Modelling the Earth’s Magnetic Field from Global to Regional Scales

Abstract

In the recent years, a large amount of magnetic vector and scalar data have been measured or made available to scientists. They cover different ranges of altitudes from ground to satellite levels and have high horizontal densities over some geographical areas. Processing these potential field data may require alternatives to the widely used Spherical Harmonics. During the past decades, new techniques have been proposed to model regionally the magnetic measurements. They complement the set of older approaches that were revived and sometimes revised in the meantime. The amount of available techniques is intimidating and one often wonders which method is the most appropriate for what purpose. In this paper, we review several modelling strategies. Starting from the Spherical Harmonics, we discuss methods with global support (wavelets, multi-scale, Slepian functions,…) and then bring the focus on regional methods with local support (Rectangular Harmonic Analysis, Cylindrical Harmonic Analysis, Spherical Caps,…). We briefly examine the theoretical aspects and properties of each approach. We compare them with the help of a unique set of perfect synthetic data that mimic an ideal spatial distribution at a fixed surface. This helps us to better emphasize the theoretical characteristics of each approach and suggest, when relevant, improvements that would be useful for future practical applications.