Spherical cap harmonic analysis of the geomagnetic field with application for aeronautical mapping

The Spherical Cap Harmonic Analysis (SCHA) is a regional modeling technique based on appropriate functions which are solutions of Laplace's equation over a constrained, cap-like region of the Earth. The concept was introduced in 1985 in the context of geomagnetism as a local or regional extension of the classic global spherical harmonic analysis. Starting from the basic principles in which the analysis method is founded, this paper describes the latest applications for the modeling of the main magnetic field and its secular variation. Although examples of applications over small areas will be given, it will be shown that, in general, the bigger the region the more appropriate the technique. Therefore, this paper focuses on the results and perspectives over continental areas, like Antarctica or Europe. The possible application to the derivation of isogonic charts for navigational purposes with suitable time predictions will be emphasized. At the same time, the limitations of the method will be examined. Although recent revisions of the technique seem to solve some of the problems, our present research focuses on the quest for solutions to the still unanswered questions.