradient like regularization of linear operators (with sparsity constraints). We will present theoretical results concerning regularization properties, convergence rates. We will also discuss numerical properties. Especially, we will show that iterative methods are a viable alternative to the variational approach of Tikhonov. The presented results are joint work with Torsten Hein, Matheon, Berlin. 155
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Frank Kutzschebauch Universität Be
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Ulrich Derenthal Ludwig-Maximilians
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Anna Dall’Acqua Otto-von-Guericke
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Eleutherius Symeonidis Katholische
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Felix Schlenk Universität Neuchât
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Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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