Regional crustal field modeling from regional satellite data with varying altitude using dedicated vector Slepian functions (Invited)

Within the last decade, high-quality magnetic data from satellite missions such as Oersted and CHAMP have enabled the calculation of detailed global magnetic crustal field models. With the launch of the Swarm satellite mission this trend is bound to continue. The geographically unevenly distributed signal quality of geomagnetic satellite data, an intrinsic property due to the shape of Earth's main magnetic field, has led to two principal approaches for the construction of global crustal field models. The first strategy consists in restricting the models to relatively low maximum spherical harmonic degrees and thereby focus on coarse details that can be resolved over the entire sphere. The second strategy invokes strong data preprocessing to increase the global signal quality. Besides these global strategies, local methods have emerged to enable the generation of higher-detail models in areas where the local data quality allows smaller spatial wavelengths to be resolved. Local methods include spherical cap harmonics, revised spherical cap harmonics, spherical wavelets, localized harmonic functions, and triangular tessellation. The amount of amplification of small features and hence also of noise when mapping models from satellite altitude to Earth's surface depends on the maximum spherical harmonic degree of the model. Therefore local methods must overcome the dilemma that their susceptibility to noise depends on a quantity associated with functions that cover the entire globe. An additional difficulty that often arises in local crustal field modeling is that the satellite trajectory deviates significantly from a perfect sphere and therefore makes the incorporation of satellite altitude variations into the method a necessity. We present a method that has the ability to calculate local crustal field models from local satellite data with varying altitude while adhering to a chosen maximum spherical harmonic degree. Our method uses a dedicated basis of vector Slepian functions that are constructed specifically to minimize the effect of the distortion of the data caused by the altitude difference between the satellite and Earth's surface. In order to prepare for the analysis of CHAMP, Swarm, and Mars Global Surveyor (MGS) measurements, we study the potential and limits of our method using artificial data.