The Influence of Correlated Crustal Signals in Modelling the Main Geomagnetic Field

Algorithms used in geomagnetic main-field modelling have for the most part treated the noise in the field measurements as if it were white. A major component of the noise consists of the field due to magnetization in the crust and it has been realized for some time that such signals are highly correlated at satellite altitude. Hence approximation by white noise, while of undoubted utility, is of unknown validity. In this paper we study two plausible statistical models for the crustal magnetization, in which the magnetization is a realization of a stationary, isotropic, random process. At a typical satellite altitude the associated fields exhibit significant correlation over ranges as great as 15 deg. or more, which introduces off-diagonal elements into the covariance matrix, elements that have usually been neglected in modelling procedures. Dealing with a full covariance matrix for a large data set would present a formidable computational challenge, but fortunately most of the entries in the covariance matrix are so small that they can be replaced by zeros. The resultant matrix comprises only about 3 per cent non-zero entries and thus we can take advantage of efficient sparse matrix techniques to solve the numerical system. We construct several main-field models based on vertical-component data from a selected 5 deg. by 5 deg. data set derived from the Magsat mission. Models with and without off-diagonal terms are compared.