Magnetic Diffusion in a Spherically-Symmetric Conducting Mantle

The diffusion of changes in the Earth's main magnetic field through a spherically-symmetric, conducting mantle is studied. It is shown that the theoretical development is independent of the assumed radial conductivity distribution. Two separate problems are considered; the diffusion of a change in the radial component of the poloidal field at the core-mantle boundary through to the surface of the Earth, which is of relevance to the determination of an effective conductivity for the lower mantle from the secular variation observations; and the diffusion into the mantle of the toroidal field induced at the core-mantle boundary by the shearing of the poloidal field in the boundary-layer, which is of relevance in the study of fluctuations in the core-mantle electromagnetic coupling. Numerical results are obtained for an assumed uniform conductivity in the lower 2 000 km of the mantle.