@misc{MinchevChambodutHolschneideretal.2009,
  author    = {Minchev, Borislav and Chambodut, Aude and Holschneider, Matthias and Panet, Isabelle and Sch{\"o}ll, Eckehard and Mandea, Mioara and Ramillien, Guillaume},
  title     = {Local multi-polar expansions in potential field modeling},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {845},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42899},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-428990},
  pages     = {1127 -- 1141},
  year      = {2009},
  abstract  = {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.},
  language  = {en}
}
@misc{LesurWardinskiAsarietal.2010,
  author    = {Lesur, Vincent and Wardinski, Ingo and Asari, Seiki and Minchev, Borislav and Mandea, Mioara},
  title     = {Modelling the Earth's core magnetic field under flow constraints},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {844},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43036},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-430369},
  pages     = {503 -- 516},
  year      = {2010},
  abstract  = {Two recent magnetic field models, GRIMM and xCHAOS, describe core field accelerations with similar behavior up to Spherical Harmonic (SH) degree 5, but which differ significantly for higher degrees. These discrepancies, due to different approaches in smoothing rapid time variations of the core field, have strong implications for the interpretation of the secular variation. Furthermore, the amount of smoothing applied to the highest SH degrees is essentially the modeler's choice. We therefore investigate new ways of regularizing core magnetic field models. Here we propose to constrain field models to be consistent with the frozen flux induction equation by co-estimating a core magnetic field model and a flow model at the top of the outer core. The flow model is required to have smooth spatial and temporal behavior. The implementation of such constraints and their effects on a magnetic field model built from one year of CHAMP satellite and observatory data, are presented. In particular, it is shown that the chosen constraints are efficient and can be used to build reliable core magnetic field secular variation and acceleration model components.},
  language  = {en}
}