On determining reference fields from ground-based and satellite field data

The physical content of simultaneous SHA internal field models for the concentric spheres for the Earth's surface and for the satellite altitude differs because of the different distances from the internal magnetic field sources. This fact is reflected in the different convergence behaviour of both the SHA expansions that can be described mathematically by the functional behaviour of the contributions of the SHA functional terms to the N . (N+2) dimensional volume in a functional space. Thereby a regularizing criterion is derived for the downward field continuation which results in a transformation formula for the Gauss coefficients. This enables to calculate all the field components. The comparison of the ground-based SHA model with that having been downwardly continued from the satellite altitude evaluates its different physical content. (C) 1999 Elsevier Science Ltd. All rights reserved.