2.1 Measurement method

The geomagnetic field is a vector field that needs to be measured in terms of its size and direction. DIMs consists of a nonmagnetic theodolite and a fluxgate sensor, are the standard instrument for measuring the geomagnetic field direction (D and I). The fluxgate sensor mounted on the top of the theodolite’s telescope is nearly aligned with the optical axis. The fluxgate sensor outputs a null signal when the geomagnetic field is perpendicular to the sensor direction. Thus, the direction of the geomagnetic field can be determined by looking for the position where the sensor’s output is null, and the position can be recorded by reading from the circle of the theodolite. For any two directions read from the circle of the theodolite, the angle between them can be obtained by calculating the difference. This is the basic principle of measurement.

The measurement of the geomagnetic declination and inclination are realized in the horizontal and vertical plane of the theodolite, respectively. To measuring the declination D, the telescope axis must be in the horizontal plane, so the first task is to level the theodolite using its bubble levels and leveling screws. As the fluxgate sensor axis perpendicular to the magnetic meridian, D is determined by the horizontal geomagnetic field and the true north direction, so there are two main steps in measuring declination. The first step is to measure the true north direction. The observer should adjust the telescope to ensure that the optical axis is aligned with the azimuth mark, and then record the reading of horizontal circle, denoted by M and shown in Figure 1. The azimuth of the mark, represented by A is already known, so the position of the true north direction can be calculated. The second step is to establish the geomagnetic field direction. The observer should adjust the telescope on the horizontal plane so that the theodolite vertical circle reading is exactly 90° or 270°, then search for the position at which the sensor output is null and record the horizontal circle reading of the geomagnetic field, indicated by D′. Finally, the geomagnetic declination D can be computed from the circle readings as:

To measuring inclination I, the telescope axis must be fixed in the geomagnetic meridian plane. The measurement is then performed by searching the sensor’s null position. This is the same process as for the declination, although the measurement is carried out without a measuring mark. This is the main measurement process.

Note that a measurement with a DIM refers to a set of measurements, as elimination of instrumental errors necessitates at least four individual measurements for the declination D and two measurements for the inclination I (Rasson, 2005). In the actual measurement procedure, four observation positions of the telescope are needed to determine one direction: telescope towards East and sensor up (D₁), telescope towards West and sensor down (D₂), telescope towards East and sensor down (D₃), and telescope towards West and sensor up (D₄). Then mean of the four readings gives the final measurement result, expressed by

The same procedure is also applied to the inclination measurement. Again, four observation positions are possible, of which two are sufficient for error correction. In this case, the observation positions are telescope towards North and sensor up (I₁), telescope towards South and sensor down (I₂), telescope towards North and sensor down (I₃), and telescope towards South and sensor up (I₄). The final inclination is the mean of the four readings, i.e.,

The misalignment between fluxgate sensor and optical axis can be compensated in this way. In addition, there are two methods for the circle reading, namely the null method (exactly zero) and the offset method (near zero). The detailed measurements procedure is described in the IAGA guide (Newitt et al., 1996). The two methods have been discussed by Xin (2003), Lu (2008) and Deng (2011). They found that if the output of the theodolite was linear, the offset method could achieve the same accuracy as the null method, even if the observer had slightly magnetic material. Usually, the modern theodolite output is highly linear, so the offset method is frequently used for the measurement. The unique absolute vector geomagnetic field can be determined by D, I and F (measured by a proton magnetometer), and the baselines of each component of the variometer can be calculated. Note that considerable effort has been directed toward the development of new observation technology (Auster et al., 2003; Rasson et al., 2011). Recently, some automatic DIMs have been realized and are performing some observations (Gonsette et al., 2017; Hegymegi et al., 2017; Brunke et al., 2018). In the future, the automatic instruments would allow completely unattended magnetic observatory operation.

2.2 Comparison method

To achieve high-quality data in geomagnetic observation, the differences between absolute instruments from different observatories should be checked. Thus, comparisons of the absolute instruments are an indispensable part of geomagnetic observation. There are two main ways to determine the difference between instruments: direct comparison by simultaneous measurements and indirect comparison by comparing the reference values. If two or more pillars are available for the absolute measurements, the instruments can be compared directly through simultaneous measurements. Both the instruments’ difference and the pillars’ difference can be obtained by interchanging the instruments’ location and applying the same observation method. The instruments’ difference for arbitrary component W and pillars’ difference for two arbitrary pillars can be calculated by the following equation:

where, p, q denote the different instruments and s, o represent the standard pillar and other observation pillar, respectively. ΔW_so is the pillar difference between the standard pillar and other observation pillar, and ΔW_pq is the instruments’ difference. As an example, W_qs represents the observation value measured by instrument q installed on pillar s.

As there are a limited number of the pillars, a large number of DIMs, and variable proficiency in the observation techniques of observers, it is difficult to complete the comparison using simultaneous measurement. As modern variometers are rather stable and offer high precision, the baselines are almost constant. Therefore, the comparison is usually achieved by comparing the adopted baseline values. The stability and accuracy of baseline values in one calibration day have been analysed by Zhang (2011), who stated that the baselines were stable during the calibration day from 8:30 to 16:30 local time, and the geomagnetic field activity showed no obvious influence on the accuracy of baseline values. Thus, it is feasible to complete the comparison by comparing baseline values. The equation for computing baseline value for arbitrary component W is given in the INTERMAGNET reference manual (St Louis, 2011) as:

where, (i:j) is the time interval (generally several minutes) for the measurement, (k) is the average time of the interval (i:j), W_o is the observed absolute field value, W_R is the minute value recorded by variometer, and W_B is the computed baseline value.

In comparison session, the reference level for arbitrary components is usually adopted from the average of all the measurements performed by the participants on the reference pillar. Since absolute measurements were made on different pillars, the baseline values measured on other pillars should be calibrated to the reference pillar for comparison. The usual calibrating method is to add a pillar difference to the results of other pillars. The pillar differences are determined by extensive measurements made prior to the comparison session. The general form of the equation for computing the difference for arbitrary component W is:

where, s and o represent the standard pillar and the other observation pillar, ΔW_so is the pillar difference between the standard pillar and other observation pillar, W_BS and W_Bo are the computed baseline values, and ΔW_Bso is the final difference between two instruments. The fluxgate theodolites from different observatories can be compared in this way, and the quality of the absolute observation data can be evaluated using these results.

3.1 The comparison results of GNC

Six comparisons have been organized by the GNC. Previously, the comparison is organized every two years following the IAGA’s guide; recently, due to the frequent turnover of staff, it is made every year. They were carried out at Changchun observatory in 2010; at Qianling, Dalian and Shaoyang observatories in 2012; at Qianling observatory in 2014 and 2016; at Urumqi observatory in 2015 and 2017. Most of DIMs from geomagnetic observatories in China have taken part in the comparison. The comparison information is list in Table 1 and the DIM types and observatories are presented in Table 2. The difference between the observation instruments and standard instruments were calculated by comparing with the standard baselines which measured by skilled observer using the standard instruments. Now, all the comparison results are collected together and sorted by DIMs. The difference in declination and inclination are, respectively, displayed in Figures 2 and 3. As shown in Figure 2, the colored dots represent the mean value, the sizes of the dots indicate the standard deviation and the colors represent the different years; the grey dots on the right show the scale of the colored dots. The grey bars, corresponding to the right-hand vertical axis, indicate the standard deviation of the comparison results of each instrument over the six years of comparisons. The right-hand panel shows the frequency distribution of all of these results. The mean and standard deviation of these results over the six years are 0.01′ and 0.15′ for ΔD, –0.02′ and 0.07′ for ΔI, respectively.

As shown in Figures 2 and 3, almost all coloured dots are distributed within one standard deviation of the mean. For ΔD and ΔI, 75% and 77% of the comparison results are within this range, respectively. To some extent, the standard deviation represents the quality of absolute observation data of the GNC. To estimate the quality, a value range of 90% of the cumulative probability is considered as the quality level of the GNC in this study. In this way, obviously wrong data can be excluded and the true level of observation quality can be accurately reflected. From Table 3, the value ranges are ±0.24′ for ΔD and ±0.11′ for ΔI. Therefore, the absolute measurement accuracy of the GNC reaches 0.24′ in declination and 0.11′ in inclination. The gray bars in the figures show the standard deviation of the instruments over the six comparison years, revealing the absolute measurement quality level of the observatories at which that instrument is located. The sizes of the dots represent the observation precision of each observer. Figures 2 and 3 show that the absolute measurement quality of most observatories and the observation level of most observers are relatively high.

By comparing Figures 2 and 3, it is clear that the distribution of the coloured dots in Figure 2 is more discrete than that in Figure 3. This indicates that the quality of the inclination observation data is superior to that of declination data. One reason for this difference may be that observers should adjust optical axis to align with the azimuth mark in the declination measurement, but it is difficult to adjust to the exactly same position each time. Thus, the declination measurement is more susceptible to error than the inclination measurement, and more observation errors may be included in declination results.

However, there are some outliers that are significantly beyond the range one standard deviation from the mean. Some of these large values can be traced back to the changes in the instruments themselves. For example, the declination difference of Manzhouli’s instrument was –0.37′ in 2010, as shown by the light green dot (No. 26) in Figure 2. This became 0.39′ in 2012 after maintenance, as displayed by the green dot (No. 26). In 2014, when sensor when was mounted on the top of the theodolite from Jinghai observatory, the difference was 0.40′, as presented by the light blue dot (No. 18). This became –0.38’ in 2016 after maintenance, as shown by blue dot (No. 18). Although the cause of these changes is not clear, it is certain that this is a systematic error, which can be tracked through the course of the comparisons.

Some other instrument problems also can be observed in these results. Because of the limitation of non-magnetic materials, the horizontal axis (the rotation axis of the telescope) and vertical axis (the rotation axis of the alignment part) of the theodolite are not as hard as the other parts. If they were damaged, the measurement accuracy would be reduced. For example, the DIM at Luoyang observatory had some problems on the vertical axis in 2014, meaning that it could not be kept horizontal during measurements. That caused the absolute observation data to be unstable and have a large standard deviation, as shown in light blue dot (No. 24) in Figures 2 and 3. There are other factors that affect the final results. The environment of some observatories in southern China is very humid, so the interior of the theodolite are become mouldy and the reading line of the theodolite can be unclear (e.g. Qiongzhong observatory, No. 34 both in Figures 2 and 3). A bad contact between the sensor and the cable can lead to unstable observation data; looseness of the sensor, resulting in its axial direction not being parallel to the optical axis of the telescope, can reduce the measurement accuracy. All of these problems can be identified through the comparison process and rectified by professionals.

The observation technology used by the observer is another important factor influencing the quality of observation data. In recent years, the staff turnover of observatory has been relatively high. For instance, in the 2015 comparison, nearly 30 percent of observers were novices. As shown in Figure 2, the degree of dispersion of the blue dots in 2015 is obviously greater than that in other years. A lack of systematic training on the principles and methods of observation means that new observer may make some mistakes in the measurement process. For example, when the telescope was not placed exactly on a horizontal plane, the declination errors of instruments No. 7 and No. 53 are –0.66′ and 0.46′, respectively, in 2016, as displayed in Figure 2; following an incorrect observation process, the declination and inclination of No. 60 are 2.37′ and 2.23′ in 2017 respectively, beyond the range shown in the figure.

3.2 The comparison results of IAGA

The international DIM comparison is organized by IAGA Working Group V-OBS, and has completed 18 sessions. Several years of the results, which are available on IAGA website, are collected here. Detailed information about these sessions and the sources of comparison results are shown in Table 4. The comparison results are sorted by country because of a lack of information on instrument types. The country serial numbers are listed in Table 5. The units of the comparison results in some years have been converted from arc second to arc minute. The mean and standard deviation of the difference of each instrument are shown in Figures 4, 5, 6, 7. The symbols in the four figures have the same meaning as those in Figure 2. Additionally, the mean and standard deviation of different elements of all the comparison results in these years are calculated; they are, respectively, 0.00′ and 0.28′ for ΔD, 0.00′ and 0.09′ for ΔI, 0.30 nT and 1.08 nT for ΔH and –0.18 nT and 0.68 nT for ΔZ, as listed in Table 6.

As shown in Figures 4, 5, 6, 7, most of the coloured dots are distributed within one standard deviation of the mean. The percentage of the data within this range is 87%, 81%, 75% and 78% for ΔD, ΔI, ΔH and ΔZ, respectively. A value of 90% was adopted as the evaluation criterion in this study. The value ranges corresponding to this percentage are ±0.35′, ±0.10′, ±1.9 nT and ±1.1 nT for ΔD, ΔI, ΔH and ΔZ, as given in Table 6. This means that absolute measurements around the world achieve fairly good observational levels. In addition, it can also be found that quality of declination is better than that of inclination in this result. A possible reason for this was discussed in Section 3.1. As depicted in Figure 4, some larger values, with large standard deviations, are obviously beyond the range of one standard deviation from the mean. A lack of sufficient information in the measurement process makes it difficult to investigate the causes. As discussed previously, it may be the result of instrument failure or operational errors. In any case, these results are good indication of the quality level of the observatory’s absolute measurements.