K. Whaler $^{a}$, R. Holme$^{b}$ and A. Jackson $^{c}$
$^{a}$ Department of Geology and Geophysics, University of Edinburgh, Edinburgh, UK $^{b}$ Department of Earth Sciences, University of Liverpool, Liverpool, UK $^{c}$ School of Earth Sciences, University of Leeds, Leeds, UK
Significant differences have emerged between models of the geomagnetic field at the core-mantle boundary (CMB) derived from surface and satellite data depending on whether the inversion was undertaken with the more usual two-norm or a one-norm measure of misfit. The residuals seem to fit a Laplacian error distribution consistent with a one-norm measure better than a Gaussian distribution, implicit when a two-norm measure is adopted. The flow at the CMB that explains the observed secular variation is usually derived from spherical harmonic models of the main field and secular variation, and we would not expect spherical harmonic coefficients to have other than a Gaussian error distribution. However, the error distribution of 'raw' secular variation data is unknown. Here, we investigate the use of orthogonal component observatory and repeat station secular variation data to model the CMB flow directly under both one- and two-norm misfit measures. We assume the main field is represented without error by a spherical harmonic model, in which case the flow inversion is linear. The ability to fit the data indicates the applicability (or otherwise) of the frozen-flux hypothesis when core flow modelling, so the sensitivity of the conclusion to the misfit measure used is of interest. Future work will investigate whether flows produced under one-norm measures are better predictors of the secular variation.