Iterative downward continuation of the geomagnetic field through a 3-D conducting mantle

SUMMARY Various methods for determining the magnetic field at the core–mantle boundary (CMB) from the observed geomagnetic core field have been explored over recent decades. These include the harmonic downward continuation of surface data and the stabilized iterative upward continuation. The instability of the inverted poloidal magnetic field at the CMB for a radial conductivity structure is complemented by the non-uniqueness of determining the toroidal magnetic field at the CMB for a laterally inhomogeneous conductivity model. We reformulate this unstable and non-unique inverse problem as an iterative upward continuation approach, in which the magnetic field at the CMB is successively updated. The uniqueness of the inverse solution is ensured by the initial choice of the toroidal magnetic field at the CMB, while the stability is achieved by stopping the iterations once the desired tolerance is reached between the spectral index of the updated solution and that obtained from numerical geodynamo simulations.We consider two significantly different radial electrical conductivity models of the lower mantle, each with conductance near $10^8$ S: conductivity model A, based on external electromagnetic sounding, which includes a significant conductivity increase in a 10 km thick layer above the CMB, and conductivity model B, characterized by a gradual conductivity increase determined from the Voigt-Reuss-Hill average of the bridgmanite-ferropericlase aggregate, with an additional conductivity increase in the 300 km thick D” layer associated with post-perovskite. Models A and B bracket the lower and upper bounds of conductivity structures derived from thermal and compositional constraints below 1600 km depth. We find that the differences between the magnetic field components at the CMB inverted for models A and B are approximately 1–2 per cent of the total field. To explore lateral variations, we construct a synthetic model of the Pacific and African superplumes by simplifying their geometric shapes, estimating the temperature increase within the plumes and allowing mantle mineral activation energies to vary only with temperature. Our results show that, in the regions of the superplumes, the poloidal and toroidal magnetic fields at the CMB change by approximately 12 000 and 2500 nT, respectively. The changes in the horizontal poloidal field at the CMB are comparable in magnitude to those resulting from substituting model A with model B. However, the changes in the radial field inverted for the 3-D plume conductivity model are significantly larger than those arising from replacing model A with model B.