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Theodolite-borne Vector Overhauser Magnetometer: DIMOVER Sapunov V 1*, Denisov A 1, Saveliev D 1, Kiselev S 1, Denisova O 1, Podmogov Y 2 Khomutov S 3, Rasson J 4 1 Quantum Magnetometry Laboratory of USTU, Mira str., 19, Ekaterinburg, 620002, Russia 2 Amakinsky Expedition, ALROSA Ltd., Saha, Mirnisky region, Ajhal, Judgnaja str., 12, 678190, Russia 3 Geophysical Observatory "Klyuchi", Koptyug av., 3, Novosibirsk 630090, Russia 4 Institut Royal Meteorologique, Centre de Physique du Globe B-5670 Dourbes Viroinval, Belgique sva@dpt.ustu.ru (Vladimir Sapunov) Abstract

This report covers results of the uncompleted long-term research directed at developing an absolute vector proton magnetometer based on the switching of bias magnetic fields. The distinctive feature is the attempt of the installation of a miniature Overhauser sensor and optimized Garret solenoid directly on the telescope of the theodolite that, in our opinion, will allow this design (Declination Inclination Modulus Overhauser magnetometer: DIMOVER) to be comparable and even better to the universally recognised DIflux device. Preliminary results, which also can be interesting to the experts in vector proton magnetometers, are presented.

1. Brief review of modern proton component magnetometers

The vector proton magnetometers were developed practically simultaneously with the availability of the method of nuclear magnetic resonance and are know since about 60 years. The basic drawback of this type of magnetometers was the significant size of the magnetic systems (up to one meter), that is caused by the high requirements for low gradient of the bias fields and the significant sizes of the proton sensors. Figure 1(a) shows an example of such system.

In recent years, the development of proton vector magnetometers achieved essential progress due to the based on application of the Overhauser effect that provide stronger proton signal from smaller sensor size. This allows to reduce dimensions of the bias systems and as consequence, allows to improve the sensitivity of measurements. The greatest successes in design and introduction in observatories practice have been achieved by in joint project of GEM Systems Inc., Eotvos Lorand Institute, and Mingeo. The Figure 1(b) shows bias system (9 rings on sphere 30 cm), and one of its co-authors L. Hegymegi.

Zhirov G. and Pack V. made the similar development in Kazakhstan and Russia in 1993 on the basis of the Braunbeck coil (magnetometer MK-2, size of magnetic system 28 cm.) with the use of the Overhauser sensor OS-2 developed by Quantum Magnetometry Laboratory of USTU. This system was successfully installed and tested during the 1994 Observatory Workshop in Dourbes (Figure 1, c).

Figure 1. Examples of the bias magnetic systems for proton and Overhauser dIdD magnetometers

a b c

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The Overhauser vector magnetometers are used for stable registration of the variations of the components and modulus of the Earth's magnetic field. One of the basic problems is the stability of installation of the magnetic system on the pillar in the observatory or the support in field conditions, which can cause baseline drifts. To solve this task, taking into account of small size of the Overhauser vector systems, GEM System has applied a proven way of vertical suspension. The device is shown in the Figure 2(a). Size of spherical magnetic system is 20 cm, 12 perpendicular rings (development of the Budapest Geophysics Institute). The drift is claimed to be below 0.1 nT/°C and a long term stability of the geomagnetic component measurement less than 1 nT/year at sensitivity up to 0.01 nT is announced.

Figure 2. Designs of the vector scalar magnetometers (a – suspended dIdD Overhauser GEM magnetometer, b – theodolite-borne proton MAGSON magnetometer, c – DIMOVER of QMLab)

The general property of the above-mentioned devices is that they are variometers of the geomagnetic

field angles (dIdD). Presently, the measurement of the absolute values of the field vector or angles I and D is carried out the only by the "DIflux" method that is used in almost all observatories together with a separate proton magnetometer.

Some years ago the firm MAGSON has made a development, which tries to unite the advantages of the DIflux method and proton vector magnetometer (Figure 2(b) shows this device). The Garret solenoid and proton sensor is mounted directly on the frame of a nonmagnetic theodolite.

We analyzed this design and it has been discussed with the designers of the Russian theodolites. They have explained that the prisms, which provide measurement of azimuth and vertical angles, are mounted directly in the telescope and that we can benefit from the special systems of self-compensation, in particular of vertical angle index. Thus it is desirable to mount our sensor (Overhauser + Garret coil) directly on the telescope to meet exact the angular disposition and compensation that is actually used in the DIflux method. Addressing the problems stated in the previous paragraph, the Quantum Magnetometry Laboratory of USTU has tried to establish a bias magnetic system and Overhauser sensor directly on the telescope of a non-magnetic theodolite. The Figure 2(c) gives a view on the prototype model (The Overhauser sensor is taken from the solenoid and is shown on the foreground). The development of the given design has required the decision of a number of theoretical and experimental tasks whose results are presented in the report.

It is necessary to mention that as scalar magnetic sensors besides proton magnetometers, there is opportunity to use quantum devices based on optical orientation of atoms. In this direction there are some problems, in particular the Cesium sensors have less perspectives taking into account their higher absolute errors. Potassium sensors developed under the direction of the academician E. Alexandrov in State Optical Institute (Russia) and GEM Systems is most interesting. The given device has subpicotesla sensitivity at sampling rate up to 10 measurements per second and an absolute accuracy of the field intensity about 0.1 nT. The drawback of the Potassium sensor, which may limit its use, is the large size of the sensor, the large power consumption about 10−20 Watts and the limited long-term reliability. While the Overhauser

a b c

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magnetometers are characterized by power about 2 Ws at the smaller speed (1−6 sec) and sensitivity of 0.01 nT to 0.1 nT.

2. Method of measurement based on switched bias field and analysis of errors

To measure the components of the geomagnetic field by a proton (scalar) magnetometer a number of methods are known. We investigate below the set-up based on the switching of bias magnetic fields (cycle +I, −I, I = 0) with the measurement of resulting total field. The vector circuit for a switching method (Figure 3) and formula (1) for calculation of the field component along bias field are shown:

Figure 3. Vector circuit for a switching method

)(22 20

21

22

21

22

TTT

TTZ−+

−= . (1)

It is a well-known formula, but, unfortunately, it gives practically no real information to choose the value

and direction of the bias field. Nor does it give the effect of the selected parameters upon the resulting random and systematic measurements errors on Z. We give below such analysis.

2.1. Sensitivity or random error of the component measurement

Using standard methods of error computation in the linear approximation (error is a lot of less of measurement value), the error on the measurement Z can be expressed as:

)()()()( 22

2

21

22

10

22

0

2 TTZT

TZT

TZZ σ⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

+σ⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+σ⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

=σ . (2)

By differentiating in (1) and by substituting, we get:

320

22

21

2222

02

22

12

21222

02

22

12

10222

12

22

02

)2(8)()43()()43()()()2()(

TTTTTTTTTTTTTTTTTZ

−+σ−++σ−++σ−

=σ . (3)

Let's assume identical sensitivity for all measurements of the module field that is σ(Т0) = σ(Т2) =

σ(Т1) = σ(Т). The value of dispersion of Z component measurement will look as follows

( ))cos31()(cos)(214)()( 220

240

22 α−+α+σ=σ BTBTTZ . (4)

Figure 4 shows σ(Z)/σ(T): the deterioration of sensitivity of the Z component magnetometer in comparison with sensitivity of the scalar magnetometer. The ratio of the geomagnetic field module to value of the bias field T0/B at various angles α between them are varied. The sensitivity of measurement of components is the best at α = 0, Т0/В = 0.5 and the loss of sensitivity σ(Z)/σ(T) is 1.58. This optimum corresponds to a direction of the bias fields parallel to the Earth's magnetic field and its value should be approximately double. Unfortunately, this case is not interesting in practice, because the increase of the bias field causes an increase of its gradient that will ask too high requirements from the bias magnetic system. Also, there is a restriction on the bias field amplitude due to the dynamic range of the proton magnetometer (usually 20000−100000 nT). More interesting is the intermediate case, when the sensitivity of component measurements does not depend on the orientation of the bias magnetic field and total intensity. This bias field should be approximately 70 % of the geomagnetic field, with a factor 3 in the deterioration of sensitivity.

⎩⎨⎧ +=

−= BTTBTT

02

01α

Z

T

−B

T T

B

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Figure 4. An inevitable loss (contoured) of sensitivity when vector

measurements are made in comparison with a scalar magnetometer

2.2. Some systematic errors of the component measurement To analyze systematic errors caused by the various reasons it is convenient to express that the bias field

are B and βB. The value Z in the switching set-up in this case is:

( )20

21

22

220

221

22

)1()1(2

)1(

TTT

TTTZβ−−β−−ββ

β−−β−= . (5)

The systematic error of the measurement is defined as follows ∆Z = Z − Z0 where Z is the measured component of the field, Z0 is the true component. 2.2.1. Errors caused by "soft" and "hard" magnetisation of the module sensors

Errors caused by the "soft" magnetisation of the magnetometer sensors are defined as ∆T1 = kT1, ∆T2 = kT2, ∆T0 = kT0. Using the formula (5) it is possible to draw a simple but important conclusion: ∆Zk = kZ. Thus the error on a component measurement caused by the "soft" magnetisation of its absolute magnetometer sensor is fully eliminated by the calibration of the module sensor.

The error due to the hard magnetisation of the module sensor means, that the sensor has its own magnetic moment due to some internal magnetic field: T0′ = T0 + h where T0′ is a result of real measurement, T0 is a true vector without the account of a field h from a magnetic impurity. The final expression of the "hard" error will be ∆Zh = h⋅cosθ, where θ is angle between the bias field vectors B and internal field h. Thus: • The systematic error of component measurement caused by the "hard" errors of the module sensors

depends only on the mutual angle of the internal proton sensor’s "hard" field and bias field. This does not depend on orientation of Earth's magnetic field.

• This error can be determined for some orientation of the vector magnetometer with the Earth's field and then be used as a correction at any field angles D and I.This error can be even nulled for a special orientation of the proton sensors to bias field (cosθ = 0).

f 0

α π/2

T0 /B

3

2

1

π/6 π/3 0

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2.2.2. Error caused by instability of the bias field or the power source This is a technically important kind of the error since it formulates the requirements to the stability of the

magnetic bias system and source of the switched current. We assume, that the fields +В and –В differ, i.e. in the formula (5) factors β = ∆β – 1. We find the error caused by the instability of the bias field or the power source as:

( ) ( )α−∆=α−∆=∆ β22

022

0 cos)(15.0cos)(1)(5.0 BTBBTIIBZ . (6)

Let's estimate the requirements on stability for the bias field or ∆I/I in conditions close to optimum (Т0/В about 1.5, B about 30000) and setting error ∆Z ≈ 1 nT. Using formula 5 the ∆I/I will be about 10–4. Thus requirements to short-term stability of the current and bias field are engineering-executed and we have errors of 0.1–1 nT for instability 10–5–10–4. It is important to note that the long-term stability does not exert influence in the switching method in contrast to a method of the field components compensation. 2.3. Error caused by the drift of the geomagnetic field

It was revealed at experimental research of breadboard models of the Overhauser vector magnetometers in laboratory conditions, which were characterized by fast changes of the geomagnetic field, that the switching method has a dynamic error. Variations of the measured component exceed the real variations. The noticed error grew at increase of speed of variations. A physical explanation is obvious enough. The basic formula for calculating the components makes the assumption of field stability. Estimations of this important kind of a dynamic error are submitted below.

To estimate the error caused by a field variation, the jump function model of a variation was simulated. Namely: at the first measurement the geomagnetic field is displaced by –∆h, in the second there is no displacement and in the third the field is displaced by ∆h. A vector proton magnetometer will calculate the Z component of field according to the basic equation (1). The error is defined as the difference between the measured and calculated component without the drift ∆h, that is ∆Z1 = Z′ – Z

[ ] [ ] BhTB

ZTTT

TTZ 00320

21

22

21

22

11

)2(22∆≤∆××=−

′−′+′

′−′=∆ hBBT . (7)

The analysis of (7) has shown that the drift error is the display of dynamic cross effect: • There is an influence (error) at the presence of variations of perpendicular components. • The error is proportional to speed of a variation to be exact is proportional to change of a field during a

cycle of measurement components (∼ the quantized time derivative of field).

Figure 5. Error caused by the drift of the geomagnetic field as result of dynamic cross effect of the proton vector magnetometers (The cycle at calculations is chosen 3 seconds)

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Figure 5 shows an example of a computer calculation of the drift error. The top figure is a simulated Z variation. The bias magnetic system is perpendicular and the measurement of H-component is made along to bias field. The variation in H direction is absent. The bottom demonstrates this error.

Some discrepancy of variation measurements by the fluxgate and the proton vector magnetometers thus should be observed. Obviously that the drift error can be excluded by some modernization of the basic formula (1) or at processing measurements taking into account speed of the components variation. 3. Breadboard model of the PC-based vector POS-1 magnetometer

The PC-based vector POS-1 magnetometer was created on the initial stage of our researches to check experimentally of the some theoretical estimation stated above. The Braunbeck coils were used as magnetic bias system (∅28 cm). The experimental research has shown the validity of the formulas presented above and of the drift error caused by fast variations in particular. Unfortunately because of volume limitation we address the readers to www.magnetometer.ru where the complete text of our poster IAGA 2004 report is submitted and where new results in this direction will also be presented.

4. Theodolite-borne vector Overhauser magnetometer

The device is based on the standard switching circuit of bias magnetic fields (cycle + J, –J, J = 0) with the measurement of resulting total field. The distinctive feature is the installation of a magnetic bias system and Overhauser sensor directly on the telescope of the theodolite. Such design provides measurement of the absolute value of a magnetic field component along the telescope optical axis with an accuracy limited potentially only by the accuracy of the theodolite, and also the total geomagnetic field.

We name the developed device and principle "DIMOVER" for "Declination Inclination Modulus Overhauser magnetometer" in analogy with the "DIFLUX" which is used presently in almost all magnetic observatories for absolute measurements together with a separate proton magnetometer.

The use of the small Overhauser sensor and optimized Garret solenoid gave the physical base for the installation of the vector sensor directly on the theodolite telescope. The usual theodolite 3T2KP of the Ural Optical & Mechanical Plant (Ekaterinburg, Russia) was demagnetized and certificated then as a DIflux magnetometer at Geophysical observatory "Klyuchi" (Novosibirsk, Russia). The Figure 2(c) gives a view on the prototype model of DIMOVER. The electronics of the standard POS-1 magnetometer is used and an additional block for the power supply of the magnetic system is added. The magnetic system is a solenoid with size ∅55×150 mm supported by a titanium pipe (the electroconductivity of titanium does not influence on polarization current switching). The internal compensating part of the Garret solenoid was optimized for the maximal time of free precession decay.

In spite of the fact that the proposed DIMOVER does not require calibration by external means, there are errors caused by the theodolite magnetic properties and with the solenoid magnetic axis discrepancy (1–3 nT depending of orientation).

It is supposed that the proposed device will find applications for geological surveys of kimberlite in complex magnetic fields connected with trap formations. There is a modification of the Z-magnetometer without theodolite, which is based on a vertically positioned solenoid so as to speed up the prospecting.

We hope that the basic application of the DIMOVER (device or its design) can be useful in magnetic observatories and field surveys because: • Co-location of the measurement of D, I and T that will allow to exclude the dT pillar correction • Only one device must be transported and powered which is important for field operations

5. Conclusion

We hope the brief review of the proton vector magnetometers is interesting and useful from the point of view of development of these devices.

We present the analysis of some random and systematic errors in the method of measuring a component by the absolute magnetometer and also the optimization of the bias field value. In particular the drift error caused by dynamic cross effect is shown.

Unfortunately, on the one hand, the presented theodolite-borne vector Overhauser magnetometer has a number of shortcomings now; namely its low speed (6–9 seconds) and low sensitivity of components measurement (up to 0.15 nT) though the total field sensitivity reaches 0.02 nT. On the other hand we hope that in this case a number of problems on the long-term stability of the measurements and the automation of the base line control can be innovatively resolved.