Geomagnetism, Earth rotation and the electrical conductivity of the lower mantle

Abstract A new approximation is derived for the electromagnetic torque acting on an electrically conducting mantle as a result of fluid flow in the core. The torque considered is that associated with the toroidal field induced in the mantle by advection of poloidal field (which is assumed to be frozen into an infinitely conducting liquid core) by the flow of liquid at the top of the core. The expression relies on the assumption that the mantle is an insulator apart from a ‘thin’ (with respect to the core radius) layer of finite conductance adjacent to the core-mantle boundary. This allows the toroidal field scalar in the mantle to be expressed as a first-order Taylor approximation. The time-dependent torque calculated at a sequence of epochs this century is compared with the torque which has previously been inferred from astronomical observations of the length of day. Although the initial results appear unpromising, a significant correlation exists when poorly determined components of the velocity field, which contribute substantially to variations in the calculated torque, are ignored. By regression analysis the conductance of the assumed thin layer is determined as 6.7 × 10 8 S and the lag of the electromagnetic torque behind the astronomical torque as 6 years, which is interpreted as the delay time for electromagnetic signals through the mantle. Finally, the implications of these results for the conductivity of the lower mantle are discussed. They imply that the bottom few hundred kilometres of the mantle probably have a conductivity of a few hundred to a few thousand siemens per metre; previously published lower-mantle conductivity models are examined in light of this conclusion. The close correlation of the variations in the calculated electromagnetic torque, which depend primarily on fluctuations in the core velocity field, with the length of day torque provides independent evidence that core flow is not steady on the decade time-scale.