Bureau of Mines Report of Investigations/1978 

Electromagnetic Technique 

for Locating Boreholes 

UNITED STATES DEPARTMENT OF THE INTERIOR 
UNITED STATES DEPARTMENT OF THE INTERIOR 

Cecil D. Andrus, Secretary 

BUREAU OF MINES 
1.1 p. . ill., (liagrs. ; 27 cnl. (Report of investigations - I3orcau of 

Slincs ; 8302) 

I. \lint rcscuc work - I-quipmcnt and supplies. 2. I%oring. 3. 

I<Icctrc~magnc.tic rncasuremcnts. I. Ilnitcci Stutrs. 13~1rcau of 

hlincs. 11. l'itlc. 111. Series: Ilnitcd Statcs. 13urr;iu of .\lines. 

Itcport of invcsrigations ; 8302- 

TN23.U7 no. 8302 622.06173 

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CONTENTS 

Abstract ................................................................ Introduction ............................................................ Acknowledgments ......................................................... Trapped miner location equipment ........................................ Transmitter ........................................................ Null detection technique ........................................... Field test ......................................................... Conclusions ............................................................. Appendix A.--Transmitter coil design .................................... Appendix B.--Coil tilt errors ........................................... 

ILLUSTRAT IONS 

Trapped miner transmitter ......................................... 3 

Trapped miner receiver ............................................ 3 

Borehole transmitter .............................................. 4 

Transmitter disassembled .......................................... 4 

Plan view of transmitter in borehole and tunnel ................... 5 

Receiver coil mounted on transit .................................. 6 

Results of field test at Ft . Ritchie, Md .......................... 7 

Coordinate system with the transmitter at the origin .............. 11 

Plane view of the coil in the null direction ...................... 11 

Effect of coil tilt on location accuracy .......................... 13 

Effect of moving transmitter above and below tunnel center line 

on location accuracy ............................................ 14 

TABLE 

1 . Minimizing error by measuring above and be low tunnel .............. 13 
ELECTROMAGNETIC TECHNIQUE FOR LOCATING BOREHOLES 

by 

H. Kenneth Sucks 1 

ABSTRACT 

The Bureau of Mines has developed hardware for electromagnetic (EM) detection and location of miners trapped in underground coal mines. This report 

describes a technique for using the developed equipment for locating uncased 

boreholes underground. Results of several field and laboratory experiments 

are described. 

INTRODUC T LON 

In many industrial situations, mining being a prime example, smalldiameter holes are drilled from the surface to intersect an underground tunnel 

or room. The correct starting point on the surface is usually determined by 

standard surveying techniques. However, because of the tendency of smalldiameter drill holes to drift, the true location of the bottom of a deep hole 

may be many feet from the expected coordinates. Often the true location will 

be determined by drilling small, horizontal. pilot holes from within the underground opening in an effort to intersect the borehole. Depending on the diameter of the original borehole, the nature of the rock, and the luck of the 

driller, success may require considerable time and expense. 

In previous work" system was described for locating boreholes electromagnetically which depends upon a known receiver sensitivity and field 

strength. In practical situations, the field strength is a function of the 

electrical properties of the surrounding rock, which is generally unknown. 

The technique to be described in this Bureau of Mines report eliminates 

this problem and it has proved to be accurate. 

' supervisory electrical engineer, Pittsburgh Mining and Safety Research 

Center, Bureau of Mines , Pittsburgh , Pa. 

'~errv, R. L. , and L. Tirrul. Lost a Borehole Recently. Can. Min. J. , 1973, 

pp. 56-58. 
Volume 1. Development and Testing of an Electromagnetic Location System 

(Research Contract H0220073). BuMines Open File Rept. 41(1)-74, 1973, 

181 pp.; available from National Technical Information Service, Springfield, 

Va. , PB 235 605/A~. 

The preceding open file reports are available for consultation at the 

Bureau of Mines facilities in Denver, Colo., Twin Cities, Minn., Pittsburgh, 

Pa., and Spokane, Wash.; at the Department of Energy facility in Morgantown, 

W. Va.; and at the National Library of Natural Resources, U.S. Department 

of the Interior, Washington, D .C . Powell, J. A. An Electromagnetic System for Detecting and Locating Trapped 

Miners. BuMines RI 8159, 1976, 15 pp. 

Westinghouse Electric Corporation. Coal Mine Rescue and Survival. Volume 2. 

Communications/Location Subsystem. BuMines Open File Rept. 9(2)-72, 1972, 

258 pp.; available for consultation at the Bureau of Mines facilities in 

Denver, Colo. , Twin Cities, Minn. , Pittsburgh, Pa. , and Spokane, Wash. ; at 

the Office of the Assistant Director--Mining, Columbia Plaza, Washington, 

D.C. ; at the National Library of Natural Resources, U.S. Department of the 

Interior, Washington, D .C. ; and from the National Technical Information 

Service, Springfield, Va. , PB 208 267. 
FIGURE 2. - T~u~ptc? r~iiricr rcceivcr. 
FIGURE 3. - Borehole transmitter. 
Figure 5 is a plan view of the transmitter lowered down the hole. The 

magnetic field lines from the transmitter coil are radial. When the plane of 

'. \ i i ,- \\ \ I I ,' .\\I/ 

TRANSMITTER 

, / I' ', , / I \ 

, 

, I ,\ I \. , I I '\ , 

, I 

'\ 

, 

, . . FIGURE 5. - Plan view of transmitter in bore- I . TUNNEL WALL hole and tunnel, 

RECEIVER LOOP NULLED ALONG 

RADIAL MAGNETIC FIELD LINES 
g

minimum for all azimuthal 

orientations. If the disFIGURE 6. - Receiver coil mounted on transit. tance into the rock to the 

transmitter were known, then 

an optimum height above or 

below the tunnel would be equal to this distance (see appendix B). 

Field Test 

In the fall of 1975, the U.S. Army Corps of Engineers requested the 

~ureau's aid in locating a 10-in-diam fresh water well in the vicinity of an 

underground tunnel at Ft. Ritchie, Md. The Bureau used the equipment and techniques just described to accomplish the task. Figure 7 shows the layout of 

the tunnel and field results. A 50-ft baseline was laid out along the tunnel 

and null measurements were taken at six positions. Multiple readings were 

taken to increase the confidence of the results. The shaded area represents 

the most likely area of the hole. 
BOREHOLE LOCATION 

/AT DEPTH OF TUNNEL 

FIGURE 7, - Results of field test at 

Ft. Ritchie, Md, 

LSURVEY BASELINE 

TUNNEL FLOOR 

The Corps of Engineers proceeded to drill a series of 2-in pilot holes on 

8-in centers starting at the suggested location, and on the 11th hole, water 

was struck at the location shown. The location error of approximately 4.5 ft 

could have been caused by several factors including metal structures in the 

tunnel, a large diesel-electric generator 100 ft away, or tilt of the coil in 

the hole. The effect of core-tilt can be quite significant (see appendix B 

for analysis), but it can be minimized by using a small-diameter transmitter 

to insure that it hangs vertically and by taking two sets of readings--one 

with the transmitter above the tunnel and the other with the transmitter an 

equal distance below the tunnel. The area enclosed by the triangulation plot 

will include the borehole. 

The effects of conducting bodies are generally impossible to predict, but 

they are not a problem unless they lie very close to the transmitter or 

receiver. 

C ONCLUS IONS 

A technique has been described for locating boreholes in underground 

tunnels using equipment developed under the ~ureau ' s trapped miner program. 

Theoretica 1 ca lculat ions and field measurements have demonstrated that accuracies of the order of lo are possible in the field. 

The Bureau is presently working on an advanced technique using frequencies below 20 Hz in conjunction with a magnetometer. Preliminary results 

indicate the system will find cased holes at distances in excess of 100 ft. 

A complete description will be available when the contract is completed, 

possibly by late 1978. 
APPENDIX A . --TRANSMITTER C.OIL DE S IGN 

The object of the transmitter coil design is to maximize the coil magnetic moment M = INA for a given package size, weight, and available transmitter power. For convenience, the following terms are defined: 

I = Coil current, RMS. 

N = Coil turns. 

A = Coil area, square meters. 

D = Coil diameter, meters. 

= Wire resistance, ohms per meter. 

a = Wire density, kilograms per cubic meters. 

Ro = Transmitter internal resistance. 

Vo = Transmitter open circuit voltage, root mean square. 

R, = Total coil resistance, ohms. 

M = INA, ampere-square meter. 

Pw = Wire resistivity, ohm-meters . 

W = Coil weight, kilograms. 

d = Wire diameter, meters. 

If the coil is tuned to the transmitter frequency so that the coil 

current is limited only by its direct current (dc) resistance, the following 

results will be achieved: 

If the wire diameter from A-3 and A-4 is eliminated, a relationship 

between N and W will result 
Using this expression for N in the equation for M the following is obtained: 

By differentiating A-6 with respect to % and setting equal to zero, the 

optimum wire resistance for a given coil weight and diameter is found. This 

procedure gives 

Using equations A-2 and A-5, these expressions can be rewritten as 

That is, for a given weight, the best coil is one that matches the transmitter for optimum power transfer. The magnetic moment is given by 

For the present transmitter and package No. 18 enameled wire was used 

which gives 

R, = 0.77 ohm, 

for No. 18 copper wire, 

P, = 1.72 x lov8 ohm-m, 

and D = 0.064 m. 

ThenW = 0.27 kg (0.6 lb), 

and N = 184 turns. 
M, = M sin no cos do, (B-3 

a nd % = M sin ri0 sin (*, , (B-4) 

where M2 = M~~ + M~~ + M~, . 03-5) 

The static fields due to each dipole component can be written as 

follows; At the receiver coil (x,y,z) it is found that 

and 

where r" = x" i- y" + z2. 
FIGURE B-1. - Coordinate system with the transmitter at the origin. 

RE

FIGURE B-2. - Plane view of the coil in the 
Each of these fields has x and y components. 

By combining the x and y components, H, and H, are found as 

Then from equation B-1, 

- 14_ - 3 yyz + 3% xy-q (x2 + z2 - zY2) 

tan - - H, 3 qxz + 3% xy-M, (y': + 2" - 2x9' 

It can be seen that if 0, = 0 then M, and M, = 0 (no tilt), and tan \Y = = tan@ 

as expected, where @ is the true angle. 

If = @ + + is allowed in equation B-11 where 6 @ is error in angle 

caused by coil tilt and convert to cylindrical coordinates by letting 

X =p cos $I, 

y = p sin 6, 

p2 = x2 + y2. 

Then it can be shown that 

(p2 + z") tan a, sin (@ - @, ) tan 

@ = 3pz + (zp2 - z2) tan P, cos (6 - a, 1. 

Figure B-3 shows the effect of coil tilt on location accuracy. The 

values of the tilt parameters were taken £ram the Ft. Ritchie, Md., experiment. 

Since the transmitter package diameter was nearly equal to the well diameter, 

we assumed the transmitter coil was alined with the wellhole; in addition, the 

wellhole is assumed to be straight. This gives 8, = 3.08O and @ = +16.2O. 

Figure B-3 shows reasonable agreement between the theoretical calculations and 

the measured data. 

Minimizing the Error 

Usually tan 9,<<1, then the minimum value of the tan 6 ii: occurs when 

z = 3. Since p is not known, this condition can be met only by using reasonable judgment when the transmitter is positioned in the hole. 
, (, ) 

302 (

) 

Equation B-13 is odd in z. If the angle Yl is measured when the transmitter is z, ft above the tunnel and an angle w2 is measured at the same horizontal location when the transmitter is z, ft below the tunnel, then the true 

angle @ is found from the average of Yl and Y2 as follows: 

(B- 14) 

This is shown in table B-1 using the estimated hole tilt values of the field 

test. 

TABLE B-1. - Minimizing error by measuring above and below tunnel 

(0, = 3.08', @, = 16.Z0, x = 29.5 ft, y = 48 ft, @ = 58.4') 

Z, y ft 

-1-5 

- 5 

+50 

-50 

Measured angle, 

degrees 

64.4 

47.4 

59.8 

57 .O 

Net error, 

degrees 

-2.5 

.O 

Error, 

degrees 

6.0 

-11.0 

1.4 

-1.4 

Average 

-I 

f 55.9 J 

> 1 58.4 2 
LSURVEY BASELINE 

TUNNEL FLOOR 

*U.S. GOVERNMENT PRINTING OFF ICE: 1978-703-103155