R. H. Church 

W. E. Webb 

BUREAU OF MINES, TUSCALOOSA, ALABAMA 

Research at the Tuscaloosa Research center is carried out under a memorandum of agreement between the 

Bureau of Mines, U.S. Department of the Interior and the University of Alabama. 

UNITED STATES 

DEPARTMENT OE 

THE XNTERIOR 
Open F;.ie Report af6-8. f 

Development of a Phase DifE3rence of Arri-~al Tzchnique For Lccation 

of Trapped Yiners 

by W. G. Hopkins, 111, R. H. Church, and W. E. Vebb 

Tuscaloosa Xesearch Center, University, Ala. 

UNITED STATES I)EPART?!ENT OF TdE INTSRIOB 

Research at the Tuscaloosa Research Center is carzied ouc under a 

nemorandum of agreement between the Sureau of Xines, U.S. Deparcnent of 

the Interior, and the Universitv of Alabzma. 
List of abbreviations ........................................ Abstract ..................................................... Introduction .................................................. Sumary of current systems ................................... The phase difference of arrival technique (PDOAT) .......... : . Sample calculations using PDOAT .............................. Deve1oprnent"of the PDOAT system .............................. Recommendations .............................................. References ................................................... Appendix A . - Fortran program for estimating phase angle 

through overburden ........................................... Appendix B . - Fortran program for determining the location 

(x, y, z coordinates) of the trapped miner ................. 

ILLUSTMTIONS 

. . Selsmic system .......................................... Electromagnetic direction-finding system ................ Electromagnetic vector field measurement technique ...... PDOAT system ............................................ PDOAT array with nomenclature ........................... Flow chart of PDOAT algorithm ........................... Block diagram of preliminary PDOAT receiver ............. Schematic diagram of high-impedence balanced input 

amplifier ............................................. Schematic diagram of narrow band-pass filter using 

twin-tee feedback.. ................................... Photograph of PDOAT system components ................... Photograph of USBH personnel depolying PDOAT receiver ... Block diagram of phase-lock loop receiver ............... 

TASLES 

1 . ~stimated position resolution. m ......................... 2 . Sensor coordinates ....................................... 
LIST OF mS35VIih? io NS 

nezaohm 

UF n.i crofarad 

R ohm 

sq mi square mile. 

m meter : 
-, . .- ..( '

D&VEIOP~~~#T OF .4 PHASE DIIFEUXC? ,Q?';\;~~IV',L 'TECH N~QUE ' 

FOR LOCATION OF Tit?iFPFD ?!IS'ERb 

By V. G. Hopkins, 111,' I?. H. church,* and W. E. \qebb3 

The develoSprnent of systems for location of miners who have becoine 

entrapped following a mine disaster has been one of the major research 

goals in the Bureau of Nines. his study details the preliininary 

development of such a system. Current technologies for locating trapped 

miners from the surface are either simple directior, finders or time 

difference pulse systems that have accuracy Limitations. Developing 

technologies using full vector field measurements at several receiving 

points are currently being studied. The necessity of measuring field 

strength with great accuracy can be a drawback in these systems. A 

system that operates with continuous wave radio signals, whose phase 

differences can be measured accurately even in weak signal conditions, 

greatly improves the location accuracy. A microcomputer would be used, 

in conjunction with the system, to gather and manipulate the data to 

automatically pinpoint the locat ion of the trapped miner. Comparison of 

this system with existing technology indicates a favorable 

accuracy/complexity ratio for the phase difference of arrival 

technique. 

~lectrical engineer (faculty) . inin in^ engineer. 

3~hysical scientist. 

Tuscaloosa Research Center, Bureau of Mines, Tuscaloosa, XL 
The &tfeau of Nines, under its mission to a.l;7ance the safety of 

Anerican miners, has undertaken and sponsored research on 

through-the-earth location and communication systens for many years. 

Experience in postdisaster. rescue ~ork has indicated a need for a 

reliable means of quickly locaring trapped miners. his was w 

particularly evident after the 1968 disaster at the Consol No. 9 ?fine in 

Famington, W. Va., where for several days the whereabouts-and condition 

of 76 men were unknown. The Farmington disaster prompted the enactment 

of the Coal Mine Health and Safety Act of 1969. The tragedy at 

Farmington focussed national attention upon the problems of mine safety, 

and particularly upon those'of postdisaster rescue. At the request of 

the Bureau of Nines, the National Academy of Engineering created the 

Committee on Mine Rescue. and Survival Techniques to "conduct a study 

program to assess the technological capabilities that czn be applied to 

survival and rzscue techniques following mine disasters." The Bureau of 

Mines was particularly interested in. the possible application of new 

technology to the problem of mine safety. The Committee on Mine Rescuz 

and Survival made numerous recommendations for research and development 

in cornminications and mine rescue. The suggestions in regard to 

communication systems led to several Bureau of Hines programs to develop 

through-the-earth comunications and trapped miner location systems. 

The phase difference of arrival technique (PDOAT) offers a new means of 

such location. The findings presented in this report indicate that such 

a system is feasible. 

*** SUMMARY OF CURRENT SYSTEMS . 

Operation of a seismic subsurface system (113 is illustrated in 

figure 1. As reported by Westinghouse ~lectyic Corp., the trapped miter 

pounds the ground by banging a hammer, rock, or similar object onto t5e 

rocky mine floor. This pounding causes vibrations in the grocnd which 

are transmitted to the surface where they are sensed by receiving 

transducers called geophones. Multiple geophones are positioned 

together for noise cancellation purposes in a form called a subarray. 

Seven different subarrays are strategically placed at known locations 

over the mine, covering an area with typically a 1,000 ft radius. 

The signals received by the subarrays are transmitted either through 

cable or radio to an instrument van which houses the electronic location 

equipment. Here the signals are processed and, knowing the subarray 

locations and the tine of arrival of the signals at each subarray, the 

location of the trapped miner is determined by computer. 

-'underlined nllinbets in parentheses refer to the list of references at 

the end of this report. 

, . D~ribg a perlbd o/' oyar 10 years, this system has been tested, 

jrn@~-oved, and refined. Studies were cond:~tted at a number of coal mines 

throughout the United States to deterair!+ the ability of the system t3 

detect typical signals from a miner pou~ding underground and thereby 

locate the miner's position. 

The results of these tests have detemined that, over a hypothetical 

area of confinement of 1 sq mi, there is a 0.85 probability of detecting 

the signal from a miner at a depth of 2,000 ft anywhere within this arza 

(6). - ' 

The components of an electromagnetic direction-finding (ENIF) system 

for subsurface location are shown in figure 2,. Position finding is 

based upon the principle that even in the presence of horizontally 

layered changes in ground conductivity, a buried 'vertical magnetic 

dipole produces a vertical magnet ic-field vector on the surface point 

directly above the dipole (5). - 

Systems for coal-mine applications use signals in the 600 to 3,000 Hz 

range to maximize the signal-to-noise ratio at the surface, The trapped 

miner carries a small transmitter-and-antenna package. In the event of 

a disaster, the mine worker must deploy the antenna, preferably by 

wrapping it around a coal pillar to produce a 30 m by 30 m one-turn 

loop, The terminals of the loop antenna are then connected to the 

transmitter, which is powered by the miner's cap lamp battery. One 

variation includes a receiver in the miner's unit; and the ability to 

answer simple yes or no questions by keying the transmitter is also part 

of the design. 

Location of the subsurface transmitter requires finding the location 

of the vertical magnetic-field component. A helic~pter with an ultra 

low frequency (ULF) receiver first searches the mining area to determine 

an approximate location. A man-portable receiver is then used to 

determine the exact location of the null. 

The electromagnetic direction-finding system provides a previously 

unavailable measure of safety to the miner. Bowever, several factors 

should be considered, including: 

(1) The accuracy with which the null in the horizontal magnetic field 

locates the underground beacon is dependent upon the horizontal 

uniformity of the rock structure. ~eviations from horizontal layering 

(for example, surface slope) may cause errors in the locatLon estimate. 

'dhile corrections for such things as surface tilt can be made for a 

homogeneous earth, their use with complicated or unknown earth 

structures becomes difficult and may be impractical. 

(2)'.~he accuracy with which the null locates the undergrouzd beacon is 

also dependent upon the underground antenna being perfectly level. A 

nonlevel mine floor produces a tilted magnetic dipole and therefore may 

introduce errors in the position estimatz. 

- % 

. - (3) The surface above a mine may contain severs1 buildings. Wh; le 

. ?--.A these ziay be priulsrily made of nonconduc tive materials, their presence 

can hinder the search process, esp~ cially if they are directly above the 

trapped miner. 

(4) Various conductive or magnetic structures, including power Lines, 

can also be present. These structures can alter the geometry of the 

magnetic fields in their vicinity; power lines will produce higher noise 

levels in their vicinity as well. Thus, if conductive structures or 

power lines are located diractly above the trapped miner, the estimate 

of his location will probably be less accurate. 

(5) The direction of the magnetic-field lines gives an indication of 

the location of the null. However, automatic interpretation of several 

such measurements to determine the location of the transmitter is 

difficult or impossible given an unknown structure of the ground. The 

electromagnetic direction-finding system requires a search and does not 

seem to be especially amenzble to automation. . 

A more recent development in the technology for detecting trapped 

miners from the surface depends upon the accurate measurement of the 

vector components of electromagnetic (EM) field at various sensor 

locations on the surface as shown in figure 3 (4). his system uses the 

same basic transmitter arrangement as EMDF. 1nan essentially lossless 

environment, such as in the atnosphere, the transmitter location map be 

exactly determined by measurement of the propagating EN waves. However, 

in a conducting median, such as the earth or water, rapid exponential 

signal attenuation results from energy dissipated through currents 

generated in the medium. At lower frequencies, the ability to 

communicate is better, and this system uses extremely low frequencies 

(ELF) to propagate an M wave (2). Measurements are made using at least 

2 three-axis field neasuremefit sensors. The report cited, (2) 

recommends 3 three-axis sensors to avoid "blind spots" and tz provide 

redundancy. This report notes also that background noise affects the 

magnitude of the field measurements. Simple noise cancellation - 

techniques such as blanking "would seriously hamper the locat ion 

process, which needs accurate amplitude measurements to achieve an 

accurate, unambiguous position fix quickly .I1 As a consequence, most of 

the report discusses signal processing techniques to minimize the 

deleterious effects of noise on the system. This system will be 

referred to as the Dl field measurement or E>fFN system. 

As an alternative ta these systems, an approach somewhat similar to 

the EM vector field msasurement technique previously described has been 

proposed. The advantage of this system, illustrated in figure 4, is 

that it depends only on the phase of the received signal at the sensor 

locations, so that the effects of at~enuation are greatly reduced, The 

proposed system uses an array of five sensors arranged in a fairly 

arbitrary, but known through measurement, array on thz surface. One 

sensor is used as a reference, and the remaining four sensors measure 

the phase difference of arrival (TDOA) wifh respect to the first sensor. 
Sensor No.1 # +Y (up) 

Sensor No. 3 / 

/ 

Sensor N 

/ Magneticdipole 

( mo;ent vector 

'4 / E, elevation an

--I-- 

-\A, azimuth 

\ 

FIGURE 3. - Electromagnetlc vector field measurement techniqu
Sensor No. 2 

Loop antenna 

transmitter 

FIGURE 4. - PDOAT syst.em 
ne co7municat ion hetween sensor posi* ions ad nhr ence could be a very 

h;:-;h frequency (VHZ) link or a ddr-cated land line. This techaique is 

referred to as the PDOAT. The details of this systeiu are discussed 1ii 

the following text which illustrates sample calculat j.oll~ 

** T'HE PHASE DIFFERENCE OF ARRIVAL TECHNIQUE 

One limiting factor in existing transmitter based trzpped miner 

location techniques is the difficulty in obtaining accurate -amplitude 

measurements of the magnetic field. This has led to the development of 

a technique which depends only on phase measurements. The system would 

used a computer algorithm to analyze the measured phases of the 

transmitted signal at multiple receiver locations. This technique 

assumes a model of the overburden strata as a homogeneous shell of 

unknown characteristics. As a byproduct of the PDOAT, the average 

characteristics of the overburden can be determiced. 

~igure 5illustrates the arrangement of sensors for k~lementing the 

PDOAT. The sensors are at known locations. These may have been 

previously surveyed or may be determined at the time of deployment of 

the system. Since it is unlikely that the terrain will be perfectly 

flat, the .sensors are assumed to have coordinates (xi, yi, zi) with 

respect to any convenient origin, which could be the location of tha 

reference sensor. Thus the reference sensor is assuxed at (0, 0, 0) 

without loss of generality. As figure 5 illustrates, the distance from 

each sensor, including the reference sensor, to some unknown location 

(x, y, z) which represents the location of an underground CW 

transmitter, can then be calculated us-ing analytic geometry. The 

underground transmitter is assumed to drive a loop antenna which then 

acts as a magnetic dipole. The same transmitter developed for the DfDF 

method could be used. As the magnetic field propagates through the 

overburden, its phase is shifted. The equations which represent this 

propagation have been documented (7-8), -- and are included here for 

completeness. Computer programs to implement the solution to these 

relationships have also been developed and documented. Thus, referring 

to figure 5, the following formulation is developed. Considering the 

loop, whose area x turn product is LA, as a vertical magnztic dipole 

results in the following magnetic fields in air (i.e. z > 0) 

and 
Z axis for loop -. 

calculations 

FIGURE 5. - PDOAT array with nomenclatu
By changing the variable of integration to x = Ah the iztegrals P 2nd Q 

are expressible in the form 
where 

and 

are dimensionless parameters. equations are now in a form 

suitable for nuxerical integration, end the previously referenced 

computer program has beenprepared to accomplish this task. A listing 

is given in Appendix A, along with run instructions. Referring again to 

figure 5, it is seen that 

d2 = x2 + y2 4- z2 (11) 

and 

Each di can be expressed as d + 6i? so that 6i represents the difference 

between d and di. A general equatlon for the biBs is thus 

(x-xi)' + (y-yi)2 + (z-z~)~ (d+6i)2 (13) 

which yields 

*2 -2 xx* + xi2 + y2 - 2yyi f JTi2 + .2 - :zzi + .-2 = 1 1 

d2 + 2d6i + 6i2 

but since x2 + y2 + t2 = d2, this reduces to 

2xix + 2yiy + 2ziz + 26id + di2 = (xi2 + yi2 + zi2) 

or (for use in the algorithm later) 
TABLE 1. - Estimated position resolution, m 

4~eference to specific brand or trade names is made for identification 

Conductivity 

s = lo-L 

s = 10'3 

s = 10'4 

only and endorsement by the Bureau of Nines is not implied, 

Frequency, Rz 

100 

0.176 

.538 

1.76 

200 

0.124 

.380 

1.245 

1, no0 

0.056 

.170 

.556 

2,000 

0.039 

.I20 

.394 
I Acquire Aj 'S 

from sensors I 

Obtain initial 

estimate of Zj 

Solve 4 linear 

equations for 

Calculate I cj=zj~m I 

Print out 

. - 

FIGURE 6.. - Flow chart of PDOAT algorithm 
--.. .- 

Since B is inversely proportional to ,/ in, i-i can be seen that 

resolution of position increased with /£- as well .as 47. Of course, 

is an assilned constant parsmeter of the overburden, but Erequzncy is a 

design parameter of the system. In order to provide adequate resolution 

but to avoid the higher frequency attenuation effects, a frequency range 

of 100 to 1,000 Hz seems satisfactory. Calculations based on some 

typical values are presented in the following sample problem using 

PDOXT . 

*** SAMPLE CALCULATIONS USING PDOAT 

Assume that the PDOAT system has been set up using 12 bit A/D 

convertors (approximately range -30' to +30') and 'the sensor sites have 

been determined relative to the reference site. These measurements are 

assumed to have been in meters. 

TABLE 2. - Sensor coordinates 

Assume further that the transmitter of the trapped miner is at 30, 40, 

and 200 m and that the constant related to the overburden and frequency 

is 1,000 (which is roughly the value at 200 Hz with cf = 

Station Distance, m 

Then the 6i's defined in the previous chapter can be found, as well as 

the corresponding Bits. Thus: 

1........... .............. 0.. 

2............................ 30 

3.......... ............. ..... -30 

4......................,.,... -25 , 

z 

5 

0 

2 

-1 
For a first test, a simple antenna and tuned circuit receiver system 

was built. A block diagram of this system is shown in figure 7. Figure 

8 shows a schematic of the input amplifier section and figure 9 shows a 

schematic of the narrow band amplifier. The antenna consists of 2,500 

turns of AWG 934 enamelled wire wound on a 64 cm diameter. The cross 

section of the antenna is approximately 2- by 2-cm. The antenna has a 

resistance of 4,500 Sl and a computed inductance of approximately 8 

henries. A Faraday shield consisting of two layers of aluminum foil 

covers the coil winding and is grounded to the receiver chassis during 

operat ion. The receiver uses a balanced high-input impedence, low noise 

amplifier circuit, followed by two stages of narrow band amplification 

consisting of 741 op-amps with twin-tee feedback networks. Each narrow 

band stage is followed by a high input impedance stage to prevent 

loading of the tuned circuits. The output consists of four stages of 

high gain unplification. The last two can be bypassed if less gain is 

needed. Low and high frequency rollof f is provided to help reject power 

line and radio frequency interference. 

This system was successfully deployed on June 2, 1982, at North River 

Energy ~or~oration's No. 1 Mine near Berry, AL. The approximate depth 

of the transmitter was 167 m. A strong signal was detected at several 

surface locations. Figure 10 shows the system components. Figure 11 

shows the system during the test. 
I 

k Buffer 

amplifier 

FIGURE 7. - Block.diagram of preliminary PDOAT recei
. . . . 

FIGURE 8. - Schematic diagram of high-Irnpedence balanced input amplifier , 
FIGURE 9. - Schematic diagram of narrow band-pass filtsr using twin-tee feedback - - - .. . . 
FIGURE 10. - Photograph of PDOAT system cornl.)onents 

After determining that the ~lgnal was padily drsectable froa the 

surface, a more alaboratC tee *as devised. For this test, a 

phase-lock-loop (PLL) chip was added to the prev'i ously designed circuit. 

A block diagram of this receiving system is shawl> in figure 12. Using 

the previously designed front end, the filtered signal was fed into a 

phase detector and the PLL chip was used to determine the relative phase 

of the received signal. A'Tektronix oscilloscope, model T-912, was used 

to observe the received signal. The output of the PLL was suitable for 

application to the A/D converter in the Tektronix 4052 and-the 

previously described algorithm then could calculate the location of the 

transmitter. 

The review of existing and developing techniques in this report 

indicates various rest riceions and expectations that must be reconciled. 

Primary items of interest are cost, complexity, and accuracy. 

The relatively low' cost and simplicity of the EXDF system lends itself 

to rapid deployment in case of an emergency. However, the less 

sophisticated rrnull-seeking't method may impose severe limitat ions in its 

use. In some cases, it may not be possible or feasible to actually 

traverse the entire cross section of a mine in order to find a null. The 

EMFM and PDOAT systems share the advantage that once deployed, no further 

excursions are required to seek the transmitter location. The primary 

disadvantage of the EHFM system is its reliance on accurate field 

strength measurements. The primary reason for its complex digital 

processing is to counteract degradation of the signal used for this 

measurement. The PDOAT system, on the other hand, relies entirely on 

phase measurements. The strength of the signal needs only to be strong 

enough to allow the phase lock loops in the sensors to lock in. 

Further research with the PDOAT is required and should include design 

and deployment of the antenna array sys tern coupled with the microcomputer 

and appropriate software to determine system performance. In addit ion, 

extensive field test ing should be conducted . 
t a t 

Narrow 

bond pass Phase 

detector 

* 

. 

. . . . .. . . . 

FIGURE 12. - Block diagram of phase-lock loop recelv

1 'Lowpair/ Amplifier -e 

filter 

* 1 I 8 

d 

\rbl tage controlled 

oscillator 

L .. 

A 

- 
1. Duda, S. J. Trapped Miner Lacatio, and b-r.ixunica~ion System 

Development Program, v. 11: ~etection a04 Location of Entrapped 2liners 

by Seismic Means: Plethods and Computer Programs. West inghouse EZectr LC 

Corp., ~altimore, MI; ~u~ines OFR 41(2)-74, May 1973, 64 pp., NTIS, 

PB-235 606. 

2. Kraichman, M. B. Handbook of Electromagnetic Propagation in 

Conducting Media, NAMT P-2302, U.S. Government Printing Office, 1970, 

p. 2302. 

3. Powell, J. A. An ~lectromagnetic System for ~etecting and Locating 

Trapped ~iners. ~u~ines RI 8159, 1976, p. 15. 

4. Rorden, L. H., T. C. Moore, E. C. Fraser, and L. R. Bulduc. 

Development of Systems Concept for Location of Trapped ~iners in Deep 

Mines by an ~lectromagnetic Xethod. Phase 1 Report, Contract No. 

50199009, Develco, Inc., Sunnyvale, CA, Oct., 1979, 119 pp. 

5. Sacks, 8. K. Trapped-~iner Location and communication Systems. 

Underground Mine Communications, Part 4, Sect ion- to-Place ~ommunications, '. 

BuMines IC 8745, 1977, p. 80. 

6. U.S. Bureau of Mines. Seismic System for Detecting and Locating 

Trapped Miners. Technology News No. 100, Bureau of Mines, May, 1981. 

7. Wait, J. R; ~lectromagnetic Induction Tschnique for ~ocating a 

~uried Source. IEEE Transactions on Geoscience Electronics. v. GE-9, 

No 2, April, 1971, pp. 95-98. 

8. . Criteria for Locating an Oscillating Magnetic Dipole Buried 

in the Earth. Proc. of IEEE, June, 1971, pp. 1033-i035. 

9. Wait, J. R. ~lectromagnetic Fields of Sources in Lossy Xedia. 

Antenna Theory, Pt. 11. R. E. Collins and P. J. Zucker, (ed). 

~cGraw- ill, New York, 1969, Ch. 24, pp. 468-471. 
Sej-srnic SYStern .......................................... Electromagnetic direction-finding system ................ Electromagnetic vector field measurement technique ...... PDOXT system .......... ;.60e*a**6....*..........*6***.... 

PDOAT array with nomenclature...... ..........*.......... 

Flow chart of PDOAT algorithm ........................... Block diagram of preliminary PDOAT receiver ............. Schematic diagram of high-impedence balanced input 

amplifier ...........,.....*6..*.d....*....o.*......... 

Schematic diagraa of narrow band-pass filter using 

twin-tee feedback... ........ ~~~~~~.*~~

Photograph of PDOAT system components,.. ................ Photograph of USBM personnel depolying PDOAT receiver.. . Block diagram of phase-lock loop receiver ......,........ 
' hpp&di A. - Fortcan program for estir2ti~G phmc angle t Lrcqgh omerbvrden 

1: 

2 : 

3 : 

4: 

5: 

b: 

.. 7: 

43: 

9: 

10 : 

11: 

12: 

13: 

Ik:4il 

15: 

16 : 50 

17: 

la: 

19: 

2il: 

21t70 

22: 

- 23: 

24: 

25: 

26: 

27:80 

28: .. 

29:93 

30 t 

31 : 

32: 100 

33: 

34 : 

35t113 

36: 

37: 

38 : 

341: 

49 : 

41: 

42 t 

43 : 

44 t 6d 

45: 130 

46 : 20 

47 : 

4d : 

49 : 

5d: 

51: 

i.Ob!PLEX ?XI PY PPZI PHI PPHI 

I IL=5 

P1=3*1415926536 

CTH=PI/l3O. 

rL3s= l 

H=.O5 

z=o.ll 

s=.03 

YL=.G 

PhI=O. 0 

OH=. i15 

i'dR=2 3 

YRIhT 40 

FORMAT (tlH~ZtStLtPHIt) 

PRIhT 50tHtZtSttLtPhI 

FORkAT(' H=*tF45.5tt Z='rF6.2rt S=t~F6.2tt YLz.8F9.41~ Phf='rF9.41 

PKIR=PHX*DTR 

CP=CCs(PtiI9) 

Sp=SIk(PaIR) 

PRIbiT 70 

FORMAT (' RtPZYAG8PR+lAGtPPHIMAGtPZPHtPRPHtPPHIPHt) 

LO 60 J=lrNR 

f?=I)H*(Jm1) 

>(=R*CP 

XD=ABS(X-5) 

IF (XD-I~E-~) 80t80r90 

R=R+. l*OH 

>r=R*CP 

Y=H*SP 

YD=ABS(Y-vL) 

IF (YO-l.E-4) 10Q~100~110 

H=R+, 1*DY 

>(=H*CP 

Y=R*SP 

CALL PINT(H~Z~X~S~Y~YL~PX~PYPPZI 

FR=PX*CP+PY*SP 

FPH I=PY*CP-P,x*SP 

PZib:=CABS (PZ 1 

PRh1=CfiBS (PR 

FPHIFI=CAaS ( PPH~ 

PZP=CANG(PZ)/DTR 

Ft?P=CANG( PR 1 /DTZ 

PPHIP=~ANG(PPHI)/DTR 

PRINT ~~~~RIPLM~PRM~PPH~.'~PFZPPPRP~PPF!IP 

FORVAT (Elq.4t6E16.5) 

COAT IFUUE 

EN0 

SUEROUTItJE PL;VT(HIZ~XPS~Y~YLVF,Y~PY~PZ) 

LOYPLEX CI~PXI~PY~~PZI~RAOPT~F~ACPPXIPY~PZ 

GKAX=(12,+H)/(l,+Z) 

RMAXI=~./SQHT((X+S)**~+~Y+YL)**~) 
. , 4 .. 1 2, 1CI It; 

hH=G:v;.d;:/t , " ,i,i< ,! 

b0 T3 -2) 

NH=G!\i ,.,X 

I\(1=2*1~h+2 

L'G=Gi*IAX/h i 

LI=(ll.tl.) 

l12=h*E 

FXI=[dmt3a) 

PYI=(O. 113.) 

PzI=(o* to* 1 

EO 4d 1=1ti'J]C 

G=OG* I 

IF '(I-NII 50tbOri~ 

CF=1 

GO 7'0 70 

CF=j.+(-l,)**l 

G2=G*G 

HAD=CSQRT(GL+CI*ri2) 

T=G*CEXP (-RAU 1 / (G+RAD 

FAC=G2*T+EXP(-G*Z) 

CALL FXI~%T(GPX,S~Y*YL~FX) 

CALL FYINT(G~x@S~Y~YL~FY) 

CALL FINT(GPX~S~YPYL~FZ) 

PXI=PXI+FAC*FX*CF 

PyI=PYI+FAC*Fy*CF 

PZI=PZI+FAC*FZ*CF 

PX=PXf *DG/3 

PY=PY L *DG/3* 

PZ=PZI*DG/3. 

FiETClRN 

EbD 

SU~RO~JTINE FI~T(GPX~SPY~YL~F) 

IF (S-YL) 10t20t20 

N=G*S 

GO TO 30 

I\r=G*Y1 

NI=2*Eu+l L 

RNP=Y 1-Y 

HFVN=-YLwY 

HDP=S-X 

RoN=-S-X 

THl=ATAN2(RkP,RUP) 

Th2=ATAN2(RhPtRah) 

TH3=ATAN2 ( RNN P RDid 1 

T~~=ATAN~(H~J~vPHDP) 

L~l=~TH2-TAl)/(hI-l) 

IF (YL-Y) 32~32~34 

OT~=(TH~-TH~)/(NI-~) 

GO TO 37 

GT2=(TH3-lH2+6.2d31d53072)/(>JI-l) 

IF (X-S) 37~37~33 

D~4=(~Hl-TH4-6.2d318550?2)/(NI-1) 

GO 'TQ 39 

CT4=(TH1-T!i4)/(NI-l) 

ET~=(TH~-~H~)/(~JI-I) 

A=4r*G*S*YL 
T11=c). 

112=0. 

T~S=U. 

TIQ=Oo 

LO 15 i=LtNI 

If (1-1) 40#4Up5:1 

CF=1 

60 Ti) 60 

IF (1-NI) 70843t40 

CF=3.+(-Le )**I 

TI=?Hl+DTl*( 1-1 1 

T2=Th2+OT2*tI-l) 

13=T~3+DT3*( 1-1 1 

T4=T~4+DT4*(1-1) 

R=RhP/SIB(Tl) I 

CALL FJl(Gdt IT) 

TIl=TIl+TT*CF 

R=RDiWCOS ( 12 . .

CALL fJI(GtHpTT) 

TI2=TI2+TT*CF 

R=RhN/S 14 ( 13 

CALL FJI(GeHtTT) 

TIJ=TI3+TT*CF 

K=RDP/COS(T4) 

CALL FJI(GPH~TT) 

T 14=TI4+TT*CF 

F=(TI~*DTl+TI2*DT2+~I3*DT3+TI4*UT4)~(3e*A) 

RETURrU 

ECuO 

SUBROUTIW FJI(G~R~P) 

ARG=G*R 

CALL JJ.X(ARGtH1) 

P=Hl*R 

RETlrHlL 

END 

SUBROLJTII~E FXIPJT(G~XPSPYPYLPFX) 

[u=G*YL 

h1=2*lt+5 

EY=YL/(N+2) . 

A=4 *G*S+YL 

FX I=O 

C.0 10 I=i~i'Jl 

IF (1-1) 20829t33 

CF=1 . GO TO 40 

If (NI-I) 20t20~50 

CF=3e+(-l0 )**l 

VP=-YL+DY~I-~) 

CALL FXJI(G#XPS~YPYP~CIF) 

TX=DIF+CF 

FXI=FXI+ TX 

Fx=FXX*OY/(3.*A) 

RETURN 

EidU 

SU~ROUTXI'~Z FYINT(GIX~S~YIYLPFY) 

Iv=C*5 

NI=2*b~+5 
\> x:.:;/ ( :;+z j 

AX%, .~-GF~FF~, 

Fvl=n. 

LO PO J=HPNL 

IF 11-LB 20cZOrSij 

CF=1. 

GO TO 40 

IF fi4I-I1 2Ijr23150 

CF=3.+(-1, )**I 

XP=-S+DX.* ( 1-1 

CALL FYJI(Gt1rYLtXtXPtDIF) 

TY=GIF*CF 

FYI=FY I+ TY 

FY=FYI*OX/ (3,wA) 

HETbHIL I 

EN3 

SUGROUTIhE FXJI(GtXtStYtYPtC1F) 

XO2=(X-S)**2 

102=(Y-YP)**2 

~=SWRT(XQ~+YD~) 

ARG=G*R 

CALL dOX(AR6rBD) 

Xs2=(X+S)**2 

RZSQRT (XSZ+YG2) 

RG=G*H 

:CALL JOX( ARGlOS) 

C. I F=BD-BS 

KETURS 

EltD 

SUEHOUTI~~E FYJI(G*YPYL~XPXP~D~F) 

YD2=(Y-Yt)**2 

x02=(x-XP)**2 

R=SGHT(X02+YD2) 

ARG=G*R 

CALL JOX(ARG~BO) 

YS2=( Y+YL) **2 

R=SCiRT(X32+YS2) 

ARG=G*R 

CALL JOX(ARGtf3S) 

b I F=SD-BS 

;iET?rHr\r 

ENC 

FUhCT iON CAPiG (Z 

LOYPLEX 2 

Zbi=CAGS(Z> 

IF (231) 10110t20 

X=HEAL(Z) 

Y =A I>iAG ( Z) 

CAIXG=ATAI\~~ (1 r k) 

GO Ta 30 

CANG=O. 

F.ETCIHI\( 

EhD 

SUEHOUTI~~E JOX( XI GJZE8O 

IF (XI 5~10~15 

il>c=->c 

GO TO 20 


tippendis B. - Focr-ran progrm for deterhinine the location (x, y, z COO rd tmtesj of tke 

trapped miner. 

.v3 DIM ki4,4),Al(4,4i,B(4,4~'3i4,4)C(4,~1)~~4) 

.a5 B = 0 

.i8C = 5 

L15 F = 0 

.SO FOR I = 1 TO 4 

169 PZI14T "INPUT THZ COORDINATES OF RECEIVER %";I 

!78 FOR 3 = 1 TO 3 

3 PRINT "INFUT ";XS:" COORDIMATE -> "; 

i5B INTUT A(I,J) 

?O9 C(I,1) = C(I,1) + A(1,Z) f 2 / 2 

zia NEXT J 

120 Z(I) = A(I,3) 

25.F = F 4 Z(I) * 2 

130 NEXT I 

243 FOR I = 1 TO 4 

25@ PRINT "INPUT THE PHASE NEASU~EMZNT OF RECEIVER #":I 

0 INPUT A(I,4) ' 

?7O A(I,3) = .5 * A(I,4) 9 Z 

288 NEXT I 

295 IF F = 0 TEEN 310 

?90 P2INT "ESTIMATE Th'E DEPTH OF THE TRANSMITTEilu; 

300 INPUT Z0 

310 FOR I = 1 TO 4 

3ZQ B(I,l) = C(I,l) - Z(I) *. ZO 

338 NEXT T 

340 A1 = INV(A) 

350 S = Al MPY B 

360 X = S(1,1) 

370 Y = S(2,1) ,+ 

380 K = SQR (S(3,1)) 

350 D = S(4,1) / K 

395 IF F = 0 T'GN 1000 

480 E = Z0 -' SQR (D * 2 - X + 2 - Y ** 2) 

$13 IF ABS (E / 23) < .001 THEN 1009 

$28 = za + E s 

430 ' GOTO 31 0 

i08Ci PRINT 

wra PRINT "x= ";x 

i220 PZINT "Y= ";Y 

1030 PRINT "z= vz0 

tG4G PRINT "K= ";K 

f9S9 PRINT "D= ":D 

3 PRINT "00 YOU UAfiT TO IKPUT NEX FXASZ MEASUFtEMEXTS?"; 

1070 INPIJT AS 

~d80 IF A9 = "Y" OR AS = "YES" THEN 240 

3399 END #