Fluxgate magnetometer's block diagram for one channel.
By gathering data with a magnetometer, comparable statistical information
on geomagnetic activity such as Q , K and Ak indices,
can be created. In order to calculate A and K indices, at least X (north)
and Y (east) components have to be measured. Absolute values are
not necessary, which makes things much easier. Commercial magnetometers
are very expensive, starting from about $5000, but such equipment can be
constructed with few hundred US dollars from generally available electronic
components.
There are several different kind of magnetometer types depending
on what kind of sensor they use. You may read more on them from this comprehensive
article.
The most simple "jam-jar" magnetometer utilizing liquid damped magnetic rod (compass) with Hall sensors and amplifier/integrator, can measure only the Y component, but in this case also the X component needs to be measured.
A Proton Precession Magnetometer can only measure total field strength. Though is it often used to hunt underwater objects and other magnetic anomalies, it can not measure the angle of geomagnetic field. The proton precession magnetometer is based on sensing the proton precession frequency (around 2 kHz in 50 uT field) with a coil wound on a container filled with alcohol or distilled water. The liquid is first magnetized with the coil and then the magnetizing current is cut off and the precession oscillation induced to the coil, is amplified and its frequency counted with a frequency counter. This frequency has certain mathematical relationship to the magnetic field strength and its absolute value can be known precisely to the nearest nanotesla. No other calibration, except that of the frequency counter, is needed.
The Fluxgate Magnetometer is capable to measure all the three
magnetic components and seems to be the proper equipment to monitor geomagnetic
activity. It was developed in 1930's for military naval use as a metal
detector. One fluxgate is flying out of the Solar system onboard Pioneer
11 probe. The working principle is based on detection of unlinear biasing
effect in a saturated magnetic core, as the surrounding magnetic field
intensity changes.
In order to understand how the (second harmonic) Fluxgate magnetometer
works and what difficulties are involved, construction, calibration and
data processing procedures are explained here in short form.
The main challenges to tackle are:
Fluxgate magnetometer's block diagram for one channel.
The Fluxgate magnetometer's sensor uses ferrite ring core driven beyond magnetic saturation with about 10 kHz sine wave drive current. The sensor's output coil is tuned to the second harmonic with a resonant capacitor. The surrounding (geo)magnetic field effects as a bias factor making the output signal (saturation) to become unsymmetric, reacting to variations of the external magnetic field in the axis for which it is sensitive to. This 20 kHz sensor output signal is amplified, detected, filtered, integrated and further DC amplified. The resulting output signal can be fed to a monitoring chart recorder and A/D converter for computer logging. IAGA recommends values to be sampled and stored at one minute intervals.
Typical sensitivity for FM-400 Fluxgate sensor is around 1 microvolts/nanotesla
(1 uV/nT). Since wide range of variations from a few nT to >500 nT
(or more depending on local K=9 value) have to be measured, there must
be voltage gain of 74 dB (~5000 * ). This may cause noise on the
output. The amplifier unit has to be DC coupled and this makes this magnetometer's
amplifier and sensor units prone to temperature drifts. More expensive
precision instrumentation class operational amplifiers must be employed
in the amplifiers. The semiconductors in the circuitry are more or less
prone to temp drifts. The ones causing problems, should be in sockets for
quick test with similar types from different manufacturers to sort out
which is the most stable. Also the resonant capacitors have to be of best
ones selected from a lot. The testing is done with cold spraying individual
components and observing the effects to the magnetometer's output. Resonant
capacitors can be tested with a digital capacitance meter by cooling the
tested capacitor with cold spray. Without fairly stable sensor room temperature
and temperature controlled thermally shielded enclosure on the amplifier,
the magnetometer can not function for extended periods without continuous
need for readjusting zero settings. The required temperature stability
for the amplifier unit is typically +-0.1 degrees C. Therefore a thermostat
type heater control will not work.
Calibration
with loop and DC current.
Calibration can be accomplished with a 50 cm diameter one turn square loop and an adjustable 5 A DC supply with digital current metering. In the final calibrating procedure the sensors are set and aligned carefully to their correct operating position, X sensor horizontally with sense marking line to N/S direction and Y sensor horizontally to E/W direction (and Z vertically, up/down). The amplifier zero settings are adjusted one channel at a time, so that all channel's outputs are at 50% (2.5 V if the output can swing from 0 V to 5 V). The loop is placed vertically at right angle from sense mark line of a sensor to proper distance (50 cm from the near side of the loop). For X sensor the loop is located East or West from the sensor and aligned E/W. For Y, the loop is North or South and aligned N/S. While adjusting, reversing and monitoring the current on the calibration loop, the current that causes a magnetic field on the sensor which equals to K=9 value (a few amperes), the amplification (gain) for that particular channel is adjusted so, that the amplifier's output will not drop below 10%, or exceed 90%, depending on the direction of DC current in the loop. This gives the meter adequate span to measure magnetic deflections up to K index of 9.
Calibration loop's DC current values corresponding K indices 1, 2, etc.
up to 9 should be cycled through and the amplifier's output voltage deviation
from 50% should be marked in the calibration tables for each index
and each sensor. Using these calibration tables it is possible later to
convert raw data to Q- and K indices. Both sensors are calibrated one at
a time in similar way. There should be minimal effect on the X output when
Y is being calibrated and vice versa, if channel separation is good. If
this is not the case, the sensor will measure also other than the desired
magnetic component, which is not the intention. Sensor cabling (wires must
have separate shields), or amplifier design/lay-out is usually the cause
for this coupling. Indices, or raw data should be later compared to a professionally
operated magnetometer data from same area to confirm correctness of calibration.
Minor differences will occur, but this has proven to be a fair way.
The processing of raw data is not overwhelmingly complex,
if one wishes to produce (Q-,) K- and Ak indices. The idea is to compare
deviations from geomagnetically quiet day (Sr: Solar regular)(curve) and
to convert these deviation magnitudes in to indices. Only difficulty is
the quiet day curve (QDC). Without this correction the afternoon
K indices rise up to K 2 or K 3 even on the quiet days, when true K is
0. I have used monthly QDCs created from median
filtered averages from
quiet days for each month initially. However, the FMI-method offers
a nice way to do the K indices with the computer.
Curves of X and Y component on a fairly quiet day (24 h).
Traditionally the K indices have been produced manually. The major cause for the daily changes on a quiet day is the Sun, and to lesser amount the Moon and some other minor effects, we call this variation just as Solar variation. One method to produce K indices is the linear elimination, or the so called FMI-method. The values for each point in Sr are formed from hourly means. Furthermore this time window, used to calculate the means, is widened for the nighttime hours and widened even more if the conditions were disturbed.
The basic width between 06...18 LT is 1 hour. 18...21 LT and 03...06 LT is 3 hours and at night 21...03 LT 5 hours (LT=local time). For each hour and for both components (X and Y), a preliminary K index is being calculated merely from the maximum deviation, which is used to widen the window during non-quiet times by K^3.3 minutes, which in practise implies: if the preliminary K is 9, the window is broadened furthermore by some +- 24 hours, which leads to the mean value for each point of the hour for the Sr, to be calculated from the data covering about two days. The original measured value is compared to the Sr value and the difference; ABS(Sr(x)-x) or ABS(Sr(y)-y), is used to create the final value of the K index from the station's own K index look-up table. This leads to the fact that the production of K indices is dragging behind up to 24 hours and the data used in the process must cover 24 h before and after the period of calculation.
Geomagnetic storm, X and Y components. 32 hour chart showing from onset to the end of event.
The method is described in 'Computer Production of K indices Based on Linear Elimination', Sucksdorff, Pirjola, Häkkinen, Geophysical Transactions 1991, Vol. 36. No. 3-4. pp. 333-345. C language source code is available on request from FMI/GEO, but coding it by the description is not an overwhelmingly diffult task.
There is a short description on the FMI-method on the Internet on: ' Quasi Real Time Determination of K-derived Planetary Indices - 1. The K Index Derivation', Berthelier & al., which also describes a modification of the FMI-method to produce near real time K indices.
Once the QDC or Sr correction table is created, algorithms for comparing deviations from QDC are fairly straightforward. The deviations can be converted using a semi logarithmic table created by Bartels, in to 15 minute Q and 3 hour K indices. The index is calculated from the more disturbed component (X or Y). K indices for a single day are converted back to linear scale with another table and summed to a daily Ak index.
At this stage I would like to point out, that if the magnetometer's
output is not linear and scaling known thru the whole measuring range up
to K 9, you may either have to linearise it in the software with suitable
algorithms before using Bartels K index table, or by doing the same (if
not allready done in the calibration process) in the K-index converting
table, by not using there the real nanotesla values, but by setting the
table so, that it produces the K indices correctly by use of non-standard
units. Do not adjust the K to Ak table!
| ak, the 3 hour
max deviation (nT) |
K index |
| <5 | 0 |
| 5-10 | 1 |
| 10-20 | 2 |
| 20-40 | 3 |
| 40-70 | 4 |
| 70-120 | 5 |
| 120-200 | 6 |
| 200-330 | 7 |
| 330-500 | 8 |
| >500 | 9 |
Converting K to Ak:
| K index | Ak index |
| 0 | 0 |
| 1 | 3 |
| 2 | 7 |
| 3 | 15 |
| 4 | 27 |
| 5 | 48 |
| 6 | 80 |
| 7 | 140 |
| 8 | 240 |
| 9 | 400 |
Daily K indices (8 pcs) are converted with this table back to
linear Ak, summed and divided by 8 for a daily Ak.
The result are like this using the FMI-method:
(NOTE: No Q indices shown here)
date K index
Ak index
1-12-99 1 1 0 1 1 1 3 1
4
2-12-99 1 1 0 1 0 1 3 3
5
3-12-99 2 2 2 3 3 4 5 4 19
4-12-99 3 2 2 4 5 6 5 3 31
5-12-99 3 2 3 3 2 3 3 2 12
6-12-99 2 4 2 2 4 3 3 2 14
7-12-99 3 2 2 3 2 3 3 3 12
8-12-99 2 2 2 2 1 3 3 3 10
9-12-99 3 3 1 2 2 2 3 3 11
10-12-99 1 1 0 1 2 3 3 2 7
11-12-99 1 1 2 1 3 2 1 0 5
12-12-99 1 2 1 1 1 3 4 3 10
13-12-99 3 4 3 3 3 3 1 0 13
14-12-99 0 1 1 0 0 1 1 1 2
15-12-99 0 1 0 0 1 0 1 3 3
16-12-99 2 1 1 0 1 1 1 2 4
17-12-99 1 1 1 1 0 3 2 0 4
18-12-99 0 0 0 3 0 2 2 2 5
19-12-99 0 0 0 2 2 2 1 2 4
20-12-99 0 0 0 0 1 1 1 1 2
21-12-99 0 0 1 0 0 1 0 0 1
22-12-99 0 1 0 0 0 1 0 0 1
23-12-99 0 1 0 0 1 1 1 2 2
24-12-99 1 1 2 1 1 1 1 2 4
25-12-99 1 1 2 1 3 2 1 1 6
26-12-99 0 0 0 1 0 0 0 2 1
27-12-99 3 2 1 1 2 1 2 1 6
28-12-99 1 1 1 2 2 1 3 3 7
29-12-99 3 2 1 0 0 2 1 3 6
30-12-99 1 1 0 1 1 1 6 5 18
31-12-99 5 3 2 3 4 3 4 5 25
Ak mean 8.1
As can be seen from these results, the lower K indices (0...2) are slightly fuzzy, because there are some weak man caused magnetic variations and marginal number of bits in the A/D converter. The contributions from all different noise sources can not be easily evaluated and since man made noise can not be eliminated by technical means, there is not much point in spending resources for solving the others. The indices are merely a way to describe the state of geomagnetic field numerically, by measuring local magnetic field variations caused by fluctuating electric currents in the ionosphere and ground.
Aurora in southern Finland can be seen usually as K index exceeds 4.
In Lapland there can be glows or arcs visible even with lower K indices.
The Magnetic Measurements Handbook, J. M. Janicke, Magnetic Research Press, 1994.
Application Note AN-103, J. M. Janicke, Magnetic Research, Inc.
Application Note AN-104, J. M. Janicke, Magnetic Research, Inc.
Application Note AN-108, J. M. Janicke, Magnetic Research, Inc.
1996 Designers Reference Manual, Analog Devices, Inc., 1996,