Multiscale Downward Continuation of CHAMP FGM-Data for Crustal Field Modelling

Summary

Crustal field determination and downward continuation from CHAMPFGM-data will be presented within a multiscale framework using scalar as well as vectorial radial basis functions. The basic idea is to formulate the problem in terms of integral equations relating the radial or tangential projections of the geomagnetic field at satellite height with the magnetic field at the Earth’s surface. In both, the radial as well as the tangential case, crustal field downward continuation turns out to be an exponentially ill-posed problem. As an appropriate solution method multiscale regularization in terms of scalar and vectorial wavelets is presented based on the knowledge of the singular systems corresponding to the aforementioned integral operators. Finally, first wavelet results of crustal field contributions at Earth level, calculated from CHAMP-FGM-data, will be presented.