This paper reports on a continuous representation of the main geomagnetic field of degree 13 for the 1900-1995 time period, including a degree 1 representation of the field of external origin, designated GSFC(S95). The model employs a cubic B-spline basis with equi-spaced knots for the temporal variation in the secular variation of the internal field. Hence, the temporal variation of the spherical harmonic coefficients is represented by integrals of cubic B-splines. In the derivation, a suite of different forms is utilized for representation of the external field: (1) GSFC(S95-a), in which the external terms are proportional to the annual averages of the as index, (2) GSFC(S95-s), in which the external terms are represented by unconstrained cubic B-splines, (3) GSFC(S95-sc), in which the cubic B-spline representation of the external field is constrained to be near the GSFC(S95-a) model for years prior to about 1940, and, (4) GSFC(S95-nx), in which there is no external field representation. The NASA candidate models for the 1995 revision of the IGRF are extracted from GSFC(S95-sc). Data sources include the Magsat and POGO satellites, observatory annual means, decimated land survey, marine total-field, aeromagnetic, and repeat data. Random data uncertainties are assigned by statistical binning procedures, while systematic error is accounted for via the correlated weight matrix procedure of Langel et al. (1989). The data are not sufficient to resolve all model parameters, and thus, regularization via quadratic penalty functions is employed. For the internal field this included minimizing the average of the square of the radial field secular variation and acceleration over the core-mantle boundary and through time. Comparison of the GSFC(S95-sc) model with the ufml model of Bloxham and Jackson (1992) for their common time span shows good general agreement, especially with respect to secular variation coefficient signatures and overall data statistics. The major differences are manifested in a better fitting of Magsat and POGO data by GSFC(S95-sc), but better fitting of early survey data by ufml. This is expected and reflects the relative influence of the data and penalty function in the particular model. The external field of GSFC(S95-sc) exhibits a very prominent solar-cycle variation in the q° coefficient, though with about a 2-year time lag. The internal field exhibits a well behaved R,,, spectrum throughout the time span indicating sufficient constraints being applied to the poorly observed, high-degree secular variation. Finally, the westward drift synthesized for degrees 2 to 5 shows a 0.76 linear correlation with the length-of-day (lod) variations of Jordi et al. (1994) when the latter leads the former by 11 years.

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All available magnetic data from observatories, satellites, repeat station measurements, and aeromagnetic, shipborne and land surveys are used to derive spherical harmonic models of the geomagnetic field from 1970 to 1990. Two models are derived, one using data from the DE-2 satellite the other not, since the quality of that data is unknown. These models are designated GSFC(11/90)D and GSFC(11/90) respectively. Main field coefficients are determined up to degree 13 and temporal variation, represented by B-splines, up to degree 10. Bias values at the fixed observatories were included as part of the solution. The secular variation models are smoothed by use of norm minimization. Both models fit the data very well.The resulting secular variation shows a jerk-like trend change in several coefficients near 1979.Candidate DGRF 1985 and IGRF 1990 models are extracted from the more general models by projecting to the desired epoch and using a truncated version of the main field spherical harmonic coefficients at those epochs.

In the absence of Magsat quality satellite magnetic field measurements, the use of data of lesser quality is sought. The DE-1 and UARS satellite magnetic field experiments were not designed for the purpose of modeling Earth's main field. The POGS satellite acquired data for modeling of Earth's main field, but at a lower accuracy than Magsat. All of these data were acquired with fluxgate magnetometers, which are subject to calibration drifts. On Magsat the fluxgate magnetometer was calibrated in-flight by comparison with a Cesium-Vapor scalar magnetometer. Such calibration is not possible on the satellites considered here, leaving uncertainty as to the accuracy of the resulting data. A formalism is developed to compare the data from these satellites with a field model derived from all other available data. This model included data from Magsat, so it is highly accurate at 1980. Its accuracy at the epochs of the satellites considered then depends upon the accuracy with which the field at 1980 can be extrapolated to future epochs. Adjustment of DE-1 data requires estimation of only two parameters for data spanning about 10 years. The resulting adjusted data are in good agreement with the model for those 10 years and exhibit residuals generally interpretable in terms of sources in the ionosphere and magnetosphere. Adjustment parameters of the POGS data vary substantially over the three years of available data. The resulting residuals indicate that the adjusted data set is suitable for main field modeling up to about degree 10, as used for the International Geomagnetic Reference Field. However, the resulting residuals are considered to be due mainly to error in measurement and not to geophysical sources. Adjustment of the UARS data is more difficult. The data used are not sufficient to resolve all of the adjustment-model parameters. If a priori information regarding the magnetic field from attitude torquer rods is included, the ambiguity is mostly resolved. Residuals after adjustment are of comparable magnitude and quality to those from POGS.

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