1 1

United States Department of Commerce

I 1I Technology Administration

1 i National Institute of Standards and Technology

NISTIR 3990

GRADIOMETER ANTENNAS FOR TUNNEL

DETECTION

David A. Hill

NISTIR 3990

GRADIOMETER ANTENNAS FOR TUNNEL

DETECTION

David A. Hill

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303

Sponsored by

U.S. Army Belvoir RD&E Center

Fort Belvoir, Virginia 22060

June 1 992

U.S. DEPARTMENT OF COMMERCE, Barbara Hackman Franklin, Secretary

TECHNOLOGY ADMINISTRATION, Robert M. White, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director
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CONTENTS

Page

1 . INTRODUCTION 1

2. MAGNETIC DIPOLE EXCITATION OF LONG CONDUCTORS 2

2.1 Formulation 2

2.2 Parallel Scan 5

2.3 Diagonal Scan 7

3. PLANE WAVE EXCITATION OF EMPTY CIRCULAR TUNNELS 8

3.1 Formulation 8

3.2 Scattered Field 10

3.3 Gradiometer Response 12

4. CONCLUSIONS 13

5 . ACKNOWLEDGMENTS 14

6 . REFERENCES 14

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GRADIOMETER ANTENNAS FOR TUNNEL DETECTION

David A. Hill

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, CO 80303

The use of gradiometer antennas for detection of long conductors

and detection of empty tunnels is analyzed. For reception in

vertical boreholes, the gradiometer consists of two vertical

electric or magnetic dipoles with a vertical separation. Both

sum and difference responses are useful, but the difference

response has the potential advantage of suppressing the primary

field and making the scattered field easier to detect. The

difference response is most effective in suppressing the primary

field for a parallel scan where the transmitting antenna and

receiving gradiometer are always at the same height.

Gradiometers are most advantageous at low frequencies where the

scattered field is small compared to the primary field.

Key words: cylindrical tunnel; electric dipole; electric field;

gradiometer; grounded conductor; insulated conductor; magnetic

dipole; magnetic field; plane wave.

1 . INTRODUCTION

A common problem in electromagnetic detection of tunnels or other

subsurface objects is that the scattered field is small compared to the

primary field and is therefore difficult to detect. This problem occurs for

detection of both empty tunnels and tunnels containing conductors . Several

methods have been used to attempt to suppress the primary field: (1) the use

of a large separation between transmitting and receiving antennas in the

detection of long conductors at low frequencies [1,2], (2) the use of a

receiving antenna that is polarized orthogonally to the primary field [3,4],

and (3) the use of a gradiometer receiving antenna [5].

This report will consider only the gradiometer method. Stolarczyk [5]

has performed low frequency measurements with a gradiometer antenna, and the

suppression of the primary field was encouraging. In this report, the

theoretical basis of the gradiometer method will be studied. Section 2

covers the application of the method to tunnels containing long conductors.

1
and Section 3 covers the application of the method to empty (air- filled)

tunnels

2. MAGNETIC DIPOLE EXCITATION OF LONG CONDUCTORS

2.1 Formulation

The geometry for excitation of a long conductor by a vertical magnetic

dipole is shown in figure 1. An infinitely long conductor of outer radius b

is centered on the z axis. A transmitting vertical (y-directed) magnetic

dipole of magnetic moment lA is located at (x^, y^, z^) . A gradiometer

receiving antenna is centered at (x, y, z) and will be described

mathematically in eqs (6) and (7). The earth has permittivity e, conductivity a, and free -space magnetic permeability /i^. We assume that the

magnetic dipole source and the conductor are located at a sufficient depth

that the air-earth interface can be neglected.

A vertical magnetic dipole antenna is well suited to detection of

horizontal conductors in tunnels because it radiates a horizontal electric

field which will excite axial currents in horizontal conductors. A

practical vertical magnetic dipole that will fit in boreholes has been

constructed using a solenoidal winding on a ferrite core [5]. The

gradiometer receiving antenna can be constructed using a pair of such

antennas

The electric and magnetic fields can be derived in terms of a ydirected magnetic Hertz vector, and the derivation is given in [1]. For a vertical magnetic gradiometer receiving antenna, only the vertical magnetic

field is required. It can be written as the sum of the primary field

Q due to the dipole and the secondary field due to the conductor:

H - + h"". (1)

y y y

2
The primary field is given by [1]

-jkr

H

d lA e

47rr

2 {k^[l

(y-y^) jkr^ + 1 3(y-y^)

•] + 1 ]}. ( 2 )

where k = and r^ = [(x-x^)^ + (y-y^)^ +

The time dependence is exp(jwt) , In general all terms in eq (2) need to be

retained.

The secondary magnetic field due to the conductor is [1]

GO “v “ ^

/ 1(A) vK^(vp) dA,

^ ^ -00 (3)

, , 2 ^ 2 , 1/2 ,,2 , 2 , 1/2 where p-(x +y) ,v-(A -k) , and

A Bessel function of the second kind [6]. 1(A)

the conductor current and is given by [1]

is the first-order modified

is the spatial transform of

1(A) - lA

27T

(4)

where p . - (x, + y.) , D(A) = K. (vb) + —^ ^ Z (A), and Z (A) is the

aU a d U 2 s s V

axial impedance (series impedance per unit length) of the conductor.

A good model for a conductor in a tunnel is shown in figure 2. It

consists of a metal cylinder of radius a surrounded by an insulating region

of outer radius b. The metal has conductivity and magnetic permeabi lity

and the insulation has permittivity and free -space permeabi lity Mq.

The axial impedance of this model is [1]

3
Z (A) ( 5 ) - Z

s m 2?rjct)€ ^ in(b/a)

,

where Z

m

^ jcj/i 1/2 I^(jk a)

1 . m . 0 m

27ra ^ a 1 (jk a) ’

III i III

jk

in (jw/i a ) m m

1/2

k.

1

1/2

and Iq and are modified Bessel functions of the first kind [6]. If we

set b = a, then Z (A) = Z , and we have a grounded metal conductor (such as

s m

a rail in a tunnel). If we set equal to the free-space permittivity

then we can model a conductor (such as a power line) suspended in an airfilled tunnel at a distance b - a from the tunnel wall.

When magnetic field reception is with a pair of magnetic dipole

antennas as in figure 1, two outputs (sum and difference) are possible, and

Stolarczyk [5] has recorded both as a function of height y. The sum output

is proportional to the sum of the vertical magnetic field at the two

dipole heights:

H (y) - H (y + s/2) + H (y - s/2). (6)

In eq (6)

,

we show only the y dependence because both terms are a function

of the same x and z coordinates. In a vertical borehole scan, only the y

coordinate is varied while x and z are held constant. In a similar manner,

the difference output is proportional the difference of the vertical

magnetic field at the two dipole heights:

If s is small, then H is given approximately by

4
Hy^(y) « s y

• VH(y), ( 8 )

where

A

y is a unit vector. Thus is proportional to the y component of

the gradient of the magnetic field when s is small, and the pair of magnetic

dipoles in the difference mode is called a gradiometer. Under the same

condition, Hy^ is given approximately by twice the value of Hy(y)

:

Hyj,(y) = 2 Hy(y). (9)

For the cases discussed in the following sections, s is not necessarily

small, and eqs (6) and (7) are used to generate the numerical results.

2.2 Parallel Scan

In a parallel scan, the source dipole and receiving gradiometer are

moved vertically together, and the heights are equal (y =>= y^)

•

The

advantage of this geometry is that the primary field is cancelled in the

difference mode of the gradiometer, and H reduces to

Hy^(y) - [Hy(y + s/2) - H^(y - s/2)] (10)

Thus the gradiometer in the difference mode responds only to the field

scattered by the conductor. In the sum mode, the primary field components

add to produce the following result for H :

Hyj,(y) - (2 H^(y + s/2) + H^(y + s/2) + H°(y - s/2)]

y^-y

( 11 )

If the

then H

primary dipole field Hy dominates the secondary conductor field H

is nearly independent of y.

cy’

5
A computer program was written to evaluate and from eqs (D-

(5), (10), and (11). The X integration in (3) was evaluated by FFT, In all

of the numerical results, we use the following values for the source,

2

conductor, and earth parameters: lA = 1 A»m , = 0, a = 0,5 cm,

o = 5.7 X 10^ S/m, n - 1, €./e^ = 1, e/e^ = 10, and a = 5 x 10 ^ S/m.

m m' 0 0 0

'

In figures 3 and 4, the magnitudes of and are shown as a

function of y for a conductor midway between the two boreholes (x = -x^ = 15

m and z = 0) . The insulation radius b is set equal to a to model a grounded

conductor. In figure 3, the gradiometer separation parameter s is varied

from 2 to 20 m. The sum response is only weakly dependent on s, but the

difference response has a higher peak value for larger values of s. However, further calculations for values of s larger than 20 m showed a decline in peak value. A perfect null is obtained at y

= 0 , and this null

should be easier to detect than the small dip in the sum response. In

figure 4, the responses are shown for various frequencies. A frequency of 1

MHz is too high because of increased attenuation in the rock, and a frequency of 10 kHz is too low because of reduced scattering from the

conductor. A frequency on the order of 100 kHz is probably optimum for the

typical distances involved (30 m borehole separation).

In figure 5, the 30 m borehole separation is maintained, but the

conductor passes closer to the source and receiver (x = -x^ = 9 m and z = 24

m) . The scattered field is larger, and even the sum response shows a significant dip at y

— 0. In figure 6, both the source and receiver are

located on the same side of the conductor (x, = -40 m, x = -10 m, and

a

z = 0) . Here the scattered field is weaker, particularly at 1 MHz, because

of the increased attenuation between the source and the conductor.

In figure 7, the effect of the insulation radius b is shown. The

scattered field is weaker for larger values of b because the current induced

on the conductor [1] is smaller than for the grounded case (b = a) shown in

figure 3. However the difference response still has its characteristic null

at y

- 0.

6
Another quantity of interest is the phase of either or [5].

Figure 8 shows phase results for the same parameters as in figure 3. The

phase of is nearly constant versus y, but the phase of has a 180°

jump at y

- 0, the location of the null. This rapid phase shift is another

possible indicator of the conductor location.

2 . 3 Diagonal Scan

In a diagonal scan, the source dipole is held fixed, and the receiving

gradiometer is moved vertically in a borehole. In a full tomography scan

[7,8], this procedure would be repeated for a full range of source heights.

In a diagonal scan, the primary field is not completely nulled out, and the

general expressions, eqs (6) and (7), are used to calculate and

In figure 9, magnitude results for a diagonal scan (y^ = 30 m) are

shown. Because the dominant primary field is not nulled out, the conductor

response does not show up clearly in either or A weak, displaced

null does appear in for the case where the conductor is located closer

to the receiving gradiometer (x - 5 m) . The phase for this same case is

shown in figure 10, and the rapid 180° jump that appeared in figure 8 is

reduced and shifted.

For an insulated conductor where the induced current does not attenuate

rapidly [1]

,

the total field is dominated by the scattered field for large

z. Here the gradiometer can still produce a good null as shown in figure 11

because the primary field is strongly reduced by attenuation in the rock.

The null is deeper at z - 200 m than at 100 m. The conductor can also be

detected by the maximum in H but the null in H , is sharper. yS yA

7
3. PLANE WAVE EXCITATION OF EMPTY CIRCULAR TUNNELS

3.1 Formulation

In this section, we consider a circular tunnel model as shown in figure

12. The tunnel of radius a (not to be confused with conductor radius a of

section 2) is air filled with permittivity and permeability . As in

the previous section, the surrounding rock has permittivity e, conductivity

a, and permeability

For detection of air-filled tunnels, both polarizations are of

interest. For simplicity we consider a plane-wave source rather than a vertical magnetic or electric dipole. The incident plane wave is

propagating in the x direction and has either E^ or polarization:

E^ - Eq exp(-jkx) or exp(-jkx). (12)

The total fields for the two polarizations are the sum of the incident and

and scattered fields:

E = E^ -h E® or H - . (13)

z z z z z z

The scattered field for E^ polarization is [9-11]

E^ - E^ S € (-1)“ a H^^\kp) cos(m«^),

z 0 m-0^m *^ mm

where a

m

k^J'(k^a)J (ka) - kJ (k^a)J'(ka)

0 m 0 m m 0 m

k-J'(k-a)Hf^\ka) - kJ„(kf,)H^^^'(ka)

U m U m m U m

€ m

1 , m - 0

2 , m # 0

^0

1/2

(14)

8
is the

( 2 ) k is given by eq (2)

,

is the mth-order Bessel Function, and

mth order Hankel function of the second kind [5]. The scattered field for

H polarization is

z

GO2 e (-j)“ b H^^\kp) cos(m<^), (15)

m-0

kJ'(k^a)J (ka) - k^J (k^a)J'(ka)

m 0 m 0 ra 0 m where b — — . kJ' (k a)Hy^ka) - k J (k )H^^'(ka)

m U m u m U m

For reception in boreholes, we are interested in the vertical (ydirected) components of the fields. The y components can be obtained from

the z components from Maxwell's curl equations. For polarization, the

component is given by

H

y jw/iQ 3x ( 16 )

For H polarization, the E component is given by

z y

T 3H

E - — T”^. (17)

y a + jw€ 5x

By substituting eqs (12) -(15) into eqs (16) and (17) and carrying out

the differentiation, we can obtain explicit expressions for and E^.

Convenient normalizations for numerical results are

Eq and Hq - 1/r; , (18)

1/2 where ry - [/^^/(a + jw€)] '

.

9
Then the incident fields are the same for the two polarizations, and H and

y

E can be written

y

H

y

) =

H

e-Jkx ^ , y

y

y where ’

} E®

y

00 a

1 ^ / /5\^r ^ ^ i.n<^ ^(2),. , , . . ^ ^ I IK-D sin(mp) m p m

m=0 m

+ k cos<^ H^^^'(kp) cos(m<^)]

m

(19)

( 20 )

Thus, the only difference between the two polarizations is in the scattering

s s coefficient: a is associated with H and b is associated with E . A

m y m y

computer program was written to handle both polarizations simultaneously.

Convergence of the m summation in eq (20) is fairly rapid so long as |k|a is

not too large.

3.2 Scattered Field

Before performing a numerical evaluation of the scattered fields, it is

useful to examine the low frequency behavior. When k^a and |k|a are small,

the Bessel functions in a^ and b^ can be replaced by their small argument

expansions [6]

For E polarization, the leading scattering coefficient is

z

^0 = (JV4) (k^ - k^)a^ (21)

3 Then the leading term in is

10
Hy = -(<f/4) (k^ (22) - kQ>a^ cos<f, H^^^'(kp).

2 2 2

The (k - hQ)a dependence in eq (22) indicates that the scattering from an

electrically small, empty tunnel is very weak. This is quite different from

E scattering from an electrically small, highly conducting cylinder where

z the scattering is strong [12]

.

For scattering, the leading scattering coefficient is

» (j<r/4) (k^ - kg)a^, (23)

s which is equal to a^ in eq (21)

.

The leading term in is

2

Ey » (jir/2) (k^ - kg)a^ H^^^kp) + cos^^ H^^^’Ckp)]. (24)

The computer program was found to agree with eqs (22) and (24) for

sufficiently low frequencies.

For all of the numerical results for the empty tunnel, we choose the

-3

following parameters: a - 1 m, a - 5 x 10 S/m. In figure

13, we show the magnitudes of the y components of the total fields as a

function of y at x - 5 m. At 10 MHz, the scattered field is weak, and the

total field is nearly constant at the incident field value of exp(-jkx). At

50 MHz, the circumference of the tunnel is approximately equal to a freespace wavelength, and the scattering is fairly strong. The two dips in the

total field (for both polarizations) have been discussed by other authors

[9,13] in tunnel detection applications. Further calculations show strong

scattering for most frequencies above 50 MHz, but weak scattering for

frequencies below about 20 MHz.

Calculations for larger values of x show weaker scattered fields and

more nearly constant total fields. This model is not well suited to

analyzing the far -field (large x) behavior of the total field because the

11
plane-wave incident field has no spreading loss while the scattered field

has inverse square root distance spreading loss. A better model for

examining the far- field behavior would have either a line source or a dipole

source. In these cases the incident field and scattered field would have

the same spreading loss.

3.3 Gradiometer Response

Since the field scattered from an empty tunnel at low frequencies is

weak compared to the primary field, we again examine the possibility of

using a gradiometer receiving antenna to suppress the primary field. For

polarization, is the vertical field component that can be received most

easily in a borehole. The gradiometer antenna for this case has already

been described in section 2, and the sum and difference responses are

proportional to and as given in eqs (6) and (7).

For polarization, is the vertical component that can be received

in a vertical borehole. In this case the two receiving antennas shown in

figure 12 are vertical electric dipoles. The sum and difference responses

are proportional to and E^^ which are given by

EyjCy) - E^(y + s/2) + E^(y - s/2) (25)

and Ey^(y) - E^(y + s/2) - E^(y - s/2). (26)

In figures 14 and 15, we show the gradiometer responses at 10 MHz for s * 2 m and 5 m. In both cases the sum response shows little variation with

y, but the difference response shows the characteristic null at y

= 0. The

peak values are greater for s - 5 m. Also, the H polarization (vertical

z E^) produces a stronger scattered field and difference response. This is

consistent with scattered field calculations by others.

Figure 16 shows gradiometer responses at 50 MHz. Here the scattered

field is strong enough that both the sum and difference responses show

12
enough y variation to indicate the tunnel height. For such cases with

strong scattering, it is not clear whether the gradiometer provides a significant advantage over a single dipole antenna.

Figure 17 shows gradiometer responses for the case where the receiving

antennas are located on the lit side of the tunnel (x = -5 m) rather than on

the shadow side. Here the scattered field is reduced, the difference

response is reduced, and the sum response shows almost no y variation.

4. CONCLUSIONS

The results presented in sections 2 and 3 indicate that a gradiometer

receiving antenna is useful in suppressing the primary field and allowing

the field scattered by an empty tunnel or a conductor in a tunnel to be

observed in the absence of the primary field. The typical gradiometer

response has a null at the height of the tunnel due to symmetry and

symmetrical peaks above and below. These features occur most prominently

with a parallel scan, rather than with a diagonal scan where the primary

field is not completely nulled out.

The best frequencies for detection of long conductors are in the

vicinity of 100 kHz, and this is unchanged from earlier results with single

dipole receivers [1,2]. The spacing between the two vertical dipole

receivers that form the gradiometer is not critical, but too small a spacing

reduces the received difference to too low a level. Too large a spacing

broadens the distance between the two peaks and degrades the vertical

resolution. Spacings on the order of 2 to 10 m yield good results.

For detection of empty tunnels, either vertical or horizontal

polarization can be used. Thus the source and gradiometer can use either

vertical electric or vertical magnetic dipoles in boreholes. Stronger

scattering is obtained for vertical polarization using vertical electric

dipoles. Frequencies of 50 MHz or higher yield strong scattering that

should be detectable with either a single antenna or a gradiometer. When

strong scattering is obtained, it is not as clear whether a gradiometer

receiver has a significant advantage over a single dipole receiver.

However, there is always some advantage because the sum response is

13
approximately the same as the response of a single dipole and the difference

response provides additional information. If lower frequencies on the order

of 10 MHz are used, gradiometers are useful in suppressing the primary field

and allowing the weak scattered field to be detected. Normally the reason

for using lower frequencies is to increase range.

Further study of several issues involving gradiometer antennas would be

useful. The idealized theoretical scans for gradiometers show a perfect

null with symmetrical peaks above and below, but preliminary measurements

[5] do not show such deep nulls. Models with less symmetry, such as

noncircular tunnels [14] or tunnels with multiple conductors, could be

studied to determine asymmetry effects on gradiometers. Imperfect alignment

and spacings of the gradiometer dipoles could degrade the null, and these

effects could be studied. We assumed a plane -wave source in the empty

tunnel analysis, but a more realistic source (such as a vertical dipole)

would be useful in predicting the proper field decay with distance. Earth

layering or inhomogenieties could also be studied to obtain an estimate of

the effects of geologic noise [15-18] on gradiometer response. The

gradiometers studied here utilize the vertical variation of the vertical

field component, but other variations and field components could also be

useful in improving the ratio of the received scattered field to primary

field if other receiving geometries could be employed in boreholes.

5 . ACKNOWLEDGMENTS

This research was supported by the U.S. Army Belvoir RD&E Center. I thank Larry Stolarczyk for helpful discussions.

6 . REFERENCES

[1] Hill, D.A. Magnetic dipole excitation of a long conductor in a lossy

medium. IEEE Trans. Geosci. Rem. Sens., GE-26: 720-725; 1988.

[2] Hill, D.A. Magnetic dipole excitation of an insulated conductor of

finite length. IEEE Trans. Geosci. Rem. Sens., GE-28: 289-294; 1990.

14
[3] Bollen, R.L. Tunnel detection by low-frequency magnetic - field

emissions and the controlled source audio magneto telluric techniques.

SRI International: January 1989.

[4] Hill, D.A. Near-field and far-field excitation of a long conductor in

a lossy medium. Nat. Inst. Stand. Tech. (U.S.) NISTIR 3954; 1990.

[5] Stolarczyk, L.G. Evaluation of RIM system II instruments, data

acquisition methods, and data processing algorithms for detection of

shallow and deeply buried tunnels with and without electrical

conductors. Stolar Inc.: May 1991.

[6] Abramowitz, M. ; Stegun, I. A. Handbook of Mathematical Functions with

Formulas, Graphs, and Mathematical Tables. Nat. Bur. Stand. (U.S.) AMS

55; 1964.

[7] Shope , S.; Greenfield, R.J. Electromagnetic cross-hole tomography for

tunnel detection. Third Technical Symposium on Tunnel Detection.

Golden, CO: January 12-15, 1988.

[8] Frank, M.S.; Balanis ; C.A. Electromagnetic tomography in tunnel

detection. Third Technical Symposium on Tunnel Detection. Golden, CO:

January 12-15, 1988.

[9] Lee, T.K.

;

Kim, S.Y.; Ra, J.W. Resonant scattering of cw

electromagnetic wave by an underground tunnel of circular crosssection. Third Technical Symposium on Tunnel Detection. Golden, CO:

January 12-15, 1988.

[10] Jones, D.S. The Theory of Electromagnetism. Oxford: Pergamon Press,

1964.

[11] Van de Hulst, H.C. Light Scattering by Small Particles. New York:

Wiley; 1957.

[12] Harrington, R.F. Time-Harmonic Electromagnetic Fields. New York:

McGraw-Hill; 1961.

[13] Lee, T.K.

;

Park, S.O.; Ra, J.W. Near-field diffraction pattern by an

underground void of circular cylinder. Microwave Opt. Tech. Let., 2:

179-183; 1989.

[14] Lytle, R.J.; Laine, E.F.; Lager, D.L.; Davis, D.T. Cross -borehole

electromagnetic probing to locate high-contrast anomalies. Geophys .

,

44: 1667-1676; 1979.

[15] Hill, D.A.

;

Wait, J.R. Theoretical noise and propagation models for

through- the -earth communication. National Telecommunications and

Information Administration; May 1992.

[16] Eaton, P.A.; Hohmann, G.W. An evaluation of electromagnetic methods in

the presence of geologic noise. Geophys., 52: 1106-1126; 1987.

15
[17] Greenfield, R. Borehole radar clutter. National Radio Science

Meeting: Boulder, CO; January 4-6, 1989.

[18] Hill, D.A. Clutter models for subsurface electromagnetic applications.

Nat. Inst. Stand. Tech. (U.S.) NISTIR 89-3909; 1989.

16
gradiometer

Figure 1. Geometry for an infinitely long conductor excited by a vertical

magnetic dipole. The gradiometer receiver consists of two

vertical magnetic dipoles separated by a distance s.

17
y

Figure 2. Geometry for an insulated conductor.

18
Vertical Magnetic Field (juA/m)

Figure 3. Magnitude of magnetic field gradiometer responses for different values of dipole separation s.

19
Vertical Magnetic Field (juA/m)

Figure 4. Magnitude of magnetic field gradiometer responses for various

frequencies

20
(LU)

A

Figure 5. Magnitude of magnetic field gradiometer responses for conductor

closer to dipole source and gradiometer.

21
Vertical Magnetic Field (^A/m)

Figure 6. Magnitude of magnetic field gradiometer responses for dipole

source and gradiometer on the same side of conductor.

22
Vertical Magnetic Field (juA/m)

Figure 7. Magnitude of magnetic field gradiometer responses for various

values of insulation radius b.

23
Figure 8. Phase of magnetic field gradiometer responses.

24
Figure 9. Magnitude of magnetic field gradiometer responses for a diagonal

scan.

25
Figure 10. Phase of magnetic field gradiometer responses for a diagonal

scan.

26
Vertical Magnetic Field (juA/m)

Figure 11. Magnitude of magnetic field gradiometer responses for large z.

27
y

Figure 12. Geometry for a plane wave incident on an empty, circular tunnel.

The gradiometer consists of two vertical electric or magnetic

dipoles

28
E

Figure 13. Field magnitudes on the shadow side of an empty tunnel.

29
Gradiometer Response

Figure 14. Magnitude of gradiometer responses on the shadow side of an

empty tunnel at 10 MHz

30
E

>%

Gradiometer Response

Figure 15. Magnitude of gradiometer responses on the shadow side of an

empty tunnel for a larger dipole separation s

.

31
Gradiometer Response

Figure 16. Magnitude of gradiometer responses on the shadow side of an

empty tunnel at 50 MHz

32
Gradiometer Response

Figure 17. Magnitude of gradiometer responses on the lit side of an empty

tunnel at 50 MHz

.

33
f
BL-114A

(5-90)

ADMAN 15.01

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBUCATION OR REPORT NUMBER

NISTIR 3990

T. PERFORMING OR(jANIZATION REPORT NUMBI

B92-0173

3. PUBUCATION DATE

JUNE 1992

4. TITLE AND SUBTITLE

Gradiometer Antennas for Tunnel Detection

5. AUTHOR(S)

David A. Hill

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BOULDER, COLORADO 80303-3328

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

10. SUPPLEMENTARY NOTES

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBUOGRAPHY Of

UTERATURE SURVEY, MENTION IT HERE.)

The use of gradiometer antennas for detection of long conductors

and detection of empty tunnels is analyzed. For reception in

vertical boreholes, the gradiometer consists of two vertical

electric or magnetic dipoles with a vertical separation. Both

sum and difference responses are useful, but the difference

response has the potential advantage of suppressing the primary

field and making the scattered field easier to detect. The

difference response is most effective in suppressing the primary

field for a parallel scan where the transmitting antenna and

receiving gradiometer are always at the same height.

Gradiometers are most advantageous at low frequencies where the

scattered field is small compared to the primary field.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITAUZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

cylindrical tunnel; electric dipole; electric field; gradiometer; grounded conductor,

insulated conductor; magnetic dipole; magnetic field; plane wave

13. AVAJLABIUTY 14. NUMBER OF PRINTED PAGES

X UNUMITED 37

FOR OFnClAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS).

4 15. PRICE

ORDER FROM SUPERINTENDENT OF DOCUMENTS. U.S. GOVERNMENT PRINTING OFFICE,

WASHINGTON, DC 20402. AO 3

X ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGHELD, VA 22161. ELECTRONIC FORM
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