Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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.
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