The magnetic field at the core-mantle boundary

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.