Bureau of Mines Report of Investigations/l982 

Performance Evaluation 

of Electromagnetic Techniques 

for the Location of Trapped Miners 

By John Durkin 

UNITED STATES DEPARTMENT OF THE INTERIOR 
Report of Investigations 8711 

Performance Evaluation 

of Electromagnetic Techniques 

for the Location of Trapped Miners 

By John Durkin 

UNITED STATES DEPARTMENT OF THE INTERIOR 

James G. Watt, Secretary 

BUREAU OF MINES 

Robert C. Horton, Director 
This publication has been cataloged as follows : 

Durkin, John 

Performance ebaluation of electromagnetic techniques for the location of trapped miners. 

(Report of investigations / United States Department of the Interior, 

Bureau of Mines ; 8 7 1 1. 

Bibliography: p. 29-30. 

Supt. of Docs. no.: 1 28.2387 11. 

1. Mine rescur mork-kquipment and supplies-b,valuation. 2. Electromagnetic fields. 3. Signal processing. I. Title. 11. Series: Report 

of investigations (United States. Bureau of Mines) ; 87 11. 

TN23.U43 lTN2971 622s 1622'.81 82-600087 
CONTENTS 

Page 

Abstract ....................................................................... Introduction ................................................................... Earth transmission loss ........................................................ General Instrument transmitter ................................................. Surface EM noise ............................................................... Surface signal-to-noise ratio .................................................. Signal detection criteria ...................................................... Recognition differential method. .......................................... Receiver operating characteristic method .................................. Probability of detection estimates ............................................. Recognition differential method ........................................... Receiver operating characteristic method .................................. Sensitivity analysis ........................................................... Summary ........................................................................ References ..................................................................... 

ILLUSTRATIONS 

Illustration of the operation of the trapped-miner transmitter ............ Trapped-miner EM transmitter with caplamp battery ......................... Caplamp voltage variation with time while operating the trapped-miner 

transmitter ............................................................. Cumulative distribution of coal mine depths throughout the Unted States ... Uplink normalized overburden signal response data and linear regression 

log (depth) model at 630 Hz ................................be........... 

Uplink normalized overburden signal response data and linear regression 

log (depth) model at 1. 050 Hz ..........................a.b.............. 

Uplink normalized overburden signal response data and linear regression 

log (depth) model at 1. 950 Hz ........................................... Uplink normalized overburden signal response data and linear regression 

log (depth) model at 3. 030 Hz ............................be....e........ 

Uplink regression results for 630-Hz-normalized vertical signal strength 

versus depth ............................................................ Uplink regression results for 1.050-H z-normalized vertical signal strength 

versus depth ............................................................ Uplink regression results for 1.950-H z-normalized vertical signal strength 

versus depth ............................................................ Uplink regression results for 3.030-H z-normalized vertical signal strength 

versus depth ............................................................ Normalized overburden response curves-- uplink regression results: Average 

surface vertical signal strength versus overburden depth by frequency ... Predicted uplink response curves for General Instruments transmitter: 

Average surface vertical magnetic field signal strength versus depth by 

frequency ............................................................... Statistical distribution of RMS surface noise at 630 Hz ................... Statistical distribution of RMS surface noise at 1. 050 Hz ................. Statistical distribution of RMS surface noise at 1. 950 Hz ................. Statistical distribution of RMS surface noise at 3. 030 Hz ................. Cumulative probability distribution of SNR expected above U.S. underground 

coal mines at 630 Hz .................................................... Cumulative probability distribution of SNR expected above U.S. underground 

coal mines at 2. 050 Hz .................................................. 
Page 

Cumulative probability distribution of SNR expected above U.S. underground 

coal mines at 1,950 Hz.................eeeeeeeeeeeeeeeememeeemeeeeeeeeee 

Cumulative probability distribution of SNK expected above U.S. underground 

coal mines at 3,030 Hz.............e...eeeeeeee~eeeeeeeeeemeeeeeemeeeeee 

Probability that mean RMS signal is greater than or equal to KMS noise for 

the General Instruments transmitter........eeeeeeeeeeeeeeeeeee.eeeee.eee 

Measured values of the critical bandwidth of the ear.. . . . . . . . . . . . . . . . . . . . . Recognition differential (auditory detection threshold) for sinusoidal 

pulses in broadband noise reduced to 1-Hz bands......................... 

Effect of repetition rate of short tones on the masked thresho1d.......,.. 

Aural probability of detection versus KMS signal-to-noise ratio for 

trapped miner pulsed with signals in Gaussian background noise.. . . . . . . . . N and SN distributions showing d' and c re1ationships..................... 

Receiver operating characteristic curve................................... 

Predicted probability of signal detection versus overburden depth by frequency for the GI transmitter as found by the recognition differential 

method.............eee.eeeeeeee.eeemeeeeee..eemeeeeeeeeaeeeeeeaeeeeeemm. 

Receiver operating characteristic curve for the trapped-miner receiver. .. . Predicted probability of signal detection versus overburden depth by frequency for the GI transmitter as found by the ROC method................ 

Predicted probability of signal detection versus overburden depth by frequency for the GI transmitter as found by the ROC method with a 3-db 

SNR improvement........eeeeee.eee.eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeem

Predicted probability of signal detection versus overburden depth by f requency for the GI transmitter as found by the ROC method with a 6-db 

SNR improvement........eeeeeeeeemeeeeee.emeee.eeeeeeeeeeeeeeeeeeeeeee

Predicted probability of signal detection versus overburden depth by frequency for the GI transmitter as found by the ROC method with a 12-db 

SNR improvement........eeeeeeemeee~ee.ee.eeeeeeee.eeeemeeeeee.eeeeeeee

Predicted probability of signal detection versus SNR improvement by f requency for the GI transmitter for a mine depth of 1,000 ft.............. 

TABLES 

Estimated parameters characterizing signal and noise distributions above 

coal ~ne~~~~..~~~~~~~~~

Probability of achieving a signal-to-noise ratio of interest above coal 

mines using General Instruments transmitters............................ 

Probability of signal detection by observer versus signal-to-noise for the 

recognition differential method......................................... 

Detection probabilities......eeeeeeeeeeeeeeeeeee.eeeeeeee.eeeeee.eeeeemeee 
PERFORMANCE EVALUATION OF ELECTROMAGNETIC TECHNIQUES 

FOR THE LOCATION OF TRAPPED MINERS 

By John Durkin 1 

ABSTRACT 

The Bureau of Mines has conducted field studies in coal mines throughout the United States to determine the effectiveness of electromagnetic 

techniques in locating miners trapped underground following a mine accident. Data from these tests have been used to generate models of 

expected signal and noise distributions as found above mines throughout 

the coalfields. These distributions have aided in placing the expected 

performance of a through-the-earth electromagnetic commnications technique into a probabilistic framework. Results show that at a 10-pct 

false alarm rate, the expected probability of detecting a miner's signal 

from a depth of 1,000 ft is 54 pct; at 500 ft it is 95 pct. These 

depths exceed the actual depths of 90 pct and 50 pct, respectively, of 

U.S. coal mines. Sensitivity studies have shown that at a depth of 

1,000 ft, for every 3 db of improvement in signal-to-noise ratio, the 

probability of detection increases 6 to 8 pct. 

'~lectrical engineer, Pittsburgh Research Center, Bureau of Mines, Pittsburgh, Pa. 
FIGURE 1. - Illustration of the operation of the trapped-miner transmitter. 

'underlined numbers in parentheses refer to items in the list of references at the 

end of this report. 
origin. Figure 1 illustrates the principle of operation of the EM trapped-miner 

signaling device and associated surface 

receiving hardware. The transmitter and 

receiver were developed by Collins Radio (1) .3 An improved version has 

recenFly been built by General Instrument 

Corp. (GI) (5) and is shown in figure 2. 

In practice, the miner would attach the 

belt-worn transmitter to a caplamp battery and deploy 300 ft of /I18 copper wire 

around a coal pillar. If the loop cannot 

be deployed around a coal pillar, it 

can be deployed along a passageway 

where attempts are made to maximize 

the loop area. The transmitter delivers 

to the loop a pulsed square wave 

voltage of 630, 1,050, 1,950, or 3,030 Hz 

of 100-msec duration and a 10-pct duty 

cycle. The established EM field is 

then detected by surface personnel. Once 

3~se of brand names is for identification purposes only and does not imply 

endorsement by the Bureau of Mines. 

FIGURE 2. - Trapped-miner EM transmitter with 

caplanip battery. 

the signal is detected, the surface crew 

deploys a large loop of wire coupled to a 

high-power audio amplifier that can be 

used for transmitting voice comrnunications to the trapped miner. The underground transmitter contains a baseband 

receiver to receive the voice signals 

from the surface, and the miner can 
respond in code by keying the transmitter 

off and on. Figure 3 shows the life 

expectancy of the caplamp battery when 

operating the transmitter. The range of 

values was obtained when using an old 

battery with an 8-hr discharge to an 

upper bound where a new battery with no 

discharge was used. A 2-ohm resistance 

was used as a load on the transmitter for 

these results. From figure 3 it can be 

seen that the transmitter can be expected 

to operate for approximately 2 to 4 

days. 

The objective of the field tests was 

twofold: First, to define a signal 

transmission measurement and analysis 

program to obtain a reliable data base 

for characterizing the signal transmission properties of overburdens in the 

U.S. coalfields; and second, to use this 

data base to predict the likelihood of 

successful performance of the EM trappedminer signaling system. The mines sampled for these tests were selected from a 

population of all coal mines on the basis 

of both the overburden depth and for the 

number of miners employed at the mine. 

The sample reflected concern both for the 

physical dependence of signal penetration 

on depth and for the number of miners 

exposed to potential emergencies within 

each depth interval. Figure 4 shows the 

cumulative distribution of mines as 

related to the maximum depth and demonstrates that approximately 90 pct of the 

coal mines within the United States are 

less than 1,000 ft deep. These tests 

were performed by Westinghouse (17) - and 

Bureau personnel. The analysis of the 

data as presented in this paper was performed by personnel of Arthur D. Little 

Inc. and the Bureau; details of this work 

can be found in an excellent report by 

Lagace (7). Numerical values of field 

strengthe and noise levels are slightly 

in error in the Lagace report owing to 

calibration errors in the antenna which 

were discovered later. Adjustments were 

made, and the data are correctly reported 

in this report. 

EARTH TRANSMISSION LOSS 

To predict the surface signal level as 

produced from an underground transmitter, 

it is necessary to understand the 

expected loss the signal incurs when 

transmitted through the earth. Unfortunately, the geological structure of the 

overburden above coal mines differs from 

mine to mine, which gives rise to differing electrical conducting properties. 

Therefore, for a given mine depth it can 

be expected that signal transmission 

characteristics will vary significantly 

from mine to mine. Consequently, one 

must rely on statistical information of 

the earth's transmission loss. A major 

objective of the 94-mine field test was 

to obtain enough data on the earth's 

transmission loss, as found over a large 

population of coal mines, to confidently 

characterize expected signal loss from an 

underground transmitter. 

To insure success in obtaining these 

data during the field tests, magnetic 

moments of the underground transmitter 

were used that were artificially higher 

than would be expected from a transmitter 

to be used by a miner. Therefore, in 

most cases, an earth transmission loss 

value for each mine was obtained. 

A strategy could then be forlned to 

predict the expected surface signal 

strength based upon a given magnetic 

moment. 

The root mean-square (RMS) values of 

the vertical magnetic field, Hz, of all 

of the data taken were normalized 

to a transmitter magnetic moment (M) of 

M = 1 amp-m*. Since the surface field is 

directly proportional to the magnetic 

moment of the underground transmitter, 

the expected level of the surface field 

for a given transmitter could then be 

found by accounting for the actual magnetic moment used. Following this normalization, statistical studies were performed to relate the surface field 

strength and mine depth at each frequency 

tested. 
MINE DEPTH, ft 

FIGURE 4. - Cumulative distribution of coul mine deptl~s throughout the United States. 
Each normalized data point can be denoted as Sij, where the subscript i 

represents the specific frequency and the 

subscript j represents the specific depth 

of test for each mine. Thus, each surf ace measurement S taken can be considered as a single observation of signal 

strength at a predetermined frequency and 

overburden depth level at a particular 

mine. 

The relationship between field strength 

and mine depth was found through regression analysis. This work assumes that 

the errors are normally distributed and 

the variance is equal across the independent variable. These assumptions were 

considered, and it was concluded that 

meaningful statistical inferences from 

the regression analysis were acceptable. 

Several linear regression models were 

hypothesized and tried. The model found 

to best fit the behavior of the data is 

one in which the mean value of the normalized signal strength S is linearly 

related to the logarithm of overburden 

depth. This is shoyn in equation 1: 

Si = ai + 13 log (depth) + E i j. (1) 

Here S is the normalized vertical magnetic fleld signal strength (expressed in 

decibels re 1 pamp/m-RMS for the ith 

frequency and depth j for a transmit 

magnetic moment of M = 1 ampm2). 

The parameters a and 6 are to be 

estimated from the data, where depth is 

known in meters. The parameter cij 

represents a random variable that is normally distributed, with expected value 

zero and variance oZi j, which is the same 

for all values of j. 

The derived regression lines for each 

of the four frequencies are plotted in 

figures 5 through 8. The ~2 statistic, a 

measure of goodness of fit, indicates 

that the log-linear relationship is 

appropriate. 

Two types of intervals have been estimated from the data. One is known as a 

confidence interval, which is defined as 

a range of values computed frorn the sample that can be expected to include the 

true (but unknown) mean value with a 

known probability. Figures 9 through 12 

display 95-pct confidence intervals with 

dashed lines. To illustrate this concept 

using figure 9, it follows from the 

field experiment that the probability is 

0.95 that the interval from -8 to -14 db 

includes the true mean normalized signal 

strength for a transmitter of magnetic 

moment M = 1 amp-m2 at 630 Hz and an 

overburden depth of 190 f t. 

While the confidence interval represents a probability statement about a 

mean value over many trials, it is also 

of interest to quantify the expected outcome of a single trial. For example, 

what signal strength could be expected if 

a test were conducted at a predetermined 

frequency and overburden depth? This 

situation is depicted by prediction 

intervals, also plotted in figures 9 

through 12. To illustrate this concept, 

again using figure 9, the probability is 

0.95 that another test performed at 

630 Hz at a depth of 500 ft would yield a 

signal strength between -51 and -24 db. 

Also plotted in figures 9 through 12, for 

comparison, is a curve of the free-space 

vertical field strength that would be 

measured on the surface in the absence 

of the lossy overburden media. 
NORMALIZED SURFACE FIELD STRENGTH (Hz), 

n - 

- db re I pamp/m 

- 

bJ- 

- - 

P 

- 

in- 

- 

in- 

- 

.4 

- 

- 

r bo- 8 - - z * CD 

D, 

3 TU- -0 

3 

- 

", 

luN 

KSu, 

P 

KgNORMALIZED SURFACE FIELD STR

db re I pamp/m 
30 200 300 400 500 703 1,000 1,500 

1 I s- Surface vertlcal magnetic field, H,,versus log (depth) for - 

- a transm~t moment M= l amp-m2 

- 

- 

I- 

'" 5 -10 - - 

n a 

- 

- 

3 

- 

Ln 

o -50- 

W 

- 

k' KEY 

J -60 - 0 Observed data values 0 0 00 

a 

-70- 

LOG (depth, m) 

FIGURE 8 - Uplink normalized overburden signal response data and linear regression log (depth) model at 3,030 Hz. 
95 pct /' 

predict~on interval 

95 pct confidence intervol 

-100 I 1 . I , ,,I I I IIlllljl I00 150 200 250 300 500 700 1.000 1.500 

OVERBURDEN DEPTH, ft 

FIGURE 11. - Uplink regression results for 

1,950-Hz-normalized vertical 

- 

95-pct prediction intervol 

- 

Free-space curve - 

- 

95-pct confidence intervol 

- 

- 

OVERBURDEN DEPTH, ft 

FIGURE 12. - Uplink regression results for 

3,030-Hz-normal ized vertical 

signal strength versus depth. signal strength versus depth. 
Figure 13 summarizes the normalized 

average overburden response as a function 

of depth and frequency by plotting the 

four regression lines and the free space 

curve on one graph. This figure shows 

that the frequency dependence of signal 

strength is relatively insignificant for 

depths less than 500 ft, and that the 

change across the band is only about 

10 db even at the maximum depth of 

1,500 ft. 

These summary normalized overburden 

response plots, together with the confidence and prediction levels of this 

section, can be used to generate 

estimates of signal strength produced 

on the surface above coal mines as a 

function of overburden depth and operating frequency for transmitters having 

any prescribed magnetic moment versus 

frequency characteristics in the 630- to 

-80 

150 200 250 300 400 500 700 1,000 1,500 2,000 

OVERBURDEN DEPTH, f t 

FIGURE 13. - Norrnali zed overburden response 

curves-uplink regression results: Average 

surface vertical signal strength versus overburden depth by frequency. 

3,030-Hz band. This assumes that, for a 

fixed magnetic moment, the size of the that the size of loop used during the 

transmitting loop has no influence on the tests and the typical offsets for measurface field. It is recognized that suring the surface field were not 

this assumption is not totally valid, as severe enough to greatly influence the 

demonstrated by Wait (16), - but it is felt results. 

GENERAL INSTRUMENT TRANSMITTER 

Using the results of the previous section on earth transmission loss sta- 6 0 

tistics, the expected surface signal 50 

strengths produced by the recently devel- - oped GI transmitter can be predicted by I 40 

I- computing the expected magnetic moment at zz 30 each frequency and then translating each 

of the overburden response curves of fig- 2 20 * 3 

ure 13 upwards by an amount equal to the nJ I0 values of the magnetic moment expressed Y ? 

in re 1 amp-m2. uv La O 

0 

-10 The GI loop antenna consists of 300 ft 5 

of !I18 copper wire, arranged in a square. * -20 

This loop configuration was chosen 

because it best represents the practi- -30 

150 200 250 300 400 500 700 1,000 1,500 2,000 

cal implementation of the strategy OVERBURDEN DEPTH, ft 

that the miners will be instructed to 

follow. Figure 14 shows the predicted FIGURE 14. - Predicted uplink response curvesfor 

surface field strength when the GI trans- General Instruments transmitter: Average surmitter is used. Also shown are the face vertical magnetic field signal strength verexpected magnetic moments for each si~s depth by frequency. 

frequency . 

I I I ' I ' I ' I ' ' I ""I 'I- 

- 

- 

- 

Magnetic moment 

of GI transmitter 

3,030 383 51 .7 \ 3,030 I I 1 I I1 1 I I I1 IIIIII I, 
SURFACE EM NOISE 

Two independent sets of magnetic field 

noise measurements were obtained during 

the measurement program. The first was 

by Westinghouse using the Collins mancarried receiver. This set of data was 

found to be in error owing to int ramodulation problems caused by the simultaneous measurement of discrete manmade noise 

and broadband noise. The second set of 

data was obtained by a Bureau team performing tests at 27 of the mines tested. 

The Bureau's data were gathered on tape 

and later analyzed in the laboratory. 

For purposes of signal detectability, 

the RMS value of the vertical magnetic 

field is of interest. The statistical 

distribution of this noise, using the 

Bureau data base, at each frequency for a 

receiver bandwidth of 30 Hz is shown in 

figures 15 through 18. 

SURFACE SIGNAL-TO-NOISE RATIO 

In the previous sections, the behavior 

of signal data and noise data obtained in 

this study has been characterized by statistical relationships. It has been 

found that both the signal and noise data 

are log normally distributed. To develop 

an understanding of detection probability, it is necessary to characterize the 

probability distributions of the surface 

RMS signal-to-noise ratio (SNK) at each 

frequency . 

The basic input for the derivation of 

RMS-SNK estimates on the surface is summarized in table 1. Mean RMS signal 

strength and standard deviation values at 

each frequency for different mine depths 

are given, adjusted to pertain to the GI 

transmitter. Mean RMS noise strengths 

and their standard deviations are also 

given at each frequency. 

TABLE 1. - --- Estimated parameters characterizing --- signal and noise 

distributions above coal mines >-- 

--- 

------- 250..................... 

500.................~... 

.................... -2.90 

----- ESTIMATED MEAN NOISE IN LIECIbELS RE 1 pamp/m / 4- 

All depths................ .T- 4.3 I -2.8 I -11.3 I -17.1 

Standard deviation.. ...... 1 13.5 1 11.5 1 12.5 1 12.5 

The independence of signal and noise 

distributions, in addition to the 

property of normality exhibited by each 

distribution, permits straight-f orward 

combination of the two distributions to 

generate SNK probability estimates. The 

sum (or difference) of two normally and 

independently distributed variables is 

also normally distributed. 

This paper is designed so that the 

mean is plotted at the 50 percentile 

point and the mean plus and minus 

one standard deviations are plotted 

at the 16 and 84 percentile points, 

respectively. Such normal probability plots are given in figures 19 

through 22 for five different overburden depths at each of the four 

frequencies. 

The SNK distributions are conveniently 

plotted using normal probability paper. 
1 I 1 I 11111 I 1 I II 1 

- - 

- - 

- - 

- - 

Mean = 4.3 ----- -- 

- - 

- - 

11111 I I 1 I II I 

CUMULATIVE NORMAL PROBABILITY, pct 

FIGURE 15. - Statistical distribution of RMS surface noise at 630 Hz. 

1.0 5 10 2030 40506070 80 90 95 989999.5 99.9 

CUMULATIVE NORMAL PROBABILITY, pct 

FIGURE 16. - Statistical distribution of RMS surface noise at 1,050 Hz. 
-40 ' 

1.0 5 10 2030 4050607080 90 95 989999.5 99.9 

CUMULATIVE NORMAL PROBABILITY, pct 

FIGURE 17, = Statistical distribution of RMS surface noise at 1,950 Hz 

CUMULATIVE NORMAL PROBABILITY, pct 

FIGURE 18. - Statistical distribution of RMS surface noise at 3,030 Hz. 

pct db), R, i Pr(SNR NORMAL PROBABILITY, CUMULATIVE 

pct db), R, i Pr(SNR NORMAL PROBABILITY, CUMULATIVE 
These four figures provide a straight- provides the probability of achieving an 

forward method to estimate the probabil- SNR value less than or equal to R, . ity of having various SNR's in actual Table 2 shows the probability of achievpractice . The vertical axis represents ing an SNR of interest for each frequency 

the area under the normal curve from at different depths . minus infinity to some SNR value R, and 

TABLE 2 . . Probability of achieving a signal-to-noise ratio of interest 

above coal mines using General Instrument transmitters 

Signal-to-noise ratio. db 1250 it 1 500 ft 1 1. 000 ft 1 1. 500 ft 

Less than -3 ....................... 

Above 12 ........................... 1. 95( 

Less than -3 ....................... 

Less than -3 ....................... -3 to 0 ............................. 0 to 3 ............................. 3 to 6 ............................. 6 to 9 ............................. 9 to 12 ............................ Above 12 ........................... 

Above 12 ........................... 3. 03( 

0.5306 

. 0821 

. 0773 

. 0697 

. 0602 

. 0497 

. 1304 

Less than -3 ....................... -3 to 0 ............................ 0 to 3 ............................. 3 to 6 ............................. . 0845 

6 to 9 ............................. . 0010 . 0809 

9 to 12 ............................ . 07 40 

0.0057 

0045 

. 0072 

. 0113 

. 0167 

. 0238 

. 9308 

0.7993 

. 0535 

. 0430 

. 033 1 

. 0243 

. 0172 

. 0296 

Above 12 ........................... . 99601 . 84411 . 2646 1 . 0561 

0.1101 

. 0446 

. 0552 

. 0653 

. 0740 

. 0802 

. 5707 

It is instructive to observe the behav- performance occurs in the upper part of 

ior of probability estimates associated the frequency band even though more loss 

with exceeding a given SNR as a function occurs through the earth at the higher 

of overburden depth and frequency . Fig- frequencies . This can be explained by 

ure 23 gives the probability of the RMS the rapid decrease in surface noise level 

signal being at least greater than as frequency increases . the RMS noise . Note that the best 
KEY 

-- 1,950 

OVERBURDEN DEPTH, ft 

FIGURE 23, - Probability that mean RMS signal is greater than or equal to Rh4S noise for 

the Genera I Instruments transmitter. 

SIGNAL DETECTION CRITERIA 

Recoanition Differential Method 

The success of a rescue effort when 

using a trapped-miner transmitter rests 

on the ability of surface personnel to 

confidently detect the signal from the 

underground transmitter. The pulsed signals from the underground transmitters 

are detected by searchers carrying rescue 

receivers equipped with a handheld loop 

antenna and headsets. The mode of detection is aural, based on the headset signals perceived by the ear. It is then 

necessary to establish a relationship 

between the nature of the signal, SNR, 

and the probability of aural signal 

detection. 

The aspects of the signal that influence detection are (a) frequency, 

(b) signal length, and (c) signal repetition. The primary aspect of the noise 

for detection considerations, besides its 

level, is its bandwidth. How each of 

these parameters affects the signal 

detection capability must be understood; 

then their results can be combined to 

generate a probability-of-detection curve 

as a function of SNR. 

The present receiver mixes the received 

signal with an internal oscillator to a 

higher frequency for purposes of narrowband filtering, and then mixes the filtered signal again to present a listening 

signal of 978 Hz to the operator. The 

ability to detect a tone masked by broadband noise as a function of frequency has 

been studied by Urick (15). - In this 

work, an entity known as critical bandwidth evolved. When the ear listens for 

a tone, it acts as a narrowband filter 

centered at the signal frequency. The 

masking of the signal by the noise will 
only be in£ luenced by the noise within systems with bandwidths approximately 

this critical band. Noise outside this one-half the critical bandwidth will 

band will have no influence on signal behave in the same manner detection-wise 

detectability. Figure 24 illustrates the as those having a system bandwidth equal 

critical bandwidth values as a function to the critical bandwidth. Therefore, 

of frequency and shows that critical for purposes of the trapped-miner system, 

bandwidth is approximately 60 Hz at the an SNK of 23-10 log 30 = 8 db is needed 

978-Hz listening frequency of the rescue to yield a 50-pct probability of 

receivers (15). - detect ion. 

The effect of the length of a pulsed 

tone is shown in figure 25. Psychoacoustic data taken by a number of investigators are combined in this figure to show 

the "recognition differential" required 

versus pulse length for a 50-pct probability of detection (15). The recognition differential is tG amount in decibels by which the signal level needs to 

exceed the measured noise spectrum level 

(noise level in 1 Hz within critical band 

of interest) to provide a 50-pct probaA final factor affecting detection is 

the signal repetition rate. Garner (4) 

provides data on the effect of the 

repetition of a pulsed tone on signal 

detectability. Figure 26 illustrates 

these findings. This work shows that as 

the repetition rate of a 50-msec pulse of 

a 1,000-Hz signal is changed from 1 per 

4 sec to 1 per sec, 2 db less SNR is 

required. Reviewing Garnerfs data would 

indicate that an even greater improvement 

night be expected for the trapped-miner 

bility of detection. transmitter, but the lack of data at 

repetition rates less than 1 per 4 sec 

The GI transmitters have a fixed pulse precludes a guarantee of this. Thereduration of 100 msec, which prescribes a fore, a conservative 2-db improvement 

recognition differential of 23 db to value will he used. The 50-pct probaachieve a 50-pct probability of detec- bility of detection SNK criterion of (8- 

tion. To determine the significance of 2) db, or 6 db, will be used. 

the 23-db recognition differential in 

terms of required SNK, a bandwidth must This work quantifies the necessary SNK 

be chosen. The bandwidth used in the to establish a 50-pct detection probabilreceiver is 30 Hz, one-half of the criti- ity. It is also necessary to extend this 

cal bandwidth of the ear at the listening work to determine detection probabilities 

frequency. It is assumed here that the at any other SNK. The results of this 

noise reaching the operator's ear is extension are shown in figure 27 and 

produced solely by the receiver and that table 3. This plot can be used with the 

the attenuation provided by the headset earlier established expected SNK for the 

is sufficient to justify disregarding underground GI transmitter to establish 

ambient acoustic noise in the area of the signal detection probabilities. 

operator. Studies (10) - have shown that 

TABLE 3. - Probability of signal detection by observer versus signal-to-noise 

ratio for the recognition differential method 

Signal-to-noise Probability of 

ratio, db detection 

Signal-t o-noise Probability of 

ratio, db detection 
RECOGNITION DIFFERENTIAL 

(AUDITORY DETECTION THRESHOLD), d b 

CRITICAL BANDWIDT

- N 

P 6,000 0 

C 000 0 
- I I I I I I II 1 I I 

- - 

- 

- I msec 

x 10 msec I 

0 15 msec - 

A 20 msec - 50 msec - 

- 

- 

- 

1 1 I 

REPETITION RATE, tones per second 

FIGURE 26. - Effect of repetitinr: rute of short tones on the masked threshold. 

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 

SIGNAL-TO-NOISE RATIO, d b 

1 I I 1 I 1 

7 

/* 

- 

- - 

- 6.0 db at 

FIGURE 27. - Aural probability of detection versus RMS signal-to-noise ratio for trapped miner 

pulsed with the signals in Gaussian background noise. 

6 

50-pct probability 

- i - 

k 

1 1 I 1 
Receiver Operating -- 

Characteristic Method 

The recognition differential, as discussed in the previous section, may provide misleading conclusions since the 

percentage of correctly identified signals is given unaccompanied by information about either false alarms or correct 

rejections. This problem occurs because 

assumptions made about an observer's perf orlnance are not necessarily correct. If 

the observer is told to be certain that a 

signal is present, then the curve of figure 27 would be shifted to the right and 

the recognition differential would be 

higher. If, however, the observer is 

told to be very sure not to miss any signals, then the curve of figure 27 would 

be shifted to the left. In the first 

case, the observer misses the signal more 

often; in the second case, the observer 

produces more false alarms. Ideally it 

would be desirable to have a criterionfree measure in order to make meaningful 

statements about an observer's performance in signal detection. 

Fortunately, this criterion-free measure can be obtained from earlier 

work by Peterson (10) on the theory of 

signal detectability-(~s~). This work 

relates statistical decision theory to 

the general detection problem. The 

theory was originally developed to 

describe mathematically ideal or optimal 

detection processes, but it has become 

apparent that it represents a good 

approximation to a descriptive theory 

of human detection and recognition 

behavior (13). - 

The fundamental detection problem of 

TSD defines two parameters, the index of 

detectability (d') and the threshold 

criterion (c), which when combined provide a useful measure of performance. To 

understand the concept of these two 

parameters, refer to figure 28. Plotted 

in this figure are the probability density functions for noise alone (N) and 

for signal plus noise (SN). The mean of 

the N distribution has been placed at 

zero so that d' is read directly as the 

position along the abscissa of the mean 

of the SN distribution. 

The distance between the means may be 

regarded as a measure of the observer's 

sensitivity. It is a measure of the difference in sensory response to noise and 

signal plus noise stimuli and is analogous to SNK. However, despite this close 

analogy, it is impossible to assign 

definite values of SNR to d'. The value 

c as shown in figure 28 is analogous to a 

threshold, and in the case for d', no 

definite value can be assigned to it. 

To obtain a measure of d' and c and of 

the effectiveness of the test system, an 

experiment is performed in which an 

observer is provided a series of observation periods. At the end of each period, 

the observer reports his or her observation as noise only, or as signal plus 

noise. To accomplish this task, the 

observer establishes a criterion, represented by c of figure 28, and responds 

"no" when a particular observation is 

less than c and "yes" when it is 

greater. 

FIGURE 28. - N and SN distributions showing d' and c relationships. 
Of the two parameters of interest, d' 

is fixed by the experimental conditions 

and defines the limitation imposed on the 

observer by the characteristics of N and 

SN, and by his or her own sensitivity to 

these characteristics. The observer to 

some degree controls c, but this control is to a large extent dictated 

by the physiological framework of the 

test. 

In a typical test, as discussed earlier, the observer may be given such 

instructions at the start of the test as 

"Don't miss any signals," or "Be very 

sure you have a signal when you say yes. " 

What it is necessary to do then is to 

structure the test properly in order to 

obtain results that will both demonstrate 

the observer's ability to accurately 

detect the signal and provide a measure 

of the false alarm rate. A form that 

provides this desired result is commonly 

known as the receiver operating characteristic (ROC) curve and is illustrated 

in figure 29. 

The ROC curve can be generated directly 

from the N and SN distributions of figure 28. The area under the N distribution to the right of c represents the 

FIGURE 29. - Receiver operating characteristic 

curve. 

probability of false alarm, P(Y I N). The 

area under the SN distribution to the 

right of c represents the probability of 

detection, P(Y ( SN) . Each possible value 

of c generates a pair of values that may 

be mapped as a point in the P(Y 1SN)- 

P(YIN) plane as shown in figure 29. The 

d' parameter value is the distance along 

the negative diagonal between the ROC 

curve and the chance line. Thus, a set 

of values of d' defines a family of ROC 

curves. 

In practice, the simplest way to obtain 

the d' value is to present to the 

observer a series of tests in which a 

signal may or may not be present on each 

test. From these tests, results are 

obtained on the probability of correctly 

identifying a signal, P(YISN); probability of false alarm, P(YIN); probability 

of a miss, P(NlSN); and probability of a 

correct rejection, P(NI N) . These values 

may then be used to enter a table of 

areas under a unit area normal distribution to obtaia d'. However, this yields 

only one point on an operating characteristic on the negative diagonal. Since 

the whole ROC curve provides important 

additional information, it is desirable 

to use a method that allows several 

points to be plotted and an ROC curve to 

be fitted to them. Such a method, called 

the rating-scale method, is made possible 

by giving the observer more than two 

response alternatives, which allows the 

observer to adopt several threshold 

criteria simultaneously. This is done by 

asking the observer to rate each test 

during which a signal might have been 

presented on a four-point rating scale; 

for example-- 

0 - Confident, signal absent 

1 - Less confident, signal absent 

2 - Less confident, signal present 

3 - Confident, signal present 

Such a four-point rating scale gives 

three points on an ROC curve. If these 

are plotted on normal-normal probability 

paper, a best-fit line may be drawn and 

d' obtained from the graph. 
PROBABILITY OF DETECTION ESTIMATES 

Recognition Differential Method 

In an actual mine emergency situation, 

many factors influence the chances of 

rescuing the miners, including time of 

arrival of the rescue team, life expectancy of the miners, search times, and 

operation time of the underground transmitter. This report has not discussed 

these points but rather has investigated 

the detection probability for an existing 

signal being measured by a rescue team ifi 

an area that in general is directly over 

a trapped miner. Even within this measurement, there are factors such as geology, noise, and depth that influence the 

probability of success. Although these 

factors preclude our stating the success 

of this measurement in a deterministic 

manner, we can, as outlined in this 

paper, quantify our chances in a probabilis tic framework. 

The probability of detection curve in 

figure 27 actually represents a conditional probability; that is, the likelihood that detection will occur given the 

presence of a fixed KMS SNR. As a consequence, the chance of detecting a signal transmitted through the earth can be 

calculated according to 

where P(D and q) represents the probability of achieving an SNK of size RK and 

also detecting the signal in the noise. 

P(RK) is the probability of the occurrence of an SNR of size RK , and P(D (%) 

is the conditional probability of detecting a signal given an SNR of size RKo 

Figure 27 gives P(D1 %), and figures 19 

through 22 show the SNR probability distributions. The latter figures show that 

these probabilities depend on frequency 

and depth. Using additional subscripts 

to account for these parameters, the 

probability of acheiving an SNR of size 

RK and detecting the signal transmitted 

from a depth i at frequency j is 

Pijk (D and %) = Pij (RK) x P(DIq). (3) 

However, the primary result is the 

expected probability of detecting a signal transmitted at a specified depth for 

a known frequency summed over all possi ble RK ' s . This is given as 

These probability formulas and concepts 

can best be illustrated by a riumerical 

example. For a transmission frequency of 

3,030Hz at an overburden depth of 

1,000 ft, the data from table 2, also 

given in table 4, can be used with the 

results shown in figure 27 to obtain 

probability of detection for each SNR 

interval. 

TABLE 4. - Detection probabilities 

Signal-to-noise 

ratio interval, 

db 

Less than -3.. ... -3 to O.......... 

0 to 3........... 

3 to 6 ........... 6 to 9........... 

9 to 12.......... 

Above 12......... 

Probability of achieving 

signal-to-noise ratio 

in interval 

0.3314 

.0804 

.0843 

.0845 

.0809 

.0740 

.2646 

Interval 

midpoint, 

db 

Less than -3 

-1.5 

1.5 

4.5 

7.5 

10.5 

Above 12 

Probability of 

detection at 

midpoint 

0.00 

.OO 

.OO 

.15 

.85 

.99 

1.00 
Applying the summation formula, equa- detection at 1,000 ft and a frequency of 

tion 4, the expected probability of 3,030 Hz is estimated to be-- 

The interpretation of this quantity is the recognition differential method of 

that a signal transmitted at 3,030 Hz observer detection. 

through an overburden depth of 1,000 ft 

has a 43-pct probability of being Figure 30 shows the extension of these 

detected on the surface in the general calculations to other frequencies and 

area above the transmitter when using depths. 

- 

KEY 

--- - 1,950 Hz - 

3,030 Hz 

- - 1,050 Hz - 

om--- Q 630 Hz 

- - 

- - 

- - 

- 

- 

- 

OVERBURDEN DEPTH, ft 

FIGlJRE 30. - Predicted probability of signal detection versus overburden depth by frequency for the 

GI transmitter as found by the recognit ion differential method. 
the SNR = 3 db wave is similar to that of 

the 0-db curve but is not shown in the 

interest of retaining clarity in the figure. Therefore, for a particular input 

SNR and preassigned PFA, it is possible 

to determine the expected PD of the 

observer. 

The practical effect of false alarms is 

increased delay due to search time. 

Hence, false alarms are important not 

only for comparing different receivers 

but also in understanding the practical 

impact a receiver may have in a search 

and find mission. 

It is the opinion of the author that an 

acceptable operating point for the 

false alarms of this system would be 

PFA = 0.10. At this PFA, figure 31 shows 

the expected PD for the observer for 

different input SNR's. 

It is now possible to recalculate the 

probability of detecting the trapped 

miner's signal based upon the ROC of the 

receiver. This work is similar to the 

method followed in the previous section, 

but the detection probabilities of the 

observer, based upon the recognition concept, are replaced by that of the ROC 

method and the data obtained by way of 

figure 31. 

These results are shown in figure 32 

and show a slight improvement over those 

shown in figure 30. 
I 1 I 1 

0 250 500 750 I ,000 1,250 1,500 

OVERBURDEN DEPTH, ft 

FIGURE 32. - Predicted probability of signal detection versus overburden d-pth by frequency for the 

GI transmitter as found by the ROC method. 

SENSITIVITY ANALYSIS 

It is informative to observe the amount for all frequencies the probability of 

of increase in signal detectability for detection increases between 6 and 8 pct 

increases in SNR of the trapped-miner at 1,000 it for every 3-db improvement in 

signal on the surface of the mine. SNR. 

Figures 33, 34 and 35 show the expected 

probability of detection as the expected 

SNR is improved over that found from the 

field tests for values of +3 db, +6 db, 

and +12 db. As expected, the probabilities increase greatly, going from 54 pct 

for no SNR improvement at 630 Hz 

and 1,000 ft to 84 pct for +12 db SNR 

improvement. 

Additional insight is provided by way 

of figure 36, where the detection probabilities are shown for each frequency at 

a depth of 1,000 ft as the SNR is 

improved. To obtain a detection probability of 90 pct at 1,000 ft, a frequency 

of 1,950 would be used and an SNR 

improvement of approximately 18 db would 

be needed. A rough estimate shows that 

Various areas of investigation may be 

studied to acquire larger SNR. The obvious first choice is to increase the 

strength of the signal source. However, 

inherent constraints due to intrinsic 

safety considerations would limit any 

gain by this technique to only a few 

decibels. Correlation techniques could 

be used where an array of receiving 

antennas could improve detectability. 

This is the objective of a current 

project (14). Incoherent integration of 

the present signal has been suggested 

by Ristenbatt (12) and is the technique 

proposed by ~enEal Instrument Corp. (6) 

in an adaptation to the present receiver. 

Noise cancellation through correlation 

techniques involving the noise at the 
PEA. = 0.10 

SNR improvement = 3 db 

FIGURE 33. = Predicted probability of signal detection versus overburden depth by frequency for the 

GI transmitter as found by the ROC method with a 3-db SNR improvement, 

I 

PEA. '0.10 

SNR improvement = 6 db 

I 

OVERBURDEN DEPTH, ft 

0 A 

250 500 750 1,000 1,250 1,500 

OVERBURDEN DEPTH, ft 

FIGURE 34. - Predicted probability of signal detection versus overburden depth by frequency for the 

GI transmitter as found by the ROC method with a 6-db SNR improvement. 
PF.*. = 0.1 0 

SNR improvement = 12 db 

I I 1 

0 250 500 750 1,000 1,250 1,500 

OVERBURDEN DEPTH, ft 

FIGURE 35. = Predicted probability of signal detection versus overburden depth by frequency for 

the GI transmitter as found by the ROC method with a 12-db SNR improvement. 

.or I I I I 1 

.8 - 

.2 - - 

I I I I 

0 3 6 9 12 15 18 

SNR IMPROVEMENT, db 

FIGURE 36. - Predicted probability of signal detection versus SNR improvement by frequency for 

the GI transmitter for a mine depth of 1,000 ft. 
receiving antenna and a distant antenna 

outside the signal's range is an area for 

future study. 

The parameters of the signal that 

affect an observer's ability to detect a 

pulsed continuous wave (CW) signal in 

noise, discussed earlier, could be 

studied to improve detectability. However, these studies must also be conscious of the efficient use of the power 

of the transmitter battery and of schemes 

used in search procedures. 

Possibly the most promising venture to 

improve signal detectability is a project 

under investigation by Develco (2). - Here, the underground transmitter is 

similar to the one discussed in this 

report except that the signal is not 

pulsed, but rather transmitted continuously. The surface receiver is a microcomputer which coherently integrates the 

transmitted signal. The principal idea 

is to exchange time for signal detectability. The receiver continually monitors the signal, and if it exists and is 

within the detectable range of the 

receiver, it will eventually be detected. 

This system was originally designed to 

detect signals transmitted from a depth 

of 3,000 ft and should be able to easily 

detect signals at a depth of 1,000 ft in 

a few minutes of operation. Location is 

performed by vector calculation of the 

signal at a number of receiving-antenna 

locations. 

SUMMARY 

This paper has discussed the results of 

an extensive field-testing program to 

evaluate the performance of the EM 

trapped-miner transmitter. Analysis of 

these data has enabled one to place into 

a probabilistic framework the ability to 

confidently detect the signal from the 

underground transmitter. Two methods 

have been used to determine the probability of signal detection. The first, 

known as the recognition differential 

method, has indicated that the probability of signal detection at a depth of 

1,000 ft is 45 pct; at 500 ft it is 

90 pct. These depths exceed the actual 

depths of 90 pct and 50 pct, respectively, of U.S. coal mines. 

The second method, which is preferred 

to the former, is known as the receiver 

operating characteristic method. This 

method relates both signal detectability 

and false alarm rate. Using this method, 

it was found that for a 10-pct false 

alarm rate the probability of detection 

at 1,000 ft and 500 ft is 54 and 95 pct, 

respectively. This information is vital 

for the future formulation and promulgation of new regulations written for the 

use of the EM system. Studies are underway to improve the detection capability 

by providing signal-processing capability 

to the receiver. Future work will look 

at a systems approach when using this 

technique. This study will investigate 

each element involved in a successful 

rescue effort, such as search strategies 

and life expectancies. Coupled with 

the results discussed in this paper, 

a thorough understanding of the effective 

implementation of the EM system should be 

obtained. 

REFERENCES 

1. Collins Radio Group. Waveform May 1979; available for consultation at 

Generator--Package and Receivers. Final Pittsburgh Research Center, Bureau of 

Report for BuMines Contract H0242010, Mines, Pittsburgh, Pa. 

April 1977, 14 pp.; available for consultation at Pittsburgh Research Center, 3. Durkin, J., and R. Greenfield. 

Bureau of Mines, Pittsburgh, Pa. Evaluation of the Seismic System for Locating Trapped Miners. BuMines RI 8567, 

2. Develco. EM Rescue System for 1981, 55 pp. 

Deep Mines. BuMines Contract 50199009, 
g

8. National Academy of Engineering, 

Committee on Mine Rescue and Survival 

Techniques. Mine Rescue and Survival, Final Report-BuMines OFR 4-70, 

March 1970, 81 pp.; available for consultation at the Bureau of Mines facilities at Denver, Colo., Minneapolis, 

Minn., Pittsburgh, Pa., Juneau, Alaska, 

and Spokane, Wash.; at the MSHA facilities at Pittsburgh., Pa., Wilkes-Barre, 

Pa., Johnston, Pa., St. Clairsville, 

Ohio, Mount Hope, W. Va., Morgantown, 

W. Va., and Norton, Va.; and at the 

National Library of Natural Resources, 

U. S. Department of the Interior, 

Washington, D.C. 

9. National Defense Research Committee (NDRC) Division 6. Principles and 

gy

BuMines Contract 50318033, December 1980; 

available for consultation at Pittsburgh Research Center, Bureau of Mines, 

Pittsburgh, Pa. 

15. Urick, R. J. Principles of Underwater Sound for Engineers. McGraw-Hill 

Book Co., Tnc., New York, 1967, 450 pp. 

16. Wait, J. Subsurface Electromagnetic Fields of a Circular Loop of Current Located Above the Ground. IEEE 

Trans. on Antenna and Propagation, July 

1972, pp. 520-522. 

17. Westinghouse Corp. Reliability 

and Effectiveness Analysis of the USBM 

Electromagnetic Location System for Coal 

Mines. Final Report for BuMines Contract 

50166060, December 1978, 151 pp. 

t7U.S GOVERNMENT PRINTING OFFICE: 1982 - 505 - 002/76