Wavelets and splines for modelling the earth’s magnetic field

At the present time there is an unprecedented opportunity to use satellite magnetometer data, as for example Oersted and CHAMP records, to improve our knowledge of the Earth’s magnetic field and its sources. These measurements contain contributions from the main magnetic field of the Earth, the crustal field as well as contributions coming from different exterior (ionospheric and magnetospheric) sources. For the mathematical analysis of the data it is critical to have in hand appropriate tools which separate these sources and which are able to analyze the different contributions independently. We present in this talk an approach in terms of (spherical) scalar and vectorial scaling functions and wavelets to handle these problems. Examples include crustal field modelling and reconstruction of ionospheric currents.