Wavelet Mie representations for solenoidal vector fields with applications to ionospheric geomagnetic data

A wavelet technique, the wavelet Mie representation, is introduced for the analysis and modeling of the earth's magnetic field and corresponding electric current distributions from geomagnetic data obtained within the ionosphere. The considerations are essentially based on two well-known geomathematical keystones, (i) the Helmholtz decomposition of spherical vector fields and (ii) the Mie representation of solenoidal vector fields in terms of poloidal and toroidal parts. The wavelet Mie representation is shown to provide an adequate tool for geomagnetic modeling in the case of ionospheric magnetic contributions and currents which exhibit spatially localized features. An important example is ionospheric currents. owing radially onto or away from the earth. To demonstrate the functionality of the approach, such radial currents are calculated from vectorial data of the MAGSAT and CHAMP satellite missions.