Main Field Model Research Articles

International Geomagnetic Reference Field: The Sixth Generation.

In August 1991 the International Association of Geomagnetism and Aeronomy revised the International Geomagnetic Reference Field (IGRF) for the fifth time. This Sixth Generation IGRF now consists of 10 spherical harmonic models of the main geomagnetic field at five year intervals from 1945 through 1990 and a secular variation model extending the main field model of 1990 through 1995. For the interval 1945-1985 the models are definitive (DGRFs), in that it is unlikely that the underlying data sets will be significantly improved so there is no plan for future revision of the models. The present revision consists of adoption of a definitive main field model for 1985, DGRF 1985, a main field model for 1990 with secular variation coefficients for 1990-1995, IGRF 1990, and a provisional model, PGRF 1985, for 1985-1990 defined as the linear interpolation between DGRF 1985 and IGRF 1990. All main field models are of degree and order 10. The secular variation model is of degree and order 8. The models were derived from five candidate main field models at 1985, five at 1990, and three candidate secular variation models at epoch 1992.5. Weighted averages of the candidate models were specified to arrive at the final models. A brief description of the development of the IGRF is given, useful formulae are reviewed, and contour maps of the geomagnetic elements D, I, H, X, Y, Z, and F at 1990 are included. The nature of and philosophy behind the IGRF are discussed and a new procedure for deriving the IGRF is proposed.

Evaluation of Models Proposed for the 1991 Revision of the International Geomagnetic Reference Field.

The 1991 revision of the International Geomagnetic Reference Field (IGRF) comprises a definitive main-field model for 1985.0, amain-field model for 1990.0, and a forecast secular-variation model for the period 1990-1995. The five 1985.0 main-field models and five 1990.0 main-field models that were proposed have been evaluated by comparing them with one another, with magnetic observatory data, and with Project MAGNET aerial survey data. The three secular-variation models that were proposed have also been compared with one another, and with estimates of recent rates of change at the observatories. The comparisons indicate that the main-field models proposed by IZMIRAN, and the secular-variation model proposed jointly by the British Geological Survey and the U. S. Naval Oceanographic Office, should be assigned relatively lower weight in the derivation of the new IGRF models.

A Comparative Analysis and Evaluation of the DGRF-85 and IGRF-90 Candidate Models.

Candidate models for the Definitive Geomagnetic Reference Field (DGRF) main field model at the 1985.0 epoch, as well as candidate models for the International Geomagnetic Reference Field (IGRF) main field model at the 1990.0 epoch along with the corresponding secular variation models at the 1992.5 epoch were evaluated against each other, and against data observations from both Project MAGNET aeromagnetic data and recently obtained Polar Orbiting Geomagnetic Survey (POGS) satellite data. Models for the 1985.0 epoch show some regional differences in model by model comparisons but, in general, are quite similar.

Comparison of DGRF85 and IGRF90 Candidate Models over Southern Africa.

This paper discusses the evaluation of candidate models, submitted to IAGA Working Group V-8 for DGRF85 and IGRF90, against results of magnetic surveys conducted by the Hermanus Magnetic Observatory over the Southern African area (Namibia, Botswana, Zimbabwe and the R. S. A.). The main field candidates are of degree 10, whereas some 1990 models also include predictive secular variation models of degree 8 for the interval 1990-1995. The epoch 1985 models are definitive main field models to replace the present IGRF, whereas the models for 1990 are non-definitive.

IZMIRAN Candidate Models for DGRF 1985, IGRF 1990 and a Secular Variation Forecast Model for the 1990-1995 Period.

Two candidate main field models for 1985 and 1990 as well as a forecast for the secular variation are represented as a series of spherical harmonic coefficients up to n=m=10 and n=m=8, respectively. IZMSV, US/UK, USGS forecasting models are compared with extrapolated secular variation observations and with one another. The IZMSV and the USGS are shown to agree best.

Analysis of Geomagnetic Secular Variation during 1980-1985 and 1985-1990, and Geomagnetic Models Proposed for the 1991 Revision of the International Geomagnetic Reference Field.

The secular variation of the main geomagnetic field during the periods 1980-1985 and 1985-1990 was analyzed in terms of spherical harmonics up to the eighth degree and order. Data from worldwide magnetic observatories and the Navy's Project MAGNET aerial surveys were used. The resulting pair of secular-variation models was used to update the Definitive Geomagnetic Reference Field (DGRF) model for 1980, resulting in new main-field models for 1985.0 and 1990.0. These, along with the secular-variation model for 1985-1990, were proposed for the 1991 revision of the International Geomagnetic Reference Field (IGRF).

Geomagnetic secular variation over Spain 1970–1988 by means of spherical cap harmonic analysis

A spherical cap harmonic analysis was applied to Spain and neighbouring areas, covering a region with a cap halfangle of 16°. The technique, due to Haines, has allowed us to obtain a model of secular variation (SV) for a time interval of 18 years reduced to the epoch 1987.5. The total number of selected data points was 1581 provided from ten observatories and 60 repeat stations. The SV model has a maximum spatial index of four and temporal degree of two. The coefficients were tested and the statistically non-significant terms removed. Another model covering a smaller region with greater density of data has been developed and both results compared. The average secular variations derived from the definitive geomagnetic reference field (DGRF) and the international geomagnetic reference field (IGRF) were compared with these models and maps plotting the calculated first field derivatives are presented. The integration of the final model will serve to update satellite data in order to produce a regional main field model.

On the use of horizontal components of magnetic field in determining core motions

SUMMARY Geomagnetic secular variation is caused by flow of fluid in the Earth's core. If electrical diffusion can be ignored, field lines are frozen to the core fluid and can be used as tracers for the flow at the top of the free stream, which lies beneath the diffusive boundary layer. In this paper we assume the flux is frozen-in and investigate the jump in the horizontal field across the boundary layer. Theoretical studies indicate that such a jump will be small (about 1000 nT); we test the hypothesis that the jump is zero within the errors of measurement of the magnetic field. Integral constraints, which are conserved if the horizontal components of field at the base of the mantle can be equated to the components at the top of the free stream, are derived and computed using seven main-field models from epochs 1935.5 to 1980.0. These main-field models have been forced to satisfy all the conditions of frozen-flux theory. The integral constraints are found to be constant within their expected errors, and we conclude that the observations are consistent with zero jump in horizontal field across the boundary layer. This result implies that use can be made of the horizontal components of field in determining core flow. We attempt to compute the flow along null-flux curves, which is not determined at all by the radial component of the field, for epoch 1970. The result is very noisy because of its reliance on gradients of the secular variation at the core-mantle boundary, which are poorly determined. We do not attempt to compute reasonable core flows consistent with these observations, although presumably many such flows exist, because they would be so poorly constrained by observation.

An attempt to obtain a detailed declination chart from the United States magnetic anomaly map.

Modern declination charts of the United States show almost no details. Greater detail may be of value to surveyors trying to follow old land deed descriptions, or to pilots of small planes or small pleasure boats operating in inland waterways. It would be extremely expensive to make adequate declination measurements needed for such a chart. It was hoped that declination details could be derived from the information contained in the existing magnetic anomaly map of the United States. This could be realized only if all of the survey data were corrected to a common epoch, at which time a main-field vector model was known, before the anomaly values were computed. Because this was not done, accurate declination values cannot be determined. In spite of this conclusion, declination values were computed using a common main-field model for the entire United States to see how well they compared with observed values. The provisional geomagnetic reference field for 1978.5 was used as the main-field model. The computed detailed declination values were found to compare less favorably with observed values of declination than declination values computed from the IGRF 1985 model itself. This result indicates that the computed anomaly elements or their combination with main-field values cannot be used as accurate anomaly values, but they may be used as an indication of where anomalies probably occur.

Some effects of quiet geomagnetic field changes upon values used for main field modeling

The effects of three methods of data selection upon the assumed main field levels for geomagnetic observatory records used in main field modeling were investigated for a year of very low solar-terrestrial activity. The first method concerned the differences between the year's average of quiet day field values and the average of all values during the year. For H these differences were 2–3 gammas, for D they were −0.04 to -0.12′, for Z the differences were negligible. The second method of selection concerned the effects of the daytime internal Sq variations upon the daily mean values of field. The midnight field levels when the Sq currents were a minimum deviated from the daily mean levels by as much as 4–7 gammas in H and Z but were negligible for D. The third method of selection was designed to avoid the annual and semi-annual quiet level changes of field caused by the seasonal changes in the magnetosphere. Contributions from these changes were found to be as much as 4–7 gammas in quiet years and expected to be greater than 10 gammas in active years. Suggestions for improved methods of improved data selection in main field modeling are given.

BGS candidate models for the 1985 revision of the international geomagnetic reference field

The British Geological Survey (BGS) proposals for the revised International Geomagnetic Reference Field (IGRF) consisted of two main-field models (with maximum degree and order n ∗ = 10 ), for epochs 1950.0 and 1960.0, based on all available near-surface survey data collected between 1940 and 1965, and a predictive model (n ∗ = 8) of the secular variation for the interval 1985 to 1990 (mean epoch 1987.5), based on the most recent observatory annual means. This note briefly describes the data sets on which the models are based and the techniques used to derive them.

IGRF candidates for 1980 and 1985

A tenth degree and order spherical harmonic model of the main geomagnetic field for 1980 has been derived using MAGSAT data supplemented by aeromagnetic vector data collected by the Project MAGNET aircraft. A secular variation model of degree and order 8 for 1982.5 based on magnetic observatory and repeat station measurements has also been developed. The secular variation model is used to project the 1980 main-field model to 1985. The 1980 and 1985 main-field models are proposed for incorporation into the revised International Geomagnetic Reference Field.

Assessment of models proposed for the 1985 revision of the international geomagnetic reference field

Geomagnetic measurements from land, marine and aerial surveys conducted in the years 1945–1964 were used to test the 14 models proposed as additions, for that period, to the series of definitive geomagnetic reference field (DGRF) models. Overall, NASA's ‘SFAS’ models and the BGS (British Geological Survey) models agree best with these data. Comparisons of the two proposed definitive main-field models for 1980.0, with each other and with the existing IGRF 1980 main-field model, show mostly close agreement, with the greatest absolute differences (several tens of nanotesla) occurring in the region of Antarctica. Comparison of the the three proposed forecast secular-variation models for 1985–1990 with estimates of recent rates of change at 148 magnetic observatories shows that the IZMIRAN (U.S.S.R.) and USGS models are in closest agreement with these data.

Testing recent geomagnetic field models via magnetic flux conservation at the core-mantle boundary

The 28 candidate main field models submitted for the International Geomagnetic Reference Field Model Revision 1985 reveal that a dramatic increase in the rate of decline of the Earth's total pole strength began around 1960. Nevertheless, all but one field model conserves the absolute magnetic flux linking the core-mantle boundary (CMB) fairly well during the 40 year time span 1945–1985. This supports the frozen-flux approximation on global length and decade time scales. Geostrophic fluid motion at the top of a frozen-flux core conserves the total magnetic flux linking either geographic hemisphere of the CMB. This constraint is poorly satisfied by the candidate secular variation (SV) models. Yet other SV models truncated at higher degree, and models based upon temporal interpolation rather than extrapolation, satisfy this constraint very well. These results lead us to make several recommendations for the 1985 and future IGRF revisions.

Evaluation of IGRF candidate models over the Australian region

Observations of declination made at magnetic observatories and repeat stations distributed throughout the Australian region are used to assess the candidate main field models proposed for the IGRF epochs 1945, 1950, 1955, 1960 and 1980.

Spherical harmonic modeling of the geomagnetic field using the fast Fourier transform

The Dilts method for computing spherical harmonic expansion coefficients of a surface function ƒ(θ, ϕ) is adapted to the inverse and forward problems of geomagnetic main-field modeling. This method, which takes full advantage of the intrinsic speed of the fast Fourier transform (FFT), can compute the coefficients of a typical degree and order 12 model in just a few seconds on most main-frame computers and therefore seems optimally suited to perform high-degree and order modeling of the Earth's crustal magnetic anomalies. Execution of the method requires the construction of an equiangular grid of geomagnetic data over the entire surface of a sphere. This is a weak point of the method since a subset of data observations must be judiciously selected from the available data to form a very thin shell that encloses the spherical surface. The data in this shell must then be very carefully averaged and interpolated to form the necessary grid. The Gauss coefficients are quite sensitive to errors in this gridding process. Satellite observations appear to be the most appropriate data source for spherical harmonic FFT modeling due to the uniform quality and global coverage that such data provide.

Geomagnetic evidence for fluid upwelling at the core-mantle boundary

Summary. Previous studies, both geomagnetic and seismic, have been unable to show conclusively whether or not there is fluid upwelling at the core-mantle boundary. Here a new method is developed, in which an attempt is made to invert geomagnetic secular variation data measured at the Earth's surface for a frozen-flux purely toroidal core-mantle boundary (CMB) velocity field, under the assumption that the mantle is electrically insulating and flux is frozen in at the CMB. These data have previously been inverted for the core-mantle boundary radial secular variation, from which the appropriate fit between model and data is known. Two different main field models were used to assess the effect of uncertainty in its radial component at the CMB. The conclusions were the same in both cases: frozen-flux purely toroidal motions provide a poor fit. A statistical test allows very firm rejection of the hypothesis that the residuals are not significantly larger, whereas there is no statistical difference between the residuals of inversions for radial secular variation and frozen-flux velocity fields at the CMB if upwelling and down-welling is included. The inherent non-uniqueness in the velocity field obtained is not of concern, since only their statistical properties are utilized and no physical significance is attached to the flows obtained.

A preliminary harmonic spline model from Magsat data

We present a preliminary main field model for 1980 derived from a carefully selected subset of Magsat vector measurements using the method of harmonic splines. This model (PHS (80) for preliminary harmonic splines) is the smoothest model (in the sense that the rms radial field at the core surface is minimum) consistent with the measurements (with an rms misfit of 10 nT to account for crustal and external fields as well as noise in the measurement procedure). Therefore PHS (80) is more suitable for studies of the core than models derived with the traditional least squares approach (e.g., GSFC (9/80)). We compare characteristics of the harmonic spline spectrum, topology of the core field and especially the null‐flux curves (loci where the radial field is zero) and the flux through patches bounded by such curves. PHS (80) is less complex than GSFC (9/80) and is therefore more representative of that part of the core field that the data constrain.

Scalar magnetic anomalies of Canada and northern United States derived from Magsat data

The total magnetic field of the earth over Canada and the northern United States is sampled along individual orbits (passes) of the magnetometer satellite (Magsat) on the basis of data extracted from the Magsat chronicle tapes. The main magnetic field at a given sample point is calculated using the main field model by Langel et al. (1982a) and then subtracted from the sampled value. The external magnetic field contribution is partially removed by a quadratic function fitted to each individual pass. The resulting magnetic residuals are resampled at 55 by 55 km grid points on an equal‐area projection and subsequently contoured. The dawn passes yield a magnetic map that is different than the dusk passes, implying that the remaining external magnetic field component has a dawn‐dusk asymmetry. The component is further suppressed by applying a band‐pass filter in the frequency domain. The magnetic anomaly map derived by averaging the dawn and the dusk band‐pass‐filtered maps shows the main features seen on the aeromagnetic maps of Canada and the United States. The map also shows that the Appalachian and the Cordilleran orogens and the Grenville‐Superior suture zone are magnetically low regions, whereas the craton basins such as the Michigan, the Thelon, and the NE British Columbia Basin are magnetically high areas.

Perpendicular error effect in the DGRF model proposals

It is known that when spherical harmonic models of the geomagnetic field are derived from data sets having insufficient component (vector) data these models are liable to pseudo-systematic errors, particularly large for the sectorial coefficients. These coefficient errors correspond to error fields having foci on and near the dip equator, and which are everywhere roughly perpendicular to the main (approximately dipole) field—the perpendicular error effect. This paper demonstrates the existence of such an effect, with foci of up to 300 nT, in the differences between the IGS, NASA, and USGS spherical harmonic models proposed for the DGRF 1965–1975, and deduces that it probably comes almost entirely from the NASA models. It is shown that, although the NASA data set contained a large amount of observatory component data, the method of analysis used by NASA meant that this data was given little weight in the main field model. It appears that ∼ 15% of component data is needed to avoid significant perpendicular error effect.