SHA vs. SCHA for modelling secular variation in a small region such as Italy

The possibility of obtaining a reasonable analytical model of the geomagnetic field secular variation (SV) in a space-time window limited to the measurements taken in Italy from 1965 onwards is discussed. The main purpose of the work is to provide a mathematical representation better for the small Italian region than the International Geomagnetic Reference Field (IGRF) which is formulated on a global scale. With this aim regional models constructed in polynomial form already exist, but they do not account for the physical constraints imposed by Laplace's equation. Spherical cap harmonic analysis (SCHA) is shown not to be suitable for SV modelling over such a small region and the final adopted model is essentially a conventional spherical expansion. It is demonstrated that it is possible to find a solution to our inversion problem that fits the data by using a limited number of harmonics, selected on the basis of significance using a regression procedure.