Translated to English from paper in Japanese, originally published in: Memoirs of the Kakioka
Magnetic Observatory, Vol.24, No.1, 1-13, 1990 with permission of the authors.

ON THE ACCURACY OF FLUX-GATE MAGNETOMETERS- Calibration Experiment –byKatsuharu KOIKE, Shinzaburo NAKAJIMA
and Yukihiro SHIMIZU
Received 11 October 1990; received in revised form 30 October 1990

Abstract
We examined the efficiency of the flux-gate magnetometers, MB-160 and MB-162, Shimadzu, which
we use for variation observation at the Kakioka Magnetic Observatory. We also examined our
method and the equipment for the calibration of the installed calibration apparatus in the flux-gatemagnetometer.
On the basis of examinations, we obtained the following conclusions:
1. Using our equipment for the calibration at Kakioka, which is composed of mainly one set of 3-axial
Helmholtz coil, we can calibrate the installed calibration apparatus within an accuracy of 0.1%.
2. When we use the flux-gate magnetometer with the resolution of 0.1 nT, we can extend the rangeof the observation from ±500 nT to ±600 nT with a sufficient linearity.
3. The output signal for the calibration which is generated by the installed apparatus in the flux-gatemagnetometer is stable. With the use of this installed apparatus, therefore, we are able tocalibrate the scale value during the observation.

1. Introduction
The torsion-type magnetic variometer has long
been used to measure geomagnetic variations.
Measurements taken by this variometer are recorded as
analog data. The resolution with which geomagnetic
variations are measured is about 0.5 nT, and it will drop
below 0.5 depending on the measurement accuracy ofthe variometer.
As data processing technology
advances, the torsion-type magnetic variometer isfalling into disuse, because the measurement involves
the manual work of reading measurements and keeping
them on record. The fluxgate magnetometer is now
widely used because it has a function of converting
analog output into digital output.
Besides the fluxgate magnetometer, other typesof instruments with the capability of outputting digitalvalues are used to observe geomagnetic variations:they include the optically pumped magnetometer,

Overhauser
magnetometer,
protonprecession
magnetometer, etc. For its price, the fluxgate
magnetometer excels all other magnetometers. At the
Kakioka Magnetic Observatory, the optically pumped
magnetometer is used because this observatory is astandard observatory and the performance of themagnetometer is given higher priority than the cost.
At Memanbetsu and Kanoya Observatories, the cost
efficiency is given higher priority, and therefore thefluxgate magnetometers are used.
The performance of the fluxgate magnetometerhas improved markedly in recent years. It is now
comparable with that of other magnetometers with adigital output function. A critical difference between
the fluxgate magnetometer and other magnetometerswith a digital output function is that the fluxgate
magnetometer is designed to observe components ofgeomagnetic variations, not to retain absolute values,

16

Katsuharu KOIKE, Shinzaburo NAKAJIMA, and Yukihiro SHIMIZU

while other magnetometers are designed to measure
total geomagnetic force and to retain absolute values.
If magnetometers other than the fluxgate
magnetometer are used to observe components ofgeomagnetic variations, they have a drawback withrespect to the stability of their compensating magnetic
field (the total magnetic force is separated vectoriallyto observe the components, and one set of forces iserased).
Therefore, there is no conspicuous
difference between the performance of the fluxgate
magnetometer and other magnetometers in terms oflong-term accuracy. After all, all magnetometersmust be calibrated based on observed absolute values.
The fluxgate magnetometer is generally
considered to be inferior to other magnetometers inreliability. This is associated with the measurement
principle of the fluxgate magnetometer: the fluxgate
magnetometer measures voltages proportional to theintensity of their magnetic field, while othermagnetometers measure frequencies proportional tothe intensity of their magnetic field. Because thesevoltage or frequency signals are very weak signals,
they must be subjected to various types of processing(noise removal, frequency multiplication, voltage
amplification, etc.) before they are introduced to final
measuring devices (a frequency counter and a
voltmeter). The voltage amplification factor of thefluxgate magnetometer has a direct effect on measured
values. (The frequencies in other magnetometers are
subjected to integer multiplication, and therefore
measurement errors do not occur.) This means thatwhen the fluxgate magnetometer is used,measurements can be brought close to the desired
values by changing the voltage amplification factor.
Although manufacturers do calibration work carefully
when making the fluxgate magnetometer to achieve ahigh level of measurement accuracy, the accuracy ofthe calibration work itself should be questioned if weare to discuss extremely small measured values.
With the above-mentioned drawback of thefluxgate magnetometer in mind, it should be pointed
out that variations in the values given by the fluxgate
magnetometer do not always represent real
geomagnetic variations. The performance of one
measuring instrument when observed in terms of thecloseness between the measured value and the realvalue is called "sensitivity," and a conversion constantused to bring a certain measurement closer to a realvalue is defined as a "calibrated sensitivity value."
The calibrated sensitivity value is expressed with thefollowing equations:
S = Ho ÷ Fo
H = Fo × S
where S is the calibrated sensitivity value, Ho is thereference magnetic-field variation, Fo is measurement
value by magnetometer, and H is the geomagnetic
variation.
The next chapter describes the present situationof the sensitivity and fluctuations, the accuracy of
calibrated sensitivity values, and other mattersregarding the fluxgate magnetometer.
2. Present Situation of the Sensitivity of theFluxgate MagnetometerAs various manufacturers make different fluxgate
magnetometers, it is inappropriate to discuss thefluxgate magnetometer without restricting our
discussion to specific magnetometer models. In thispaper, Models MB-160 and MB-162 made by
SHIMADZU CORPORATION are discussed.
Bothmodelshavebuilt-inreferencemagnetic-field signals to allow for easy verification of
measured value. The reference magnetic-field signal
can be generated in increments of 20 nT over therange from 20 nT to 100 nT. By operating the switch
on each model, a reference signal can be generated andsuperposed on a geomagnetic field being measured.
Specifically, a measured value changes by the size of areference magnetic field the instant the reference
magnetic field is applied or removed.
(Strictly
speaking, the change in a natural magnetic field is alsosuperposed.)
The manufacturer maintains that
because the reference signal is calibrated correctly, thesensitivity of the magnetometer can be calibrated
equally correctly.
The calibrated sensitivity value obtained byoperating the switch should always be 1.000 if both themeasuring instrument and reference signal are
calibrated correctly. In reality, however, this value is
not always 1.000. It is not a rare occurrence that adifference of about ±1% occurs with themagnetometers installed at geomagnetic observatories.
Furthermore, reports are that annual variations
deemed to be associated with sensor temperatures
were observed, and the range of variations reachednearly 0.5% (Figure 1). This indicates that either theOn the accuracy of flux-gate magnetometers

calibrated reference signal or the measurement
system or both should be questioned with respect tospecific accuracies, depending on the circumstances.
Judging from the state of distribution of repeatedly
measured values, the accuracy of a calibrated
sensitivity value obtained by operating the switch isestimated to be 0.1% to 0.5% (Figure 2). The
obtained accuracy varies depending on the number oftimes of repetitions (as far as the accuracy alone isconcerned, the larger the number of times ofrepetitions, the higher the accuracy becomes),variations of a natural magnetic field when a reference
signal is superposed (it is better to superpose areference signal when geomagnetic variations are in acalm state), the strength of the reference signal
applied (a stronger signal produces better results), andother factors. If the number of times of measurement
is increased to 10 to 20 and if the strength of thereference signal applied is increased to 100 nT (themaximum strength to which the built-in reference
signal can be set), it will be possible to achieve a levelof accuracy of about 0.1%. The sensitivity value isusually calibrated this way when steady-stateFig. 1- Calibration Experiment -observations are to be made.
Considering the 1% difference in the previously
mentioned calibrated value relative to the 0.1%
accuracy, the 1% difference is not negligible at all,because it is too large a measurement error. On thecontrary, the 1% difference has a considerable effecton measured values. For example, because thediurnal variation of the "D" component is about 100 nT,
a measurement error of about 1 nT will be contained.
Other types of errors arising from factors related to
the fluxgate magnetometer (the resolution of
measured values, the stability of baseline values
affected by temperature and level changes, mutualinterference when three axes of a sensor do not crossat right angles, errors resulting from the conversion of
the amount of the "D" component to an angle, and soforth) have much less impact on the measurement
accuracy.
For this reason, it is necessary torecalibrate the sensitivity value of the fluxgate
magnetometer by using a reference signal other thanthe built-in reference signal of the fluxgate
magnetometer.

Change in the sensitivity of the fluxgate magnetometer (change in the output relative
to the built‑in reference signal of 100 nT)‑ Extracted from Gijutsu Hokoku, no. 85 ‑Calibrated sensitivity

Distribution of calibrated

Reference signal (large coil)Fig. 2

17

Reliability of the calibrated sensitivity value (the state of distribution of
repeatedly measured values and the strength of a reference signal)

18

Katsuharu KOIKE, Shinzaburo NAKAJIMA, and Yukihiro SHIMIZU

It is theoretically possible to measure theintensity of a geomagnetic field as is, if themeasurement range of the fluxgate magnetometer canbe extended. In this case, because the number ofeffective measurement digits of the fluxgate
magnetometer is limited, the resolution required tomeasure geomagnetic variations becomes insufficient.
In general, direct-current components are erased byadding a compensating magnetic field (the stability ofthis compensating magnetic field, which directly
affects the stability of the fluxgate magnetometer, hasrecently improved greatly, and good results can now be
obtained) so that only variations are measured. The
measurement range is determined by operating thedial indicator on the panel of the fluxgate
magnetometer. It is usually set to ±500 nT. In thismeasurement range, geomagnetic variations can bemeasured with the resolution of 0.1 nT, so that
ordinary geomagnetic variations, such as the ones that
occur during geomagnetic storms, can be measured
with sufficient margins.
One single calibrated sensitivity value is usuallyused on the assumption that the sensitivity is uniform
in the range of ±500 nT. Regarding the uniformity ofthe sensitivity inside a smaller range of ±100 nT, someexperiments were conducted using the built-in
reference signal and the results were reported. We
conducted experiments by extending the range beyond±100 nT to check the uniformity of the sensitivity. In
conducting experiments, we used the following two
methods:(1) Overall connection method: We used a set value asa mid-point and measured the sensitivity within arange of ±100 nT with a built-in reference signal.
While applying the compensating magnetic field
previously mentioned, we measured the sensitivity
values by successively moving the set point
gradually.
(2) Sensitivity measurement method: The magnetometer
was set to produce an output near zero under normal
operating conditions. In this setup, we measured
the sensitivity in the measurement range by using
an external reference signal (generated by a large
Helmholtz coil and other devices to be explainedlater).
As shown in Figure 3, the sensitivity values
obtained are linearly distributed. Figure 3 shows only
the results of an experiment conducted using one

specific magnetometer (MB-162 No. 8901) and themethod (2) mentioned above.
The same linear
tendency, however, was noted with the results of anexperiment conducted using another magnetometer(MB-162 No. 8302) and the method (1) mentioned
above. It was verified that sensitivity values are
uniform in a wide range and that the same calibrated
sensitivity value can be used as a typical, uniform
value if we want to improve the accuracy of thecalibrated sensitivity value to 0.1%.
Figure 3 shows the calibrated sensitivity values
represented as digital output values. The sametendency as observed with digital output values isnoted with analog output values.
Sensitivity values are dispersed at the central
portion (where the strength of the applied reference
signal is less than 100 nT) more than at other portions,as shown in Figure 3. This shows that the accuracyof the calibrated sensitivity values is poor. Thisdispersion is attributed to the fact that the appliedreference signals were weak, and as a result, therequired level of relative resolution for the measured
values could not be obtained. This means that if weare to obtain high-accuracy sensitivity values by using
weak reference signals, it is important to makemeasurements
repeatedly(reports
arethatmeasurement must be made repeatedly 10 to 20
times).
Calibrated sensitivity values are also shown in theregion beyond the range of ±500 nT, and they can beconsidered to be a continuation of sensitivity values in
the range of ±500 nT. This means that even if themeasurement range is set to ±500 nT, it is possible to
make measurements in the range up to ±600 nT.
The fluxgate magnetometer consists of threeparts: a sensor, a measurement system, and a cable.
Although these parts are usually used as one set, anyof these three parts can be replaced with one part ofanother compatible measuring instrument.
If afluxgate magnetometer with a part of anothercompatible measuring instrument assembled is used
to make measurements, the output values may vary by
several percent of error or up to 10% of error. As
explained earlier, the fluxgate magnetometer can
output correct measurements after being calibrated.
The manufacturer calibrates it by adjusting the coilconstant of a sensor, the supply current for sensitivity
calibration of a measurement system, the amplification

- Calibration Experiment -19

Calibrated sensitivity value

On the accuracy of flux-gate magnetometers

Reference signal
Linearity of sensitivity values of the fluxgate magnetometerfactor of voltages to be output by a sensor, etc., all as
one set. Therefore, if parts of another measuring
instrument and those of the fluxgate magnetometerare combined as one set, this set must be considered
to be a new set and it must be newly calibrated. If it
is not calibrated, the measured values are unreliable,
except for a case in which only a cable is replaced.
We conducted an experiment by replacing a 100-meter
cable with a 300-meter cable and found that there wasno significant difference between the sensitivity values
measured using the 100-meter cable and thosemeasured using the 300-meter cable. This is thought
to be due to the fact that the resistance of the cables isso small as to be negligible compared with theresistance in the measuring instrument itself. (SeeFigure 4.)
In making measurement for the long term, it isimportant to take into consideration the change in thesensitivity of the fluxgate magnetometer over time.
An example of this change in the sensitivity over timeis shown in Figure 5. As shown in Figure 5, as thetemperature of a detector or the measuring instrument
itself changes by 10 degrees, the sensitivity changes
by a maximum of 0.1% (Z component). This is asignificant change that exceeds the measurement
accuracy (about 0.05%) obtained by increasing thenumber of times that the measurement is repeatedly
made.
With regard to the D component, however, no
noticeable change in the sensitivity is observed.

Calibrated sensitivity value

Fig. 3

Cable length
Detector
Controller

Fig. 4 Calibrated sensitivity values relative to compatible
magnetometers

Considering the case of MB-160 shown in Figure
1, it would be more sensible to make the measurementby assuming that the calibrated sensitivity values dochange over time. The sensitivity changes as sensor
temperatures change, as shown in Figure 1, and thesensitivity values remain unaffected by the types ofreference signals, as shown in Figure 5. (Thesubscript "i" attached to a straight line means that thebuilt-in reference signal was used, while the subscript"o" means that an external reference signal was used.)
Therefore, it is presumed that the built-in reference
signal remains unchanged.

Katsuharu KOIKE, Shinzaburo NAKAJIMA, and Yukihiro SHIMIZU

Calibrated sensitivity value

20

Temperature of the measuring instrument
Fig. 5 Dependence of the calibrated sensitivity value on
temperatures

This assumption indicates that a built-in reference
signal calibrated using a certain method at a certain
time can be used throughout the service life of themagnetometer.
Judging from the results of two experiments(Figures 1 and 5), it is thought that the sensitivity
changes as sensor temperatures change and that thesensitivity changes at the rate of less than 0.05%/°C.
To keep the sensitivity measurement error to about
0.1%, therefore, the change in the sensor temperaturemust be kept below 2°C. If the change in the sensor
temperature exceeds 2°C, another different sensitivity
value must be applied.
3. Sensitivity Calibration Methods and Resultant
Accuracy
In the previous chapter, we discussed the present
situation of the sensitivity of the fluxgate
magnetometer, and indicated that the sensitivity must
be calibrated using appropriate calibration methods inorder to measure geomagnetic variations with a highlevel of accuracy by using the fluxgate magnetometer.
This chapter describes the sensitivity calibration
methods and resulting accuracy.
A method of calibrating the sensitivity using thebuilt-in reference signal of the fluxgate magnetometeris generally used. This is the simplest method:
applying the reference signal by pressing asensitivity-calibration push button and reading thechange in the measured value shown on themagnetometer. Because the fluxgate magnetometer
usually has a built-in reference signal of about 100 nT
and is capable of resolution up to 0.1 nT, the sensitivity
can be calibrated with a degree of accuracy as high as
0.1%. The reference signal and natural variations in
the magnetic field are superposed, causing
interference to the process in which themagnetometer produces a sensitivity value. If thisinterfering effect is strong, the degree of calibration
accuracy will drop. By making measurements when
the geomagnetic variations are in a calm state andusing mean values obtained through repeatedmeasurements, it is possible to achieve 0.1% accuracy.
One problem of this method is the reliability of thebuilt-in reference signal. That is, although it is statedin the specifications that the reference signal accuracy
is 100 nT, 100.0 nT is not necessarily a guaranteed
figure. As mentioned in the previous chapter, it
would be safer to assume that ±1% of a margin of error
is contained in the stated signal accuracy.
With the second method, geomagnetic variations
are measured using the fluxgate magnetometer, whileat the same time they are measured using a standard
measuring instrument specially designed forobservation of geomagnetic variations. Using thismethod, the reference signal used to calibratesensitivity is the value of geomagnetic variation
designated by the standard measuring instrument.
Although this method has the advantage thatsensitivity variations can be checked and calibrated bycontinuing to make measurements over a long periodof time, it has a drawback with respect to thecalibration accuracy.
If we are to achieve asatisfactory level of calibration accuracy by using thismethod, the following requirements must be met:
・Geomagnetic variations at a point where there is astandard measuring instrument must be exactly thesame as geomagnetic variations at a point where
there is a calibrating meter.
・If rapid geomagnetic variations are to be measured,
measurement must be made with exactly the sametiming.
・If slow geomagnetic variations are to be measured,
long-time stability is required.
Furthermore, the intensity of geomagnetic
variations to be measured is generally very small, andOn the accuracy of flux-gate magnetometers

the geomagnetic variation of 100 nT required toachieve the 0.1% accuracy seldom happens. To
compensate for the insufficiency in the relative
resolution due to the small amount of variation, it ispossible to increase the apparent resolution to morethan 0.1 nT by superposing similar phenomena (forexample, the amplitude of diurnal variations on theorder of some 10 nT). However, this technique does
not always produce good results.
The crucial drawback of this method is that thereference value must be provided by a standard
measuring instrument in parallel, and measurement
must be made for the long term to calibrate the correct
sensitivity values.
With the third method, a device for making an
artificial magnetic field is used together with thebuilt-in reference signal for calibration. To makeartificial magnetic fields, large Helmholtz coils andpower supplies are installed at the Kakioka Magnetic
observatory. The accuracy of an artificial magnetic
field required to calibrate the sensitivity value
correctly is determined by the coil constant and thecurrent accuracy. Although the coil constant andcurrent accuracy values are known values, we
examined and evaluated them and described theresults in this paper.
If the sensitivity of the magnetometer iscalibrated using the large Helmholtz coils, thedirection of magnetic-field measurement (sensor
direction) using the magnetometer must match theorientation of a magnetic field formed by theHelmholtz coils. Although the match accuracy should
be as high as possible, it is a waste of time to attempt
to increase the match accuracy above a certain
required level. If the orientation of a magnetic field"A" formed by the Helmholtz coils deviates from thedirection of a geomagnetic field to be measured(sensor direction of the magnetometer) by θ °, therelationship between the orientation of the magnetic
field "A" and the size of the magnetic field "B" formedin the sensor direction is expressed as follows:
B = A × cos θ
B/A directly affects the accuracy of sensitivity
calibration. Because the accuracy of calibrating thesensitivity by monitoring the state of distribution ofsensitivity values is 0.1% at best, 2° should besatisfactory as the value of θ . Factors that lead tothe occurrence of errors must be reduced to a

- Calibration Experiment -21

minimum, and therefore it is recommended that θ
should be adjusted to about 0.2°. To confirm that thedirection of magnetic-field measurement matches theorientation of the magnetic field formed by theHelmholtz coils, the amount of magnetic variations in
the orthogonal direction (Z or D when H is calibrated)must be checked by turning the current to theHelmholtz coils on and off. If a deviation of θ ° is
noted, the relationship between the size "A" of themagnetic field formed by the Helmholtz coils and thesize "C" of the magnetic field in the orthogonal
direction can be expressed as follows:
C = A × cos θTo bring θ within 0.2°, C should be less than 1.5
nT if A is 500 nT. 0.2° is a figure determined with asufficient margin, and there should be no problem even
if C is set to 15 nT, 10 times as large as 1.5 nT. This
technique of checking the sizes or intensities ofmagnetic fields assumes that the orthogonality of themagnetometer sensor is correct.
Results ofexperiments conducted in the past show that theorthogonality was on the order of a few minutes (0.1°),
which was quite satisfactory (refer to the report of
Kamii for further details). In the setup describedabove, turn the current to the Helmholtz coils on andoff and read the values given by the magnetometer.
As mentioned earlier, the relative resolution can beincreased if a larger current is supplied to theHelmholtz coils. Because the measurement range ofthe magnetometer is usually set to ±500 nT, theartificial magnetic field should be increased graduallyfrom about ±50 nT to ±500 nT, and sensitivity values
should be examined to check the uniformity while
monitoring the values given by the magnetometer. If
the intensity of the artificial magnetic field is low, therelative resolution is also low, and therefore thecalibration accuracy must be increased by making
measurements repeatedly.
We will here discuss the reference-current
accuracy and the coil-constant accuracy of a device forgenerating a reference magnetic field at eachgeomagnetic observatory.
A stabilized power supply (TYPE2852) made by
Yokogawa Electric Corporation was used to generate
the reference current. Because an indication ofcurrent instabilities was noted, another different
model (TYPE2561) made by the same company is now
used. Although both power supplies can maintain an

22

Katsuharu KOIKE, Shinzaburo NAKAJIMA, and Yukihiro SHIMIZU

Measured current/set current

accuracy of ±0.03%, they must be tested and calibrated
periodically to maintain this accuracy level. The
effective calibration period, however, has already
expired for reasons of operating conditions and costs.
It is desirable to ask the manufacturer to test andcalibrate the reference current and to obtain an official
calibration certificate. In conducting the present
experiment, however, we tried to calibrate it byourselves within the scope considered appropriate byusing measuring equipment that we owned. We used
three digital multimeters (Model TR6851 made by
Advantest).
A maximum deviation of measured
values given by these three multimeters was 0.02%,
and the mean value of all measurements made was±0.01%, which was considered to be correct. We
found that the output of the stabilized power supply(TYPE2561) was larger than the set value by 0.02%.
Considering that the measurement accuracy of thevalue of a dummy resistor used to convert current into
voltage was ±0.03%, it was thought that an appropriate
margin of error could still be maintained. Morespecifically, the current value set using the dial
indicator on the power supply unit was thought to beconstant within the range of ±0.03%. It remained
constant in the measurement range of 1 mA to 100 mA
that we used for this experiment, and no deviationfrom the range of ±0.03% was noted even if themeasurement range was changed (Figure 6). In
discussing the 0.1% accuracy with which thesensitivity value must be calibrated, the set current
value should be considered to be sufficiently reliable.
The stabilized power supply (TYPE2852) wasused for about 10 years after it was calibrated, and its
output value could not be trusted. Considerable
dispersion was noted in the range from 1 mA to 100
mA (maximum deviation: ±1%), and a considerable
difference was also noted between different set ranges.
Digital multimeter (K)Digital multimeter (G1)
Digital multimeter (G2)

range

Set current

Fig. 6 Accuracy of the current used to form a reference
range
magnetic field (type 2561)

Differences in the measured values given by
previously mentioned multimeters were also large,
indicating that the output current was unstable. It isvery regrettable that, by continuing to calibrate thesensitivity, we have continued using this power supply
with confidence until just recently.
The coil constants of the Helmholtz coils now
being used are shown in Table 1 (values adopted in thepast). They were calculated using the equations
shown in Figure 7, based on the sizes of coil frames
and the number of coil turns.
As is apparent from the equations, thecoil-constant accuracy calculated is dependent on theaccuracy of measuring the coil lengths and intervals.
Judging from how the coil lengths and intervals
entered in the test report were different, the limit of
the coil-constant accuracy was considered to be 0.1%.
It would be safer to define it as about 0.2%.
In this experiment, we determined the coilconstants using a method that was not influenced by
the accuracy of measuring the coil lengths andintervals. Specifically, we used a magnetometer set
in the center of the coil to check the variations of areference magnetic field formed by the Helmholtz
coils and the power supply system.
To check the change of the magnetic field, weused an optically pumped magnetometer (MQM-100)
made by Mitsubishi Electric Corp. The value givenby
thismagnetometerdoes
notcontainsensitivity-related errors that accompany themeasurement of variations, as previously described.
Furthermore, the correctness of the values given by
this magnetometer was verified through a comparison
with the values given by an optically pumped
magnetometer that we owned (made by NEC Corp; itis part of the KASMMER system).
The optically pumped magnetometer measures
only the intensity of a geomagnetic field (totalmagnetic force), and cannot measure only variations ofa geomagnetic field formed by the Helmholtz coils in a
specific direction. The intensity of a magnetic field
formed by the Helmholtz coils in a horizontal orvertical direction was converted to total magnetic
force, and the total magnetic force value was comparedwith actual measurements (inclination values usedwere the values that we collected during observations).
In this case, although the orientation of the Helmholtz
coils is a factor responsible for causing conversion errors,On the accuracy of flux-gate magnetometers
Table 1

- Calibration Experiment -23

Coil constants of the large Helmholtz coils

Values adopted in the past
Accuracy of above values
Measured values
Accuracy of above measured values
Difference (values adopted in the past measured values)

North-south coil(nT/mA)
11.2320.010
11.2220.001

East-west coil(nT/mA)
11.6330.010
11.6280.004

Vertical coil(nT/mA)
10.8660.010
10.8690.002+ 0.010+ 0.005- 0.003

Current: I
The numberof turns: N
Interval: 2bLength: 2a

C: Coil constant (nT/mA)
2a: Length of one side of a rectangular coil (m)2b: Interval between a pair of rectangular coils (m)N: The number of turns of the coil
Bz: Intensity (nT) of a magnetic field formed in the Z direction
I: Current supplied to the coil (mA)
C: Coil constant (nT/mA)
Fig. 7

How to calculate the coil constanterrors, there should be no problem if both horizontal
and vertical coils are tilted by less than 2°. According
to the results of experiments that Kamii et al.
conducted at a later date, the tilt was less than 10', andthis should cause no problem at all. Coil constants
calculated are shown in Table 1 (values measured inthis experiment).
The coil constant of the coil for forming ahorizontal magnetic field in the east-west direction
could not be calculated by using this method because alarge error might occur when the intensity of themagnetic field formed in the east-west direction wasconverted to total magnetic force and the required
coil-constant accuracy could not be obtained. As asolution, variations of the magnetic field formed by theHelmholtz coils were measured using the fluxgate
magnetometer.
The sensitivity of this fluxgate
magnetometer was calibrated using the coil forforming a horizontal magnetic field in the north-south
direction. Coil constants calculated this way are
shown in Table 1 (values measured in thisexperiment).
The difference between the values adopted in thepast and those measured in this experiment ranged
from 0.01 (0.1%) to - 0.003 (0.03%). It is notnecessarily a significant difference if we consider theaccuracy of values adopted in the past. However,
because the measurement accuracy is 0.05% in thisexperiment, it was thought that the values adopted in
the past should be changed.
Although concern
remains as to the calibrated reference current value(the stabilized power supply, TYPE2561, was later
calibrated by the manufacturer and 0.01 % wasachieved), we propose that the coil constants
determined in this experiment be used from now on.
If we are to calibrate the sensitivity of thefluxgate magnetometer with the accuracy of 0.1%
(sensitivity values are generally calibrated with theaccuracy of 0.1%), this level of accuracy can beachieved by applying the artificial magnetic field
formed by the Helmholtz coils and the reference
current.
There are three methods for obtaining sensitivity
values, as previously described. The good and bad
points of these three methods are summarized in Table
2.

Katsuharu KOIKE, Shinzaburo NAKAJIMA, and Yukihiro SHIMIZU

24

Table 2

Reference value
Large Helmholtz coilGood and bad points of the three sensitivity calibration methods

Good point
The reliability of the reference
value is high.

Internal calibration signal

Variations can be monitored
easily.

Geomagnetic variations

Variations can be monitored.

If we are to obtain highly accurate measured
values by making measurements for a long time using
the fluxgate magnetometer, the following methodshould be used to calibrate the sensitivity values:(1) Calibrate the built-in reference signal of themagnetometer using the large Helmholtz coils.
α = So / SI
α : Calibration coefficient of the built-in reference
signalSo : Sensitivity value of the magnetometermeasured using the large coils
SI : Sensitivity value of the magnetometermeasured using the built-in reference signal(2) While the fluxgate magnetometer is used, thesensitivity values must be checked periodicallyusing the built-in reference signal, and thesensitivity values to be adopted must be determined
and used.
S = α × SI
S: Sensitivity value to be adopted
4. Accuracy of the Fluxgate Magnetometer
The measurement accuracy of the fluxgate
magnetometer is affected most by sensitivity-related
factors, as described earlier. If the sensitivity iscalibrated using the methods described in the previous
chapter and if measured values are corrected properly,
the accuracy of values given by the fluxgate
magnetometer will be improved.
Because thesensitivity can be calibrated with the accuracy of 0.1%,
measured values can also be obtained with the samelevel of accuracy. That is, if a variation of about 100
nT occurs (this is equivalent to diurnal variation), theresolution of 0.1 nT, which is 0.1% of 100 nT, can be
maintained, and this resolution level compares with

Bad point
The state of variations that occur cannot bemonitored (measurement is impossible after setting).
The reliability of the reference value is low.
Variations of the reference signal cannot bemonitored (the reliability is low).
Geomagnetic variations must be measured using thefluxgate magnetometer, while at the same time theymust be measured using a standard measuring
instrument.
(High-reliability equipment is required.)
It takes time and labor to process data.
(A large quantity of data is required.)that of the optically pumped magnetometer, amagnetometer of the highest-level accuracy available
today. If a variation of more than 100 nT occurs (thisis equivalent to "Dst" of a geomagnetic storm, when
variation close to 1000 nT is experienced), there is thepossibility that errors on the order of about 1 nT arecontained in the measured values, and therefore theoptically pumped magnetometer still excels thefluxgate magnetometer in this regard.
Another concern is the stability of calibrated
sensitivity values. The sensitivity value can becalibrated with an accuracy higher than 0.1% under the
given conditions in which the fluxgate magnetometeris placed (under conditions in which the sensitivity iscalibrated). However, after a lapse of a certain time
length, it is unknown whether the calibrated value isstill maintained or not. Sensitivity values calibratedusing the built-in reference signal change over theyears, as previously mentioned. If this change is thechange in the sensitivity (output values ofgeomagnetic variations), not in the built-in reference
signal, there is a remedy that we can use to correct
this change. Specifically, we would like to proposethat the built-in reference signal be calibrated using
the large Helmholtz coils (the true value that allows
100 nT to be maintained constantly) and thatsensitivity values be obtained using the built-in
reference signal during measurements.
It wasreasoned from past data on the secular change incalibrated values that what changes over the years isthe sensitivity, not the reference signal. The grounds
for this reasoning are as follows:(1) The change in the sensitivity calibrated with thebuilt-in reference signal is associated with thechange in sensor temperatures. It is thoughtOn the accuracy of flux-gate magnetometers

improbable that the change in the sensitivity is
associated with the measurement system (thepower supply section that generates the built-in
reference signal is located inside this measurement
system).
(2) If what changes over the years is the reference
current, the change in the reference current should
be proportional to the change in the baseline value
because the V/I conversion circuit is used to erase
the background magnetic field. This proportional
relationship, however, cannot be observed.
(3) The sensitivity of the fluxgate magnetometer
calibrated through a comparison with values givenby the optically pumped magnetometer also changes(details are unknown due to a lack of accuracy).
This indicates that what changes over the years is
not the built-in reference signal.
(4) The change in the sensitivity cannot be explainedeven if we examine the change in the coil constantof a sensor coil. In the fluxgate magnetometer, one
single coil is used to calibrate sensitivity to erase
background magnetic fields. However, how thesensitivity changes is quite different from how thebaseline value changes. The cause of the change inthe sensitivity is not known as of this moment.
Nakajima, one of the authors of this paper, isconducting research to verify whether the
hypothesis that the built-in reference signal remains
stable is correct by comparing the values given by
the fluxgate magnetometer with those given by the
optically pumped magnetometer.
5. Summary
Although the performance of the fluxgate
magnetometer has been improved considerably inrecent years, some sensitivity-related matters are notyet resolved completely, and the fluxgate
magnetometer is still behind the optically pumped
magnetometer in performance. In this paper, we
described the sensitivity of the fluxgate magnetometer(MB-160 and MB-162 made by SHIMADZUCORPORATION), as well as the calibration methods.
The main points presented in this paper are
summarized as follows:- Calibration Experiment -25(1) The measurement accuracy based on the calibrated
sensitivity value is 0.1% at best under thecircumstances.
(2) The values given by the magnetometer are uniform
over a wide range. In the ±500-nT range, it ispossible to measure the intensity up to ±600 nT.
(3) Complete confidence should not be put in thebuilt-in reference signal.
(4) The sensitivity could be calibrated with theabsolute accuracy of 0.1% when we used the device
for forming a reference magnetic field (a large
Helmholtz coil and a power supply combined) at the
Kakioka Magnetic Observatory.
(5) Research is being conducted on the calibrated
sensitivity values. We see a good possibility of
being able to calibrate the sensitivity by using theinternal reference signal calibrated by the large
Helmholtz coils.
Acknowledgments
We would like to extend our sincere appreciation
to Mr. Kuwajima, former manager of the Engineering
Section (presently the assistant officer at the
Earthquake Prediction Information Section, theSeismological and Volcanological Department at theJapan Meteorological Agency) for his support inwriting this paper and all the staff of the Engineering
Section for their cooperation in conducting
experiments.
References
Observation Guideline: Gijutsu Hokoku special issue,
no. 26
Uwai, T. et al., Survey of the orientation of large
Helmholtz coils at the Nishidai comparison andcalibration room, Gijutsu Hokoku, no. 89 (inJapanese)
Koike, K. et al., Operating test for optically pumped
magnetometers, Gijutsu Hokoku, no. 87 (inJapanese)
Koike, K. et al., Performance of the fluxgate
magnetometer as compared with that of the
optically pumped magnetometer, Gijutsu Hokoku,
no. 85 (in Japanese)