Modelling geomagnetic secular variation by main‐field differences

SUMMARY Secular variation of the geomagnetic field is required in main‐field modelling for updating data and for model prediction. In either case, it is differences between field values at two different epochs, at any given location, that is required and that therefore is to be estimated by a given model. Analytically, this has been done previously by including an ‘anomaly bias’ in the solution which otherwise is strongly influenced by crustal sources, or by numerically estimating derivatives of the field by taking consecutive first differences. The anomaly bias technique is inherently not well conditioned and furthermore requires the solution of many parameters not actually needed in the model, while the derivative technique is not amenable to a full main‐field solution; neither technique works well for repeat‐station data. By taking differences relative to the means over observatory or repeat‐station data, secular‐variation fields can be modelled accurately because the anomaly biases cancel out in taking such differences. By also including, with appropriate weighting, the observatory and repeat‐station means themselves, as well as any aeromagnetic, satellite, or other available main‐field data, the full main field may be modelled. A very simple algorithm is derived for modelling either secular variation or the full main field.