Determination of surface motions of the Earth's core

The general problem of inferring fluid velocities at the surface of the earth's central core from magnetic data is discussed and previous results are compared. Earlier analyses are extended by allowing for small contributions to secular change from magnetic diffusion, while constraining the velocity to satisfy a quasi-geostrophic condition. The latter dynamic condition is derived from first principles and allows for electromagnetic forces in addition to the Coriolis force. The under-determined system of equations is solved by applying a variational principle that requires nonsingular solutions corresponding to a given ‘effective’ magnetic Reynolds number. Solutions are shown for several values of the Reynolds number and for the first time include estimates of surface electrical-current patterns. The solutions represent observed secular change data to within rms errors of 13% and 33% for Reynolds numbers of 1.2 and 4.3, respectively. A theoretical argument is given for the plausibility of these heuristically derived ‘effective’ Reynolds numbers, which are one to two orders of magnitude below those commonly assumed for the whole core.