Research Article  Open Access
Improving Earth’s Magnetic Field Measurements by Numerical Corrections of Thermal Drifts and ManMade Disturbances
Abstract
This contribution deals with challenges encountered in realworld geomagnetic measurements and is focused on improving the performance of two variometer stations of Kelčany and Polom, which have been recently established in the Czech Republic. It is shown that a carefully designed fullfield instrument, despite lacking temperature stabilization, can provide vectorial and scalar data accurate to a few nT, if the raw data were postprocessed by compensating for gain temperature coefficients—we show how this can be obtained by a precise calibration and longterm scalar measurements. We also show a method for suppressing nTlevel spikes in the data due to nearby car traffic, by utilizing gradiometric measurement for detecting the car occurrences and by employing a linear optimization problem in order to find the parameters of the moving magnetic dipole and compensate for it. In this manner, we were able to reduce the anthropogenous noise due to car traffic while keeping as much original information as possible.
1. Introduction
Vectorial magnetometers which serve for monitoring of Earth’s field variations due to diurnal field changes, geomagnetic storms, etc., are standard instruments deployed at geomagnetic observatories and variation stations; they are mostly based on fluxgate sensors [1]. To achieve the best magnetometer (variometer) performance, it will usually be installed in a temperaturestabilized environment, either by the use of an active and magnetically clean heatingsystem or by selecting a highly temperaturestable location, preferably underground. This approach is of course demanding on the site selection and/or the necessary infrastructure. However, the variometer performance improved recently not only in terms of noise (the current stateoftheart noise limit of fluxgate sensors is about 3–5 pT/√Hz @ 1 Hz) but also in temperature stability [1–3]. Also, with the advent of dcprecise 24bit A/D converters, it is possible to build a “fullfield” instrument which not only can monitor the magnetic field variations but also can provide the vector magnitude (scalar) from the three vector components. To achieve this, precise magnetometer calibrations are needed [4, 5], and the calibration parameters need to be longterm stable. The calculated total field value can be further used for temperature compensations.
An important aspect of realworld deployment of variometers is the anthropogenous noise at the selected site, which is at least in the Central European region difficult to obey by placing the instrument in a remote locality—due to extensive urban development, DCrailways, pipelines, etc. [6]. Thus, the anthropogenic noise should be estimated and, if a better location is not viable, a compensating or at least a detection method should be developed; the latter is the case mainly if the occurring disturbances are on localscale, i.e., car traffic—we will show this is the case of one of our localities.
The following results were obtained from magnetometers running at three different localities in the Czech Republic. The reference lownoise data was obtained from the established INTERMAGNET geomagnetic observatory Budkov (BDV) in Southern Bohemia, which employs passive and active temperature stabilization. Two variometer stations were recently established—Polom (PLM) in Eastern Bohemia at the CzechPolish border and Kelčany (KEL) in south Moravia—see Figure 1. The motivation to have all three stations is clear—first, having data redundancy is important for magnetic field observations, forecasts, and data services; moreover, from the three measurements, it would be theoretically possible to suppress the anthropogenous noise which occurs on localscale—the only correlated information is the Earth’s field variation, which is homogeneous enough across the three stations span (100–200 km). From Figure 1, it is evident that mainly the DC railways (which are far away from BDV observatory) will have a detrimental effect on anthropogenic noise on both variometers running at PLM and KEL. The site of Průhonice (PRU) just at the outskirts of Prague is also shown; it served as a geomagnetic observatory station from 1946 to 1967, when the magnetic observations have been moved to a much quieter location of Budkov.
2. Instrument Setup and Site Limitations of PLM and KEL Stations
The station of Polom (PLM) has been in service since late 2016. The site is a property of Czech Army and is being run in collaboration with the Institute of Geophysics, CAS and provides important seismic, meteorological, and geodetic data [8]. CTU and IG CAS took the opportunity to install a fluxgate variometer instrument [4] in the already magnetically prescreened and prepared locality. Because of the recent installation, the temperaturestabilized hut is not yet available, and therefore, the variometer sensor and also electronics are operating at ambient temperatures, although protected from the elements. The site is also equipped with nonmagnetic pillars for obtaining “absolute” magnetic measurements, i.e., measurements of local inclination and declination handtohand with total field intensity, which are usually obtained using a portable Overhauser magnetometer [9].
The station of Kelčany (KEL) is privately owned and is being run by the members of Magnetic Laboratory at the Department of Measurement, FEE CTU Prague. The advantage of the site compared to PLM is the underground location of the sensor and electronics (in a dualpurpose winecellar), which allows for less than ±5°C yearly temperature variation. Careful magnetic mapping has been done before installation, the site was cleaned of ferromagnetic objects and a nonmagnetic pillar for the instrument was built. The site is running since 2015 and is, advantageously, on roughly the same latitude as the BDV observatory. The data are publicly available [10].
The magnetometers installed both at KEL and PLM stations were manufactured at the CTU using lownoise racetrack fluxgate sensors, exhibiting ~20 pT digital noise floor and showing high geometrical and temperature stability. The triaxial sensor head at PLM is moreover made from MACOR machinable ceramics; the head is further fixed on a marble plate [3]—see Figure 2. Neither KEL nor PLM facilitate a scalar magnetometer; thus, the total field data are calculated from the three orthogonal field components.
(a)
(b)
After initial trials at the PLM station, where the ambient temperature can change from −20°C to +40°C, we decided to orient the sensor to the “UVZ” orientation [11]. This means that the two horizontal axes are oriented ±45° from local meridian—in this manner, both horizontal axes are measuring roughly the same magnetic field (about 15,000 nT at our location). The NEZ or HDZ components are computed numerically [9], so the offset drifts and mechanical instability in azimuth are of less significance than if measuring the E or D component directly. Also, the compensating current in all axes is large enough (few mA) not to be influenced by cable leakage currents. The UVZ orientation is also beneficial for obtaining a simple thermal drift model as shown later.
A comparison of anthropogenous noise observed at BDV, KEL, and PLM stations is shown in timedomain in Figure 3, where the calculated total field from both KEL and PLM vectorial readings is compared to total field measurements at BDV observatory provided by Overhauser magnetometer.
(a)
(b)
The anthropogenous noise at both PLM and KEL is larger than at the BDV observatory (about 0.2 nT peakpeak); however, at KEL also isolated peaks occur with an amplitude up to several tens of nT pp, which have been later traced down to be caused by nearby car traffic, as further shown in Section 2.1.
Figure 4 further shows aligned spectrograms from three days of 1second data obtained at all three sites (21–23/7/2017). At PLM, the clean nights are alternated with noisy daytime periods due to the ~40 km distant DC railway and light urban rail. Although the noise at BDV station is very low, the used instrument (DMI fluxgate variometer) has large intrinsic noise, so actually, during the quiet night periods (with almost no electric train traffic), the PLM data are less noisy due to the used variometer. The KEL data on the other hand suffer from increased anthropogenic noise even during the night, since the sensor is located in a residential location—the broadband daytime noise is another 10 dB above PLM. Another 10–20 dB noise increase in short bursts has been traced down as local car traffic.
2.1. Car Traffic and Magnetic Noise
To confirm the origin of the excessnoise at KEL site, the passing cars (the local street is about 25 m away from the sensor location) have been observed by a webcamera and by a cellphone video recording, respectively, and compared to magnetic data—a sketch displaying the actual setup at KEL site is shown in Figure 5.
To be able to detect, mark, and possibly remove the passing car’s magnetic signature, an axial (dB_{y}/dy) fluxgate gradiometer has been created in NS direction by placing a second sensor coaxial to the variometer head. This second sensor has been placed approx. 5 m away from the variometer (position 1), closer to the street; later also a shortbaseline gradiometer was placed at position 2. The peaks obtained from the axial gradient data correspond with the peaks of the variometer data; however, the gradiometer noise floor is still high for detecting spikes less than about 5 nT pp.
In Figure 6, the vehicle occurrences have been drawn into the magnetic field recorded. Axial gradient (in NS direction) and magnetic field (NS component) are shown—the recorded spikes are in the order of tens nT pp (even larger for vans/busses); we show that there is a clear correlation of the spikes and car traffic.
3. Methods of Improving the RealWorld Performance at KEL and PLM Stations
At KEL and PLM sites, we are experiencing two difficulties: temperature drifts due to seasonal and diurnal changes of the ambient temperature (PLM) and large noise due to car occurrences (KEL). It should be noted that the carinduced spikes cannot be simply filtered out with a lowpass filter since the peaks in the individual axes are not bipolar, thus any lowpass filtration would introduce artefacts in the measured data. Moreover, for a strong magnetic source (e.g., a buscoach), the disturbance occurs even for 20 seconds.
3.1. Correcting for Temperature Drifts (PLM)
It is obvious that if the temperature coefficients of the sensor are known (i.e., offset and gain temperature coefficient), one could recalculate and obtain driftfree data. However, the temperature drift in a fluxgate magnetometer (assuming that the electronic is driftfree) is caused by multiple effects [12], e.g., by the temperature of the excitation tank capacitor, by the dimensional expansion of the feedback/pickup coil, or due to the expansion of the triaxial holder material and its base. Moreover, it is difficult to calibrate the whole setup as the sensor, and its base are quite bulky. As we have selected the UVZ orientation of the sensor, the ~20–30 ppm⋅K^{−1} sensitivity drifts dominate in all axes, simplifying further modeling of thermal response (With NEZ orientation, the E axis drift would be dominated by the offset drift which is a combination of electronic and sensor drifts; however, the electronics and sensor head are in our case at different positions and temperatures and exhibit different thermal mass. With HDZ orientation, the D component (~2000 nT) would be influenced both by the offset and gain drifts. In both NEZ and HDZ cases, also mechanical directional instability would have to be modeled.). The predicted sensitivity drift is 0.4 nT⋅K^{−1} for each horizontal axis and 1.1 nT⋅K^{−1} for the vertical axis, respectively. Utilizing a “fullfield” variometer, thus measuring in a feedback loop all the three vector components of the magnetic field at once, allows us for calculation of the total magnetic field (the scalar vector magnitude). Both variometers at PLM and KEL have been calibrated with the “scalar method” [4] for their offsets, gains, and orthogonalities, so the only difference to a driftfree scalar measurement from an Overhauser magnetometer are then the magnetometer drifts itself.
We did this for the PLM variometer by comparing the Overhauser readings obtained at BDV observatory to the calculated total field from PLM—in this case, we assume that on the local scale, the measurements at the two localities, which do not exhibit geologic anomalies, will differ only by a stable offset B_{Off}. This was also verified during multiple onsite measurements with an Overhauser magnetometer at different times and temperatures (we could not yet perform a longterm scalar measurement due to the lacking infrastructure).
To find the actual variometer drifts in all three axes, we have utilized a leastsquares fitting method, which generally minimizes the difference B_{Diff} between the scalar reading B_{BDV} at the BDV observatory and the calculated scalar value at PLM from the three individual components B_{1}, B_{2}, B_{3}. Thus we try to minimize B_{Diff} from a large set of following equations:
The solution of equation (1) was found with a constrained fminsearch function in MATLAB R2015 [13], and the offset agreed well with the one obtained from onsite Overhauser measurements. After correcting on the obtained drift constants α, β, and γ [T⋅K^{−1}], we were able to largely suppress the temperature drifts in all three axes. The dataset we have used was from February 2018, which allowed for large temperature span between +17°C and −12°C, see Figure 7.
(a)
(b)
We could improve the results even further by introducing a lag of 800 s which was experimentally obtained by calculating the crosscorrelation between the total field differences and temperature—this delay is believed to originate from the fact that the temperature measurements occur at the MACOR cube where the sensors are located, but significant part of the drifts can be caused by the excitation capacitor temperature coefficient [14]—the capacitor is heated only by radiation, since it is thermally connected to the MACOR cube only by its thin leads. After introducing this delay, the calculated values were the following:
The value of α roughly corresponds to the 30 ppm predicted drift (vertical axis measuring approx. 44,000 nT). Also, the γ value corresponds to an expected value for a horizontal sensor. However, the obtained value of β is unexpected, since both horizontal sensors should exhibit the same values or at least the same order of magnitude. We cannot currently offer other explanation than a faulty sensor deployed at this position.
After rotating the temperaturecompensated PLM vector readings with a 3 × 3 matrix, which reorients the sensor at PLM to the orientation at BDV, we were able to show that the temperature compensation was successful also in the individual components, see Figure 8.
3.2. Suppressing the CarInduced Disturbances (KEL)
As we have shown in paragraph 2.1, there is a clear correlation between the disturbances occurring at KEL and the car traffic. Thus we decided to create a simple model, assuming the following simplifications: (1)The car at the ~25 m+ distance can be well modeled as a single magnetic dipole(2)We neglect the road curvature and assume it in EW direction (xaxis)(3)The magnetic moment magnitude and orientation are stable during the car passage, since it keeps its orientation to the Earth’s magnetic field(4)The occurrence of the maximum axial gradient in the yaxis, which occurs when the car radial distance to the sensor is smallest, defines the symmetry point of the car movement(5)The maximum axial gradient in the yaxis (NS component) occurs defines symmetry of the car movement(6)The car does not change its speed significantly(7)In 10 seconds, the car is distant enough not to give any significant (>0.1 nT) disturbance(8)During the ~20 s car passage, the Earth’s magnetic field changes only linearly(9)The occurrences of cars in both lanes are not frequent.
Thus when fulfilling the above assumptions, we can write for the vectors of observed field and vector of car disturbance field utilizing the wellknown equation for magnetic field of a magnetic dipole with magnetic moment position vector and an (orthogonal) rotation matrix : where the position vector size (radial distance) is calculated as
The position vector coordinates of equations (3) and (4) are aligned with the magnetic moment coordinates of the dipolar source (hence the need for rotational matrix to align with the coordinates). However, we are not interested in the real orientation of the magnetic moment vector in this case, so there is no need to calculate for , which would further complicate the problem.
To find the “true, disturbancefree” of equation (3), we have implemented a leastsquares fittingbased algorithm, which relies on reading from a gradiometer placed close to the street, allowing for detection of the passing cars through the “point of symmetry”. In other words, we are trying to fit the magnetic field at every sampling point using equation (3). To achieve this, we implement a set of equations which describe the magnetic field during the short disturbance, which occurs due to the moving magnetic moment. The dataset for the optimization is centered at the gradient peak and is usually 10 + 10 seconds long (Figure 4). Since we assume a simple trajectory as of Figure 4, we are trying to find position components x and y, whereas the only changing is the x, since y is constant and equals zero in our case. Due to the constant sampling time, we can express x as a linear function of time and vehicle speed , both of which we assume constant. Since the sensor at KEL is sampling at 206.5 samples⋅s^{−1}, there are enough equations during the car passage, even after FIR filtering of the data (to remove 50 Hz mains disturbances) and smoothing. The optimization result of equation (3) is then the “true” Earth’s field vector , the magnetic moment vector , the car speed , the initial position x_{0}, and the constant y distance together with the timederivative of the Earth’s magnetic field during the fitting period.
The optimization started only when the gradient amplitude in the observed interval crosses a preset threshold in order to run only for disturbances significantly larger than overall system noise. In our case, the threshold has been set to 2 nT⋅m^{−1}. The algorithm also contains bounds and tests to compensate only using the expected values (car speed ~ 5–20 m⋅s^{−1}, y between 20 and 30 meters, fitted m below 600 A⋅m^{2}). For details of the algorithm and used functions, see Appendix.
3.2.1. WebcamTrial: Magnetic Moment Statistics
We applied the compensating algorithm on the dataset from the verification video trial (see Chapter 2.1) in order to check the feasibility of our model. In the 50minute dataset, we had ~270 car passages: 2 buscoaches, 4 vans, and 17 motorbikes and the rest were passenger cars (see Figure 6 for the induced disturbances); they were evenly distributed in the close and far lane (130 vs. 133 occurrences). The resulting “typical” magnetic moment for passenger cars and busses was found as 250 ± 50 A⋅m^{2} and 520 ± 50 A⋅m^{2}, respectively (the compensating algorithm did not start for the motorbikes due to the gradient threshold). In Figure 9, we show statistics of the individual magnetic moment components (only passenger cars shown), from which it is evident that the largest component is the vertical one which tends to be oriented along the magnetic flux lines, i.e., the component does not change its sign depending on car trajectory orientation.
(a)
(b)
(c)
3.2.2. Compensating the Disturbances
An example result for compensating a single car disturbance is shown in Figure 10—the original data, the fitted dipole from moving the car, and the data after disturbance compensation are shown for x, y, and z field components. The noise clearly decreased in the cleanedup dataset—see Figure 11 for a closeup of timedomain and Figure 12 for two spectrograms of 14hour data.
(a)
(b)
(c)
(a)
(b)
(a)
(b)
4. Conclusion
We show an approach on how to deal with (1) unstabilized ambient temperature and (2) manmade disturbances occurring at two variometric stations. Whereas the first problem is usually solved by temperature stabilization—active or passive [15]; our approach shows that a “moderate” performance can be achieved even at ambient temperatures. Although the presented method seems straightforward, we are not aware of other ambienttemperature magnetic field stations utilizing such longterm calibration and compensation. The overall maximum residual drift of 5 nT pp during 30°C temperature swing was achieved, which is even in accordance with INTERMAGNET standards [16], where the instrument should keep 0.25 nT⋅C^{−1} for vectorial readings, but it still does not fulfill the required 1 nT accuracy for scalar values. However, for our purposes, this approach brings fast and reliable results as we can really choose the ambientrun site at PLM as a redundant source of magnetic data. The steps and results shown here can be beneficial to many “repeat” stations, which usually run at ambient temperatures and which are supplementing the magnetic observatories. Even better results can then be expected if the sensor is, i.e., buried at 12 meters to avoid such large temperature fluctuations, and of course, when utilizing at least a moderate temperature stabilization (±2°C), the residual drifts after fitting would be one order of magnitude less than those presented.
As for the second problem, fitting and cleaning of a 14hour 1second dataset took less than 60 seconds on a Corei7 PC using MATLAB R2015, so offline postprocessing of daily data could be viable even in embedded systems running Linux and using Python fitting libraries. The fitting speed and accuracy can be improved by having an a priori knowledge of the target ydistance (i.e., knowing the lane) and/or the car speed. For achieving this, distance calculation from axial gradiometer reading [17] or speed measurement with magnetic sensor [18] could be used. Also, improved detection of the passing cars can be facilitated with a shortbaseline gradiometer placed as close to the street as possible, which also results in a better approximation of the gradient by the calculated field difference. As for the problem with two cars passing in adjacent lanes, it could be possibly solved by employing a second order model with two car trajectories and vector summation of the magnetic signature; for detection of this situation could symmetrically deploy two shortbaselines along the street and observe their output in time.
We again emphasize that this method, when compared to the usual ways—disregarding or interpolating the data heavy lowpass filtering [9, 19]—allows not only to keep the true DC value but also does not destroy the “high frequency” component originating from various physical phenomena (field oscillations, solar storm onsets, etc.).
Appendix
The basic MATLAB function utilized in the optimization problem for carinduced disturbances cancelling is shown in this appendix. The fieldfit function enters the leastsquares curvefitting algorithm lsqcurvefit of the Optimization Toolbox (MATLAB 2015) with a guess of the values and lower and upper bounds, where xdata is the time vector and B_{Obs} is the vector of the observed magnetic field. The function dip2B to calculate the field from a pointlike dipolar source follows the dipolar term in equation (3); an example implementation can be accessed, e.g., in [20].

Data Availability
The geomagnetic data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare no conflict of interest.
Authors’ Contributions
Conceptualization, investigation, software, methodology, data curation, and visualization was provided by M. J.; writing was performed by M. J., M. V., and T.B.; resources and data collection were provided by M. B., M. J., M. V., and T. B.
Acknowledgments
We would like to thank the Military Geographic and Hydrometeorologic Office of the Czech Army for the possibility to work and acquire data at the Meteorologic and Seismic station Polom, including the complimentary accommodation. We would also like to thank Jaroslav Pokorný for his logistic and technical support during onsite measurements.
References
 L. W. Pedersen and L. Merenyi, “The FGE magnetometer and the Intermagnet 1 second standard,” Journal of Indian Geophysical Union, vol. 2, pp. 30–36, 2016. View at: Google Scholar
 A. Marusenkov, “Possibilities of further improvement of 1 s fluxgate variometers,” Geoscientific Instrumentation, Methods and Data Systems, vol. 6, no. 2, pp. 301–309, 2017. View at: Publisher Site  Google Scholar
 M. Janošek, V. Petrucha, and M. Vlk, “Lownoise magnetic observatory variometer with racetrack sensors,” IOP Conference Series: Materials Science and Engineering, vol. 108, article 012026, 2016. View at: Publisher Site  Google Scholar
 V. Petrucha, P. Kaspar, P. Ripka, and J. M. Merayo, “Automated system for the calibration of magnetometers,” Journal of Applied Physics, vol. 105, no. 7, article 07E704, 2009. View at: Publisher Site  Google Scholar
 N. Olsen, L. TøffnerClausen, T. J. Sabaka et al., “Calibration of the Ørsted vector magnetometer,” Earth, Planets and Space, vol. 55, no. 1, pp. 11–18, 2003. View at: Publisher Site  Google Scholar
 N. Kompein, R. Pleschberger, R. Egli, B. Leichter, and R. Leonhardt, “A comparison between Conrad Observatory and the old Wien Cobenzl observatory: insights into anthropogenic ground currents,” in Book of Abstracts  XVII IAGA Workshop on Geomagnetic Observatory Instruments, Data Acquisition and Processing, p. 83, Dourbes, Belgium, 2016. View at: Google Scholar
 “SŽDCoperation of infrastructure,” June 2018, http://provoz.szdc.cz/PORTAL/ViewArticle.aspx?oid=594598. View at: Google Scholar
 L. Laža, “Four decades of the Polom station, Vojenský geografický obzor 2014,” vol. 2, pp. 4–33, 2014, June 2018, http://www.vgo.army.cz/sites/vgo.army.cz/files/dokumenty/zakladnistranka/vgo_2014_02.pdf. View at: Google Scholar
 J. Jankowski and C. Sucksdorff, Guide for Magnetic Measurements and Observatory Practice, International association of Geomagnetism and Aeronomy, Boulder, 1996, June 2018, http://www.iagaaiga.org/data/uploads/pdf/guides/iagaguideobservatories.pdf.
 “Geomagnetic observatory of Kelčany,” June 2018, https://maglab.fel.cvut.cz/geomagnetic. View at: Google Scholar
 G. Schultz, “Geomagnetic results Wingst, 2001 Yearbook No. 47,” in Yearbook Magnetic Results 2001, 2002, 2003, H. J. Linthe, Ed., p. 59, GfZ Potsdam, 2007. View at: Google Scholar
 Y. Nishio, F. Tohyama, and N. Onishi, “The sensor temperature characteristics of a fluxgate magnetometer by a widerange temperature test for a mercury exploration satellite,” Measurement Science and Technology, vol. 18, no. 8, pp. 2721–2730, 2007. View at: Publisher Site  Google Scholar
 J. D'Errico, “Bound constrained optimization using fminsearch,” Math WorksFile Exchange, June 2018, https://www.mathworks.com/matlabcentral/fileexchange/8277fminsearchbndfminsearchcon. View at: Google Scholar
 A. Cerman, J. M. Merayo, P. Brauer, and F. Primdahl, “Selfcompensating excitation of fluxgate sensors for space magnetometers,” in 2008 IEEE Instrumentation and Measurement Technology Conference, pp. 2059–2064, Victoria, BC, Canada, May 2008. View at: Publisher Site  Google Scholar
 M. Korte, M. Mandea, H. J. Linthe, A. Hemshorn, P. Kotzé, and E. Ricaldi, “New geomagnetic field observations in the South Atlantic anomaly region,” Annals of Geophysics, vol. 52, no. 1, pp. 65–81, 2009. View at: Publisher Site  Google Scholar
 B. J. StLouis, E. A. Sauter, and R. L. Coles, “INTERMAGNET technical reference manual, version 4.6, INTERMAGNET 2012,” June 2018, http://www.intermagnet.org/publications/intermag_46.pdf. View at: Google Scholar
 M. Janošek, A. Platil, and J. Vyhnánek, “Simple estimation of dipole source zdistance with compact magnetic gradiometer,” IOP Conference Series: Materials Science and Engineering, vol. 108, no. 1, article 012025, 2016. View at: Publisher Site  Google Scholar
 V. Markevicius, D. Navikas, A. Idzkowski, A. Valinevicius, M. Zilys, and D. Andriukaitis, “Vehicle speed and length estimation using data from two anisotropic magnetoresistive (AMR) sensors,” Sensors, vol. 17, no. 8, p. 1778, 2017. View at: Publisher Site  Google Scholar
 J. J. Curto, S. Marsal, J. M. Torta, and E. Sanclement, “Removing spikes from magnetic disturbances caused by trains at Ebro Observatory,” in Proceedings of XIII IAGA workshop on geomagnetic observatory instruments, data acquisition and processing, pp. 60–66, Boulder, CO, USA, 2009, US Geological Survey Open File Report 1226. View at: Google Scholar
 University of British Columbia, “Potential fields in Earth and planetary sciences,” June 2018, https://www.eoas.ubc.ca/~malasad/EOSC450. View at: Google Scholar
Copyright
Copyright © 2018 Michal Janošek et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.