CONVENTIONAL SPHERICAL HARMONIC-ANALYSIS FOR REGIONAL MODELING OF THE GEOMAGNETIC-FIELD

Spherical Harmonic Analysis (SHA) is normally used to model the three-dimensional global geomagnetic field. To address the same problem in regional modelling, Haines (1985) proposed Spherical Cap Harmonic Analysis (SCHA). This regional technique involves the computation of more complex Legendre functions with real (generally non-integer) harmonic degree. Here a new more practical technique is described; it is called Adjusted Spherical Harmonic Analysis (ASHA) because it is based on the expansion of conventional spherical harmonics after the colatitude interval is adjusted to that of a hemisphere. This kind of analysis can also be applied to modelling general two-dimensional functions.