THE INFLUENCE OF CORRELATED CRUSTAL SIGNALS IN MODELING 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 magnetizat ion in the crust and it has been realized for some time that such sign als are highly correlated at satellite altitude. Hence approximation b y white noise, while of undoubted utility, is of unknown validity. Lan gel, Estes & Sabaka (1989) were the first to evaluate the influence of correlations in the crustal magnetic field on main-field models. In t his paper we study two plausible statistical models for the crustal ma gnetization described by Jackson (1994), in which the magnetization is a realization of a stationary, isotropic, random process. At a typica l satellite altitude the associated fields exhibit significant correla tion over ranges as great as 15 degrees or more, which introduces off- diagonal elements into the covariance matrix, elements that have usual ly been neglected in modelling procedures. Dealing with a full covaria nce matrix for a large data set would present a formidable computation al challenge, brit fortunately most of the entries in the covariance m atrix are so small that they can be replaced by zeros. The resultant m atrix comprises only about 3 per cent non-zero entries and thus we can take advantage of efficient sparse matrix techniques to solve the num erical system. We construct several main-field models based on vertica l-component data from a selected 5 degrees by 5 degrees data set deriv ed from the Magsat mission. Models with and without off-diagonal terms are compared. For one of the two Jackson crustal models, k(3), we fin d significant changes in the main-field coefficients, with maximum dis crepancies near degree 11 of about 27 per cent. The second crustal spe ctrum gives rise to much smaller effects for the data set used here, b ecause the correlation lengths are typically shorter than the data spa cing. k(4) also significantly underpredicts the observed magnetic spec trum around degree 15. We conclude that there is no difficulty in comp uting main-field models that include off-diagonal terms in the covaria nce matrix when sparse matrix techniques are employed; we find that th ere may be important effects in the computed models, particularly if w e wish to make full use of dense data sets. Until a definitive crustal field spectrum has been determined, the precise size of the effect re mains uncertain. Obtaining such a statistical model should be a high p riority in preparation for the analysis of future low-noise satellite data.