Geomagnetic field models usually consist of coefficients of a truncated spherical harmonic analysis derived by a weighted least squares analysis. The data are typically assumed to be uncorrelated, and an estimated, diagonal, data covariance matrix is incorporated as an inverse weighting function. Accuracy estimates on the derived coefficients are taken to be the usual output covariance matrix. This procedure does not take into account the field from the truncated terms, the presence of crustal fields, or the presence of external fields, such as Sq. The resulting accuracy estimates are believed to be too low by factors of 2--10. A formalism is presented within which approximate account can be taken of these neglected fields. This formalism includes a weight matrix in which the observations are suitably correlated. A priori statistics describing the truncated main field, the crustal field, and the Sq field are required. An estimate of the properties of the crustal field is made which is consistent with both surface and satellite data. The properties of the Sq field are inferred from the model of Malin <1973>. Given these estimates, computation of the elements of the weight matrix is straightforward. For surface data the weight matrix is adequately approximated as diagonal for moderate sized data sets and, in those cases, is easily incorporated into the least squares formalism. However, for satellite data and for large quantities of surface data, the matrix is ''full,'' and an approximation is adopted to make the analysis tractible.

Models are derived using a selected subset of Magsat data, both with and without the correlated weight matrix. Inclusion of the correlated weight matrix increases the error estimates of the coefficients by a factor of up to 7.5. Calculation of such models using no approximations in the correlated weight matrix are limited by computer size to observation sets of about 1500 points or less. However, using the approximation, much larger data sets can be accommodated, and it becomes practical to perform the calculations on satellite data sets. The GSFC(12/83) model, based on Magsat data, was rederived using this method. The coefficient uncertainty estimates increased by factors of 4--70, while the coefficient values remained essentially the same. ¿ American Geophysical Union 1989