A seventh-generation revision of the International Geomagnetic Reference Field (IGRF) was adopted by the International Association of Geomagnetism and Aeronomy (IAGA) at the XXI General Assembly of the International Union of Geodesy and Geophysics in July 1995. The new spherical harmonic models adopted are based on weighted averages of candidate models submitted by NASA's Goddard Space Flight Center, the Russian Institute of Terrestrial Magnetism, Ionospheric, and Radio Wave Propagation-IZMIRAN, and jointly by the US Naval Oceanographic Office and the British Geological Survey. The revised IGRF specifies the Earth's main field from 1900 to 2000 and is declared to be definitive from 1945 to 1990. This paper lists the IGRF coefficients, describes the derivation of the new IGRF models, and examines aspects of the IGRF's accuracy, continuity, and behaviour during this century.

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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 ufm1 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 ufm1. 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 q₁⁰ coefficient, though with about a 2-year time lag. The internal field exhibits a well behaved R_n 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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The method of natural orthogonal components (NOC) analysis, which separates temporal variations, and spherical harmonic analysis, which models spatial distribution, were combined to model the spatial-temporal variations of the geomagnetic field over the globe. NOC's obtained in this way describe the temporal variations year by year without smoothing. Use of combined observatory and satellite magnetic survey data for developing a spatial-temporal model of equal accuracy on the globe and over the time interval of the data is proposed.

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We present the methods used to derive mathematical models of global secular variation of the main geomagnetic field for the period 1985 to 2000. These secular-variation models are used in the construction of the candidate US/UK models for the Definitive Geomagnetic Reference Field at 1990, the International Geomagnetic Reference Field for 1995 to 2000, and the World Magnetic Model for 1995 to 2000 (see paper II, Quinn et al., 1997). The main sources of data for the secular-variation models are geomagnetic observatories and repeat stations. Over the areas devoid of these data secular-variation information is extracted from aeromagnetic and satellite data. We describe how secular variation is predicted up to the year 2000 at the observatories and repeat stations, how the aeromagnetic and satellite data are used, and how all the data are combined to produce the required models.

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This paper presents the 1995 main-field revision of the World Magnetic Model (WMM-95). It is based on Project MAGNET high-level (≥15, 000 ft.) vector aeromagnetic survey data collected between 1988 and 1994 and on scalar total intensity data collected by the Polar Orbiting Geomagnetic Survey (POGS) satellite during the period 1991 through 1993. The spherical harmonic model produced from these data describes that portion of the Earth's magnetic field generated internal to the Earth's surface at the 1995.0 Epoch. When combined with the spherical harmonic model of the Earth's secular variation described in paper I, the Earth's main magnetic field is fully characterized between the years 1995 and 2000. Regional magnetic field models for the conterminous United States, Alaska and, Hawaii were generated as by-products of the global modeling process.

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A global evaluation is made of the candidate geomagnetic field models for the DGRF 1990 (main field) and IGRF 1995 (main field and secular variation). An evaluation of these models is also made with respect to the previous (6th generation) IGRF. The models are compared with each other and, where possible, with recent data from observatories, magnetic surveys including repeat stations, Project MAGNET and marine surveys. It is concluded that, although there are some large differences between the candidate models, there is not enough evidence to recommend one model in favour of another. The 6th generation IGRF, however, fits the Project MAGNET data better than any of the candidate models. It is suggested that each model be given equal weight in the production of DGRF 1990 and IGRF 1995 main-field models.

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Three candidate models for the IGRF 1995 description of the 1995.0 main field are evaluated. These are GS-95 proposed by the Goddard Space Flight Center (U.S.A.), IZ-95 proposed by IZMIRAN (Russia) and UB-95 proposed jointly by the US Navy (U.S.A.) and the British Geological Survey (U.K.). These models are tested against a set of December 1994 and January 1995 preliminary monthly mean values kindly provided to us by 73 observatories distributed throughout the world. This procedure has at least two advantages. First, no secular variation corrections are required for the test to be carried out. Second, all datasets used in the construction of the candidate models include observatory annual means up to at most 1993.5 and share similar links to our independent test data set. We, therefore, expect the test to be reasonably unbiased towards any of the models. The procedure has the inconvenience of being sensitive to local crustal anomalies, as pointed out by Langel et al. (1982). Indeed, directly comparing predictions from the candidate models to the observed monthly means reveals little else than a common, correlated, hardly discriminating, disagreement mainly due to crustal anomalies. We repeated the comparison after correcting the monthly means for the crustal anomalies derived by Bloxham and Jackson (1992). This second test was much more significant and showed that the models do a comparable job, UB-95 being marginally better. We recommand equal weighing between the two GS-95 and IZ-95 candidate models, and a slightly larger weight for UB-95.

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The 1995 revision of the International Geomagnetic Reference Field (IGRF) includes a definitive main-field model for 1990.0, a main-field model for 1995.0, and a forecast secular variation model for the interval 1995-2000. The four 1990.0 main-field models and four 1995.0 main-field models that were proposed as candidates have been evaluated by comparing them one with another, and also with magnetic observatory data. The comparisons indicate that the accuracies of the main-field models proposed by IZMIRAN are one and a half times higher than those of the other candidate models. The two secular variation models that were proposed have also been compared; averaging of the two models is appropriate.

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Several innovations have been introduced in the production of the Canadian Geomagnetic Reference Field (CGRF) for 1995. The secular variation and main field were modelled simultaneously using the recently developed method of main field differences. The degree of the temporal polynomial was varied depending on the spherical cap harmonic spatial degree. Modifications were made to allow the use of scalar, as well as vector, data in the analysis. Use was made of several data sets not used in previous versions of the CGRF, including Project Magnet data, POGS data, low-level scalar aeromagnetic data, and scalar marine data. A spherical cap harmonic model was produced for a spherical cap of 30° radius centred at 65°N, 85°W. The maximum spatial index of expansion was K=16, and the maximum temporal expansion was 7. The CGRF results in an error variance to the data over the modelling area that is 19% lower for the main field data and 55% lower for secular variation data than does the IGRF.

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Regional spatial-temporal models of the geomagnetic field have been produced by a variety of techniques. Recently, spherical cap harmonic analysis has gained wide acceptance as a means of modelling the magnetic field over a portion of the globe. Time variations of the field are commonly represented by polynomials or trigonometric series. The Canadian Geomagnetic Reference Field for 1995 (CGRF) is an example of a model produced in this manner. There are, however, other techniques that may offer advantages for some applications. The method of natural orthogonal components is one of these. To demonstrate this method, a spatial-temporal model of the geomagnetic field changes over Canada (ROM-Canada) has been produced using North American observatory annual means and Canadian repeat station data. These data were fitted with rectangular Legendre polynomials using natural orthogonal components as the temporal functions. Overall, total-intensity first-differences computed from the CGRF and ROM-Canada model the observed first-differences with comparable accuracy. ROM-Canada appears to be somewhat more accurate in the centre of the modelling area, but less accurate near the edges. Moreover, the ROM-Canada models of the vector components are less accurate than the CGRF.

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The 1995 revision of the International Geomagnetic Reference Field (IGRF) comprises a definitive main-field model for 1990.0, a main-field model for 1995.0, as well as a prediction secular-variation model for the period 1995-2000. The proposed main-field models have been evaluated by comparing them with results of magnetic surveys conducted by the Hermanus Magnetic Observatory over the Southern African sub-continent, including countries like South Africa, Namibia, Botswana, and Zimbabwe. The secular-variation models on the other hand have been compared with secular variation estimates based on rates of change as observed at the various field stations during 1990-1995.

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Three candidate models for DGRF 1990 and three candidate models for IGRF 1995, two of which include models of the secular variation for 1995-2000, were evaluated by comparison with observations from throughout the New Zealand region. No candidate model stands out as being significantly better or worse than any other candidate model from the same category. UB-90 has the poorest fit to the vertical component (Z) for 1990 but has the best fit to the total intensity (F). IZ-95 has the poorest fit to both the east component (Y) and Z for 1995 and, as a consequence, to F also. The adopted model for IGRF 1995 (main field) differs less on average from updated values of Y and Z than does the adopted model for DGRF 1990, although the range of differences is greater for all components. The candidate models for secular variation underestimate the magnitude of the north component (X) by 5-9 nT/yr on average but fit Z (and F) well (within 2 nT/yr on average).

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The possibility of obtaining a reasonable analytical model of the geomagnetic field secular variation (SV) in a space-time window limited to the measurements taken in Italy from 1965 onwards is discussed. The main purpose of the work is to provide a mathematical representation better for the small Italian region than the International Geomagnetic Reference Field (IGRF) which is formulated on a global scale. With this aim regional models constructed in polynomial form already exist, but they do not account for the physical constraints imposed by Laplace's equation. Spherical cap harmonic analysis (SCHA) is shown not to be suitable for SV modelling over such a small region and the final adopted model is essentially a conventional spherical expansion. It is demonstrated that it is possible to find a solution to our inversion problem that fits the data by using a limited number of harmonics, selected on the basis of significance using a regression procedure.

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The aim of this study is to analyse the integration of sparse three component magnetic observations from observatories and repeat stations with dense total field values from aeromagnetic data, into a homogeneous description of the magnetic field. The methodology followed implies the independent computation of main and crustal field contributions, each one incorporating the constraints of harmonicity. The crustal anomalous field is calculated for 1980 by digital filtering of the total field values from aeromagnetic surveys; the convolution is made in the spatial domain with space varying coefficient sets to account for the change in direction of the main field. The main field is estimated by updating the DGRF80, whose agreement with the Iberian data has already been demonstrated, with a SCHA model for the secular variation deduced from 360 three component observations over the Iberian Peninsula for the period 1980-1991. The combination of these two contributions permits one to compute magnetic component maps for the 1991.0 epoch that agree, in the least-squares sense, with the observational data while respecting the mathematical characteristics of a potential field. This methodology seems to be an effective way to produce regional estimations of the internal field.

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The historical field work inside the current Mexican area since the XVII century is presented as an introduction to the comparison study done on three examples of these magnetic surveys during the XX century, in particular the years 1907, 1952 and 1990, in order to find how well the IGRF fits this area. The magnetic declination was used because of the better availability of the magnetic declination maps for the period studied. The values given by the IGRF were compared with the values from magnetic surveys in the Mexican Republic. Results of these comparisons show RMS differences for the magnetic declination of 52.5' for 1907, 115.4' for 1952 and 18.7' for 1990. Means and standard deviations of the residuals are discussed. The isolines shows a possible underestimation of the surface field in 1907 and an overestimation in 1952 by the IGRF. Long-wavelength features were found to be correlated with aeromagnetic and satellite magnetic anomalies, but, in any case, the IGRF seems to be a satisfactory geomagnetic reference model for the area and epochs studied.

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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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Models of the geomagnetic main field of degree and order 13 are constructed for epoch 1992.5. These are based on combinations of (quiet-time, low activity) Polar Orbiting Geomagnetic Survey (POGS) total intensity data, and various near-surface, largely vector, measurements. We consider the significance in the fit of models to data of: (a) the spatial sampling interval; (b) the estimated ionospheric field corrections at POGS satellite altitude produced by Quinn et al. (1995); (c) the degree and order one external field coefficients; and (d) the relative proportions of POGS and near-surface data. At this degree and order it is found that: (a) the main-field model accuracy is relatively insensitive to the average sampling interval over a 15:1 range of intervals; (b) the most accurate models are those in which the estimated ionospheric field corrections are not included; (c) the external dipole term is of the order of +20 nT and hence has a marginal impact on model accuracy at the Earth's surface; and (d) a relatively high ratio, of order 4:1, of POGS to surface data optimizes model accuracy at both POGS satellite altitude and ground level, although only a low ratio of POGS to surface data, of order 1:9, is required for high model accuracy at the Earth's surface alone. Overall, the most accurate main-field model produces spot values at the surface of the Earth with residual standard deviations between 96 nT and 120 nT, depending on component. An estimate of a typical “true”, or absolute, model accuracy is also given, by comparing computed values, from a simplified model, with measured data from an independent near-surface data set. It is concluded that the absolute model accuracy at the Earth's surface is of the order of twice the accuracy of the model fit to its input data, again depending on component.

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POGS total intensity data were analysed over the Southern African region between 10° South and 45° South in latitude and between 5° East and 40° East in longitude. Satellite data were selected corresponding to magnetically quiet conditions during local night times before carrying out an analysis of external fields by subdividing winter and summer data into Dst bins 5 nT wide, centred at multiples of 5 nT. Spherical Cap Harmonic Analysis (SCHA) was then applied to each of these Dst data bins to obtain external field coefficients corresponding to k = 1. Residual POGS data were downward continued by means of the equivalent layer magnetization model and modelled by SCHA to reveal component data at ground level.

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Scalar magnetic data from the POGS satellite are analysed for the 1991-1993 period. Models of the main geomagnetic field are computed using an iterative least-squares method. Vector components of the field derived from these models display large errors known as the Backus effect. A method for estimating the noise level in global data in the form of an equivalent gaussian noise is introduced and POGS data are shown to have a standard deviation of about σ = 45 nT. Despite this high noise level, it is shown that POGS data can be used to improve models derived from observatory vector data. It is also shown that the Backus effect can be significantly reduced by using some accurate vector ground-based measurements of the main field at observatories located near the equator. Monthly models are computed using both POGS and observatory data for which monthly mean values are available at POGS period. Local corrections applied to observatory measurements are computed by comparing observatory monthly mean values with Magsat models. The results are shown to be improved when these corrections are applied to the observatory data, confirming that they correspond essentially to stationary short-wavelength crustal anomalies.

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