A time-dependent model of the Earth's magnetic field and its temporal change of the period 1957 to 2005.

We will present an extended version of a previously published time-dependent geomagnetic main field model (Wardinski & Holme, 2006). The new version of this model covers the period from 1957 to 2005 and includes annual differences of monthly or annual observatory means, secular variation estimates from repeat station data and ship data. Similar to the previous model the new version will be constrained to fit satellite main field models in 1980, 2000 and 2005. Although, we use secular variation estimates to set up the model, we expect external field variations to contaminate these annual first differences. In order to find the most likely set of Gauss coefficients which account for the observed secular variation and to solve inverse problem, we apply an iterative least square approach. Usually, the error covariance matrix within the least square solving is assumed to be diagonal. However, we set up the error covariance matrix to be non--diagonal. This allows a better distinction between internal field variations and contamination due to external field variations. The time--dependent model of the main field and its variations will be used to provide constraints on fluid motions at the surface of the Earth's core, and the core--mantle coupling.