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Local multi-polar expansions in potential field modeling

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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.


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Correspondence to B. Minchev.

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Minchev, B., Chambodut, A., Holschneider, M. et al. Local multi-polar expansions in potential field modeling. Earth Planet Sp 61, 1127–1141 (2009) doi:10.1186/BF03352965

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Key words

  • Potential fields (gravity, geomagnetism)
  • inverse problem
  • spherical harmonics
  • satellite data
  • size reduction