A statistical approach to the Earth's main magnetic field

Abstract

Based mainly on historical magnetic data and following indications derived from paleomagnetic data, we suggest that the Earth's main magnetic field can be described as a two scale process. The first scale is characterized by a mainly axial dipolar geometry and long time constants (much longer than several hundred years). It could be maintained at the core-mantle boundary by diffusion from within the core as the likely tangentially geostrophic flow at the top of the core gives special status to this axial dipole field. The second scale is characterized by a far more complex geometry and short time constants (of the order of a couple of hundred years). It encompasses the observed non-dipole field, possibly the equatorial dipole field and is a likely signature of the convective term in the induction equation. Most of the observed axial dipole secular variation is probably also related to it. The stationary isotropic statistical model defined describes the behaviour of the field in statistical terms. This model provides a pertinent formalism for characterizing both the main field and secular variation spectra, and makes it possible to define ‘typical correlation times’, thus allowing a discussion of the two scale process we propose. It also makes it clear that historical data do not support the separation between dipole and quadrupole families, a view which has sometimes been advocated.