On the determination of the size of the Earth’s core from observations of the geomagnetic secular variation

Abstract

When the magnetic field of a planet is due to self-exciting hydromagnetic dynamo action in an electrically conducting fluid core surrounded by a poorly-conducting ‘mantle', a recently proposed method (Hide 1978,1979) can in principle be used to find the radius r c of the core from determinations of secular changes in the magnetic field B in the accessible region above the surface of the planet, mean radius r s , with a fractional error in r c of the order of, but somewhat larger than, the reciprocal of the magnetic Reynolds number of the core. It will be possible in due course to apply the method to Jupiter and other planets if and when magnetic measurements of sufficient accuracy and detail become available, and a preliminary analysis of Jovian data (Hide & Malin 1979) has already given encouraging results. The ‘magnetic radius’ ̄r̄ c of the Earth’s molten iron core has been calculated by using one of the best secular variation models available (which is based on magnetic data for the period 1955-75), and compared with the ‘seismological’ value of the mean core radius, r c = 3486 ± 5 km. Physically plausible values of r̄ c are obtained when terms beyond the centred dipole ( n = 1) and quadrupole ( n = 2) in the series expansion in spherical harmonics of degree n = 1,..., ^ n ,..., n * are included in the analysis (where 2 ≼ ^ n ≼ n *≼ ∞). Typical values of the fractional error ( r̄ c - r c ) / r c amount to between 0.10 and 0.15. Somewhat surprisingly, this error apparently depends significantly on the value of the small time interval considered; the error of 2% found in the first case considered, for which ^ n — n * = 8 and for the time interval 1965-75, is untypically low. These results provide observational support for theoretical models of the geomagnetic secular variation that treat the core as an almost perfect conductor to a first approximation except within a boundary layer of typical thickness much less than 1 km at the core-mantle interface.