sented by: R n = 1.349 X 109 (0.270) n (nT) 2 for the core and R n = 37.1 (0.974) n (nT) 2 for the crust. These representations can be used to establish order of magnitude inaccuracies in core field models due to crustal fields and due to inability to "observe" the core field wavelengths beyond n = 13 which are totally obscured by the crustal field.

Magsat data has been analyzed as a function of the Dst index to determine the first degree/order spherical harmonic description of the near‐earth external field and its corresponding induced field. The analysis was done separately for data from dawn and dusk with the following results: dusk external: q10 = 20.3 ‐ 0.68 Dst (nT); dusk internal: g10 = 29987.7 + 0.240q10 (nT); dawn external: q10= 18.62 ‐ 0.63 Dst (nT); dawn internal: g10 = 29992.3 + 0.287q10 (nT), where g10 and q10 are the degree 1, zero‐order, internal and external coefficients, respectively, in a spherical harmonic potential function describing the near‐earth magnetic field. Comparison with POGO data indicates that the constant term relating q10 and Dst has changed about 20 nT between 1970 and 1980, presumably due to an increase in the average ring current intensity. A local time variation of the external field persists even during very quiet magnetic conditions. Both a diurnal and 8‐hour period are present. A crude estimate of sq current in the ±45° geomagnetic latitude range is obtained for 1966–1970. The current strength, located in the ionosphere and induced in the earth, is typical of earlier determinations from surface data, although its maximum is displaced in local time from previous results.

Data from the Magsat spacecraft for November 1979 through April 1980 and from 91 magnetic observatories for 1978 through 1982 are used to derive a spherical harmonic model of the earth's main magnetic field and its secular variation at epoch 1980.0. The model is called GSFC(12/83). Constant coefficients are determined through degree and order 13 and secular variation coefficients through degree and order 10. The first‐degree external terms and corresponding induced internal terms are given as a function of Dst. Preliminary modeling using separate data sets at dawn and dusk local time showed that the dusk data contain a substantial field contribution from the equatorial electrojet current. The final data set was therefore selected first from dawn data and then augmented by dusk data to achieve a good geographic data distribution for each of three time periods: (1) November–December 1979, (2) January–February 1980, and (3) March–April 1980. A correction for the effects of the equatorial electrojet was applied to the dusk data utilized. The solution included calculation of fixed biases, or anomalies, for the observatory data. Although similar in many respects, GSFC(12/83) differs from International Geomagnetic Reference Field 1980 by 3.6 nT in the g10 term and shows a slightly negative B in the northern polar region as well as other differences in secular variation pattern.

No abstract

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.