An extended version of the C3FM geomagnetic field model: application of a continuous frozen-flux constraint

A recently developed method of constructing core field models that satisfies a frozen-flux constraint is used to built a field model covering 19572008. Like the previous model C3FM, we invert observatory secular variation data and adopt satellite-based field models to constrain the field morphology in 1980 and 2004. To derive a frozen-flux field model, we start from a field model that has been derived using classical techniques, which is spatially and temporally smooth. This is achieved by using order six B-splines as basis functions for the temporal evolution of the Gauss coefficients and requiring that the model minimizes the integral of the third-time derivative of the field taken over the core surface. That guarantees a robust estimate of the secular acceleration. Comparisons between the classical and the frozen-flux field models are given, and we describe to what extend the frozen-flux constraint is adhered. Our models allow the interpretation that magnetic diffusion does not contribute to the observed secular variation. Additionally, the resulting frozen-flux field model shows a more or less constant spatial complexity, so that the spatial complexity of the magnetic field imposed by the 2004 satellite field model is maintained backward in time to the beginning of the model period, 1957. Therefore, we understand the frozen-flux constraint as an instrument that aids the backward projection of high spatial resolution in core field models to earlier times.