TY  - GEN
A1  - Minchev, Borislav
A1  - Chambodut, Aude
A1  - Holschneider, Matthias
A1  - Panet, Isabelle
A1  - Schöll, Eckehard
A1  - Mandea, Mioara
A1  - Ramillien, Guillaume
T1  - Local multi-polar expansions in potential field modeling
T2  - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2  - The satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 845 
KW  - potential fields (gravity, geomagnetism)
KW  - inverse problem
KW  - spherical harmonics
KW  - satellite data
KW  - size reduction
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-428990
SN  - 1866-8372
IS  - 845
SP  - 1127
EP  - 1141
ER  - 
TY  - JOUR
A1  - Hayn, Michael
A1  - Holschneider, Matthias
T1  - Directional spherical multipole wavelets
N2  - We construct a family of admissible analysis reconstruction pairs of wavelet families on the sphere. The construction is an extension of the isotropic Poisson wavelets. Similar to those, the directional wavelets allow a finite expansion in terms of off-center multipoles. Unlike the isotropic case, the directional wavelets are not a tight frame. However, at small scales, they almost behave like a tight frame. We give an explicit formula for the pseudodifferential operator given by the combination analysis-synthesis with respect to these wavelets. The Euclidean limit is shown to exist and an explicit formula is given. This allows us to quantify the asymptotic angular resolution of the wavelets.
Y1  - 2009
UR  - http://jmp.aip.org/
U6  - https://doi.org/10.1063/1.3177198
SN  - 0022-2488
ER  -