Geomagnetic field analysis--III. Magnetic fields on the core--mantle boundary

The method of stochastic inversion, previously applied to secular variation data, is applied to main field data. Adaptations to the method are required: non-linear, as well as linear, data are used; allowance is made for crustal components in the observatory data; and the prior information is specified differently. The requirement that the models should satisfy a finite lower bound on the Ohmic heating in the core provides strong prior information and gives finite error estimates at the core—mantle boundary. The new method is applied to data from the epochs 1969.5 and 1980.0. The resulting field models are very much more complex than other models, such as the IGRF models extrapolated to the core, and show considerable small-scale detail which, on the basis of the error analysis, can be believed. The flux integral over the northern hemisphere is computed at each epoch; the difference between the two epochs is approximately one standard deviation, suggesting that the question as to whether the decay of the dipole is consistent with the frozen-flux hypothesis has been resolved in favour of the hypothesis.