Reference

NBS

PUBLICATIONS

NBSIR 84-3017

AlllDb D3nbD

MICROWAVE DETECTION OF LOST

WELLS AND UNKNOWN WATER-FILLED

VOIDS IN COAL MINES

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

September 1 984

-QC

100

.U56

84-3017

1934

V

UBSART

NBSIR 84-3017

MICROWAVE DETECTION OF LOST

WELLS AND UNKNOWN WATER-FILLED

VOIDS IN COAL MINES

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

September 1984

Prepared for Bureau of Mines

United States Department of the Interior

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

D. R. Belsher

R. H. McLaughlin

A. G. Repjar

H. E. Bussey

r

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

99TTJ-yfi^ ______

REPORT DOCUMENTATION

PAGE

l. REPORT NO. X. R^CipMflC't

4. ntl« «r>d SAjbCrtl* Microwave Detection of Lost Wells and Unknown

Water-Filled Voids in Coal Mines

s. Raeon ora September 1984

7. AutftorCt) D.R. Belsher, R.H. McLaughlin. A.G. Reoiar. H.E. Bussey

S. Parforminc Orssn^otlon Rast. No. NBSIR 8A-3017

f. Parforminc OryanUatton Nama and Addrasa Electromagnetic Fields Division

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

JO. Pretaet/TaaA/Vtorfe UnK No. 7233410

XL ContraettO ar OranMQ) No. «3 H0272007

(Q

12. Soonaotinc Onaintaation Nama and Addroas United States Department of the Interior

U.S. Bureau of Mines, Denver Mining Research Center

Denver Federal Center, Denver, Colorado 80225

U. Type o# Raeort 4 Parted Cdaorad Final - Phase II Jan. 1979 to March 1984

14.

IS. Sepptamanta ry Netaa

14. AlMtract (Unde 200 «*orda) Work on contract H0272007 is summarized for the period of January 1979

through March 1984. The development of improved antennas useable with both

a pulse system or an FM-CW system is described. The development of a field

prototype pulse sampling system is described. Initial theoretical work on the problem of dielectric loading of antennas as well as a study of notential

system range is included.

17. Oeeunwnt AiMlyra s. Omerteton Detection of mining hazards

Detection of coal mining hazards

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3
FOREWORD

This report was prepared by the National Bureau of Standards (NBS),

Electromagnetic Fields Division, Boulder, Colorado, under USBM Contract number

H0272007. The contract was initiated under the Minerals Health and Safety

Program. It was administered under the technical direction of the Premining

Hazards Division, Denver Research Center, with Mr. Richard L. Myers acting as Technical Project Officer. Mr. Dennis Maez was the contract administrator for

the Bureau of Mines. This report is a summary of the work recently completed

as a part of this contract during the period 23 January 1979 to 1 March

1984. This report was submitted by the authors on 1 May 1984 and published in

September 1984.

The NBS thanks other staff members not named as authors who contributed

indirectly to this work: Doyle A. Ellerbruch for helpful discussions on techniques, Douglas T. Tamura for assistance in the field, and James R. Andrews

for helpful discussions on pulse theory.

The authors also wish to acknowledge the considerable help provided by

the staff of the Kaiser Coal Mine at Raton, NM, especially that of Mr. Ed

Moore, Mr. Richard E. Hood, Mr. Rod Lawrence, Mr. Terry Jordan, Mr. Ron

Chavez, and Mr. Harry H. Elkin.

The assistance provided by personnel of the Bureau of Mines, Denver

Research Center, is greatly appreciated, most notably that of project monitor

Mr. Richard L. Myers and also Mr. R. J. Leckenby.

The authors regret the unavoidable delay in concluding this project.

Progress was stopped for more than two years while manufacturers of critical

sub-assemblies worked to meet the specifications.

4
CONTENTS

Page

FOREWORD 4

1. INTRODUCTION 11

2. ANTENNA CHARACTERISTICS 12

2.1 Antenna Construction 12

2.2 Antenna Response 13

2.3 Antenna Pattern 13

2.4 Isolation in the Bistatic Configuration 13

2.5 Operation Close to Surfaces.. 14

3. POTENTIAL FOR DIELECTRIC LOADING OF ANTENNAS 14

3.1 Infinite Bow-Tie Antenna 14

3.2 Finite Bow-Tie Antenna 15

3.3 Dielectrical ly Loaded Antennas 16

3.4 Directional Bow-Tie Antenna ...17

3.5 Conclusions and Recommendations 17

4.

SUBSURFACE RADAR RANGE LIMIT STUDY 18

4.1 Introduction 18

4.2 The Radar Equation 18

4.3 Interface Transformati on Factors, I C^^ 20

4.4 Attenuation in the Medium 24

4.5 Radar Range Calculation from S/N 25

4.6 Radar Cross Section 25

4.7 Electromagnetic Theory of Scattering Cross Sections

of Extended Targets 26

4.8 Cross Section of a Planar Interface 27

4.9 Half-period (Fresnel) Zones 27

4.10 The Strip Approximation of a Tunnel 29

4.11 Cross Section of a Dielectric Tunnel at Broadside Incidence ... .30

4.12 Cross Sections of Circular Cylinders (Boreholes) 31

4.13 Computer Routine for S/N Versus Range 33

4.14 Conclusions 33

5. PULSE RESPONSE SIMULATIONS 34

5.1 Waveform Comparisons... 35

5.2 Borehole Detection Estimates 36

6.

PULSE SYSTEM EQUIPMENT 37

6.1 High Voltage Impulse Generator 37

6.2 Receiver Preamplifier 37

6.3 High-frequency Sampler 38

6.4 Fiber-optic Transmission System 39

6.5 Digital Acquisition System 40

5
7. FIELD TESTING 40

7.1 NBS Test Range 40

7.2 Coal Mine Results 41

8. ADAPTATION OF SEISMIC DATA METHODS 41

9. FUTURE DIRECTIONS FOR RADAR DETECTION OF UNDERGROUND ANOMALIES 42

9.1 Mining Needs 42

9.2 Antennas 42

9.3 Future System Types 43

9.4 Accessibility to Mine Test Areas 43

10. REFERENCES 43

APPENDIX A. COMPUTER PROGRAM FOR SI GNAL-TO-NOISE RATIO, AS A FUNCTION

OF DISTANCE (RANGE) TO A SUBSURFACE TARGET 82

6
LIST OF FIGURES

Page

Figure 1. Reflections due to the NBS-TQ antenna without the

resistive material (1) and the same antenna with

the resistive material (2) 47

Figure 2. Transmitted waveform from the TG antenna (curve 1) and the

TQ antenna (curve 2) 48

Figure 3. Relative transmission in dB for the TG antenna (plain line)

forward direction, the TO antenna (squares) forward

direction, and the TQ antenna (triangles) reverse direction at a range of 3/4 49

Figure 4. Baffle arrangement for isolating TQ antennas when operated

bistatical ly 50

Figure 5. Response (1) of the system with the TQ antenna pair

pointed at the sky and (2) to a 1.2 meter square metal

plate 5 cm in front of the baffle 51

Figure 6. Pulse system antenna return from an air-filled box target

buried at 0.6 meter (1) and the same* return corrected by

subtraction of the sky return (2) 52

Figure 7. Non-coplanar fin antenna schematic 53

Figure 8. Characteri sti c impedance of the non-coplanar fin antenna

with equal fin angles (plotted from data presented by

Carrel [9]) 54

Figure 9. Input impedance of biconical antennas with 5.4° cone angle

and 0.054° cone angle as a function of the length, Jl, of

the cone in wavelenqtns, \ (plotted from data presented by

Kraus [12]) 55

Figure 10. Input impedance of single cones with ground plane as a function of cone length, A, in wavelengths, X. Cone

angles are 10°, 20°, 40°, and 60° (plotted from data

presented by Kraus [12]) ,....56

Figure 11. Input impedance of single cone with ground plane versus

kS.. K is the wave number, Z is the cone length, and the

cone angle, 9^, is 60° (plotted from data presented by

Papas and Ki ng [13] ) 57

Figure 12. Characteri sti c impedance of a biconical antenna with equal cone angles, (plotted from data presented by Carrel [9]) 58

7
59

Figure 13a.

Figure 13b.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Sketch of the rays from source to field point (target). Rays

are refracted into the second medium and partially reflected,

"o<"l

Geometry for calculating Sommerfeld interface transmission.

In this example, the source is in denser medium with

refractive index nQ>nj^ 59

Signal-to-noise ratio for a CW radar system with the

following parameters: 500 MHz source; horn antennas 50.8 cm

X 76.2 cm; frequency = 0.5 GHz; complex permittivity = 9-jO

for low loss curves, 4-j0.16 for medium loss curves, 9-j0.9

for high loss curves. The upper curve of each group is for

a flat mine tunnel wall 1.5 m high of infinite length with

water in the tunnel. The lower solid curve of each group

is for a 30 cm diameter cased borehole. The dashed curve

is for a water-filled borehole without casing having a 30 cm diameter. The system noise is assumed to be 8 dB

greater than Johnson noise in a 1 MHz bandwidth and clutter

is ignored 60

Simulated impulse waveforms having widths of 5, 2, 1, and

1/2 ns at the 50% point 61

Resulting spectral energy distribution of the impulses

shown in figure 15 in dB relative to 10"^ volt-seconds 62

The signals resulting from transmission of the

impulses shown in figure 15 over a 1 .5 meter

path with the TQ antennas 63

Simulated sinusoidal pulse waveforms having 8, 4, 2, and 1 cycles 64

Resultant spectral amplitude of the sinusoidal pulses shown

in figure 18. 8-cycle pulse, dotted curve; 4-cycle pulse,

triangles; 2-cycle pulse, squares;. 1-cycle pulse, solid

line with no marker 65

"he signals resulting from the transmission of the sinusoidal pulse waveforms shown in figure 18 over a 1.5 meter

path using TQ antennas 66

Simulated linear chirp pulse waveforms. 250-500 MHz

in 10 nanoseconds, plain curve. 250-1000 MHz in 10

nanoseconds, square markers. 250-1000 MHz in 20

nanoseconds, triangle markers 67

Resulting spectral amplitudes of the linear chirp pulse

waveforms shown in figure 21. The curve markers correspond

to figure 21 68

8
Figure 23. Resulting signals after transmission of the linear chirp

pulses over a 1 .5 meter path using TQ antennas. The curve

markers correspond to figure 21 69

Figure 24. The result of transmitting a 300-600 MHz linear chirp pulse over a 1.5 meter path using the TQ antennas 70

Figure 25. The result of autocorrel ation of the waveform of figure 24 71

Figure 26. Autocorrelation of the transmitted waveform of the 4 cycle

250 MHz sinusoidal pulse 72

Figure 27. Simulated response in relatively damp coal for a 15 cm radius hole at 1 meter range. (1) cased hole, (2) airfilled hole, (3) water-filled hole 73

Figure 28. Simulated response in relatively damp coal for a 15-crn

radius hole at a range of 1 meter (1), 2 meters (2), and 5 meters (3). The amplitude of the response at 5 meters has

been amplified 50 times 74

Figure 29. Simulated radar response in relatively damp coal for a 1 .0 volt, 1 nanosecond input pulse reflected from a borehole.

The given dimension is the borehole radius 75

Figure 30. Simulated radar response in relatively dry coal for a 1.0

volt, 1 nanosecond input pulse reflected from a borehole.

The given dimension is the borehole radius 76

Figure 31. Preprototype pulse system block diagram 77

Figure 32. Output waveform of the high-voltage impulse

generator 78

Figure 33. NSB range for subsurface anomaly measurements 79

Figure 34. Pulse system response averaged over a sequence of 26

measurements (1). Single response from over the 0.6 meter deep

air-filled target (2). The resulting response showing the

target signal enhancement (arrow) obtained by subtracting

sequence average from the response at one position (3) 80

Figure 35. A stacked series of modified responses obtained by

subtracting the average response of the series from

each measured response. Target signal at arrow 81

9
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03
MICROWAVE DETECTION OF LOST OIL WELLS AND

UNKNOWN WATER-FILLED VOIDS IN COAL MINES

D. R. Belsher (retired), R. H. McLaughlin,

A. G. Repjar, H. E. Bussy (retired)

Interference Characterization Group

Electromagnetic Fields Division

National Bureau of Standards

Boulder, CO 80303

1. INTRODUCTION

This is the final report for work (Phase II) carried out by the National

Bureau of Standards (NBS) under contract H0272007 with the Bureau of Mines.

Many thousands of oil wells pass through the coal beds of the United

States. Of these, a very large number are in active underground coal mining

areas. The casings of these wells are found, when possible, on the surface,

and their underground positions are determined from drilling data or costly

well-logging techniques. Many of these wells were drilled and abandoned years

ago and are often impossible to locate at the surface. The drilling logs for

those that can be located at the surface often do not exist. These "lost"

wells are believed to have caused some major coal mine explosions. Some coal

mine explosions have resulted in the loss of over a hundred lives in a single

catastrophic event. The hazard is produced when the cutter teeth of a mining

machine contact and penetrate a steel well casing. The resulting sparks can easily ignite the casing gas and the coal gas and dust present at the mining

face. Where the location of a well casing is known, the law requires a coal

pillar to be left surrounding the underground position. Even wells whose

positions are known both on the surface and underground may be penetrated when

new or inexperienced personnel misjudge their underground positions. The

underground position of a cased well is often different from the surface position since many wells are not drilled vertically. As a result, mine managers

must constantly check for any one of the many thousands of lost or undocumented cased and uncased wells.

Flooding is another coal mine hazard. Experience has shown that flooding

generally occurs when coal is mined within approximately 3 m (10 ft) of a flooded area in a previously worked mine. Severe flooding can also occur by

cutting into a water-filled well. This happens even when 6.10 m (20 foot)

horizontal drilling guidelines are followed and mining is restricted to more

than 15.3 m (50 feet) from old workings. Testing for old workings by drilling

is often a cause of dangerous flooding since the drill hole can easily be

enlarged by water flow. Also, old workings can be missed when mining

personnel test by drilling.

11
A microwave technique appears to offer an excellent chance for success in

detecting voids and well casings to ranges of 15 m (50 feet) or more. All of

the prominent microwave techniques have potential advantages over other

techniques in that:

(1) The antenna need not physically contact the working face;

(2) the antenna can be mounted on room and pillar mining machinery, or on longwall mining machinery, or it can be hand carried;

(3) measurements can be made quickly with minimum interference to production; and

(4) data can be analyzed and made available for immediate use by production personnel.

It was felt that the maximum benefit, for the available time and money

provided in Phase I of this work, would be achieved by improvements in the

antennas which would be useful for any microwave system. Accordingly, in

Phase II of this work, the goals were to provide additional antenna improvements and to assemble a pre-prototype impulse radar system for delivery to the

Bureau of Mines. Additional effort has been expended on studies of potential

range (see section 4) and a study of dielectric loading of antennas (see sec- tion 3). A short comparison study of possible pulse types useable in underground radar has been included (see section 5). The general layout of the

prototype impulse system is described.

2. ANTENNA CHARACTERISTICS

2.1 Antenna Construction

During Phase I of this contract, a broadband, TEM-type antenna was developed. Designated the NBS-TG, it consisted of two tapered leaves and had

an impedance which varied exponentially from 50 ohms at the feed to 377 ohms

at the aperture. The antenna has been improved by encasing it in a shielded

enclosure and is now known as the NBS-TQ. This shielding improves the frontto-back ratio as well as the isolation when the antennas are used

bi statically. Shielding was added by placing the antenna in a metal box having an aperture at the open end of 50 cm by 80 cm. The box was 63 cm deep and was lined with a 3/4-inch thickness of a commercially available conductive

foam to suppress surface currents in the box. Additionally, two sheets of

resistive material (approximately 100 ohms per square) 8 cm wide by 15 cm long were riveted to the tips of the antenna halves. The resistive sheets were not

terminated on the box but were spaced away from the metal. The resistive

strips were added to provide lower reflections at the aperture. Figure 1 shows a comparison in the time domain of the reflections due to the NBS-TQ

antenna without the resistive material, curve (1) and the same antenna with

the resistive material added, curve (2). Notice that the right-hand peak,

which is the aperture reflection, is much reduced. The incident signals were

1/2 ns duration impulses of equal amplitude.

12
The antenna feed is by way of a type N feedthrough connector at the box

and a 0.6-m length of RG-58 coaxial cable connected to the antenna using an SMA connector. The remaining space in the shielding box is filled with low

density styrofoam to completely fill the box and support the antenna firmly in

position. The aperture was covered with sheet plastic and sealed with heavyduty tape.

2.2

Antenna Response

The measured transmitted pulse response, using an electrically small

resistive dipole as a standard receiving antenna, of both the MBS-TG and the

NBS-TQ antennas is compared in figure 2. It is obvious that the isolating box

does introduce some changes in the transmitted waveform, but the reduction in

transmission to the sides and back should make the overall system performance

much better.

Unless otherwise noted, all measurements shown were made with the

equipment described in the Phase I Final Report for this contract. That

system included a commercially available digital -processing oscilloscope and

an NBS-constructed impulse generator having a 45-volt amplitude into 50 ohms

and 1/2-ns width (FWHM--full width, half maximum, or 50% amplitude points).

2.3

Antenna Pattern

A comparison of the forward and reverse transmitting transfer function

amplitudes with the probe at a 3/4 m distance from the nearest antenna surface

of the NBS-TG and the encased version, the NBS-TQ, is shown in figure 3. The

transmitting transfer function characterizes the electromagnetic fields which

are generated at a given distance by a known signal applied at the feed and

has the units of volts/meter/volt. This concept is discussed in reference

[3]. The front- to-back ratio for the NBS-TG is approximately 1; so even with

some reduction in forward signal, the improvement in front- to-back ratio for

the NBS-TQ is quite worthwhile. The improvement in front- to-back ratio is

very important for use in the close confines of a mine and especially where

noisy and highly reflective mining machinery is present. Thus, this task was given high priority.

2.4

Isolation in the Bi static Configuration

A pair of the NBS-TQ antennas were mounted with the E-field directions

parallel. They were then tested with different spacings between the antennas,

different baffle configurations between the antennas, and different standoff

distances from material surfaces. The results of this work generally showed

that an optimum spacing between antennas should be about 36 cm with a baffle

centered between the antennas and extending about 68 cm to the front. The

most effective baffle tested consisted of a thin dielectric material (1/4-inch

plywood) with a sheet of absorber glued to both sides (see figure 4). A metal

baffle gave more isolation between antennas, but interacted with the antennas

and the ground to give other responses which were undesirable.

13
2.5 Operation Close to Surfaces

For operation near a coal face, for example, the antennas should change

their characteristics as little as possible as the surface is approached.

This means that the effect of variations in spacing from the coal surface

encountered during use will not be a source of confusion. If the antenna performance is insensitive to distance from the coal face, it is possible, as a first step in processing the measurement data, to subtract a background signal

which is common to the system. The background signal can be obtained by

pointing the antenna pair at the sky in a position where it is not near reflecting objects. Figure 5 shows a comparison of the response of the TQ

antenna pair with the baffle pointed at the sky with the response from a metal

plate. Figure 6 shows how this same system sky response may be subtracted

from a ground signal to yield an enhanced response from a buried target. It can be noted that even though the target response (see arrow) is down in absolute amplitude, its relative amplitude increase makes it visually more obvious

in the corrected waveform.

3. POTENTIAL FOR DIELECTRIC LOADING OF ANTENNAS

The infinite "bow-tie" antenna belongs to the frequency independent class

of antennas because its shape is defined entirely by angles [1,2]. As a result, its impedance, polarization, pattern, etc., are independent of frequency and the antenna is said to be broadband. The characteristics of such

broadband antennas are necessary for accurate impulsive electromagnetic field

measurements [3] which can be used for the detection and analysis of prominent

features in a geophysical environment [4].

The overall purpose of this section is to investigate the characteristics

of a practical, i.e., finite, bow-tie antenna with the following specifications. The antenna should be broadband, matched to a 50-ohm source line, and

have some directionality [5,6]. The frequency range of interest for this

study is specified to be from 10 MHz to 1 GHz. To achieve these goals, con- siderations are given to dielectrically filling the antenna which also

increases its electrical size [5]. Resistively loading the antenna to achieve

broadbanding from 500 MHz to 1 GHz is currently being studied at NBS [7,8].

First, the characteristics of the infinite bow-tie antenna as a function

of its shape [2,9] will be presented. Also, the effect of a dielectric medium

on its electrical properties is shown. Next, the "finite" bow-tie antenna is

considered, followed by a discussion on dielectrically loading antennas. By

the use of non-symmetrical dielectric loading, a directional bow-tie antenna

is then investigated. Finally, conclusions and recommendations are presented.

3.1 Infinite Bow-Tie Antenna

The problem of finding the characteristic impedance, Zq, of an antenna

consisting of two infinitely long conical conductors which have a common apex

has been solved by Carrel [9]. The examples presented include the coaxial

biconical antenna [10], the non-coaxial bi coni cal antenna [11], the coplanar

fin antenna, and the non-coplanar fin antenna. The infinite bow-tie antenna

14
can be simply treated as a special case of either of the latter two examples. See figure 7. Due to recent interest in TEM horns [7], it is appropriate to consider the infinite bow-tie antenna as a special case of the non- coplanar fin antenna (see figure 7). The solution for the characteristic

impedance, Zq, is given by

= nK/K' ( 1 )

where n = / ^

intrinsic impedance of the medium between the conductors. Here, it is only necessary to mention that K and K' are the complete

elliptic functions and inevitably depend only on the angles and Sq defined

in the figure. u and e are, of course, the permeability and dielectric

constant of the medium, respectively.

In figure 8, the characteristic impedance of the non-coplanar fin antenna

with equal fin angles is given as a function of and 9 q. For the infinite

bow-tie antenna, 0^ = 180 degrees. It should be noted that the values

obtained from figure 8 are for an antenna in free space which has a dielectric

constant, e^.

In a dielectric medium with a relative dielectric constant, e^, the

characteristic impedance , Zq (e^), is

Z

0

Z0

( 2 )

where Zq (gq) is the characteristic impedance in free space.

It is apparent that the characteristic impedance of an infinite bow-tie

antenna thus depends on both the fin angle, t|;q, and the dielectric constant.

These factors should be considered when matching the antenna to a 50-ohm

source line and/or a dielectric medium.

3.2 Finite Bow-Tie Antenna

The input impedance equals the characteristic impedance for the infinite

bow-tie antenna and for the infinite biconical antenna [12]. However, the

theoretical input impedance has only been obtained for the "finite" biconical

antenna. For the finite biconical antenna whose half-angle, is less than

about 3 degrees, the input impedance has been calculated [12]. For the wideangle biconical antenna, the input impedance has been calculated [12, 13].

For these cases, it is significant that the wider biconical antenna has not

only a lower characteristic impedance, but also an input impedance that is more constant as a function of cone length than the narrower antenna (see fig- ure 9). From this result, it has generally been concluded that wider antennas

are more suitable for broadband application. To further substantiate this

trend, Kraus shows that, for cones with half angles of 5°, 10°, 20°, and 30°

15
[12] and characteristic impedances of 188, 146, 104, and 80 ohms, respectively, the input impedance variation reduces with increasing cone angles (see

figure 10). It also appears evident that the input impedance varies about the

characteristic impedance, as is further seen in figure 11. The existence of

these factors should be determined by measurement for the finite bow-tie

antenna so that matching to a 50-ohm source line may be accomplished. It

should be noted that the results in [12] and [13] are for the cases where the

lower cone is replaced by a ground plane. Hence, the impedance values are half of those which would be obtained for the bi coni cal antenna. For

reference, the characteristic impedance of the infinite bi coni cal antenna with

equal cone angles is given in figure 12.

3.3 Dielectrically Loaded Antennas

The basis for determining the characteristics of the bow-tie antenna in

the presence of a dielectric has, in part, been discussed earlier in this sec- tion. To extend this basis, it is appropriate to study the cases where either

a dipole [14] or bi coni cal antenna [15] is imbedded in a spherical dielectric

of radius a, since the case for the bow-tie antenna has not been solved. By

letting a approach infinity, one could then study the effect of matching the

dielectric filling to the dielectric medium [16].

For the above cases, consider the dielectric sphere to have a dielectric

constant, e^, and let the dielectric constant of the medium be e

2

* For the

dipole case and for and k

2 a < 1, the radiation resistance decreases as ei

increases [14]. However, the radiation power factor, which denotes the available product of bandwidth and efficiency [14,17], increases only slightly for

1 < e < 4, where e e ^i/c 2 , and decreases for larger values of e. Over the

range 1 < e < 4 the radiation resistance decreases by a factor of 4. Hence,

although the resistance can be varied to possibly match to a 50-ohm line,

which is in itself desired, one might not expect a significant increase in

bandwidth.

For the wide-angle bi coni cal antenna and for and k

2

a < 1, the radiation power factor decreases as the dielectric loading, e, increases [15].

Also the conductance is independent of e. It should be pointed out that the

above results assume the electric field to be tangential to the dielectric

boundary. However, these results, along with those for the dipole case, may

be indicative of what to expect for the bow-tie antenna; that is, that the

power factor may not significantly increase and the radiation resistance may

decrease as e decreases. Dielectric loading may not offer a significant

improvement in antenna performance unless the antenna can be placed in contact

with the medium of i nterest--the coal seam in this case.

16
3.4 Directional Bow-Tie Antenna

Lytle [6] has shown that a miniaturized directional antenna can be

obtained by placing sources offset in material with a high dielectric constant. In a similar manner, one could offset the bow-tie antenna in a dielectric sheet such that the radiation would be maximized in one-half plane and

would be minimized in the other half plane. In principal, the wavelength in

the dielectric material, is

Xo

X. = (3)

where X

2 is the wavelength in the medium and e = where ei and C2

the dielectric constants in the material and medium, respectively. Hence, by

offsetting the antenna from one side of the dielectric sheet a distance d^^,

such that d]^ = (2s, + 1) Xj^/4, i an integer, and requiring the width of the

material to be such that the antenna is a distance, d£, from the other side,

where d

2 = nX]^/2, n an integer, one would maximize the radiation on the former

side and minimize the radiation on the latter side. This design can only be

optimized over a narrow bandwidth using frequency independent dielectrics.

Further work is required in order to develop dielectrics or ferroelectrics

which have dielectric constants inversely proportional to the square of frequency over the bandwidth of interest.

3.5 Conclusions and Recommendations

The input impedance of an infinite bi coni cal or infinite non-coplanar fin

antenna, which may be an infinite bow-tie as a limiting case or an infinite

TEM horn, depends only on the angles defining the antenna and on the permeability and dielectric constant of the medium. When these antennas become

finite, it appears that the input impedances of the wide-angle antennas are more constant as a function of frequency than are narrow-angle antennas and

vary about the character! Stic impedance. Such antennas, which include the

wide-angle bow-ties, are considered to be broadband.

By enclosing the bow-tie antenna in a sheet of dielectric, one may

increase the directional i ty of the antenna in a given band of frequencies, but

the radiation resistance may decrease as the dielectric constant increases.

Based on the above, one can design either a wide-angle TEM horn or bowtie antenna such that the input impedance is known within bounds for a given

dielectric medium. Thus, one can optimize the antenna so that its input

impedance can be matched to a 50-ohm source to maximize power transfer. Using

dielectric media such as air and water, it is recommended that the theory be

verified to determine its applicability. In particular, the input impedance

for the antenna in both media should be measured over the frequency range from

10 MHz to 1 GHz. It would then be feasible to increase the directionality of

17
the antenna over a frequency range by enclosing the antenna In a dielectric

sheet. The accuracy of the theory could be verified and the bandwidth of the

antenna immersed in the dielectric sheet could be compared to those obtained

for the infinite media.

The above recommendations could effectively be accomplished by using

image theory and performing the experiments using a ground plane, thereby

avoiding the use of a broadband balun, which can be a drawback for precise and

accurate measurements.

This section gives theoretical estimates of the radar range limit of buried targets. Cook, in 1974 and 1975 [18,19], investigated the subject. The

main parameters of the radar range equation are discussed, and the detection

range is found with appropriate receiver noise assumed and no clutter.

The theory needs to be augmented by practical experience with "radar

clutter," i.e., reflections from miscellaneous targets. This clutter is

rather analogous to precipitation and atmospheric turbulence clutter during

aircraft detection. The coal "atmosphere" has inhomogeneities that may act as false targets, giving clutter.

The desired targets considered are a borehole and a mine tunnel. The

radar cross sections of these targets are obtained by suitable modifications

of known theory for homogeneous dielectric and metallic cylinders and for a strip approximating an old workings tunnel. An outline of this section is as follows: The radar signal equation is given which contains the source power,

the antenna gain and area, the dielectric loss, interface loss, and inverse

distance loss of propagation in the medium, and the radar cross section of the

target. Cross sections for the targets of interest are derived in some detail, including new results for cross sections that depend on range. Finally,

with assumed system parameters, including the noise figure, the radar range

equation is solved (Appendix A).

The radar equation is developed in many radar books, e.g., Berkowitz

[20]. In our application, the radar back scattered received signal power in a homogeneous lossy atmosphere (the coal) is calculated as

4. SUBSURFACE RADAR RANGE LIMIT STUDY

4.1 Introduction

4.2 The Radar Equation

-4oR

1

( 4 )

18
where

P = emitted power during the rf pulse, or the effective

power level of the "continuous" wave of an FM-CW radar,

watts

,

Gj^, &2= gains of transmitting and receiving antennas (gains may

differ from specifications if target is closer than

diam^/wavelength)

,

0 = target radar cross section area,

Xq = wavelength of EM wave in air,

a = attenuation coefficient of the EM field due to the

material dielectric, loss specifically, a = the real

part of (-o)2ye)l/2 where w is the radian frequency and y and e are the magnetic permeability and electric

permittivity of the material,

e = £Q(e' - je"), where cq is the permittivity of vacuum,

and e' , e" are the real and imaginary parts of the

relative complex permittivity e* = e' - je" (with

exp(+jwt) time dependence), and n = / e* , a useful

refractive index for finding 9 in Snell's law.

1 = the reflection power loss at the air-to-material interface counting both the entrance and the exit of the

radar beam,

D = a dispersion effect which arises only from the broadening and consequent decrease in height of the signal

pulse due to dielectric dispersion in the medium. An

extended target (noncompact) may broaden the pulse. The

radar antennas and components may disperse the pulse.

Both of these effects are included in the FFT synthetic

pulse calculations in section 5 and are not included in

D,

R = range, distance from radar antenna to target,

= the part of the range distance that is in the coal,

Gj = convergence-divergence product to give the change of the

signal S due to refraction of the incident and the target returned signals through the interface.

In (4), the first fraction is the power density at the target and the

second fraction is the returned power density at the radar, both in assumed

free space. The third fraction is the receiving area of the radar. The terms

Cj, D, exp(-4aRi) represent various losses due to the ponderous medium and

i nterface.

In the remaining discussion, the case of Rj^ R will be recognized only

for the factors D, C(j|, and exp(-4aRi)*

19
Separation of the attenuation, exp(-4aR]^), from the dispersion effect, D,

is an approximation. In section 5, these factors are taken into account by

convolving the impulse response of the dispersive medium with transmitted and

reflected pulses.

4.3 Interface Transformation Factors, I

Factors of the interface problem are obtained by what is often called

Sommerfeld's method for a dipole in a half space. Hufford, in 1969 [22], gave

a rigorous derivation and practical results for the far field (obtained by

geometrical optics) and for the ground wave, both in the air half space with a buried electric or magnetic dipole source. The treatise by Banos [34], is

detailed; see especially his "Expansions valid over an entire hemisphere."

Brekhovski kh ' s 1980 treatise [35] is useful because, with the source in either

space, it gives specific equations for the geometrical optics term, the ground wave term, and a third term--the lateral wave. One of the authors of this

report (HEB) has extended the geometrical optics solution to all ranges, from

the interface to infinity in the refracted beam (as was necessary because the

target was usually quite near the interface). Although our solution looks

different, it agrees exactly with Brekhovski kh ' s first term.

Our solution will be briefly developed for an isotropic point source of

power in a half space and assuming classical geometrical ray optics with

energy conservation in the reflected and refracted ray-bundles (infinitesimal

solid angles) of the problem--see figure 13. Finally, to get the radar factors I and of equation (4), the results must be applied twice. The point source in air transmits to the target which then transmits back to the radar.

The geometry of the problem in a spherical coordinate system is com- pletely specified by assigning z^, the perpendi cul ar distance from the source

to the interface, n^ and n^ the refractive indices of the source space and the

other half space, respectively, and the location of the receiving point (field

point) at a distance, from the interface and from the z axis. From

Snell's law, the ray paths are found giving the angles 9^ and 0^, and r^ and

the distances from the source to the point of refraction and from there to

the field point, respectively. The source power is denoted as W_ watts. The

power density at distance r^ is Sq(Cq) = Wq/(4 n r^'^) W/m*^ in homogeneous

space

.

Now consider the power transport by the rays in an infinitesimal solid

angle, dQ^, at incidence angle, 0^, that will refract to the target. The

incident rays from the source are homocentric. Therefore, the power flow in

the solid angle is dW^ = SQ(rQ) dQ^ at distance r^ as it intersects the

interface. Note that the E-field rms magnitude may be obtained from

So = Eq Oq Yq where Yq is the wave admittance of the vacuum. The transmitted

power of the refracted rays is the incident minus the reflected power. Thus,

20
Fresnel's interface reflection coefficient, r, gives the power transmission

coefficient, (1 - |r|^). The power density, s-^y of the refracted beam based

on energy conservation is expressed as

s^ (R^) da^(R^) = s^(r^) da^(r^) (1 - |rl^) , (5)

where da is the area of a solid angle at the distance indicated.

It remains to find da^ of the refracted beam. The solid angle of an incident beam element at angle 0^ may be written in spherical coordinates as

dfi = sin 0 d0 de , 0 0 ^0 0 ’

where <}> = azimuthal angle and 0 = polar angle.

For the refracted rays by symmetry, d^^ = d^Q and by Snell's law

d0, = (n /n, ) cos 0 d0 /cos 0, . 1 0 1 0 0 1

However, to find the area of the refracted beam, we must recognize the

astigmatism of the refraction. At distance in the solid angle dQ^, the

range distance back to the apparent source of the ray bundle in medium 0, as determined by tracing back two rays diverging by d(j)]^ s d(t)Q, is R^^ + r^^ where

r, = r n, /n

1 0 1 0

(From this we find that the origin of the segment r^^ is a point on the z axis.) Therefore, one dimension of the refracted solid angle, dQ^, is

(R^ + r^) sin 0^ d(])^ .

The range distance to an apparent source point as determined by tracing back

two rays diverging by the angle d0^ is (R]^ + r 2

) where

r„21'= r^ (cos 0,/cos 0 ) 1 o'

21
The cross-section area of the refracted rays is then obtained at any distance,

doj^(R^) = + r^^) (Rj^ + r^) sin dcj)^^ de^ . ( 6 )

Finally, substituting into (5), including Fresnel's r, we find the transmitted

power density, Sj^,

h<"l' . 'o

yrp- (Kj + r^) (K^ + r^)

n^ cos ~Z

n^ cos

0 0

n^n, cos 0^ cos e, 0 1 0 1 cos 0Q + r\y cos 0j^)

TE

(7)

where TE denotes the TE mode, i.e., when the E-field is parallel to the interface. For the TM mode, replace the TE quantity by

2 (n^ cos 0, + n. cos 0^) 0 11 0

Equation (7) may be evaluated at the interface R]^ = 0. It reduces to

l£^(Rj^ > 0)/E^(r^)| = 2 n^ cos cos 0^ n^ cos 0^)

and, similarly, for the TM mode, both agreeing exactly with Fresnel's interface transmission coefficients (Stratton, 1941) [36].

We will show next that (7) reduces to Hufford's far-field solution as R^

tends to «. First, we must renormalize (7) to Hufford's reference field,

Ef. The field, E^, is defined as the field that would exist at the receiver

from the isotropic power source, Wq, if all space were homogeneously filled

with the material having refractive index n^^,

E^(r) = W^/(4 TT r^ n^Y^) , (8a)

and r is the direct distance from the source to the receiving point. The

incident Eq and Sq have already been defined in terms of Wq and rQ. After

taking the square root of (7) with Rj^ = «, which makes r

= «, and replacing

Eo(ro) by Ef(r) (r/ro) , we have

Ei(Ri) 2 cos 0^

T72

(n cos 0 + n, cos 0,

)

0 0 1 1 TE

(8b)

22
For the TM nx)de, use (Rq cos 9]^ + cos Equation (8b) agrees exactly

with Hufford's far-field result for his interface transmissions ]L Cg| and |L

C^l (TE and TM) when specialized to his case; namely, n^ = 1 in the air and nQ

is of the dense material in which the source is buried. Also, Hufford

obtained (Re n^)^/^ instead of our n^^^^ and he gave the phase of E^^/Eq.

Having started with power densities, we lose the phase and must assume the

dielectric loss tangents are less than 0.1 to yield square roots of Oq and n^

with less than 1% error.

The following tabulation gives computer results for 1E]^(R^)/E^ ( r) j (found

from equations (7) and (8a), valid at any value of Ri consistent with

the wavelength in medium (1), of figure 13, and also gives results for

Brekhovskikh' s f(Ri) multiplied by r--the distance defined in E^, equation

8a. Reciprocal paths were calculated. The fields, exhibit reciprocity as expected. The last column shows that 1 E]^/E^/'f(R 3^) j = (n^^/n^)^/^.

lo/l^i ^0 ^0. |El/Efl r'F(R^) E^/(E^rf(

2 20.7° 1, 1 0.546 0.7724 0.707

1/2 45° 1, 1 1.092 0.7724 1.414

2 20.7° 5, 1 0.788 1.115 0.707

1/2 45° 1, 5 1.577 1.115 1.414

The refraction contributes divergence when n^/nj^ > 1 and convergence when

nQ/n^ < 1. Hufford's normalization is especially appropriate for practical

calculation because |Ej^/E.pj^ is the power loss (or gain) of the interface.

|E]^/Ef| correctly changes value accordingly as divergence or convergence, d or

c, occurs. The separate factors I and are given, respectively, by

(1 - jrj^)^ (which is the last fraction in (7) squared) and by the first two

fractions in (7) evaluated in each direction and multiplied. The total

interface radar power transfer is

I = |Et/E^| 2 l^l/^fl^ ’

' " ‘d ‘ ‘c

evaluating equation (7) first with subscript o denoting parameters in the denser medium and 1 denoting the rarer medium, convergent case, and then again

with all parameters interchanged, divergent case. For the above example,

where r^ and R^ are 1, 5 and then 5, 1 on return, the value of IC^ is " 1.545,

using the table.

23
Summarizing, we have developed a convenient expression for Sommerfeld's

geometrical optics term which is valid from the interface, to R

2 = ®.

The ground and lateral wave terms have not been included, a valid approximation when 0Q and 0-j^ are small and and z^ are greater than and in the

two media. However, when the source is at or on the interface, Engheta, [37]

and Lewis [38] have demonstrated large correction of the optical term.

Our expression for this area in the refracted beam seems to be new, but

agrees with Brekhovski kh . His area term is somev/hat remeniscent of an equation in optics for the caustic which gives the location of the origin of our segment, V 2

» cf. Martin and Wei ford [39]. Their equation is ax^"^^ + b = 1 in a Cartesian system, where a and b are functions of n^, n^^, and z^.

Our caustics may be described as follows: The origin of rj^ is in medium

0 on the z-axis at a distance

Z, = z tan 0 /tan 0,

1 0 0 1

from the interface. The origin of r^ is found by tracing the refracted ray at

angle 0j^ backward into medium 0 a distance

2 ^2 " ^0 e^/cos 0q) .

These equations hold no matter which medium contains the source.

4.4 Attenuation in the Medium

The term exp(-4aR2^) gives the power loss in the medium during the round

trip. The factor a is the attenuation factor of the propagation constant in

the medium.

a + jp = ( -co^ \ie) (9)

A good approximation for coal media at frequencies of interest is

a = 0 ,5p e' tan6 (10)

1/2 where tan6 = e"/e' for the medium,*^000 and 6 = w ( a e ) , the phase factor of

free space. The error of the approximati on, (10), is proportional to 0.5

tan^6 i f tan6 <0.1.

24
Section 5 uses exact complex scattering coefficients of a homogeneous

cylinder to obtain exact synthetic pulse computer predictions of signatures of

the various cylinders. Synthetic pulse trials also allowed the factor D of eq

(4) to be estimated by comparing the pulses in dispersive coal and fictitious

nondispersi ve coal. From this we chose a very approximate value of D = O.S,

for a range sufficiently large to bring S/N down to approximately 2. (To a good approximation, D is proportional to de'/du in the radar frequency band,

and to range R^. Lynch [42] approximates de'/dco as proportional to tanS.

4.5 Radar Range Calculation from S/N

Tne ultimate radar range may be defined by setting the signal power, S,

of equation (4) equal to the noise power, N, of the radar receiver

S/N = 1, ( 11 )

and solving for R.

The noise power must be suitable for the type of radar, detection method,

search method, time duration of display, etc. However, we will use the noise

power often given for common rf pulse radar,

N = kTB NF (12)

where the Boltzman constant, k = 1.38 x 10"^^ watt/Hz Kelvin, T = temperature

= 290K, B = receiving bandwidth in Hz, and NF is the multiplicative noise figure. We have used NF = 6.31, which is 8 dB . This figure is somewhat higher

than that for well designed systems where 4 dB to 5 dB might be attained. The

noise figure theory is discussed in Mumford and Scheibe [23]. For baseband

pulse radar, the S/N may be obtained using the reflected pulse voltage, S,

divided by the rms noise voltage, N, of the usual A-scope presentation. By

signal processing, S/N can be enhanced by integration over many pulses with a sampling scope. The latter method may detect a signal smaller than noise, but

may require a significant amount of time depending on the pulse repetition

rate, pulse broadening by dispersion, and volume in the earth to be examined.

4.6 Radar Cross Section

Tlie factor a is given by the equation (Bovmian, Senior, and Uslenghi,

equation 1.30) [24],

2 2 2

1 i m ( R ^ “>

) a | E ^. | = 4i; R I ^

^

| , (13)

25
where is the field strength of the wave incident on the target and is

the field strength of the scattered field at the receiving antenna. R is the

separation distance of the target and radar. E^ must be either calculated or measured. Approximate calculations for a borehole and dielectric strip are given in sections 4.7 through 4.14 and used in Appendix A. (Exact cylinder

scattering was used in section 5.)

The use of a in (4) is simply a way of stating the value of [E^/E^l^ of

the target. The use of a/^% in (4) requires the a defined in (13). The

so-called cylinder cross section, ^ cannot be used directly, even for a cylinder, in solving equation (4).

Values of a are often available based on the theory of a plane wave, the source at infinity. As will be discussed, we deduce correction factors of 0.5

and 0.25 to the theoretical o of infinite cylinders and an infinite plane,

respectively, when the source is at a finite distance as for practical radar.

4.7 Electromagnetic Theory of Scattering Cross Sections of Extended Targets

The radar cross section in (4) and (13) may be essentially constant,

i.e., independent of range, R, for compact targets. Then, e.g., a of a large

O metal sphere is % r'^, r = sphere radius R >> r > \. For a general convex,

large, compact metal body

where rj and r 2 are the two radii of curvature at the reflection point.

For extended bodies, however, the cross section is usually a function of

the range distance, R. For example, a of an effectively infinite planar

metallic interface is % R^. With this cross section, the signal in (4) decays

as R“^, instead of R"'^ as for compact targets. Cook [19] deduced R"^

dependence, qualifying it as being only for a rough surface.

The references on radar cross sections, (Berkowitz, p. 556) [20], (Kerr,

sect. 6.2) [25], (Ruck) [26], and the basic EM scattering treatises, e.g.,

(Bowman, Senior and Uslenghi) [24], do not specifically give these rangedependent cross sections. The basic theory is the basis for the cross sections that we will give for cylinders representing boreholes, and for

strips representing old workings tunnels. The purpose here will be to obtain

theoretical values for such targets, including the necessary range

dependence. Tarantolo and Unterberger [27] deduced a dependence on range,

beamwidth, and pulse length. Our results differ from theirs. In particular,

the beamwidth is not a necessary parameter for usual conditions.

26
4.8 Cross Section of a Planar Interface

Consider, as a simple example, a small radar antenna interrogating an infinitely extended flat metallic interface. The field is at 1 m from the

source point. The incident field at the target at distance R is then

Ei = Eq/R.

By image theory, the radar receiving antenna may be at distance 2R with the

interface removed . Therefore, we deduce that the received (scattered) field

i s

Es = E^/2 . Eq/2R.

These fields in eq (13) give

- a = 71 R (14)

dependent on range as was stated previously.

4.9 Half-period (Fresnel) Zones

Radar aspects of scattering from a plane, a strip, and a cylinder may be

obtained by Ki rchhoff-Fresnel -Huygens ' concepts of wave surfaces and scattering surfaces as intermediate sources. There are half-period (Fresnel) zone

areas on the surfaces that contribute a range of phases from zero to n, n to

2 ti, and so on. Kerr [25], section 6.2, obtained radar cross sections of plane

and curved surfaces by the vector Ki rchhoff -Huygens method. He states, p.

417, that Fresnel zones may be defined on reflecting surfaces.

The scalar Ki rchhoff-Huygens method will be used here to obtain an approximate solution for a strip, and to obtain a rather good estimate of the

difference between theoretical plane wave incidence, and practical pointsource, radar cross sections. First the planar surface will be reconsidered

and (14) redeveloped from diffraction theory to illustrate the Kirchhoff

method

.

In a Cartesion coordinate system, consider a planar reflecting intermediate surface lying in the yz-plane at x = 0 with a point receiver at x = R and

a point source at x = R', both on the x-axis. The radius of the circular

first half-period zone on the intermediate surface is

r^ = /R' R\/(R' + R) , (15a)

assuming R, R' >> X. In the case of monostati

c

radar R' = R,

27
= /R X/2 . (15b)

In the case of a fictitious plane wave incident radar, R 00

r, = /RX . 1 (15c)

There are successive annular half-period zones surrounding the first zone.

For more discussion see, e.g., Jenkins and White [31], chapter 18, and Kerr

[25], chapter 5.

The total reflected field from a smooth flat or curved intermediate sur- face is almost proportional to the area of the first zone. For a planar target, the areas and consequent relative scattered fields, , for monostatic

and for bistatic plane wave incident radar are proportional to the circle

areas, % R X/2 and n R X, respectively, from (15b, 15c). The scattered fields

proportional to these areas are (by a calculation similar to Fresnel's

integrals in equation (17))

where m denotes monostati

c

, and pwi denotes plane wave incident radar.

The interesting conclusion may be drawn that the concept of half-period

zones enables us to solve, approximately, the problem of how to obtain monostatic point-source radar cross sections from known canonical plane wave incident scattering solutions, as will be further demonstrated below.

For the radar interrogation of an infinite planar interface, equations

(16a) in (13) give

(16a)

E

i

* s , pwi

2 a TX R m

2 (16b)

here correctly agrees with equation (14).

28
4.10 The Strip Approximation of a Tunnel

Consider next an infinitely long dielectric strip representing one side

wall of an old workings tunnel. The reflection of the farther side wall of

the tunnel will be discussed qualitatively later. Assume that the width of

the strip is 1.5 m (5 feet), which equals 1 to 5 wavelengths in air (more in

coal), for radar whose main spectrum is in the band 0.2 GHz to 1.0 GHz. With

these parameters, the reflection coefficient of the assumed strip may be represented by a physical optics approximation, which means that the discontinuities at the edges of the strip are disregarded.

a metallic strip initially instead of the dielecthe radar (which is located on a of the order of the strip width, 2 w

or less, the cross section is

2 approximately that of an infinite planar interface, i.e., a ~ tt R , from

(16b). The reflection will be relatively strong at such a close distance. It

may be shown by means of Fresnel integrals that o will vary by about ± 2.5 dB

from IT k^, depending on w/rj^ (w = half width of strip).

It is useful to discuss

trie interface strip. When the range,

normal from the center of the strip) is

(~ 1.5 m), of the order of a few wavelengths

The important case of the strip far from the radar, presenting a small cross section, may be solved by application of the Ki rchhoff-Huygens method.

Assume the width, 2w > x, so that the discontinuities at the edges of the

strip may be neglected, and the range, R >> w, so that the waves are approximately at perpendicular incidence over the first Fresnel zone. The

results for plane wave incident (pwi) radar and for monostatic radar looK the

same; E-scattered is

Es = [C (u) - j S(u)] (17)

where E^- is incident field, C and S are Fresnel's cosine and sine integrals

(tabulated functions) and u = /2 w/r^. (The total phase lag of R' + R is suppressed.) For pwi radar R' -> «> and (15c) is used. For monostatic radar

R' = R and (15b) is used. For the conditions assumed, especially R >> w which

gives r^ > 2w, the approximations C(u) = /? w/r^ and S(u) =0 hold, giving

IE /E. I = /~Z w// XR (monostatic) , (13a)

' s 1 'm

l^s/^ilpwi = 2 w/AxR (pwi) . (18b)

These field ratios in (13) give range-dependent cross sections,

= 8 IT R w^/X = 4 w^ R , (19a)

Vi " = 8 k^ w^ R . (19b)

29
It may be confirmed that these results are a good approximation by suitable

comparison with eq 7.4 - 17 (Fig, 7-17) of Ruck [26], which gives

o'^ ~ 1 + (2 w)^ (20a)

where is the cylindrical cross section per unit length, not a function of

range, R. The cylindrical cross section in (20a) is defined as = lim 2 -n R

p |E^/E.jp, in the limit as R (As was discussed, the correct a radar is

obtained by putting E^/E^- in equation (13)). However, for the present com- parison, we want (from (18b)) which is obtained as

= 8 u w^/\ , / = 16 T? w^/\^ = (2 k^w)^ , (20b)

almost agreeing with Ruck, i.e., with (20a) but missing the 1 of (20a) because

we have neglected edge effects, which is valid because w/\ > 1. It is con- cluded that our range-dependent cross sections (19a) and (19b) are correct

approximations, neglecting edge effects.

4.11 Cross Section of a Dielectric Tunnel at Broadside Incidence

The necessary next approximation is to assume that the cross section of a dielectric strip interface may be obtained from that of a metal strip by the

rel ation

a.. T = a . T Irl^ (21) diel metal ' ' '

where r is the reflection coefficient at the tunnel interface. Using the

1/2 notation refractive index, n = e* , the reflection coefficient in passing

from medium 1 to medium 2 is

r = (n^ - n 2 )/(n^ + n^) .

For example, r from coal with = 5 and a water-filled shaft, e2

= 81, is

r = - 0.60

w

30
and from coal to a gas such as methane or air is

r = + 0.38 . d

These values in (21) show that a of a water-filled shaft is 2.5 times greater

than for a gas, depending upon the assumed permittivity of the coal medium.

The farther wall of a tunnel has a reflection coefficient of the same magnitude as the first wall. There are multiple reflections in the time domain.

However, the EM power returned by the second wall is

(1 - | r|^)2 ( 22 )

weaker than from the first wall, due to the transmission loss in each direction at the first wall. (Equation (22) is the square of the factor in (5).)

These multiple reflections will be seen as successively smaller reflections in

the time domain, or as interfering varied amplitude returns with an FM-CW

swept radar.

We note that, with gas in a shaft, the sign of the reflection coefficient

at the first wall is positive. With water, the sign is negative. The opposite occurs at the second wall. In effect, this is also true for detecting a borehole when k^an

2 is large.

We conclude that, at least theoretically, the radar return signature may

be used to identify the target, i.e., to solve the inverse problem. The

magnitude and sign of the reflection coefficient, and/or the rate of decay of

successive reflections (influenced by attenuation of water) may give the width

of the shaft and distinguish between water and gas filling. Successive

reflections are seen in the simulated pulse study in section 5.2. Thus,

detailed data could contribute to solving the inverse problem. Wittmann [40]

has demonstrated comparable synthetic pulses in a planar layered medium. Roe

and Wittmann [41] gave a synthetic analysis of the phasor signals of the FM-CW

radar scattering from a planar layered medium, to distinguish n^^ < or > n 2

«

4.12 Cross Sections of Circular Cylinders (Boreholes)

The radar scattering of circular cylinders involves concepts similar to

those brought out in the scattering of a strip (tunnel). Just as for the

strip, we will convert to the monostatic radar case by observing that the significant excited length along the cylinder is 0.707 of that for the canonical

plane wave incidence case.

The scattering of a small cylinder is much greater with TM polarization

than with TE polarization. Only the TM case will be discussed. In the mine,

the antennas should be oriented to give a vertical E-field. However, it would

be useful to rotate them by 90° in trying to solve the inverse problem of

identifying a target, e.g., to distinguish a borehole from a tunnel and to

identify clutter.

31
The scattering from a metallic cyl inder with plane wave incidence and the

receiving point at distance p >> a, a = cylinder radius, is

lim(p > - E. (2/n P , (23)

p = - J (-1)" cosn4./H<^)ka) (24)

where = 1 for n = 0 and = 2 otherwise, and

k = . (25)

The Jpi are Bessel functions, 4

> = 0 for monostatic radar, and the are

Hankel functions for outgoing waves, section 2.2.1 [23], [26]. In (23) the

phase factor, exp(- jkp - jtx/ 4) , has been omitted. The e* is of the

surroundi ng medi urn.

Using Eg/E^- of equation (23) in (13), which amounts to assuming that

there is a bi static radar with the source at infinity and the receiver at R = p, we get

a . = 8 R|P|^/k . (26) pwi ' ' '

However, for practical monostatic radar the^

is removed from the numerator

of (23) giving

= 4 R|P|^/k . (27)

As in equation (16) for the strip, a = 0.5 a •. The k is in the medium.

It may be shown that in the geometrical optics approximation, i.e., a > \,

|P|^ = kii a/4, which in (27) gives

"^m,G.O. ~ R ^ 3 • (28)

The dependence of cross section on range, R, was also demonstrated in the

development of equations (14) and (19a, b). The change in cross section for

the case of plane wave incident radar and monostatic radar, a factor of 4 in

(17b) and factor of 2 in (19a, b), was deduced. The reasons for all of these

results may be based on the concept of the first Fresnel zone area as a function of R and the consequence that = 0.5 for a long cylinder.

32
The method of obtaining the monostatic cross sections of strips and

cylinders by multiplying , by 0.5 furnishes a very simple approximation

which avoids difficult calculations for a full wave [28], point source radar

solution in place of eq (23). Our approximate results are, however, believed

to be reasonably accurate for R >> a, R >> X. (We recently found that Brysk

[32] deduced the factor 0.5 = a range dependent a.)

4.13 Computer Routine for S/N Versus Range

The appendix lists a computer program for calculating the signal/noise

ratio, S/N, of an FM-CW radar. The program is in BASIC language and is suitable for a desk top computer. It solves for S of (4) divided by N of (12) as

a function of range, R. The approximation of equations (21) and (22) are rea- sonable for large water-filled bore holes; but for air filling, the ranges are too optimi sti c--especi al ly if the hole diameter is less than the wave length

in the coal. (For the tunnel, (21) and (22) are good approximations.)

Figure 14 shows curves of S/N as a function of distance for detecting a 3u-cm diameter well. Reasonable values for two coal "atmospheres" and three

borehole contents: metal, water, and gas are assumed.

The exact solution (23) is used for metallic cylinders in the intermediate range, ka, of the order of 1. For small ka, an accurate Rayleigh-type

approximation is used. For large ka, the geometrical optics value,u a, as modified (28) for monostatic radar, is used. The cross sections with

dielectric filling were assumed to be the above multiplied by | r| , equation

( 21 ).

4.14 Conclusions

The radar signal equation was modified to take into account changes in

the signal due to the coal "atmosphere". These effects include mainly the

air-to-coal interface, the attenuation of the waves by the dielectric loss,

and the spreading of the pulse by dielectric dispersion in the coal. The last

effect had to be estimated; more research on dispersion could be useful.

Regarding the target locations, they were idealized as being straight

ahead of the working antennas. A borehole off to the side would, theoretically, give a weaker signal because the radar antenna gives maximum gain

straight ahead. Preliminary experiments to evaluate the degradation of the

range capability for off-side boreholes would be useful.

The old tunnel may give a small cross section if it is higher or lower

than the radar antennas and, also, when it is not perpendi cul ar to the working

tunnel surface. Regarding the relative heights, the inevitable roughness of

the old tunnel wall will furnish some non-specular reflections, thus permitting some reflection, though weak compared to the specular reflection cross

33
section used in (19a). For non-perpendicular intersection of the old and new tunnels, the antenna gain pattern, Gq, of the radar antennas for the ray angle

that arrives at perpendicular incidence on the old tunnel will determine the

change in the cross section.

There is a real need for experience with clutter. The scattering of var- ious clutter targets both attenuates the wave to and from the desired target

and gives interfering signals that may, in effect, raise the noise figure, NF,

of (13).

It may be noted that Ruck [26], devoted Chapter 9 to rough surface

effects. Their work could be useful in extending the present work.

We have attempted to give a clear explanation of the cross sections of

infinite planes, cylinders, and strips. Some of our results may be new. Tine modification of plane wave scattering theory for point-source radar scattering

c c was investigated and solved. To find a for eq (4) from a use a = 2Ro .

Finally, it seems necessary to caution that with the targets off-side,

higher and lower, walls not perpendi cul ar, rough targets, and also clutter, we cannot expect ranges to be as great as those calculated in the figures.

The antenna pattern in the material is limited to forward directions.

For example, if the pattern in air covered the whole forward hemisphere, then

the pattern in coal with e' = 9 would cover only 19.5° from straight ahead of

the significantly illuminated area of the interface.

5. Pulse Response Simulations

Impulsive signals have typically been used at NBS for geophysical probing

because they are relatively easy to generate at high repetition rates, and

they have a broad spectral content and a short duration which permits discrimination between closely-spaced returns. On the negative side, it's very

difficult to construct efficient, portable antennas with sufficient bandwidth. In addition, the higher frequency components of the 1/2-ns NBS impulse

generator are severely attenuated in lossy materials such as coal.

At the contract monitor's suggestion, a comparison of potentially useful

pulse waveforms was done by simulating the transmission between the two TQ

antennas in air. The received signals are examined for amplitude, width,

distortion, and for the feasibility of using additional signal -process! ng

techniques. The analysis is extended to include transmission through a lossy

medium and reflection from a borehole as described in chapter 4. The result

is an estimate of the likelihood of detecting a borehole at a given range with

an actual measurement system.

34
5.1 Waveform Comparisons

The two TQ antennas, separated by 1.5 m, are treated as a two-port network. The simulated response of this network to any signal is the convolution

of the input waveform with the measured network impulse response. Impulses of

1-volt amplitude and 1/2- , 1-, 2-, and 5-ns duration at the 50% point were approximated by the raised cosines shown in figure 15 with the spectral distributions of figure 16. Clearly, the 5-ns impulse has so little energy in

the pass band of the antennas (see figure 3) that only a very small signal

would be expected at the receiving antenna terminals. The results of the con- volution operation (figure 17) confirm that impulses with a duration of much

more than 2 ns will be too inefficiently transmitted to be useful with the TQ

antennas.

Similar comparisons using 1 volt peak-to-peak sinusoids of 1, 2, 4, and 8

cycles are illustrated in figures 18 through 20. The carrier frequency was chosen as 250 MHz to approximate the transition duration of the impulse generator to be delivered to the Bureau of Mines as a part of this contract. The

monocycle, with its reduced energy at lower frequencies, may be an improvement

over the impulse. The received signal is no better for the other three 250

MHz examples, and the additional pulse width would make detection of adjacent

geologic features more difficult.

Above-ground radar systems use pulse compression schemes to combine a narrow response with higher average power. This can be accomplished by transmitting a carrier frequency which is a linear function of time, a so-called

chirp, and cross correlating the returns with a replica of the chirp. Hard- ware is becoming available which could potentially perform the same function

quickly in a coal mine environment without extensive computer processing.

A set of linear chirp waveforms are shown in figure 21. These were

chosen as an estimate of what might be usefully transmitted using the TQ

antennas. The three waveforms are: 250-500 MHz in 10 ns, 250-1000 MHz in 10

ns, and 250-1000 MHz in 20 ns. The spectra of these pulses are shown in

figure 22. The resulting received waveforms, after transmission over a 1.5 m

path with a pair of TQ antennas, are shown in figure 23. Correlation

techniques would be less effectively applied to the upper waveform which shows

little evidence of the frequency change. The higher frequencies of the other

two waveforms would be severely attenuated in the coal. That additional

distortion could limit the system's effectiveness. A fourth chirp was numerically generated covering 300-600 MHz with a 20-ns duration. Figure 24

shows that the simulated received waveform retains the chirp characteristic.

The autocorrelation of that waveform as depicted in figure 25 demonstrates the

extent of the pulse compression possible. Compare this result to the

autocorrelation of the 4-cycle, 250 MHz sine wave presented in figure 26.

Both received waveforms are about 25 ns in duration, but the chirp has a much narrower autocorrelation function.

Multi -cycle sinusoids will be less effective sources than will simpler

waveforms until rapid coding schemes can be perfected. Chirps, on the other

hand, offer distinct advantages if the "clutter" signals can be suppressed.

Some additional work is certainly warranted in this area. At present, it seems that 1- to 2-ns wide impulses or monocycles are optimal choices for the

antennas and detection system.

35
5.2 Borehole Detection Estimates

It is helpful to have a method which predicts the response of a measurement system to a particular mining threat. One can combine an incident wave- form with the antenna impulse response as was done in the previous section,

correct for the attenuation in a lossy dielectric material, include the

reflection characteristics of a given target, and thereby estimate the amplitude and form of the received signal. The analysis can predict the ability of

a given system and data processing technique to discriminate between targets

and background responses and can estimate the limiting range of the system.

A 1-volt amplitude, 1-ns duration impulse (figure 15) was chosen as the

incident waveform and convolved with the TQ antenna impulse response. The

antennas were assumed to be immersed in the dielectric medium, i.e., no cor- rections were made for the air/coal interface in the simulation. The antennas

might well be placed directly against the work face when the system is to

achieve maximum range. Typical surface roughness and contours add great

uncertainties to any estimate of the reflection at that interface.

The coal seam was modeled as a frequency independent dielectric with

infinite extent. Dry coal was assigned a relative dielectric constant of 3.65

and a loss tangent of 0.03; for damp coal, it was 6.5 and 0.05,

respectively. These are reasonable approximations since our primary operating

range lies above 200 MHz. When measured values of dry coal permittivity

versus frequency were substituted for the frequency independent value, the

results were not substantially changed. We are not aware of measurements on damp coal covering a broad enough spectrum for this analysis.

Vertical boreholes representing the uncharted, abandoned wells are the

mining threats of greatest interest for this work. Based on Bowman [24], the

complex reflection coefficient was computed at each of the component

frequencies of the simulated pulse for several types of boreholes in dry and

damp coal. The antennas are considered as point sources. The responses to a metal-cased 15-cm radius borehole, an empty hole, and one that is water-filled

are given in figure 27 for a 1-m range. As expected, the response from the

cased hole is larger and inverted when compared to the empty hole return. The

water-filled, uncased pattern is much more complicated. The slightly saline

solution delays the signal enough that each reflection across the diameter of

the pipe is distinct and inverted from the previous one. Thus the sign,

amplitude, and pattern of a response may well indicate the type of threat

encountered. Figure 28 illustrates the rapid attenuation of the response to a cased 15-cm radius borehole in relatively damp coal as the target range is

increased. The received signal drops by more than 30 dB as the range is

increased from 2 m to 5 m.

A summary of these simulations is presented in figures 29 and 30. The

predicted responses from five types of boreholes at ranges to 10 m in dry and

damp coal are shown. Since the noise introduced by the sampling circuitry of

a time domain receiver is on the order of 1 mV, high voltage pulses, preamplification, and signal averaging will be required if the system is to

recognize boreholes at even a five meter range. Electromagnetic (EM) techniques have been used over large ranges in salt domes. The response of the

36
system to a 15-cm borehole in rock salt at various ranges is also shown on figure 29. A relative dielectric constant of 6.5 and a loss tangent of 0.001

was assumed for rock salt. Clearly, operation at much larger ranges is

possible in a low loss material such as salt.

6. Pulse System Equipment

A prototype time domain measurement system has been assembled for delivery to the Bureau of Mines at the conclusion of Phase II. The design goals

emphasized a portable system that could be readily interfaced to the existing

equipment at both the Bureau of Mines and NBS and which offered flexibility

and fast waveform acquisition. As shown in figure 31, the equipment includes

the TQ antennas described in chapter 2, and an impulse generator and equivalent-time sampler located at the antennas. A two-channel fiber-optic link

carries the analog signal and trigger to a remotely-located digital acquisition unit where the waveforms are analyzed and stored on floppy disks. In this arrangement, laboratory equipment has been integrated into a wide bandwidth system useful for a variety of subsurface measurements.

6.1 High-voltage Impulse Generator

A specially constructed pulser supplies 500-volt high, 2-ns wide

impulses to the 50-ohm transmitting antenna at a pulse repetition frequency

(prf) of 10 kHz (see figure 32). The spectral content of the pulse overlaps

the operating ranges of the TQ's and other Bureau of Mines' antennas. A

stable pretrigger, adjustable from 50 ns to 300 ns, is furnished to the highfrequency sampler. The unit may be operated from either the power line or a 12-volt battery. Always set the 10-turn voltage control to 0 (full counterclockwise) and the RATE switch to OFF before turning the power ON. Allow a two-minute warm up, set RATE to ON to enable the clock circuitry and pretrigger, and increase the 10-turn voltage control. Set that control to 0 again

before turning the pulser OFF.

6.2 Receiver Preamplifier

An optional 29-dB amplifier between the receiving antenna and the highfrequency sampler provides two functions in the system. It boosts low-level

signals of up to 30 mV. The amplifier has good fidelity and a bandwidth of

10 MHz to 2 GHz. In addition, it acts as a limiter for signals of up to

1/2 volt at its input, holding the output to about 1 volt maximum. The amplifier compresses the signals from the receiving antenna, enabling the sampler

to recover returns which otherwise would be buried in the sampling noise while

protecting the sampling diodes from damaging voltages. The unit has a quick

recovery from saturation. The input to the amplifier must be limited to not more than 7 volts for 3 ns or the unit may be damaged. When using the highvoltage impulse generator, take care that the peak received signal (usually

from the air/coal interface) does not exceed 1/2 volt. Add attenuators and/or

remove the amplifier when large signals are likely.

37
6.3 High-frequency Sampler

The sampler is used to construct a discrete, equivalent- time replica of

the repetitive signal from the receiving antenna/preampl ifier. By sequentially acquiring one point per repetition at increasingly delayed times over

1024 signals, the system assembles a waveform which resembles the input signal

but with a duration of about 100 ms instead of 200 ns. This longer waveform

can easily be digitized in real time and transferred to a computer for further

processi ng.

The high-frequency sampler is a modified version of a commercial oscilloscope plug-in and is compatible with the present equipment at both NBS and the

Bureau of Mines. The unit uses replaceable sampling heads which offers several advantages. First, if a sampling diode bridge were damaged on a field

measurement, the head alone could be exchanged; there would be no need to send

the modified sampling plug-in for repair. Second, a higher performance sam- pling head could be substituted if wider bandwidth signals were to be measured. The sampling head furnished with this system covers dc to 1 GHz at

- 3 dB, but models are available with responses to 12 GHz. Finally, the sam- pling head is quite small, and possibly a long extender cable could be integrated into the sampler in the future to allow the head to be lowered into a borehole. This potential was attractive to the Bureau of Mines. The normal

input range of the sampler is up to 1 volt peak-to-peak with a tangential

noise of 1 mV, indicating a dynamic range of 54 dB without signal averaging.

The high-frequency sampler could be set up as follows for a coal-seam

measurement:

With that arrangement, a 200-ns time window would be acquired which represents

a 10- to 15-m range. Since the time corresponding to the left edge of the

window can be varied from 0 ns to 1000 ns, the total observable range is from

0 m to between 60 m and 90 m, depending on the permittivity of the coal. If

shorter ranges are desired, set the time-distance dial to X.l, which permits a viewable range in damp coal of at least 10 m from the face.

The output of the sampling process is a discrete waveform resembling a staircase in which each step corresponds to a single sample. The frequency at

which the samples are taken is constant regardless of the time window selected

and is equal to the prf of the impulse generator. The SCAN control must be

adjusted to set the width of the equivalent-time waveform so that enough sam- ples are included to accurately characterize the sampler input signal. At

TIME-DISTANCE : TIME/DIV ; PRESET : HIGH RESOLUTION : mV : ATTENUATOR : STABILITY : LEVEL : SLOPE

0, XI

20 ns Out

Out

In 200 mV/di

V

ccw

cw

+

38
least 5 samples/nanosecond are required for the high-voltage impulse generator. The product of that number, the TIME/DIV setting, and 10 divisions

yields the total number of samples in the equivalent-time waveform--in this

case, 1000. The duration of that waveform is the number of samples divided by

the impulse generator pulse repetition frequency, 10 kHz for this case. Thus,

the impulse generator prf (or 30 kHz, whichever is less) dictates the rate at

which samples are taken, the scan control determines the number of samples in

the equivalent- time waveform, and the TIME/DIV setting maps the real time window into equivalent- time. At full clockwise, the SCAN control selects about

512 samples. That number increases as the knob is turned counterclockwise.

Connect an oscilloscope to the SWEEP OUT jack, and adjust the SCAN control

until the ramp is the correct duration.

The plug-in "blanking" signal provides the trigger marking the start of

the equivalent-time waveform. The output waveform is derived from the plug-in

"VERT SIG OUT" which is scaled to 1 volt peak-to-peak to be compatible with

the fiber-optic system. The high-frequency sampler may be connected to the

digital acquisition system through the fiber-optic link or through up to 20 m

of coaxial cable by reconnecting two coaxial cables within the sampler. The

plug-in may also be removed from the sampler and inserted directly in an oscilloscope for laboratory use.

6.4 Fiber-optic Transmission System

A two-channel, fiber-optic transmission system provides low noise signal

paths from the high-frequency sampler, which is located at the receiving

antenna, to the digital acquisition system at a remote point. The system

consists of two channels, one used to transmit the equivalent-time replica of

the received signal and the second for a trigger marking the start of that

waveform. Each path consists of a transmitter, approximately 125 m of fiberoptic cable, and a receiver. The system has a maximum signal, in or out, of

1 volt peak-to-peak and a frequency response of 15 Hz to 25 MHz. The dynamic

range has been verified at greater than 50 dB.

Both commercial transmitters have been modified. The input impedances

have been increased to 600 ohms to reduce the loading of the previous

stages. In addition, an R-C differentiating circuit was added to the transmitter in the trigger path to condition the TTL "blanking" signal to the bandwidth and input voltage limits of the fiber-optic system. As a result, the

transmitter units are not interchangeable and damage may result if the cables

to the transmitters are reversed.

The receiver units require 50-ohm terminations. A feedthrough terminator

must be used on the signal path. The trigger signal is terminated and transformed to > 2 volts to reliably trigger the digital acquisition system. No

additional termination is required for that channel.

39
6.5 Digital Acquisition System

The digital acquistion system consists of a microprocessor-controlled

waveform recorder, monitor, and 5 1/4-inch floppy disk drive. The waveform

recorder can acquire up to 10,000 points at a 66 kHz rate with 12-bit A/D

conversion. It can average repetitive waveforms to reduce the effects of ran- dom noise, correct for time and amplitude scaling, apply tiine-weighted-gain

functions, and subtract previously acquired waveforms such as background or clutter waveforms. The measurements, setups, and procedures are stored on diskettes or transferred to a controller/computer via either RS-232 or GPIB

interfaces.

The unit would normally be used in the averaging mode, external trigger

at 10% level, with the sweep time equal to the duration of the high-frequency

sampler's equivalent- time waveform, and with 1000 element arrays.

7. FIELD TESTING

7.1 MBS Test Range

An indoor test range has been installed at NBS (see figure 33). This

test range holds both air-filled and water-filled voids for use in checking

underground void measurement or imaging systems. The loss in the soil of the

range goes from about 25 dB per meter at 300 MHz to about 50 dB per meter at

1 GHz. This loss is quite high for operation of any radar system at these

frequencies and thus represents a rather stringent test of any detection system.

Several series of measurements were taken with the pulse and FM-CW systems using different antennas and antenna arrangements. Using the TQ antennas

with a center baffle (as described in section 2.4), a sequence of 26

measurements was made starting at the end of the range having the air-filled

targets. The transmitting and receiving antennas with the septum were moved

along the range as an assembly. Responses were recorded at 5-cm intervals.

Figure 34 shows a typical result using a possible data handling method. Curve

1 shows the average background response for the series. Each point on that

curve is the mean of the 26 responses at that relative time. Curve 2 shows

one of the response curves taken over the 0.6-m deep target. Curve 3 is

obtained by subtracting an average background from a response taken over a target to show how the target signal may be enhanced. The target response is

shown by the arrow in figure 34. A series of enhanced responses is shown

stacked in figure 35. The hyperbolic contour of the target signal (arrow) can

be relatively easily seen.

Other approaches to the deconvolution problem were tried, but at this

time no significant results are available. A large number of measurements

were made using the FM-CW system with very similar results to those of the

pulse system.

40
7.2 Coal Mine Results

Measurements of borehole returns were made at the Kaiser mine near Raton,

New Mexico. The useable boreholes were located in a bench of coal approximately 1.6-m thick which was left in an open pit area of the mine. The

borehole diameter was 12 cm. All the measurements made at the mine site were

done with the FM-CW system.

The most notable result is that there was much more consistency from

point to point in a series of measurements with the hole refilled and tamped

with coal than in a similar series run with the boreholes either empty or with

a metal pipe inserted. Placing a pipe in the hole especially alters the

response pattern over a wide frequency range and a wide special range much more than would be indicated by simple theory. Probably, more theoretical

work is needed on the FM-CW system before proceeding much further with hard- ware implementation.

Some series were run using a variable-densi ty recorder to display

results. It appears that this approach may be useful to help visually

interpret a large amount of data.

Long delays in delivery of equipment ordered for this project precluded

additional tests that had been planned for that site and a location at the

Pittsburgh seam.

8. ADAPTATION OF SEISMIC DATA METHODS

A local commercial company, suggested by the Bureau of Mines, was approached to suggest methods for applying its proprietary seismic data

analysis techniques to electromagnetic pulse-type responses. The results of

the initial discussion seem promising; but thus far in the program, we have

not been able to provide the multiple results in the pattern which their

method demands.

It should be noted that the suggested approach utilizes a modification of

the common depth point (CDP) method. This is not an ideal approach for an underground radar, since one must know approximate range or position of the

target in advance and multiple sets of measurements must be made. This technique is not amenable to a near, real-time scan method at a coal face, but may

have some value for other survey work.

41
9. FUTURE DIRECTIONS FOR RADAR DETECTION OF UNDERGROUND ANOMALIES

9.1 Mining Meeds

This contract was initiated with the goal of developing a system to

locate old mine workings and old wells penetrating coal seams near present

coal mining activity. The next phase in this ongoing program is to be devoted

to the construction and testing of a model system that will detect these hazards. It is believed that the goals should be expanded to cover clay veins

and faults in coal seams in any future effort. The time allocated to the

overall effort would have to be increased, but the expenditures of funding

would be more effective if applied to these closely related problems in the same program.

The location of clay veins and faults in coal seams has become of much

greater importance in the last few years, since these situations are severe impediments to production, especially when mining is done with longwall

machinery. The location of clay veins is important, since the coal seam may

have different heights on each side. This situation is difficult to mine

effectively with longwall machinery because the longwall machine cannot be

angled up or down enough to accommodate the sudden shift in coal height. The

clay can be hard enough to damage the cutters on mining machines. The roof

structure near faults or clay veins is usually unstable and requires extensive

bolting. It would be helpful to know ahead that such a situation exists so as

to start turning a longwall machine or to make the most economic choice on allocating manpower or machinery to the job of mining the clay vein. Since a clay vein may act as a partial barrier to methane drainage, the mining through

a clay vein may suddenly release large quantities of gas. This gas can quickly become a safety problem which can be best solved when one is forewarned. As a consequence, one future goal should be to make any hazard detection system adaptable to use with longwall mining machines.

9.2 Antennas

The antennas developed for this work are useable with both the FM-CW system and pulse system. This development effort has been carried only as far as

is consistent with progress in other areas of the work. The work done on them

to this point indicates further improvements in performance can be made. The

present indications are that improvements can best be brought about by careful use of dielectric loading to reduce the physical size, resistive loading to

reduce unwanted reflections, and perhaps by investigating the general bow-tie

antenna (see section 3) or a wideband microstrip approach [30].

42
9.3 Future System Types

This effort, in both the Phase I work as well as Phase II work, has been

confined to exploiting the time domain or pulse- type system primarily and the

Frequency-Modulated, Continuous-Wave (FM-CW) system to a lesser degree.

Recent improvements to both systems continue to make them important candidates

for an ultimate solution. .Geophysical hazard detection is a very difficult

problem. The solution requires many design compromises which subsequently

limit the system applications and the analysis of the responses. At this

writing, no technique is clearly superior to all others. It is important to

this program that a number of methods are developed in parallel and that new designs are carefully evaluated.

NBS has done some introductory theory development work on the Planar Near

Field Reconstruction (PNFR) technique and also, more recently, has made some beginning measurements to verify this theory [4]. The results have been good

enough to suggest that this system should also be looked at very seriously in

any underground radar mapping work.

9.4 Accessibility to Mine Test Areas

In any future effort, a test area meeting several requirements is crucial. It must have a well-described physical arrangement of rock and coal as well as the anomaly to be detected. The anomaly must be available at the

proper ranges and be of the appropriate type. A very important feature of any

test area is that access be available for a relatively long period of time.

This should be done so that comparisons of test results can be made to detect

small changes or improvements in system performance as the work progresses.

The test range constructed by NBS during this phase has been invaluable

to this work, but it does not provide all the elements needed. It is felt

that a dedicated test area in an actual mine environment is necessary for this

type of work.

10. REFERENCES

[1] Rumsey, V. H., Frequency Independent Antennas. Academic Press, New York

(1966).

[2] Carrel , R. L., The Character! Stic Impedance of the Fin Antenna of

Infinite Length. Antenna Laboratory Technical Report No. 16, Electrical

Engineering Research Laboratory, Engineering Experiment Station, University of Illinois, Urbana, Illinois (1957).

[3] Lawton, R. A. and Ondrejka, A. R., Antennas and the Associated Time

Domain Range for the Measurement of impulsive Fields. Nat. Bur. Stand.

(U.S.) Tech. Note 1008; 1978 November.

43
[4] Jesch, R. L., Johnson, R. B., Belsher, D. R., Yaghjian, A. D., Steppe,

M. C., and Fleming, R. W., High Resolution Sensing Techniques for Slope

Stability Studies, FHWA-RD-79-32 (January 1979).

[5] Buettner, H. M., Antenna Design for Geophysical Application. URSI

Digest, North American Radio Science Mtg., Laval University, Quebec,

Canada (June 2-6, 1980).

[6] Lytle, R. J, and Laine, E. F., Design of a Miniature Directional Antenna

for Geophysical Probing from Boreholes. IEEE Trans, on Geoscience Electronics, Vol . GE-16, No, 4, (Oct. 1978).

[7] Kanda, M., The Effects of Resistive Loading on TEM Horns. Nat. Bur.

Stand. (U.S.) NBSIR 79-1601; 1979 August.

[8] Kanda, M., The Characteri sties of a Linear Antenna with Tapered Resistive and Capacitive Loading. Digest of lEEE/AP-S International Symposium, Laval University, Quebec, Canada (June 2-6, 1980).

[9] Carrel, R, L., The Characteri sti c Impedance of an Infinite Biconical

Antenna of Arbitrary Cross Section. Antenna Laboratory, Technical

Report No. 25, Electrical Engineering Research Laboratory, Engineering

Experiment Laboratory, Engineering Experiment Station, University of

Illinois, Urbana, Illinois (1957).

[10] Schelkunoff, S. A., Electromagnetic Waves. D, Van Nostrand Co. Inc.,

New York, (1943).

[11] Schelkunoff, S. A., Advanced Antenna Theory. John Wiley and Sons, Inc.,

New York (1952).

[12] Kraus, J. D,, Antennas. McGraw-Hill Book Co, Inc., New York, (1950).

[13] Papas, C. H. and King, R., Input Impedance of Wide-Angle Conical

Antennas Fed by a Coaxial Line. Proc. of I.R.E., pp. 1269-1271, (Nov.

1949)

.

[14] Galeis, J., Antennas in an Inhomogeneous Medium. Pergamon Press,

New York, (1969).

[15] Galejs, J., Dielectric Loading of Electric Dipole Antennas. Journal of

Research of the Nat. Bur. Stand. (U.S.), Digest Radio Propagation, Vol.

66D, No. 5, (Sept. -Oct. 1962).

[16] Balanis, C. A., Jeffrey, J. L., and Yoon, Y. K., Electrical Properties

of Eastern Bituminous Coal as a Function of Frequency Polarization and

Direction of the Electromagnetic Wave and Temperature of the Sample.

IEEE Trans, on Geoscience Electronics, Vol. GE-16, No. 4 (Oct. 1978).

[17] Wheeler, H. A., Fundamental Limitations of Small Antennas. Proc.

IRE(12), 1479-84, (1947).

44
[18] Cook, J. C., Status of Ground-Probing Radar and Some Recent Experiments. Reprinted by Am. Soc. of Civil Engrs., from Proc. of Engineering

Foundation Conference on "Subsurface Exploration for Underground

Excavation and Heavy Construction", Henniker, N.H., Aug. 1974.

[19] Cook, J. C., Radar Transparencies of Mine Tunnel Rocks. Geophysics,

vol. 40, pp. 865-885, 1975.

[20] Berkowitz, R. S., Modern Radar (Analysis, Evaluation, System Design).

John Wiley & Sons, New York, 1965.

[21] Bussey, H. E.; Larsen, E. B., Buried Antenna Performance; Development of

Small Resonant Antennas. Rome Air Development Center, Griff iss AFB, New

York, RADC-TR-74-169, June, 1974 (Defense Documentation Center No. AD

783-274).

[22] Hufford, G. A., UHF Propagation from Buried Antennas. ESSA Research

Laboratories, ITS, Tech. Memorandum ERLTM-ITS191, 68 pp, July, 1969.

[23] Mumford, W. W., Scheibe, E. H., Noise Performance Factors in Communication Systems. Horizon House-Microwave, Inc., 1968.

[24] Bowman, J. J., Senior T. B. A., and Uslenghi, P. L. E., Electromagnetic

and Acoustic Scattering by Simple Shapes. North Holland Pub. Co.,

Amsterdam, 1969.

[25] Kerr, D. E., Propagation of Short Radio Waves. McGraw Hill Book Co.,

New York, 1951

[26] Ruck, G. T., Barrick, D. E., Stuart, W. D., and Krichbaum, C. K., Radar

Cross Section Handbook. Plenum Press, New York, 1970.

[27] Tarantolo, P. J. and Unterberger, R. R., Radar Detection of Boreholes in

Advance of Mining. Geophysical Prospecting, vol. 26, pp. 359-382, 1978.

[28] Wait, J. R., Electromagnetic Radiation from Cylindrical Structures.

Pergamon Press, New York, 1959.

[29] Jesch, R. L., Void Detection. Final report to Navy, National Bureau of

Standards, Boulder, CO (August, 1980).

[30] I-Ping, Yu, Multiband Microstrip Antenna. NASA Tech Briefs, vol. 5, no. 1, Spring 1980.

[31] Jenkins, F. A.; White, H. E., Fundamentals of Physical Optics. McGrawHill, 1937.

[32] Brysk, H., The radar cross section of a semi-i nfini te body. Can. Jour.

Physics, vol. 38, pp. 48-56, 1960.

45
[33] Bussey, H. E.; Richmond, J. H., Scattering by a lossy dielectric circular cylindrical multilayer, numerical values. IEEE Trans, on Ant. & Propa., vol . AP-23, pp. 723-725; September 1975.

[34] Banos, A., Jr., Dipole radiation in the presence of a conducting halfspace. Pergamon Press, New York, 1966.

[35] Brekhovski kh , L. M., Waves in layered media. Academic Press, New York,

Second Edition, 1980.

[36] Stratton, J. A., Electromagnetic theory. McGraw-Hill, New York, 1941.

[37] Engheta, N.; Papas, C. H.; Elachi, C., Radiation patterns of interfacial

dipole antennas. Radio Science, vol. 17, No. 6; November-December 1982.

[38] Lewis, R. L., Ear-field computaion inside a dielectric media for an antenna above a planar interface. National Radio Science Meeting, U.S.

Nat. Committee/URS I, 24-28 May 1982, Univ. of New Mexico, Albuquerque.

[39] Martin, L. C.; Welford, W. T., Technical optics, vol. I. Pitman Pub.

Corp., New York, 1966 (second edition).

[40] Wittmann, R. C., Simulated pulse techniques for measuring coal layer

thickness. Ch. 6, pp. 287-297 in J. R. Wait, Ed., Analytical bases for

electromagnetic sensing of coal properties, final technical report to

U.S. Dept, of Energy ET-75-G-01-8972, July 1978.

[41] Roe, K. C.; Wittmann, R. C., Improved coal interface detector, report to

U.S. Dept, of Energy. Nat. Bur. Stand. (U.S.) NBS IR-82-1663, 1982 May.

[42] Lynch, A. C., Relationship between permittivity and loss tangent. Proc.

IEEE (London), vol. 188, pp. 244-246, 1971.

46
Relative

Amplitude

Figure 1. Reflections due to the NBS-TQ antenna without the resistive

material (1) and the same antenna with the resistive material

( 2 ).

47
Relative

Amplitude

lL-3 u TRANSMISSION OF ANTENNAS TO REFERENCE DIPOLE AT 3/4 M.

Figure 2. Transmitted waveform from the TG antenna (curve 1) and the TQ

antenna (curve 2).

48
Relative

dB

dB above 1 V/M/V

Figure 3. Relative transmission in dB for the TG antenna (plain line)

forward direction, the TQ antenna (squares) forward direction

and the TQ antenna (triangles) reverse direction at a range of 3/4 m.

49
A=0.15 m

Figure 4. Baffle arrangement for isolating TQ antennas when

operated bi statically.

1.22

50
Relative

Ampl

itude

Time in Nanoseconds

Figure 5. Response (1) of the system with the TQ antenna pair pointed at

the sky and (2) at a 1.2 meter square metal plate 5 an in front

of the baffle.

51
Relative

Ampl i

tude

iE-3 U AHTENNrtS OUER WOODEN BOX .6 M DEEP IN SOIL

Figure 6. Pulse system antenna return from an air filled box target buried

at 0.6 meter (1) and the same return corrected by subtraction of

the sky return (2).

52
Figure 7. Noncoplanar fin antenna schematic.

53
Characteristic

Impedance,

Z

,

in

Ohms

0 20 40 60 80 90

Fin Half-angle, in Degrees

Figure 8. Characteristic impedance of the non-coplanar fin antenna with

equal fin angles (plotted from data presented by Carrel [9]).

54
Reactance

in

Ohms

Resistance in Ohms

Figure 9. Input impedance of biconical antennas with 5.4° cone angle and

.054° cone angle as a function of the length, ji, of the cone in

wavelengths, X (plotted from data presented by Kraus [121).

55
Reactance

in

Ohms

Figure 10. Input impedance of single cones with ground plane as a function

of cone length, sl, in wavelengths, X . Cone angles are 10°, 20°,

40° and 60° (plotted from data presented by Kraus [12]).

56
Input

Impedance

in

Ohms

Figure 11. Input impedance of single cone with ground plane versus k£. K is the wave number, £ is the cone length and the cone angle, 0q,

is 60° (plotted from data presented by Papas and King [13]).

57
Characteristic

Impedance,

Z

,

in

Ohms

Figure 12. Characteri Stic impedance of a biconical antenna with equal cone angles, (plotted from data presented by Carrel [9]).

58
INTERFACE

AIR

<1

/

//

4

BoT

NORMAL TO

INTERFACE 7

/

/

r//

/

>

/

MEDIUM (COAL)

DIRECT RAY TARGET -O

Te.

Figure 13a, Sketch of rays from source to field point (target).

Rays are refracted into the second medium and partially

reflected, n^<n^.

;'Eoiu‘T (coAL^ ^

air

-icj'^e 15 d. 3eo~etry for calculating Sommer-i'eld interface transmission.

In chis example, the source is in the denser medium with

re'ractive index n >n,.

0 1

59
Radar Range in Meters

Figure 14. Signal -to-noi se ratio for a G4 radar system with the following

parameters: 500 MHz source; horn antennas 50.3 cm by 76.2 cm; frequency = 0.5 GHz; complex permittivity = 9-jO ft)r low loss

curves, 4-j0.16 for mediim loss curves, 9-J0.9 for high loss curves. The upper curve of each group is

for a flat mine tunnel wall 1.5 meters high of infinite length

with water in the tunnel. The lower solid curve of each group

is for a 30 cm diameter cased borehole. The dashed curve is for

a water filled borehole without casing having a 30 cm diameter. The system noise is assumed to be 8 dB greater than

Johnson noise in a 1 MHz bandwidth and clutter is ignored.

60
Relative

Amplitude

(volts)

SIMULATED TIME DOMAIN WAUEFORMS

5, 2, 1 AND 1/2 NS WIDE AT THE 50'/. POINT

U

Figure 15. Simulated impulse waveforms having widths of 5, 2, 1, and 1/2 ns

at the 50% point.

61
DB SPECTRAL AMPLITUDE OF SIMULATED IMPULSES

Frequency in Gigahertz

Figure 16. Resulting spectral energy distribution of the impulses shown in

-9

figure lb in dB relative to 10 volt-seconds.

62
Relative

Amplitude

(millivolts)

IE -3 U SIMULATED IMPULSE TRANSMISSION ODER 1.5 M WITH TQ ANTENNA

Figure 17. The signals resulting from transmission of the impulses shown in

figure 15 over a 1.5 meter path with the TQ antennas.

63
Relative

Amplitude

(volts)

U SIMULATED TIME DOMAIN WAUEFORMS

Figure 18. Simulated sinusoidal pulse waveforms having 8, 4, 2, and 1 cycles.

64
DB SPECTRAL AMPLITUDES OF SIMULATED 230 MHZ WAUEFORMS

Frequency in Gigahertz

Figure 19, Resultant spectral amplitude of the sinusoidal pulses shown in

figure 18, 8-cycle pulse, dotted curve; 4-cycle pulse,

triangles; 2-cycle pulse, squares; 1-cycle pulse, solid line

with no marker.

65
Relative

Amplitude

(millivolts)

lE-3 US 1 MULCTED 250 MHZ TRANSMISSION OUER 1.5 M WITH TQ ANTENNAS

Figure 20. The signals resulting from the transmission of the sinusoidal

pulse waveforms shown in figure 18 over a 1.5 meter path using

TQ antennas.

66
Relative

Amplitude

(volts)

Time in Nanoseconds

Figure 21. Simulated linear chirp pulse waveforms.

250-500 MHz in 10 nanoseconds, plain curve. 250-1000 MHz in 10 nanoseconds, square markers.

250-1000 MHz in 20 nanoseconds, triangle markers.

67
DB SPECTRAL AMPLITUDES OF CHIRPS WITH RESPECT TO lE-9 US

Frequency in Gigahertz

Figure 22. Resulting spectral amplitudes of the linear chirp pulse waveforms shown in figure 21. The curve markers correspond to

figure 21.

68
lE-3 M SIMULATED CHIRP TRANSMISSION OUER 1.5 M WITH TQ AHTNNAS

Time in Nanoseconds

Figure 23. Resulting signals after transmission of the linear chirp pulses

over a 1.5 meter path using TQ antennas. The curve markers

correspond to figure 21.

69
Relative

Amplitude

lE-3 U

Figure 24. The result of transmitting a 300-600 MHz linear chirp pulse over

a 1.5 meter path using the TQ antennas.

70
Relative

Amplitude

1.2

1

.8

.6

.4

0

-2

-.4

-.6

-8

X Aa^ '^\IV\ v\l

0 5 10 15 20 25 30 35 40 45 50

Time in Nanoseconds

Figure 25. The result of autocorrel ation of the waveform of figure 24.
Relative

Amplitude

Figure 26. Autocorrel ation of the transmitted waveform of the 4 cycle, 250

MHz sinusoidal pulse.

72
Relative

Ampl i

tude

lr-3 U SIMULATED RESPONSE > DAMP COAL, 15 CM HOLE AT 1 M

Time in Nanoseconds

Figure 27. Simulated response in relatively damp coal for a 15 cm radius

hole at 1 meter range. (1) cased hole, (2) air-fi1led hole, (3)

water -filled hole.

73
Relative

Amplitude

IE-3 U SIMULATED RESPONSE. DAMP COAL, 15 CM CASED HOLE

Figure 28. Simulated response in relatively damp coal for a 15 cm radius

hole at a range of 1 meter (1), 2 meters (2), and 5 meters (3).

The amplitude of the response at 5 meters has been amplified 50

times.

74
Response

Voltoge,

peak

-to

-peak

10mV

Figure 29. Simulated radar response irrelatively damp coal for a 1.0 volt,

1 nanosecond input pulse reflected from a borehole. The given

dimension is the borehole radius.

75
Response

Voltage,

peak

-to

-peak

10 mV

1 mV

lOO^V

10/tV

1/iV

O.litVL

0

Figure 30.

i

.

L

. . . . ;

'

'

- -

: - ^ - .

. . . . ...

, ^

‘

I L . . 1 . ,

:

i

1

- * " - - .

15. cm, metal cased

7.5 cm, metal cased

15. cm, water filled

15. cm, air filled

7.5 cm, water filled

2 4 6 8 10 12 14

Target Range in meters

Simulated radar response in relatively dry coal for a 1.0 volt, 1 nanosecond input pulse reflected from a borehole. The given

dimension is the borehole radius.

76
77

Figure

31.

Preprototype

pulse

system

block

diagram.
Vol

ts

U

Figure 32. Output waveform of the high-voltage impulse generator.

78
Figure 33. NBS range for subsurface anomaly measurements.

79
Relative

Amplitude

lE-3 UTQ ANTENNAS OUER 2 FOOT DEEP AIR BOX/ AUERAGED BACKGROUND/

Figure 34. Pulse system response averaged over a sequence of 26 measurements

(1). Single response from over the 0.6 meter deep air-filled

target (2). The resulting response showing the target signal

enhancement (arrow) obtained by subtracting the sequence average

from the response at one position (3).

80
Scan

Distance

TQ ANTENNAS MITHOUT PRE-AMP SCANNING OUER 2 ' TARGET

FILE TQ65MN.5 FROM 0 TO 2.49023E-08 MINUS TQ65MN.5AU

Time in Nanoseconds

Figure 35. A stacked series of modified responses obtained by subtracting

the average response of the series from each measured

response. Target signal at arrow.

81
APPENDIX A

COMPUTER PROGRAM FOR SIGNAL-TO-NOISE RATIO,

AS A FUNCTION OF DISTANCE (RANGE) TO A SUBSURFACE TARGET

The program listing, written in BASIC language, is included in this

appendix. Some results from the program are shown in figure 14, which shows curves for the si gnal -to-noi se ratio, S/N, as a function of distance for specific coal "atmospheres," specific targets, and a specific radar system model.

The radar system has some constant parameters and others as input variable. The constants are given in statement 20 (S20). The variable parameters

required are frequency (S60), antenna dimensions (S90), dielectric permittivity and loss tangent of coal (S120), coal conductivity (if the dielectric

tangent was entered as zero), and one of the five targets considered as described in S240 and S260, and the target dimension S550. The source power,

10 mW, and the frequency, 500 MHz, are assigned in S116 and S70, respectively.

The noise is that for a classical CW radar with Johnson noise in a 1 MHz

bandwidth augmented by an 8 dB noise figure, i .e., multiplied by 6.31. The

noise power is calculated as 06 in S490.

The received power is calculated as S4 in S670. The S/N is calculated in

line S680.

S/N for other radar systems may require running the program. However,

for simple cases, the graph may be rei nterpreted . For example, if the source

power is increased by 10 dB, the S/N at any range is increased by 10 dB . If

the noise is 5 dB greater, then S/N is 5 dB smaller.

With different target dimensions and a different frequency, it is necessary to rerun the program. The statements from 750 to 1800 are used to calculate target cross section as a function of frequency and dimensions. The

methods are approximate. The strip validity is discussed in the text. The

method for the cylinder cross section branches to one of three methods depending on the ka. The small and large cases are well known approximations. The

intermediate case, S840 to S1020, uses forward recursion to evaluate the

cylinder functions (see S1350, S1360), which is ultimately an unstable procedure for S/N. However, for the present usage in the intermediate range, 0.05

< ka < 5.99, the resulting truncated Bessel function series is accurate within

± V/o except for an anomaly for ka near unity.

It may be noted that the ratio of source power to noise power, with no propagation loss, is 0.01 W/0.0252 pW, or about 116 dB

.

The ultimate range of a radar is often taken to be S/N = 0 dB . With signal processing, it may be at less than 0 dB . With clutter, it may be considerably above 0 dB

.

82
Example of Results of the Radar Range Program

RRIiRR RRHGE FOR DETECT I OH OF SUBSURFRCE TRRGETS s TUNNEL WRLL OR BOREHOL

FREQ = NEGRHZ; DIMENS = CN. W= PIPE DIRN?OR HEIGHT OF TUNNEL. FI LEI 3-27

INPUT F0

RNTENNR RPERTUREB: ? C:N = ERRTH DIEL CONST iiTRNGNT= TO USE CONDUCTIVITY ENTER O)

9 0.1 3.00373S342 0.149S13315

TRRGET C0DE: 1=METRL NELL? 2=NRTER NELL?3=RIR NELL

CODE= 1 4=NRLL NITH NRTER? 5= NRLL N/fllR NOISE FIGURE DB 3

VELOC OF LIGHT= 29979.25 CM /MICROSEC

S.-N OF 0.01 N RRDRR IN HRLFSFRCE? NOISE= 3 DB RBOVE KT IN IMHZNIDTH

F0= 500 E1jT1= 9 0.1 L1?L2= 50.3 76.2

TRRGT= 1 LRMDH= 59.9535 INTERFRCE NMISSION= 0.749532926 NCHSE=

2.52336E-14 N0= 1 N = KR EXRCT: /S=RERL /S=IMRG

4.72 1526373 1.3 14397197 1.

20 4 .

3

5 0 6 7 E - 0 3 1 1 3 . C! 6 4 9 1 Ci 40 1 . 54333E-04 97. 3 7 9 5 3 7 3 4

60 1 . 30706E-05 37. 14230353

3 0 1 . u7047E~06 . "I 4 Fi i-'1

1 00 2 . 29009E-07 69. 577 3 6 9 3 2

150 3 . 9 3 7 3 6 E — 0 50. 65 '3 916 3 2

200 5. 36433E-1

1

33 . 27454000

250 i . 13396E-12 16. 7 1 0 3 4 3 3

300 2. 97353E-14 0. 719372779

350 3. 1 1971 F-i

h

-14., Q v=; V 4. =; i4

333392003

RRTIO

1 . 0223712

I Signal-to-Noise Ratio (dB)

Received Signal Power (Watts) — Range (cm)

83
5 F'EM RRIiRR RRHGE

b PRINT "RRIiRR RRHGE FOR DETECTIOH OF SUBSURFRCE TRF:GETS: TUNNEL WRLL OR BOREHOL"

7 REM H.E.BUSSEH»DIV 723. 02, NRTIONRL BUREAU OF STANDARDS » BOULDER C0.

10 REM FILE 10-27 AS MODIFIED 12/12/SO

20 REM OF .OllJRTT RRDRR INHALF SPACE. W/NOISE =+BDB ABOVE KT IN IMHZ WIDTH"

30 VI =29979. 25

40 PRINT "FREQ=MEGAHZ;DIMENS=CM. W= pipe DIRM.OR half HT of tunnel. FILE10-27"

50 REM TO CHANGE UNITS. SAY, METERS REPLACE VI BY VI IN METERS/MICROSEC

b0 PRINT "INPUT F0">

70 INPUT F0

S0 REM L1.L2=H0RN DIMENSIONS. IF CIRCULAR DISH: USE L1=L2=0. 886*DIAM.

90 PRINT "ANTENNA APERTURES . CM= "

i

100 INPUT L1.L2

110 REM P0=EFFECTIVE CW RARAR POWER IN WATT

lie P0=0.01

120 PRINT "EARTH DIEL CONST &TANGNT=(TO USE CONDUCTIVITY ENTER 0>"!

130 INPUT El.Tl

140 IF T1>0 THEN 190

150 PRINT "INPUT CONDUC. MHOS -'METER" 160 INPUT SI 170 T1=S1-<E1*3.S54E-06*F0»2*PI)

ISO REM COMPLY REFRACTIVITY N5&N6

190 N1=SQR<0. 5*E1

)

200 T =SQR 1 +T 1 *T 1

)

210 N5=Nl*SQRc:i+T>

220 n6=hi*sqR'.;-i+t;'

230 PRINT ei;ti;n5;n6

240 PRINT " TARGET CODE: 1=METAL WELL? 2=WATER WELL.3=AIR WELL"

230 INPUT C7

260 PRINT "C0DE="C7" 4=WALL WITH WATER; 5= WALL W- AIR

270 NS=S

2S0 PRINT "NOISE FIGURE DB"N3" VELOC OF LIGHT="V1" CM -MICROSEC"

290 REM G5= POWER REFLECTION OF TARGET=1 FOR METAL. =.25 FOR GASS<WATER

300 G5=l

310 IF C7<2 THEN 330

311 IF C7=2 OR C7=4 THEN 315

312 C5=O.N5-l)/<H5+l>>t2

313 GOTO 330

315 G5= < N5-9 ) / < N5+9 > > t2

330 PRINT "S.-'H OF 0.01 W RADAR IN HALFSPACE. NOISE= 3 DB ABOVE KT IN IMHZWIDTH"

350 L=V1/F0

360 K0=2-PI.''L

370 K=K0*N5

3S0 REM N7=KT NOISE IN IMHZ WIDTH

390 N7=4E-15

400 REM 1-WAY POWR .YMISS. OF INTERFACE =I 410 I=4-*N5/< 1+N5)*< 1+N5> > 420 REM DISPERSION MULTIPLIER=D

430 D=0.5

450 A0=0. 55*L1*L2

460 G0 = A0*4*PI.-(L*L>

470 Gl=G0*El

430 REM D6=NF=N0ISE FACTOR

490 D6 = N7*EKP ( 2 . 302b4H3*0 . 1 '' 500 PRINT "F0="F0"El.Tl="Ei;Tr'Ll.L2="Li;L2

510 PRINT "TARGT="C7; "LAMDA="L; " INTERFACE XMISSION=' I "N0ISE="D6; "X0="

1

520 REM S4= POWER*GAINS

530 S0=P04G 1 *A0*0. 0625* I * I *D ( P I *P I

)

540 REM S3 IS RELATED (E SC ATT. E INCID>SQUARED: GOT EiY CYL SUBROUTINES. OR KIRCHHO

84
S50 "W= "! TcM iriFIJT W 570 IF C7 4 THEN 770

580 PEM SThTEM60O THRU 630* 720j 730» GI VE VARIED RANGE STEPS. METHD 570REQSb3O-75O

530 FOP R=30 TO 100 STEP 20

600 GOTO 630

610 R! = R + 5 0

620 IF R=150O THEN 740

630 GOSUB C7 OF 750 > 750 > 750 » 1630 k 1630

640 REM S= CROSS SECTI0N=4*PI*R*R«( <E SCATT/E INCIDI SQUARED)

650 S=S3*4*PI*R*R

660 A6=Ei iP ~4*K0*N6*R

)

670 S4=S*S0*A6/<R*R*R*R)

6S0 PRINT R;S4; 10*LGT(S4 'D6>

630 IF R.101 THEN 710

700 IF RM00 THEN 610

710 NEXT R 720 P=100

730 GOTO 610

740 END

750 S3=S7. R 760 RETURN

770 PEM METAL CYL SCATTERING

"^SO DIM J[16]jYC16]

800 PRINT " KA EXACT! •^S=REAL ''S=IMAG S7 RATIO"

810 H=W*0.5

820 X=K*

A

830 IF X<0.05 THEN 320

840 IF X<5.39 THEN 1020

850 PEM NEXT STEP=SCATTER I NG RATIO BY GEOM OPT I CS=LFlRGE KA

860 S8=P I *A* 1 . 008

870 P3=S8.'(PI*A)

880 S7=G5*0. 25*A*1 . 008

830 PRINT " "X" "S7;R8

300 GOTO 580

310 PEM SMALL CYL SCATTER (RAYLEIGH)

320 D 1 =LOG ( 0 . 5*X

)

330 D2=D 1+0. 5772157

340 ri=H2*D2+0.25+PI*PI

350 Sl=-0. 25+PI*PI ."D 360 32=0 . 5*P I *D2-'D 370 F3=S1 +S1+S2+S2

380 S7=G5+F8.- (PI*K)

3 30 P 7 = 4 * F 8 • ( P I * X

)

1 000 PR I NT X 5 S 1 5 S2 ? S7 5 R7

1010 GOTO 580

1020 PENEESSEL (INTERMEDIATE CYL)

1030 X=X

1040 IF X>2.33 THEN 1150

1050 V=X+X."3

1 060 V6=V* ( 1 . 265620S+V* ( -O . 3 1 63866+V+ ( O . 0444473+V* ( -O . O033444+0 . 00O2 1 +V ) ) )

>

1 070 V6= 1 + V+ ( -2 . 2439337+V6

)

1080 V7=V*(-0. 74350334+V*(0. 253001 17+V*( -0. 04261214+'/*(0. 0O427316-V+O. 00024846,' )

1 030 V7=2*L0G (0. 5+X) *V6/P I +0 . 3674669 1 +V+ ( O. 60553366+V7)

1 1 00 V3=0 . 2 1 093573+V* ( -0 . 033542S3+V* ( 0 . 004433 1 3+V+ ( -O . O003 1761 +V* (1.1 03E-05 ) ) )

)

1110 V8=X* ( 0 . 5+V* ( -0 . 56243385+V*V8 )

)

1120 V3=V*(2^1682709+V*(-1 . 3164827+V*(0. 3 12335 l + v*(-0. O400376+V+O. 0027873) > )

)

1 1 30 V3=2*L0G ( 0 . 5*X > +V8/P I + ( -0 . 6366 1 38+V + ( 0.221 203 1 +V3 > ) /X

1140 GOTO 1230

1150 V=3/X

1 160 V6=V*(-0. 0055274+V*(-0. O0O03512+V*(O. O0137237+V*(-0. OO072805+V+O. OOO 14476

85
1 170 V6 = 0 . 797SS456+V* ( “7 . 7E-07 +V6

)

1 1 80 K8=V* ( -0. 00003954+ V* < 0 . 00262573+V* < -0.00054 1 25+V*< -0. 00029333+V+0 . 000 1 355

1190 K3=.-:-0. 785398 16+V+(-0. 041 66397+K8>

1200 X2=SQRX

1210 V7=SINK3*V6-'X2

1 220 Vb=C 0SK8*V6''X2

1230 V8=V*C.0.01659667+V*( 1 . 7105E-04+V+<-0. 0024951 1+V*c;0. 001 13653+V*-0. 00020033

1240 V8=0.79783456+V*a.5fc':E-06+V8)

1250 K8=V*(;5.65E-05+V*<-0. 00637879+V+C0. 00074348+V*(0.00079824+V*C-0. 00029166)

1260 K3=X-2. 35619449+V*<0. 1 24996 12+K8)

1270 V9=SIN<K8)*V8/X2

1230 V8=C0S<K8)*V8/X2

1290 REM

1300 J[1]=V6

1310 J[2]=V8

1320 VC1]=V7

1330 YC2]=V9

1340 FOR F-2 TO 15

1350 JCP+1 ]=<2+P-2)*JCP]/X-JCP-l ] 1360 VTP + 1 ]=(2*P-2) + YCP]/X-YCP-l ] 1380 IF YIPK-9E+05 THEN 1400

1390 NEXT P 1400 P1=P

1410 81=0

1420 82=0

1430 N=-l

1440 FOR P=1 TO PI 1450 N=N*-1

1460 Q2=JCP]*J[P3

1 470 D 1 =Q2+YC P 3*Y[ P

]

1480 IF P>1 THEN 1510

1490 Q7=l

1500 GOTO 1520

1510 Q7=2

1520 Fl=Q7.- ril 1530 S1=81-F1*Q2*N

1540 S2=82 + F1* J[ P ]*Y[ P ]+H

1550 REM IF Y[PJ>-lE+05 THEN 1570

1570 NEXT P

1 5 8 01 F 8 = 8 1 + 8 1 + 8 2 + 8 2 1590 87=G5*F3/(PI*K)

1600 R 6 = 4 * F 8

' (PI* X > 1610 PRINT X ! 8 1 5 82 5 87 ! R6

1620 GOTO 580

1630 REM KIRCHH0FF-FRE8NEL FIELD OF H 8TRIP,TflPE #20, FILE 30

1640 REM N( CM )=HflLF WIDTH; LENGTH=INFINIT; C&:8F0R Z = 8QR2*W -R1 1650 REM WIDTHi:<RFlNGE IN CM. FR8NL C I 8 DEFINED IN fiMS55 EQ7.3.l:lc2

1 6 6 0 R: 1 = 8 0 R ( 0 . 5 * R * L

' N 5

)

1670 Z=8QR2*W'R

1

1630 U=0.5*PI*Z*Z

1690 F=( 1+0. 926*2 >• (2+1 . 792*2 + 3. 104*2*2)

1 700 G= 1

' ( 2+4 . 1 42*2 + 2*2* ( 3 . 492+6 • 67 *2 )

)

1710 81=SIN(U)

1720 C1=C0S<U)

1730 C=0. 5+F*81-G*Cl

1740 39=0. 5-F*Cl-G*Sl

1760 E2=0. 5*(C*C+S9*S9)

1770 S3=G5*E2

1780 PRINT "2 C 89 S3=E2*G5"Z; C; 89j S3

1790 RETURN

1800 END

86
bibliographic data

SHEET 'S ff insryciions'

1. publication or report no.

2. Performing Organ. Report No. 3. FubI 1 cation D ate

NBSIR 84-3017 "

-

4. title And Subtitle

Microwave Detection of Lost Wells and Unknown Water-Filled Voids in Coal Mines

5. AUThOR(S)

D.R. Belsher; R.H. McLaughlin; A. 6. Repjar; and H.E. Bussey

6 . performing organization (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

S. Type of Report 8< Period Covered ,

S. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. Stote. ZIP)

10. SUPPLEMENTARY NOTES

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

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

bibliography pr literature Survey, mention it here)

Work on contract H0272007 is summarized for the period of January 1979 through

March 1984. The development of improved antennas useable with both a pulse system

or an FM-CW system is described. The development of a field prototype pulse

sampling system is described. Initial theoretical work on the problem of

dielectric loading of antennas as well as a study of potential system range

is included.

12. KEY WORDS (Six to twelve entries; olphapeiical order; capitalize only proper names; and separate key words by semicolor s antennas; dielectric load; pulsed system; radar range

13. AVAILABILITY

[T^Unlimited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S, Go ve rnment Printing Office, Vvashington, D.C. 20402.

'

I ] Order From National Technical Information Service (NTIS), Springfieic VA. 22161

14. NO. OF

printed pages

86

15. Pf.

. % ' C'AJw- :

' • ‘ 4 > •- • r
‘A**’ ^51^'