A Fractal Interpretation of the Topography of the Geomagnetic Scalar Potential at the Core-mantle Boundary

The spatial power spectrum of the scalar potential (V) of the main geomagnetic field shows a power-law behaviour at the core-mantle boundary (CMB) and an almost uniform distribution of the corresponding phases. This is strong evidence for a fractal topography of V having a non-integer dimension of 2.2 (with an uncertainty of 90.1) which is, indeed, found from an analysis of the power spectra of 32 spherical harmonic models of V spanning the interval 1647 to 1990.