Global versus regional internal--external potential field separation

Internal--external field separation is crucial for many aspects of geomagnetism, aiming at distinguishing contributions of the magnetic field generated within a given observation surface from those generated in the exterior.

When data are available on a full spherical observation surface, this separation is a standard, stable, and widely used procedure dating back to Gauss.

However, when data are only available in a subdomain of the observation surface (as is the case for aeromagnetic and ground-based surveys), the situation drastically changes.

Here we show that, without prior assumptions, an internal--external field separation is not uniquely possible.

Given the geophysically reasonable assumption that the exterior sources, e.g., magnetospheric and ionospheric current systems, are located above a source-free spherical shell, we show that a unique separation becomes possible but that it is highly unstable.

The results are based on the spherical Hardy--Hodge decomposition and explain the intrinsic difficulties of regional data-based internal--external potential field separation.