Geostatistical methods applied to field model residuals

The geomagnetic field varies on a variety of time- and length scales, which are only rudimentary considered in most present field models. The part of the observed field that can not be explained by a given model, the model residuals, is often considered as an estimate of the data uncertainty (which consists of measurement errors and unmodelled signal), and is typically assumed to be uncorrelated and Gaussian distributed. We have applied geostatistical methods to analyse the residuals of the Oersted(09d/04) field model [http://www.dsri.dk/Oersted/Field_models/IGRF_2005_candidates/], which is based on 5 years of Ørsted and CHAMP data, and includes secular variation and acceleration, as well as low-degree external (magnetospheric) and induced fields. The analysis is done in order to find the statistical behaviour of the space-time structure of the residuals, as a proxy for the data covariances. Once these are known, they can be used in the modelling process to improve the model, estimate its uncertainty and eventually determine the optimal sampling rate in time and space. The uncertainty estimate on the field model can be used to estimate the uncertainty on quantities deduced from the field model, when the field model is used for geophysical interpretations.