The poloidal geomagnetic field in a differentially rotating upper core layer

Abstract

SUMMARY This paper deals with the inverse solution of the induction equation accounting for moving core material. In a layer of the fluid outer core we prescribe the associated velocity field by a differential rotation. The angular velocity near the core–mantle boundary (CMB) corresponds to the mean westward drift of the geomagnetic field. We solve the induction equation for the poloidal magnetic field in both the mantle and the fluid outer-core layer using the magnetic field as the boundary value at the Earth's surface and the assumed velocity field as the prescribed model parameter. The numerical solution of the induction equation is based on a modified Tikhonov regularization of an integral equation approach described in a previous paper by Ballani et al.. This numerical experiment shows both the scope of our method with respect to highly conducting material and the effect of the motion of the conducting material on the penetration behaviour of field variations. The results indicate that the downward continuation of the field by our method is possible to about 100 km below the CMB in the decadal time scale. The penetration depth mainly depends on the high conductivity, while the effect of the relative rotation is marginal in the uppermost 25 km and becomes more significant in deeper parts. Solutions become more unstable for depths of the outer core below 100 km, and no relevant solution fitting the data within 10 per cent can be reached, i.e. decadal field variations at these depths cannot be fully causally related to those observed at the Earth's surface.