New representation of geomagnetic secular variation over restricted regions by means of spherical cap harmonic analysis: application to the case of Spain

A model of the secular variation (SV) of the geomagnetic field over Spain and adjacent regions, using a particular application of spherical cap harmonic analysis (SCHA), is given. SCHA was directly applied as presented in a previous paper; however, some drawbacks were detected, making evident the limitations of the technique for fields with low spatial harmonic content, as in the case for SV over relatively small regions. After trying some alternative approaches to the conventional procedure, it has been discovered that the solution lies in increasing the cap half-angle (but the data continue to be restricted within the original cap) to obtain more suitable harmonic contributions. It is shown that inspection of the spatial power spectra of the SV field on different spherical caps is useful in selecting the cap half-angle.