Geomagnetic field modeling incorporating constraints from frozen-flux electromagnetism

Abstract A spherical harmonic representation of the geomagnetic field and its secular variation for epoch 1980, designated GSFC(9/84), is derived and evaluated. At three epochs (1977.5, 1980.0, 1982.5) this model incorporates conservation of magnetic flux through five selected patches of area on the core-mantle boundary bounded by the zero contours of vertical magnetic field. These 15 nonlinear constraints are included like data in an iterative least squares parameter estimation procedure that starts with the recently derived unconstrained field model designated GSFC(12/83) (Langel and Estes). Convergence is approached within three iterations. The constrained model is evaluated by comparing its predictive capability outside the time span of its data, in terms of residuals at magnetic observatories, with that for the unconstrained model. The new model demonstrates significantly improved predictability. Next, it is established that the flux of magnetic secular variation out of the northern (or southern) geographic hemisphere of the core-mantle boundary is nearly conserved by a remake of the field model designated GSFC(9/80). The GSFC(9/84) model is then examined and found to satisfy this independent linear constraint on secular variation very well.