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Volume 58 Supplement 4

Special Issue: Swarm—The Earth’s Magnetic Field and Environment Explorers

Introducing localized constraints in global geomagnetic field modelling


A set of functions is defined that can be used for modelling the internal part of the geomagnetic field. These functions are represented in term of spherical harmonics of a given maximum degree L and are centred at specific latitudes and longitudes. The number of functions needed and the positions of their centres are such that any potential field of maximum spherical harmonic degree L can be modelled. Formulae are obtained to transform between the potential field representation using these functions and a classic spherical harmonic representation. The shape of these functions can be optimized to make them reasonably localized, and from there it is shown how a localized constraint can be applied to an internal geomagnetic field model. The technique is demonstrated by means of models built from a few months of the Swarm mission synthetic data set.


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Correspondence to Vincent Lesur.

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Lesur, V. Introducing localized constraints in global geomagnetic field modelling. Earth Planet Sp 58, 477–483 (2006).

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Key words

  • Geomagnetism
  • Geomagnetic Field
  • Swarm
  • Localized constraints
  • wavelets