NIST

PUBLICATIONS

A11102 ^

b 5 5 3

iniioTIR 88-3098

MAGNETOSTATIC MEASUREMENTS

FOR MINE DETECTION

Richard G. Geyer

National Institute of Standards and Technology

(formerly National Bureau of Standards)

U.S. Department of Commerce

Boulder, Colorado 80303-3328

October 1988

8-3098

.988

;.2

m

NISTIR 88-3098

MAGNETOSTATIC MEASUREMENTS

FOR MINE DETECTION

Richard G. Geyer

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

(formerly National Bureau of Standards)

Boulder, Colorado 80303-3328

October 1988

Sponsored by

U.S. Army Belvoir Research & Development Center

Fort Belvoir, Virginia 22060-5606

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

Abstract 1

1. INTRODUCTION 2

2. FACTORS AFFECTING MAGNETIC SUSCEPTIBILITY 2

3. MEASUREMENT TECHNIQUES 3

4. FREQUENCY LIMITATIONS FOR TEST MEASUREMENTS 8

5. SUSCEPTIBILITY MEASUREMENT OF U.S. ARMY BELVOIR MINE LANE

MAGNETITE- SAND MIXTURE 10

6. APPLICATION TO PASSIVE MAGNETOMETRIC DETECTION 13

6 . 1 Theory 13

6.1.1 Magnetization Vector in Same Direction as Inducing Field 13

6.1.2 Magnetization Vector in a Direction Different

from Inducing Field 17

6.2 Sensitivity Analyses 21

7. CONCLUSIONS 27

8. REFERENCES 30

iii

Magnetostatic Measurements for Mine Detection

Richard G . Geyer

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, Colorado 80303

The use of a Maxwell inductance bridge and calibration

procedure for measuring the magnetic susceptibility of magnetically linear, homogeneous, and isotropic materials are reviewed. A complication in this measurement exists since

electromagnetic induction sensors respond to the product of the

magnetic permeability and electrical conductivity. For this

reason, frequency limitations resulting from sample size and

conductivity must be considered. Such limitations can be specified by examining the in-phase and quadrature components of

the induced dipole moment of a conductive, permeable sphere

of diameter equivalent to that of the bridge test coil in a uniform alternating magnetic field and by choosing a maximum

allowable test frequency that gives an induction number much

less than 1 within the sphere.

Magnetic susceptibility measurements are applied to the

passive magnetometric detection problem of an arbitrarily shaped

susceptible (metallic) mine buried in a magnetically permeable

earth. For analysis purposes a conservative susceptibility con- trast between a typical metallic mine and host soil having the same measured magnetic characteristics as the U.S. Army Belvoir

Research and Development Center (BRDC) magnetite-sand mine lane

mixture was assumed. Anomalous detection limits were then calculated for various total field intensity (proton precession) sensor

head heights and offset distances, given mine dimensions as small

as 7.6 cm on a side.

Key words: inductance bridge, magnetic permeability, magnetic

susceptibility, magnetometric detection, magnetostatic

1
1 . INTRODUCTION

Magnetic susceptibility is a fundamental physical property of a material

medium. The degree to which a body is magnetized when placed in a magnetic

field is given by

I = k H, (1)

— “ where I is the magnetic polarization in A/m, H is the applied magnetic field

intensity in A/m and k is the susceptibility (dimensionless) relating the

applied field to the intensity of magnetization.

For a magnetically linear, isotropic substance, the constitutive equation

— relating the magnetic flux density B within a substance to the external

magnetic field H due to magnetization is expressed by the vector equation,

B = Mo (1 + k)H = (2)

where na is the permeability in vacuum (4it x 10' 7 H/m) and k is the

susceptibility given in eq (1).

2. FACTORS AFFECTING MAGNETIC SUSCEPTIBILITY

The magnetic susceptibility of soils depends on the component magnetic

minerals derived from chemical and mechanical breakdown of bedrock. Magnetic

minerals of importance are few in number, and those most commonly encountered

are the iron and titanium oxides which form several solid solution series in

rocks (fig. 1 [1]). Depending on the fractional composition of any solid

solution series, the susceptibility may vary widely (fig. 2 [2]). In addition

to specific chemical composition, the susceptibility depends on grain size and

the intensity of the magnetizing field. Thus, considerable variation in the

susceptibility of rocks (and soils) can occur. A general description of

2
typical magnetic susceptibility values for various rocks and minerals is given

in Table 1 [ 3 ]

.

Figure 1. Composition diagram of natural magnetic minerals

(after reference [1]).

3

.

MEASUREMENT TECHNIQUES

Many techniques are available for the measurement of the magnetic

properties of materials. Most techniques for determining magnetic

susceptibility involve placing the sample in a weak uniform and time -varying

source field (less than 47r x 10

" 3 A/m) which does not saturate the sample so

that the so-called initial susceptibility obtained is independent of the

magnetizing field and hysteresis effects are avoided. As Anderson [4] notes,

3
Table 1. Magnetic susceptibility of rocks and minerals (after reference [3]).

Magnetic minerals Susceptibility k/47r

Magnetite crystals 6.3 to 24.0

Magnetitie 0.04 to 2.0

Ilmenite 0.03 to 0.14

Franklinite 0.036

Pyrrho tite 0.007 to 0.028

Specularite 0.003 to 0.004

Chromite 0.002

Major rock types

Basic effusive 0.001 toi 0.004

Basic plutonics >0 . 000 1 toi <0.004

Granites and allied rocks >0 . 000 1 toi <0.001

Gneissed, schists, and slated >0.000 1 to <0.001

Sedimetaries >0.000 1 to <0.001

Specific rock types

Igneous rocks

Basalt 0.000 68 to 0.006 3 Diabase 0.000 078 to 0.004 2 Gabbro 0.000 44 to 0.004 1 Granite 0.000 03 to 0.002 7 Porphyry 0.000 023 to 0.000 5

Metamorphic rocks

Serpentine 0.000 25 to 0.014

Slate 0.000 039 to 0.003 0

Gneiss 0.000 01 to 0.002 0

Schist 0.000 026 to 0.000 24

Sedimentary Rocks

Shale 0.000 04 to 0.000 5 Clay 0.000 2 Sandstone 0.000 005 to 0.000 017

Dolomite 0.000 0009 to 0.000 014

Limestone 0.000 004

Iron ores and minerals

Siderite 0.000 1 to 0.003

Limoni te 0.000 1 to 0.000 2 Hematitie 0.000 04 to 0.000 1 Ankerite 0.000 02 to 0.000 1

4
Table 1. Magnetic susceptibility of rocks and minerals (after reference [3])

(cont . )

.

Typical sulfide minerals

Arsenopyrite 0.000 005 to 0.000 2 Chalcopyrite 0.000 005 to 0.000 2 Chromite 0.000 005 to 0.000 2

Markasite 0.000 005 to 0.000 2 Pytite 0.000 005 to 0.000 2

Diamagnetic minerals and rocks

Anhydrite and gypsum - 0 , .000 001 1 to - 0 ..000 01

Quartz - 0 ,.000 001 1 to - 0 ..000 001 2 Sylvite - 0 .000 000 9 to - 0 ..000 001 1 Calcite - 0 ..000 000 6 to - 0 ..000 001 0

Rock salt - 0 ..000 000 4 to - 0 .,000 001 3

5
SUSCEPTIBILITY

/4

(MAGNETITE) (ULVOSPINEL)

FRACTION Fe

2

Ti04

Figure 2. Susceptibility of the magnetite-ulvospinel series

(after reference [2]).

measurement techniques often involve balancing a Maxwell inductance bridge with

the sample inserted into one solenoidal inductance arm of the bridge (fig. 3).

Another approach is to note the change in mutual reluctance between two coils

set up in a coaxial or orthogonal relation to each other when the magnetic

sample material is placed near the coils. The system is calibrated with a

standard of known susceptibility and measurements are normalized to an

equivalent half space composed of material of identical susceptibility as that

of the sample. One paramagnetic standard often used for calibrating

susceptibility bridge measurements is ferrous ammonium sulfate, Fe(NH4 ) 2

6
( S0A ) 2 • 6H2 0 , with a molecular weight of 392.15. The susceptibility of this

salt is 32.6 x 10~ 6 x U-n .

Figure 3. Typical susceptibility bridge schematic detecting inductance change in test

coil C2 by action of the coil's

field on a sample having unknown

susceptibility.

A typical susceptibility bridge schematic is shown in figure 3. The inductance

change in test coil C2 by action of the coil's field on a sample having unknown

susceptibility is measured. Coils C x and C 2 are solenoids carefully matched

for inductance. Mx and M2 are identical variable inductors. In operation, the

bridge would be balanced with no specimen in either coil through variable

resistor R and inductor Mx

. The specimen is then inserted into C 2 (test coil,)

and the bridge balanced with inductor M2 where the inductance adjustment is

proportional to the susceptibility. Calibration of the inductance M2 may be

achieved by balancing the bridge with standard substances placed in a test tu:

in the coil C2 containing a known weight of a paramagnetic compound such as

ferrous ammonium sulfate of known susceptibility. Calibration would be si:rp'.

accomplished by balancing the bridge with inductor M2 when the test statu!..:'! .

7
placed in C2

. The test tube can then be removed and bridge balanced with

variable inductor . The same test tube with the same amount of the same

standard substance is again inserted into coil C2 and the bridge balanced with

M2

. This process is repeated throughout the inductance range of C2 so as to

obtain a calibration curve referenced to the known standard. If ferrous

ammonium sulfate is used, it should be kept in a fresh, sealed bottle since the

salt is slightly hygroscopic.

4. FREQUENCY LIMITATIONS FOR TEST MEASUREMENTS

In the above techniques, the sample is energized with a low-frequency

field. It is, of course, essential that this field have a frequency

sufficiently low that no conductivity response of the sample will be observed.

A model which provides a general rule of thumb for the highest usable frequency

is that of a conducting permeable sphere in a uniform alternating magnetic

field,

H, = H0 e'

1Wt

, (3)

as shown in figure 4. Ward [5] has slightly rewritten (for e lwt time

dependence) Wait's [6] original results for the in-phase M and out-of-phase N

components of the induced dipole moment of a sphere in a uniform alternating

magnetic field when the wavelength in the external host medium is much greater

ii H

than the radius of the sphere ( | a | « 1 where = [iu>n 1 o 1 + w

z

/i 1 e

1 ] ),

2/i 2 (tana - a) - ft i (a - tana 4- a

2 tana)

M - iN =

2/i2 (tana - a) + 2 ^1 (a - tana + a

2 tana)

a = ( i«/i2

cr 2 ) \

,

and a is the radius of the sphere in meters.

( 4 )

8
The in-phase and quadrature components of the induced dipole moment of a sphere

are shown plotted as a function of the response parameter of a sphere,

u

6 = (oxj 2 m2 ) a, in figure 5. These components are shown in parametric fashion

for /j 2 /Mi equal to 1 (free space) to nz /^i equal to 1000 (steel sphere).

Figure 4. Conducting permeable sphere of radius a in uniform

alternating magnetic field H0 e . Sphere has

conductivity, permeability, and permittivity of

a2 , n2 • c 2 » respectively, while host medium has

conductivity, permeability, and permittivity of

al • Ml CiIn order that the conductivity response of the sample be small, we see

from figure 5 that 0

2 = (w/i2

<7 2)

a

2 should be « 1. In the case of pure

magnetite, the permeability /i 2 is approximately 1.5 x 4* x 10' 7 H/m and the

conductivity a2 is about 1.5 x 10* S/m. Thus, for a 2.5 cm diameter sphere and

the condition that 9 2 =0.1, we find that the maximum allowable frequency is

approximately 400 Hz. Of course, for samples that are considerably less

conductive than pure magnetite, the maximum allowable frequency may be higher

while still avoiding sample conductivity response. If we ignore the effect-; nf

9
Figure 5. In-phase M and out-of-phase N components of

induced dipole moment of sphere in uniform

alternating field for |7xct| « 1.

(After reference [5]).

the air-earth interface, Wait's work [6] can also be used to quantitatively

assess detection limits for both conductivity and permeability contrasts.

5. SUSCEPTIBILITY MEASUREMENT OF U.S. ARMY BELVOIR MINE LANE

MAGNETITE- SAND MIXTURE

A susceptibility meter [7], was used in measuring the susceptibility of a

sand and magnetite mix provided to NBS by Dr. Lee Anderson of BRDC . The sample

consists of silica sand and magnetite of about 30 mesh size. This susceptibility meter is quite portable (0.5 kg with dimensions of 190 x 80 x 30 mm,

operating on one disposable 9 V battery)

.

10
In this meter there are two coils placed orthogonally to each other in

the detector head, which is mounted in the bottom of the instrument case

(circuit diagram shown in fig. 6). In a nonmagnetic environment the voltage

induced in the receiver coil by the transmitter coil is zero. When a sample

100k

Figure 6. Circuit diagram for susceptibility meter [7],

is brought near the coils, a voltage proportional to the magnetic

susceptibility of the sample is induced in the receiver coil. The received

signal is detected by a phase-locked amplifier and after rectification is used

to drive an analog panel meter, which is thermally compensated and

directly calibrated for susceptibility. Field strengths are less than

Un x 10' 3 A/m at 1000 Hz so that with the phase sensitive receiver circuit the

influence of electric conductivity in most samples is usually eliminated. As

stated by Anderson [4], calibration is usually done for a half-space geometry,

which is convenient when measurements are performed in the field. When

11
laboratory samples are measured, a multiplicative correction factor should be

applied according to the soil sample size. A chart indicating this halfspace correction factor is given in figure 7 from information provided by the

manufacturer

.

SAMPLE SIZE OR CORE DIAMETER (mm)

Figure 7. Half-space multiplicative correction factor for

susceptibility measurements.

The silica sand-magnetite mixture's susceptibility (=330 g sample, =50 mm

diameter) was measured and found to be approximately 175 000 x 10' 6 uncorrected

for sample size. After a sample size correction factor of 2.0 from figure 7 is

used, the susceptibility of the 330 g sample is determined to be 350 000 x

10~ 6

. For mine detection standards purposes, such measurements can provide the

12
practical property range limits for which detection feasibility of various mine

detection systems can be judged. Similar comments can be made about other

physical property contrast limits, i.e., complex permittivity (as a function of

frequency), density, and acoustic velocity.

6. APPLICATION TO PASSIVE MAGNETOMETRIC DETECTION

Magnetic anomaly signatures from metallic mines that can be detected

passively result from magnetization of the metallic enclosure within an

applied inducing (static) field. The character of the magnetic signature

depends on the geometric disposition of the mine, its equivalent volume -percent

magnetite content (that is, the susceptibility of the mine to magnetization)

and the direction and magnitude of the inducing field. In addition, for manmade iron and steel (not stainless) objects the magnetization can also have a

permanent component which is independent of the induced component so that the

total magnetization is the vector sum of the two. For metallic mine detection

it would be useful to examine the sensitivity of passive magnetometry to

various metallic, permeable mine standards enclosed in various soil types for

varying heights and offsets of the sensor head to the buried mine.

6.1 Theory

6.1.1 Magnetization Vector in Same Direction as Inducing Field

Almost any model source geometry of a metallic mine (fig. 8) may be

approximated by a suitable arrangement and number of prismatic elements.

Therefore a prismatic element is considered as a basic building block for

passive magnetometric detection of buried metallic mines (fig. 9).

13
Figure 8. Arbitrary geometry of a magnetically permeable mine

or firing pin as observed at a field point P(r).

The expression for the total anomalous magnetic field intensity in the

direction of the applied vector field, Ht , due to a prismatic model of a

single metallic mine at an arbitrary field observation point P (x,y,z) (that

would be sensed by a typical proton precession magnetometer) is somewhat

tedious to derive. Essentially,

d d

Ht (x , y , z) = - — V(x,y , z)cosI + — V(x , y , z) sinl , (5)

14
X

N

T

T

i

Figure 9. Geometry of prism describing metallic mine (or firing

pin) relative to magnetic north at depth D and having

cross-sectional dimensions L and W, thickness T, and

magnetic susceptibility k.

where I is the inclination of the (earth's) applied uniform (inducing) field

and where the coordinate system is configured such that x is directed north,

z is positive downward, and V is the magnetic potential defined by the volume

integral

V (x , y , z) = /// ^ *,?" dx' dy' dz ' (6)

volume of prism

where M denotes the direction and magnitude of magnetization of the prism block

and r' is the position vector from an element of integration at (x',y',z') to an arbitrary field point P (x,y,z). After much algebraic manipulation, the

anomalous total magnetic field due to a single rectangular prism at any point

in the x-y plane, after rotation of coordinates such that coordinate surfaces

coincide with the surfaces of the prism (fig. 10), may be shown to be

Ht (x,y,0) sin<5 cos£ in

7(x

u

-x) 2 + (yy-y) 2 + D i - (yy-y)

7(x

u

-x) 2 + (yy-y) 2 + d

2 + (yu-y)

15
sin£ cos<5 Hn

/(*y-x ) 2 + (y L

-y) 2 + Df - (yL-y)

J(Xy-x) 2 + (yL

-y) 2 + D

2 + (yL

-y)

sin2 5 tan

(Xy-x) (yy-y)

(Xy-x) 2 + D 1 /(x

u

-x2

) + (yy-y) 2 + D

2 + D

2

-

1

+ sin2 5 tan

( VX> <yL

_y)

(Xy-X) 2 + DiVcxy-x) 2 + (yL-y ) 2 + Df + D

2

+ cos2 6 tan

-

1

(Xy-x) (yy-y)

Dx J( Xy

_ x) 2 + (yTT -y) 2 + D

2 U

- cos2 5 tan

- l (X

U'

X) (yL

_y)

D1 VCXy-x) 2 + (yL

-y) 2 + D

2

- sin5 cosS Jin 7(xt -x) 2 + (yy-y) 2 + D

2 - (yTT -y) U

/(x

L

-x) 2 + (yy-y) 2 + D

2 + (yy-y)

+ sinfi cos S ^n

7(xl-x) 2 + (yL

-y) 2 + D

2 - (yL

~y)

7(x

l

-x) 2 + (yL

-y) 2 + D

2 + (yL

~y)

+ sin2 5 tan

(xL

-x) (yy-y)

(xL-x) 2 + D 1 7(xl

-x) 2 + (yy-y) 2 + Df + Df

16
- sin2 6 tan

- l (xL

-x) (yL-y)

(xL

-x) 2 + D x 7(x

l

-x) 2 + (yL

-y ) 2 + Df + Df

cos2 6 tan

-

1

(xL-x) (yy-y)

D x 7 (xl

-x) 2 + (yy

-y) 2 + D

2

+ cos2 5 tan

-

1

(xL-x) (yL

-y)

Di 7(xl

-x) 2 + (yL

-y) 2 + D

2

(7)

where S = 90° - I. Equation (7) is an exact expression for the (static) total

magnetic field at any point in the x-y plane for a prism with large depth

extent whose magnetization vector is in the same direction as that of inducing

field and whose magnetization is uniform throughout the prism. Effects of

shape demagnetization are incorporated into the value assigned to | M |

.

The

values of x^, x^, y^, y^ are referenced in figure 10. Equation (7) is readily

used to obtain the total field intensity for magnetized bodies of finite

vertical extent (such as the magnetized mine or firing pin of interest here) by

considering a prismatic body having its top at depth and its bottom at a depth D2

. The fields due to two bodies of infinite depth extent are first

determined, one at depth Dx and the other at a depth D2

. If we subtract the

latter from the former, the anomalous field signature for the mine body of

finite depth extent is obtained.

6.1.2 Magnetization Vector in a Direction Different from Inducing Field

When the magnetization vector of the subsurface metallic mine is in a

direction different from that of the static inducing field (that is, when

permanent magnetization is present), the following expression for the total

magnetic field signature at an arbitrary point of observation P (x,y,0) in the

17
x-y plane due to a single prismatic element (see fig. 9) of large depth extent

T results from eq (6),

Figure 10. Rotated prismatic element whose geometry is

specified by eight ordered coordinate triplets.

Ht (x.y.O) ! m | cosl sinl,, sin# in

2

/(xy-x) 2 + (yy-y) 2 + D

2 - (Xy-x)

/(Xy-x ) 2 + (yy-y) 2 + Df + (Xy-x)

cosl sinl„ sin# in

7(x

L

-x) 2 + ( yu

-y) 2 + D

2 - (x

L

-x)

2

cosl sinl„ sin# in

/(x

L

-x) 2 + (yy-y) 2 + D

2 + (x

L

-x)

7(x

IJ -x) 2 + (yL

-y ) 2 + D? - (Xy-x)

2 J(Xy-x ) 2 + (yL

-y) 2 + D

2 + (Xy-x)

18
+ cosl sinl„ sin# in

7(xl-x) 2 + (yL-y) 2 + Df - (xL

-x)

7(xl-x) 2 + (yL

-y) 2 + dl + (x

L

-x)

+ (cosl sinl + cosl sinl0 cos0) in

J(Xy-x) 2 + (yy-y ) 2 + D

2 - (yy-y)

7(Xy-x) 2 + (yy-y) 2 + D

2 + (Yy-y)

- (cosl sinl + cosl sinl cos0) in

/(Xy-x) 2 + (yy-y ) 2 + D

2 - (Yy-y)

7(Xy-x) 2 + (Yy-y)

z + D

2 + (Yy-y)

- (cosl sinl + cosl sinl cos#) in

7(Xy-x) 2 + (yL

-y) 2 + D

2 - (yL

-y)

/(Xy-x) 2 + (yL

-y ) 2 + D

2 + (yL

-y)

+ (cosl sinl + cosl sinl cos 9 ) in

/(Xy-x ) 2 + (Yy-y ) 2 + D

2 - (Yy-y)

7(Xy-x) 2 + (yy-y ) 2 + D

2 + (Yy-y)

cosl cosIQ sin 9 in

7(xy-x) 2 + (Yy-y ) 2 + D

2 + D x

7(Xy-x) 2 + (yy-y ) 2 + D

2 + D x

+ cosl cosIQ sin 9 in

7(Xy-x) 2 + (yy-y ) 2 + D

2 + Dj

7(Xy-x) 2 + (yy-y ) 2 + D

2 + D x

19
- cosl cosIQ

+ cosl cosIQ

+ cosl cosIQ

- cosl cosIQ

+ sinl sinl

sinl sinl

- sinl sinl0

cos 9

-

l

tan

(Xy-x) (yy

-y)

(Xy-x) 2 + D^CXy-x) 2 + (yy-y) 2 + Df + Df

cos$

cosd

-

1

tan

-

1

tan

(xL-x) (yy-y)

(xL-x) 2 + D^CXy-x) 2 + (yy-y) 2 + D

2 + D

2

<VX> <yL'y)

(Xy-x) 2 + d1 7(x

u

-x) 2 + (yL

-y) 2 + of + Df

cosd

- 1 tan

(xL-x) (yL

~y)

(Xy-x) 2 + D1 7(Xy-x) 2 + (yy-y) 2 + D

2 + D2

- i tan

(Xy-x) (yy-y)

D1 7(Xy-x) 2 + (yy-y) 2 + Df

-

1

tan

(Xy-x) (yy

-y)

Di y( Xy-x) 2 + (yy-y) 2 + D

2

-

1

tan

(xu'x) (yL' y)

Di^( xu

" x )

:i + (yL

-y>“ + Di

20
+ sinl sinl ( 8 ) 0

-

1

tan

(xL-x) (yL

-y)

Di-/(xL

-x ) 2 + (yL

-y ) 2 + D\

The inclination of the static inducing field, as measured from the

surface, is represented by I Q , whereas the inclination and azimuth of the

magnetization vector within the prismatic body are given by I and 9 . For

sensitivity analyses of a body of small thickness T, eq (8) may be used in a

manner analogous to eq (7) . In practice it is difficult to predict any

component of permanent magnetization. However, approximate anomalous static

field signatures can be predicted in this passive detection scheme for ranges

of the susceptibility contrasts measured for most metallic mines and for

various soil types. These anomalous signatures can be predicted for various

horizontal offsets and heights of the sensor from the actual buried mine so as

to indicate threshold sensitivities required in any actual field

instrumentation.

6.2 Sensitivity Analyses

For most iron and steel objects a conservative range of the magnetic

susceptibility k is between 1 and 10. Anderson [4] has reported background

magnetic susceptibilities of various soil types, and the measured

susceptibility of the U.S. Army BRDC magnetite-sand mine lane mixture is

350,000 x 10“ 6

. These values are summarized in Table 2. The contrasts in

susceptibility between measured permeable soils and metallic mines or firing

pins may be used in sensitivity analyses for either passive schemes (such ns

that described here) or active electromagnetic induction sensing.

21
Table 2. Magnetic susceptibilities of various soil

types (after Anderson [4]).

LOCATION SOIL TYPE PARENT ROCK

TYPE

_k ( xlO6

) 4?r Fairfax Co., Va. Congarie silty

clay loam

Alluvial clay 15

Fairfax Co . , Va. Susquehanna loam Heavy coastal deposits 75

Fairfax Co. , Va. Chester loam Granite , granite

gneiss and schist 20

Panama Canal Zone Coastal sands Basic ferromagnesian

igneous

50,000 to

150,000

BRDC Magnetite -sand

mixture

27,800

Table 2 shows that a minimal contrast in magnetic susceptibility between the

highly magnetic Panama Canal Zone coastal sands and a steel clad metal mine is

10.68. For purposes of this sensitivity analysis the dimensions of the mine are

taken to be 76 mm x 76 mm x 76 mm, and the mine model is a solid with a

minimal susceptibility contrast of 10.68. The magnetization vector is also

taken as vertical in an inducing field of 50 000 nT.

Relative anomalous magnetometric signatures for variable offsets and

heights of a total field head from the buried metallic mine are shown in

figures 11, 12, and 13. Heights of the sensor head were taken as 0.3 m, 1.5 m,

and 3 m, respectively. For a sensor head which is just 0.3 m above the burial

depth of this modeled mine, the detection range is 2.4 m. A threshold offset

detection range for this mine size is given as a function of sensor height in

figure 14. Clearly, a larger metallic mine would have a much greater

detection range, while that of a permeable firing pin would be much less.

22
Applied Field: 50 000 nT 0 0.6m

Susceptibility Contrast: 10.68 LubbbTM"?

Mine Dimensions: 76 mm x 76 mm x 76 mm

Inclination of Polarization Vector: 90°

Sensor Height Above Mine:0.3 m

Contour Interval: Variable nT

Horizontal = Vertical Scale

Figure 11. Anomalous total magnetic field intensity for passive magnetometric

mine detection (magnetically permeable host medium)

.

23
Mine Dimensions: 76 mm x 76 mm x 76 mm

Inclination of Polarization Vector: 90°

Sensor Height Above Mine: 1.5 m

Contour Interval: 1.0 nT

Horizontal = Vertical Scale

Figure 12. Anomalous total magnetic field intensity for passive magnetometric

mine detection (magnetically permeable host medium)

.

24
Mine Dimensions: 76 mm * 76 mm x 76 mm

Inclination of Polarization Vector: 90°

Sensor Height Above Mine: 3m

Contour Interval: 0.5 nT

Horizontal = Vertical Scale

Figure 13. Anomalous total magnetic field intensity for passive magnetometr i

c

mine detection (magnetically permeable host medium)

.

25
Referred to Background Micropulsation Noise Level of 1 nT \IY\z

Figure 14. Threshold offset detection range versus sensor height for 7.6 cm x

7.6 cm x 7.6 cm buried magnetic mine.

26
7 . CONCLUSIONS

The magnetic susceptibility of soils depends on the component magnetic

minerals derived from chemical and mechanical breakdown of bedrock. Magnetic

minerals of importance are few, and those most commonly encountered are the

iron and titanium oxides. One measurement technique for determining material

magnetic susceptibility is to observe the inductance change required to balance

a bridge circuit when the sample under test is inserted into a solenoidal test

coil composing one arm of the circuit. The inductance adjustment is

proportional to the susceptibility of the sample, and calibration is achieved

by balancing the bridge with known weights of a paramagnetic compound such as

ferrous ammonium sulfate. In order to avoid a conductivity response of the

sample in the weak time-varying source field of the bridge test coil, a maximum

allowable test frequency is chosen so that the induction number within the

sample under test is much less than 1. This criterion can be deduced from an

examination of the in-phase and quadrature components of the induced dipole

moment of a conductive permeable sphere in a uniform alternating magnetic

field.

Magnetic susceptibility and conductivity measurements provide practical

property range limits from which sensitivity analyses for active or passive

metal detection systems may be performed. Examination of the induced dipole

moment of a conductive, permeable sphere, placed in a permeable medium and

excited by a uniform alternating magnetic field, also reveals that the

operating frequency of an active detection system can be chosen so that the

quadrature response is maximized for a given diameter of the buried sphere.

This size discrimination capability is possible when the relative magnetic

27
permeability contrast between the target sphere and enclosing soil medium is

known, as well as the conductivity of the sphere.

An example of the use of magnetostatic measurements for passive detection

of buried metallic mines has been considered which allows an arbitrary geometry

of the mine in an arbitrary inducing field and in a magnetically permeable

background medium. Typical commercial proton precession magnetometers have

tuning sensitivities permitting total magnetic field intensity measurements

accurate to ±0.5 nT. In a field of 50 000 nT and time-varying ambient noise

levels (over the tuning period) of ±0.5 nT, a metallic mine 7.6 cm on a side

would have an anomalous signature of 1000 nT at zero offset and would still be

detectable (over background noise levels) at offset distances of about 2 m for

a sensor height of only 0.3 m. However, at sensor heights of 3 m the presence

of a mine 7.6 cm on a side would be barely detectable, giving a maximum

anomalous total magnetic field strength at zero offset of only 1.3 nT.

Although not performed here, the same type of sensitivity analyses for

electromagnetic induction detection schemes can be made on the basis of

magnetic permeability and electrical conductivity measurements. The total

magnetic field signatures due to metallic firing pins would be lost in ambient

noise levels. However, the very low inherent noise levels of superconducting

quantum interference device (SQUID) sensors suggest that SQUID magnetic

gradiometers might be a useful detection tool for such a case. The quantity

measured by such a system will be the gradient tensor, the spatial rate of

change of the vector components of the magnetic field. The resulting tensor

components could then be downward continued to accentuate anomalous

28
signatures, and it may be possible to invoke depth estimation procedures to

filter out magnetic surface clutter. These problems are worthy of further

theoretical and experimental study.

29
8 . REFERENCES

[ 1] Nagata, T. Rock magnetism. Tokyo: Maruzen Press; 1961. 350 p.

[2] Akimoto, S. Magnetic properties of ferromagnetic oxide minerals as a

basis of rock magnetism. Adv. Phys. 6(288); 1957.

[3] Heiland, C.A. Geophysical exploration. Englewood Cliffs, New Jersey:

Prentice Hall; 1940. p. 310-314.

[4] Anderson, L. Private communication. U.S. Army Belvoir RD & E Center,

Countermine Systems Directorate, Fort Belvoir, VA 22060-5606; 1987.

[5] Ward, S.H. Electromagnetic theory for geophysical applications. Mining

Geophys. II: 78; 1967.

[6] Wait, J.R. A conducting sphere in a time varying field. Geophys.

16:666; 1951.

[7] Geoinstruments, model JH-8*.

^Certain commercial equipment, instruments, or materials are identified in this

in order to specify the experimental procedure. Such identification does not

imply recommendation or endorsement by the National Institute of Standards and

Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

30
NBS-t 14A (rev. 2 -gc) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NT STIR 88-3098 October 1988

4. TITLE AND SUBTITLE

MAGNETOSTATIC MEASUREMENTS FOR MINE DETECTION

5. AUTHOR(S)

Richard G. Geyer

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. National Institute of Standards and Technology

NATK>f4At--By-R€Ay-G-F--STAN-B-Afl-B$

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

U.S. Army Belvoir Research and Development Center

Fort Belvoir, Virginia 22060-5606

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11.

ABSTRACT ( A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

The use of a Maxwell inductance bridge and calibration procedure for measuring the magnetic susceptibility of magnetically linear, homogeneous, and isotropic materials are

reviewed. A complication in this measurement exists since electromagnetic induction

sensors respond to the product of the magnetic permeability and electrical conductivity

For this reason, frequency limitations resulting from sample size and conductivity must

be considered. Such limitations can be specified by examining the in-phase and quadrature components of the induced dipole moment of a conductive, permeable sphere of diameter equivalent to that of the bridge test coil in a uniform alternating magnetic field

and by choosing a maximum allowable test frequency that gives an induction number much

less than 1 within the sphere.

Magnetic susceptibility measurements are applied to the passive magnetometric detection

problem of an arbitrarily shaped susceptible (metallic) mine buried in a magnetically

permeable earth. For analysis purposes a conservative susceptibility contrast between

a typical metallic mine and host soil having the same measured magnetic characteristics

as the U.S. Army Belvoir Research and Development Center (BRDC) magnetite-sand mine lane

mixture was assumed. Anomalous detection limits were then calculated for various total

field intensity (Proton precession) sensor head heights and offset distances, given

mine dimensions as small as 7.6 cm on a side.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s inductance bridge; magnetic permeability; magnetic susceptibility; magnetometric

detection; magnetostatic

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