Earth Planets Space, Vol. 58 (No. 4), pp. 477-483, 2006
British Geological Survey, Murchison House, West Mains Road, Edinburgh, EH9 3LA, UK
(Received November 18, 2004; Revised August 16, 2005; Accepted August 25, 2005; Online published April 14, 2006)
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.
Key words: Geomagnetism, Geomagnetic Field, Swarm, Localized constraints, wavelets.