The goal of magnetic observatories is to measure and provide a vector magnetic field in a geodetic coordinate system. For that purpose, instrument set-up and calibration are crucial. In particular, the scale factor and orientation of a vector magnetometer may affect the magnetic field measurement. Here, we highlight the baseline concept and demonstrate that it is essential for data quality control. We show how the baselines can highlight a possible calibration error. We also provide a calibration method based on high-frequency “absolute measurements”. This method determines a transformation matrix for correcting variometer data suffering from scale factor and orientation errors. We finally present a practical case where recovered data have been successfully compared to those coming from a reference magnetometer.
Most magnetic observatories are built according to a standardized or universally adopted scheme (Jankowski and Sucksdorff, 1996) including at least a set of three major instruments: a variometer, an absolute scalar magnetometer, and a declination and inclination flux instrument (DI-flux instrument). The different data streams are combined to build a unique vector of magnetic field data. The variometer is a vector magnetometer, which records variations of the magnetic field components at a regular interval (e.g. at 1 Hz). However, this is not an absolute instrument. In particular, reference directions, the vertical and geographical north, are not available. They usually work as near-zero sensors, so that an offset must be added to the relative value of each component in order to adjust it and therefore determine the complete vector. Those offsets or baselines should be as constant as possible but may drift more or less depending on the environment stability and device quality. For instance, thermal variations may affect the pillar stability. A baseline can also suffer from sudden variation due to an instrumental effect after a (unwanted) motion like a shock due to maintenance staff or a change in the surrounding environment (Fig. 1). A regular determination of the baselines is thus necessary to take their change into account. This is the main goal of the well-known “absolute measurements” that are carried out by the two other instruments.
First, a scalar magnetometer records the intensity of the field
The last instrument serves to determine the magnetic field orientation according to reference direction. Magnetic declination is the angle between true north and the magnetic field in a horizontal plane, and the inclination is the angle between the horizontal plane and the field. In a conventional observatory, a DI-flux instrument (non-magnetic theodolite-embedding single-axis magnetic sensor) is manipulated by an observer according to a particular procedure (Kerridge, 1988) taking about 15 min per measurement. This instrument is also considered absolute because angles are measured according to geodetic reference directions. Due to this manpower dependency, the frequency of absolute measurements does not exceed once per day (St Louis, 2012). However, new automatic devices such as AutoDIF (automatic DI-flux instrument; Gonsette et al., 2012) close the loop by automatising the DI-flux measurements procedure. Moreover, AutoDIF is able to increase the frequency of baseline determination by performing several measurements per day.
After collecting synchronised data from the three instruments, baselines are
computed by using the relation for the Cartesian coordinate system:
Equation (2) assumes a variometer properly set up with the
Baseline example computed from conventional manual measurements (dark blue) and the automatic system (light blue). In mid-2013, a baseline jump corresponding to an instrumental effect occurred, proving that regular absolute measurement are crucial.
A correct orientation is usually ensured by paying attention during the
set-up step, but its stability in time is not always evident. Permafrost areas
are examples of drifting regions (Eckstaller et al., 2007) where variometer
orientation is not guaranteed. If the orthogonality errors are neglected,
the problem of calibration can be expressed as follows:
The method presented in this document is related to a variometer in XYZ
configuration. However, other configurations may also be considered. For
instance, many observatories set up their magnetometers in an HDZ
configuration,
where
Before solving the calibration problem, it could be useful to give some clues for detecting required adjustments. Indeed, it is difficult, when only examining definitive data, to detect a few nanotesla errors in daily amplitude. Direct comparison with other observatories requires them to be close enough while many observatories cannot afford to buy an auxiliary variometer. Fortunately, baselines are useful tools for checking data. As described below, they are affected by calibration errors, and, if they are measured with a sufficiently high frequency, particular errors can be highlighted.
Let us consider an observatory working with a variometer, such as a LEMI-025,
in a Cartesian coordinate system. Each sensor converts a real magnetic
signal expressed in nanotesla into a more suitable format (usually a
voltage). This converted signal passes through an ADC providing, in turn, a
digital representation of the initial signal. A scale factor is then used to
convert the true signal into a digitised signal. Consider the
Supposing now a difference between the digital and real variation of a component
resulting from a badly calibrated scale factor, the baseline measurement
will be affected by this error:
The scale factor is usually factory calibrated and should be stable
over time. It is certainly true but there are many situations for which
the scale factor is not known exactly (e.g. a homemade instrument) or differs
from its factory value (e.g. a repair after a lightning strike may affect the
instrument parameters). The impact of a scale factor error also depends on
the magnitude of the magnetic activity. A 1 % error for the
Now, let us consider once again the same XYZ variometer but this time
presenting an orientation error. That could be due, for instance, to a
levelling error caused by a bad set-up or an unstable basement and/or an
Rasson (2005) treated the simplified case of a rotation
Light blue:
The general case is much more complex in particular if the orientation error
is combined with a significant scale factor error. Indeed, the term
Absolute measurements, before giving baselines, provide absolute or spot values of the magnetic field. When performed with a sufficiently high frequency (e.g. once per hour), the generated magnetogram can be compared to the variometer value. Therefore, a vector calibration can be done as if a reference variometer was available.
A DI-flux instrument, either a manual system such as a Zeiss 010-B or an automatic system like
the AutoDIF, is affected by the sensor offset and misalignments errors. A
single spot measurement is therefore computed from a set of four declination
(index 1 to 4) and four inclination (index 5 to 8) records. The eight synchronised
variometer values as well as the eight scalar measurements are averaged. Thus,
each spot value and corresponding variometer value is computed as
follows:
Let us consider a series of
A LEMI-025 variometer has been installed in the Dourbes magnetic observatory. The device has deliberately been set up in a non-conventional orientation as shown in Fig. 3. The levelling and orientation error have been strongly exaggerated compared to those encountered in conventional observatories, but, if we consider a possible future automatic deployment using systems such as a GyroDIF (Gonsette et al., 2017), the orientation could be completely random. An AutoDIF installed in the Dourbes absolute house has been used for performing absolute declination and inclination measurements because of its high-frequency measurement capability. An Overhauser magnetometer recorded the magnetic field intensity at the same time. One measurement every 30 min has been made during 4 days from 20 to 24 July 2016. The mean Kp index over this period is 2 while the maximum is 5 (only three periods of 3 h reached level 5 of the Kp index).
LEMI-025 installed in the Dourbes magnetic observatory. The red arrow indicates the true north direction. The orange arrows highlight the bubble-levels saturation.
LEMi-025 baselines. Light blue: before processing. Dark blue: after processing.
Before processing, the baseline computation clearly highlights the set-up
error as shown in Fig. 4. Actually, such big variations do not meet the
international standards (St Louis, 2012) and could discard the concerned
magnetic observatory. Indeed, most observatories perform absolute
Variometer difference between a reference variometer and the case study variometer. The value are clearly within 1 nT.
A second LEMI-025 is installed in the variometer house of the Dourbes
observatory. This one is correctly set up, so it could be used for a
posteriori comparison. Figure 5 shows the difference between vector
components built from the case study variometer and the reference
variometer. Notice that, even if both are separated by as much as 10 m, the
observatory environment should ensure minimal difference. If we exclude the
borders for which the cubic-spline baselines are badly defined, the three
curves meet the INTERMAGNET 1 s standards requiring an absolute
accuracy not worse than
In this paper, the measurement errors have not been taken into account. In particular, absolute measurements were performed sequentially so that the magnetic field could be changed between the first and the last measurement. Equations (12)–(14) do not take the variations between the mean declination time and the mean inclination time into account. Indeed, using Eqs. (19)–(22) with the badly set up variometer for compensating the magnetic activity would lead to a non-linear system. Nevertheless, AutoDIF achieves a complete protocol of absolute measurement within less than 5 min including the geographic north measurement at the beginning. Because of the high number of measurements during a few days, the error due to this delay can be considered as random. Assuming that the measurement errors are a random noise, their effects are therefore cancelled according to the Gauss–Markov theorem.
Jankowski and Sucksdorff (1996) suggested taking advantage of a disturbed day in order to maximise the effect of a set-up error. However, the global measurement noise may increase, in particular at high latitude. Indeed, the synchronisation between instruments may become critical. Additionally, a rapid change in the magnetic field may induce soil current that could affect both the DI-flux instrument and the variometer. Fortunately, as the noise is random and this is even truer during chaotic magnetic activity, it has no effect on the final results.
Equation (16) supposes a constant baseline so that a small variation will contribute to the residues. However, the use of an automatic DI-flux instrument provides a large number of measurements within a short time period. The case study has been performed during only 4 days, within which the baseline variations are reasonably considered small. Their contribution to the error can therefore be considered negligible compared to the possible scale factor and orientation parameter effects. Nevertheless, INTERMAGNET recommends performing absolute measurements with an interval ranging from daily to weekly (St Louis, 2012).
The baselines and absolute measurements are powerful tools for checking data quality and for highlighting possible gross errors. The present paper has demonstrated that even with a strong set-up error, it is possible to recover good magnetic data meeting the international standards. It also contributes to automatic installation and calibration of magnetic measurement systems. Future observatory deployments will be more and more complex, with automatic dropped systems in unstable environments. The challenges of tomorrow are in Antarctica, the Earth's seafloor or even Mars (Dehant et al., 2012). The application of theses methods will contribute to reaching those objectives. They will require not only automatic instruments but also regular and automatic control.
Data are available upon request from the corresponding author at agonsett@meteo.be.
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 acknowledge the Royal Meteorological Institute of Belgium, which allowed this research. We also acknowledge the editor and the reviewers who contributed to the improvement of this article. Edited by: Arnaud Chulliat Reviewed by: Santiago Marsal and one anonymous referee