The U.S. Geological Survey (USGS) Geomagnetism Program has developed and tested the residual method of absolutes, with the assistance of the Danish Technical University's (DTU) Geomagnetism Program. Three years of testing were performed at College Magnetic Observatory (CMO), Fairbanks, Alaska, to compare the residual method with the null method. Results show that the two methods compare very well with each other and both sets of baseline data were used to process the 2015 definitive data. The residual method will be implemented at the other USGS high-latitude geomagnetic observatories in the summer of 2017 and 2018.

Geomagnetic observatories are unique facilities. They measure the variation
of the three vector components of the geomagnetic field at 1 min or
1 s time resolution and they also measure the absolute value of the
geomagnetic field (see, e.g., Rasson et al., 2017; Matzka et al., 2010; Love
and Chulliat, 2013; Chulliat et al., 2017). The vector components are
typically measured with a three-axis fluxgate magnetometer. The absolute
measurements are used to generate baseline values, which are the difference
between the absolute values and raw variation data, for each magnetic
component. The baseline values are used to calibrate the variation data to
produce final definitive data. Since the first systematic geomagnetic
observations in the 16th century (Malin, 1987), there has been
continued development and improvement of instruments to measure absolute
values of the geomagnetic field. Some of these instruments measure the
strength of a magnetic vector component, the magnitude of the entire vector,
or the angles of the orientation of the geomagnetic vector. Beginning in the 1970s
the most common instruments employed are the proton precession
magnetometer that measures the magnitude (

The point of the residual method is to allow readings of the horizontal or vertical circle for positions where the output of the fluxgate, termed the residual value in nanoteslas, is not exactly zero. This makes it easier to cope with rapid changes of the geomagnetic field. It also allows the observer to be farther away from the DIM, reducing the possibility of contaminated measurements. Additionally, as in the case for Zeiss 020 theodolite, the circle reading can be set exactly to a whole-minute value and the output of the DIM magnetometer can be used to mathematically compensate for the resulting small deviation in angle between the whole minutes as opposed to estimating tenths of minutes by eye. The residual method presented here was developed for the Danish geomagnetic observatories at Danish Technical University (DTU), originally part of the Danish Meteorological Institute. The method and computations are based on a document written by Kring Lauridsen (1985), a book by Jankowski and Sucksdorff (1996), and a study by Matzka and Hansen (2007).

This paper presents the updated computational scheme used by the U.S. Geological Survey (USGS) and shows comparisons of the two methods employed at the USGS College Magnetic Observatory (CMO), Fairbanks, Alaska.

For the sake of simplicity, all of the following equations will use angles in radians, unless indicated otherwise. For programming purposes, angles measured in degrees or gradians will need to be converted to radians as appropriate. Instrument orientations, such as west down, refer to the direction the telescope is pointing and the position of the fluxgate sensor mounted on the telescope. The definitions used can be found in the Appendix.

The inclination angle computations are discussed first because the
horizontal baseline value,

For the residual method, the computations involve some additional steps.
Each inclination reading (AI

The individual

The final inclination value

Computing the absolute value for declination, using the null
method, from the declination measurements is fairly simple. The magnetic
meridian is computed as the average of the four declination readings. The
four mark readings, which are sightings on the true azimuth mark before and
after the declination measurements, are also averaged. The computation of
the absolute value for declination, using the null method, can be described
in simple terms as

The exact formula for the declination conversion uses the simple
trigonometric relation that the declination angle can be computed from the
inverse tangent of the value of

A comparison of the difference between the computation of declination
from

The USGS declination measurements are in the following order: west down,
east down, west up, and east up, which correspond to AD

The mean of the four angles

In this method, the absolute values for

There are five separate error parameters that can be computed from the measured declination and inclination angles that are useful for diagnosing the quality of measurements performed with the DIM.

For the

Declination diagnostic parameters from absolute observations for the first 2 months of 2016, plotted with an arbitrary vertical scale. The graph shows the four individual observations and their average. There is an outlier value observed on day 51 that is probably a bad measurement that should be eliminated before processing.

The declination sight error, in arcseconds, designated as

The inclination sight error, also known as the misalignment in the vertical
plane, in arcseconds, designated as

Comparison of baseline measurements using the null and residual methods
at College Magnetic Observatory in 2014 and 2015. The three graphs show that
there is considerable agreement between the null and residual methods. The

The residual method was tested at most of the USGS observatories by USGS
staff during site visits over the course of a year, and the agreement
between the null and residual methods was satisfactory. More extensive
testing was performed at the CMO. This was a
logical choice because the observatory has good baseline stability and is
located at high geomagnetic latitude, 65

In the comparison of the two sets of baselines, there are agreements and differences. The baselines for declination show differences that are mostly on the order of a tenth of a minute apart. These differences could be easily explained by round-off error, but it is also possible that it could be due to differences in computation schemes, with the residual method deriving more accurate baselines because the observer does not have to null the sensor during active periods of magnetic activity. The null method uses the traditional small angle computation to convert nanoteslas to minutes. The residual method uses the exact conversion from nanoteslas to minutes. Also, some of the larger differences could be attributed to observer error or a higher level of magnetic activity.

Differences in the horizontal component (

The vertical baselines (

Since 1996, the USGS has usually performed absolute observations, using the
null method, with four separate measurements or sets over about an hour.
Four sets were also measured when using the residual method. Four separate
measurements make it possible to evaluate the range or spread of the
measurements. At CMO, the residual method showed a consistently smaller
value in the range of the four measurements, especially in the

The 14 months of baseline data shown, using the two measurement methods, were combined and used for the final processing of the definitive data for 2015. A few measurements using the null method were removed from the data set due to possible contamination; none of the data from the residual method were removed because of possible contamination. The residual method has been implemented at both College and Deadhorse observatories. The USGS plans to implement the residual method at the remaining USGS observatories in Alaska in 2018 and in all observatories by 2019.

From the data presented above, it is evident that absolute measurements using the residual method are comparable to measurements with the null method. While it is difficult to judge the absolute accuracy of the results, the residual method, with a smaller range in the four sets of observations, demonstrates more precise results, suggesting an increase in the accuracy of the baseline measurements. With well-trained observers, both methods should yield similar results. When processing data from a high-latitude observatory such as CMO, there are some baseline data values that are removed from the data measured using the null method when the magnetic activity is high. With the residual method, the amount of baseline data removed due to high magnetic activity is less than half than was removed from the data measured with the null method.

The residual method presented also offers the possibility of more precise results for the absolute and baseline measurements. The use of the exact computation, for the conversion from nanoteslas to arcminutes, does provide a more accurate calculation for the declination results because the small angle approximation is eliminated.

We have demonstrated that the residual method is at least as good as the null method. In some cases, it is better because the nature of the method makes it more accurate during higher levels of magnetic activity, typically seen at high magnetic latitudes. This provides for extra baseline data for the times when the null method would not be possible due to high magnetic activity. The residual method also makes it possible to move the observer away from the fluxgate sensor on the DIM to avoid contamination. This is especially helpful for observers who wear glasses. For example, at Brorfelde Observatory (BFE), Denmark, the observer is 1–2 m away from the instrument. Personnel from DTU, German Research Centre for Geosciences (GFZ), and USGS have learned that when training new observers it is easier to teach the residual method than the null method; that way, the observers can get consistent results sooner.

The College Magnetic Observatory definitive data, for 2014 and 2015, have been
published on the Intermagnet web site at

The authors declare that they have no conflict of interest.

This article is part of the special issue “The Earth's magnetic field: measurements, data, and applications from ground observations (ANGEO/GI inter-journal SI)”. It is a result of the XVIIth IAGA Workshop on Geomagnetic Observatory Instruments, Data Acquisition and Processing, Dourbes, Belgium, 4–10 September 2016.

We would like to thank Carol Finn, Karen Remick, Tim White, Jill McCarthy, and Janet Slate for their helpful comments and suggestions. We also would like to thank Lon Sonsalla, Karen Remick, and Tom Yenchesky at College Magnetic Observatory for their absolute measurements. In addition, we would like to thank the anonymous referee and Lars Pedersen for their valuable suggestions. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. government. Edited by: Alexandre Gonsette Reviewed by: Lars W. Pedersen and one anonymous referee