The International Geomagnetic Reference Field (IGRF) 10th Generation was adopted in 2004 by the International Association of Geomagnetism and Aeronomy (IAGA) Working Group V-MOD. It is the latest version of a standard mathematical description of the Earth's main magnetic field and is used widely in studies of the Earth's deep interior, its crust and its ionosphere and magnetosphere. This generation differs from the previous generation with the replacement of the secular-variation model for 2000.0-2005.0 with a main-field model at 2005.0 and a secular-variation model for 2005.0-2010.0. The IGRF is the product of a huge collaborative effort between magnetic field modellers and the institutes involved in collecting and disseminating magnetic field data from satellites and from observatories and surveys around the world. This paper lists the new coefficients and includes contour maps and pole positions.

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When deriving spherical harmonic models of the Earth's magnetic field, low-degree external field contributions are traditionally considered by assuming that their expansion coefficient q⁰₁ varies linearly with the D_st-index, while induced contributions are considered assuming a constant ratio Q₁ of induced to external coefficients. A value of Q₁ = 0.27 was found from Magsat data and has been used by several authors when deriving recent field models from Ørsted and CHAMP data. We describe a new approach that considers external and induced field based on a separation of D_st = E_st + I_st into external (E_st) and induced (I_st) parts using a 1D model of mantle conductivity. The temporal behavior of q⁰₁ and of the corresponding induced coefficient are parameterized by E_st and I_st, respectively. In addition, we account for baseline-instabilities of D_st by estimating a value of q⁰₁ for each of the 67 months of Orsted and CHAMP data that have been used. We discuss the advantage of this new parameterization of external and induced field for geomagnetic field modeling, and describe the derivation of candidate models for IGRF 2005.

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Following the call for candidates for the 10th generation IGRF, we produced and submitted three main field and three secular variation candidate models. The candidates are derived from parent models which use a standard quadratic parameterisation in time of the internal Gauss coefficients. External magnetospheric fields are represented by combined parameterisations in Solar Magnetic (SM) and in Geocentric Solar Magnetospheric (GSM) coordinates. Apart from the daily and annual variations caused by these external fields, the model also accounts for induction by Earth rotation in a non-axial external field. The uncertainties of our candidates are estimated by comparing independent models from CHAMP and Ørsted data. The root mean square errors of our main field candidates, for the internal field to spherical harmonic degree 13, are estimated to be less than 8 nT at the Earth's surface. Our secular variation candidates are estimated to have root mean square uncertainties of 12 nT per year. A hind-cast analysis of the geomagnetic field for earlier epochs shows that our secular acceleration estimates from post-2000 satellite data are inconsistent with pre-2000 acceleration in the field. This could confirm earlier reports of a jerk around 2000.0, with a genuine change in the secular acceleration.

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In this paper we describe the derivation of the BGS candidate models for the 10th generation International Geomagnetic Reference Field. Our data set comprised quiet night-time data from the Ørsted and Champ satellites spanning 1999.2-2004.6 and observatory hourly means spanning 1999.0-2004.0. To improve the secular variation estimates for 2005.0-2010.0, predictions based on application of linear prediction filters to long series of observatory annual means were also used. These data were fitted by a spherical harmonic “parent”model with an internal field of maximum degree 36, a quadratic dependence on time up to degree 8, a linear dependence on time up to degree 12, an external field of maximum degree 2 with linear dependence on time, annual and semi-annual variations, and Dst dependence for degree 1 terms. Additionally for the external field, non-zonal degree 1 coefficients in the Geocentric Equatorial Inertial reference frame with annual variations and dependence on the Interplanetary Magnetic Field Y -component are included. The candidate models were then based, for the main field, on an extrapolation to 2005.0 of the truncated parent model, and for the secular variation, on its extrapolation to 2007.5. This latter set of coefficients was then used to generate a synthetic data set at the Earth's surface and this set was augmented with long term linear predictions of observatory annual means, to produce the final candidate secular variation model at 2007.5.

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A simple method is proposed for constructing a space-time model of the main magnetic field based on the high-accuracy satellite survey data. At the first stage, we expand the CHAMP daily mean data into spherical harmonics with constant coefficients. It provides us with a series of the daily mean spherical-harmonic models (DMM) over a survey interval of several years, which are, then, expanded into the natural orthogonal components (NOC). It is shown that the NOC series converges rapidly, and that the accuracy of the space-time model over the time interval under consideration is no worse than the accuracy of the traditional models.

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The recent satellite magnetic missions, combined with high quality ground observatory measurements, have provided excellent data for main field modelling. Four different groups submitted seven main-field and eight secular-variation candidate models for IGRF-10. These candidate models were evaluated using several different strategies. Comparing models with independent data was found to be difficult. Valuable information was gained by mapping model differences, computing root mean square differences between all pairs of models and between models and the common mean, and by studying power spectra and azimuthal distributions of coefficient power. The resulting adopted IGRF main-field model for 2005.0, an average of three selected candidate models, is estimated to have a formal root mean square error over the Earth's surface of only 5 nT, though it is likely that the actual error is somewhat larger than this. Due to the inherent uncertainty in secular variation forecasts, the corresponding error of the adopted secular-variation model for 2005.0-2010.0, an average of four selected candidate models, is estimated at 20 nT/a.

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This paper presents the various candidate models used in deriving the 9th generation IGRF. Based on notes submitted to the IAGA working group V-MOD with the Gauss coefficients, a brief description of the data used and the method of modelling for each of the candidate models is given. The six candidate models for epoch 1995.0 and the five for epoch 2000.0 are presented. Improvements gained by the new models are also discussed.

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As part of the 9th generation of the IGRF defined by IAGA, we proposed a candidate model for DGRF 1995 and two candidate models for DGRF 2000. These candidate models, the derivation of which is described in the present note, are based on the “Comprehensive Model, Version 4 (CM4)”, and on the “Ørsted Main and Secular Variation Model (OSVM)”; two parent models that have been published elsewhere (Olsen, 2002; Sabaka et al., 2004; Lowes and Olsen, 2004). However, the main field part of OSVM is contaminated by “leakage” of the ionospheric field and its induced counterpart, which affects mainly the zonal coefficients g⁰₁, g⁰₃, . . ., by 1-2 nT. We describe the reason for this contamination, and present a method to correct for it. Since not only OSVM, but probably all main field models that are derived primarily from data around local midnight suffer from this effect, the presented scheme can also be applied to approximately correct these models.

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Two geomagnetic main-field models for epochs 1995.0 and 2000.0 were proposed as candidate models for DGRF 1995 and DGRF 2000. A main-field model was derived for epoch 2000.0, using the high-quality data provided by the Ørsted satellite around this epoch. Since no high-quality satellite vector measurements of the magnetic field were acquired between 1980 and 1999, our approach was to extrapolate this 2000.0 accurate model back to 1995. To do this we produced a secular-variation model for the time-span 1995-2000, from ground measurements. The models obtained were incorporated into DGRF 1995 and DGRF 2000 as part of the 9th generation of the IGRF in 2003.

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It is well known that models of the global geomagnetic field constructed from only measurements of the field intensity suffer from large errors arising from the Backus or perpendicular error effect. Knowledge of the location of the magnetic dip equator is in principal sufficient to eliminate this error. We investigate constraining the location of the dip equator using observations of the equatorial electrojet in intensity measurements made from the CHAMP satellite. While the models generated are inferior compared with models obtained from oriented three-component vector data, they may be of sufficient quality to allow construction of future global geomagnetic reference models in the absence of vector data.

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An exposed cross section of the tilted Tottabetsu plutonic complex allows direct evaluation of its original 2-D cross-sectional shape and pretilting vertical density variations in both the pluton and the country rocks, which serves as a strong constraint in gravity modeling that complements information on the ‘missing’ pretilting horizontal dimension of this tilted pluton. The pluton is stratified with the uppermost thin granitic unit (-1-km thick) and the underlying thick gabbro-diorite units (-9-km thick) that preserve a stratigraphic record of numerous hotter replenishments in the form of alternation of originally horizontal mafic sheets and cumulate layers. Both the pluton and the country rocks show systematic density increase with pretilting crustal depth, but density contrast of the pluton with the country rocks varies between each unit. The 2-D cross-sectional shape and gravity analysis revealed that the pluton had a vertically-elongated shape with vertical side walls before tilting. The vertical side walls, together with the stack of the originally horizontal sheets and cumulate layers, suggests that the pluton grew only vertically by piston mechanism. The very thick, exposed cross section provides unequivocal evidence for development of such a pluton with this unusual shape and mass distribution, which has been inferred elsewhere only by some geophysical studies.

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