On the strength of electric currents and zonal magnetic fields at the top of the Earth's core: Methodology and preliminary estimates

Abstract

A new method is described for estimating: (a) the meridional electric current density, j θ , (b) the vertical growth rate of the zonal magnetic field, ∂B φ / ∂r, or its scale-height, B φ / ∂B φ / ∂r) and (c) the vertical growth rate of the vertical current density, ∂j r / ∂r, at a few isolated points on the top surface of the Earth's core from observations of the internal geomagnetic field at the Earth's surface. The theoretical technique rests on combining unaccelerated, gravitationally-driven Boussinesq fluid dynamics of the core with frozen-flux electromagnetism, the mantle being treated as a spherically symmetric insulator. Insertion into this theory of main field models for epochs 1965, 1975 leads to preliminary values for these quantities of magnitude: (a) j θ ∼ 1 A/ m 2, (b) ∂B φ / ∂r ∼ 10 −6 T/m or B φ /( ∂B φ / ∂r) ∼ 10 m, (c) ∂j r / ∂r ∼ 10 −6 A/m 3. Some geophysical implications of these estimates are discussed.