On the derivation of the Earth's conductivity structure by means of spherical cap harmonic analysis

After Haines & Torta (1994) applied spherical cap harmonic analysis (SCHA) to deduce the formulation of equivalent currents in terms of spherical cap harmonic coefficients, it seemed appropriate to extend the same scheme that relates global spherical harmonics with the Earth's conductivity structure to regional modelling of geomagnetic-field variations. From the considerations made in this paper it seems difficult or even impossible to obtain either a conductivity-depth profile (by assuming a homogeneous mantle conductivity within the region) or a 3-D structure, from a regional analysis of global-scale phenomena such as the regular daily variation, by using the same formulations as employed in global analyses. There exist, in addition, some intrinsic limits of SCHA itself, which, although in general do not decrease its potential in regional geomagnetic modelling, can affect the derivation of a proper conductivity estimation.