By John Durkin and Roy J. Greenfield 

UNITED STATES DEPARTMENT OF THE INTERIOR 
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 

Evaluation of the seismic system for locating trapped miners. 

(Report of investigations / Bureau of Mines ; 8567) 

Bibliography: p. 48-50. 

1. Mine rescue work-Equipment and supplies. 2. Seismometers. I. 

Greenfield, Roy J. 11. Title. 111. Series: Report of investigations (United States. Bureau of Mines) ; 8567. 
CONTENTS 

Abstract ................................................................ 1 

Introduction ............................................................ 1 

Acknowledgments ......................................................... 2 

System description and operation ........................................ 3 

System deployment .................................................. 3 

System instrumentation ............................................. 7 

Seismic noise ........................................................... 9 

Theoretical seismic waveform modeling procedure ......................... 11 

Signal amplitude model derived from field tests ......................... 21 

1976 Kentucky coal mine results .................................... 21 

Signal amplitudes from the 1977 field tests ........................ 25 

Signal amplitude model for various sources .............................. 27 

Detection criterion ..................................................... 29 

Detection range ......................................................... 29 

Subarray performance .................................................... 30 

Probability of detection ................................................ 34 

Location accuracy ....................................................... 45 

Sumary ................................................................. 47 

References .............................................................. 48 

Appendix A*-- Relation of the amplitude distribution of narrow-band noise 

envelope to rms level ................................................. 51 

Appendix B.--Nomenclature ............................................... 53 

ILLUSTRATIONS 

Seismic van ........................................................ Ideal array configuration .......................................... Subarray configurations of 7 geophones and 24 geophones ............ Miner pounding while surface personnel listen for signal ........... Seismic system block diagram ....................................... Seismic record showing signal and noise before digital notch 

filtering and after filtering .................................... Flow chart of waveform modeling procedure .......................... Man signaling with timber on roof of mine .......................... Surface force-time function ........................................ Geometry and parameters used in waveform modeling procedure ........ Comparison of observed and theoretical seismograms at -800-ft depth 

Orient /I6 Mine ................................................... Spectrum of Orient /I6 data compared with spectrum from WMP ......... Comparison of observed and theoretical seismograms at 1.80 0-ft 

depths. King Mine ................................................ Comparison of observed and theoretical amplitudes at -800-ft depth. 

Orient /I6 Mine ................................................... Effect of soil layer thickness on vertical seismograms ............. Effect of force pulse width r, 12 ................................... Geometry for signal amplitude model and the form of model for earth 

velocity. V, ..................................................... Surface P-P particle velocity versus horizontal offset for A, model 
Page 

Comparison of A, model predictions for signal amplitudes with 

Westinghouse data from the Hamilton /I1 Mine..................... 25 

Cumulative probability of At coefficient and A2 coefficient for 

three Kentucky mines............................................ 26 

Maximum horizontal detection range versus source depth............ 30 

Geometry for calculation of detection probability............ ..... 35 

Chi-square fit to cumulative probability of T..................... 36 

Probability of detection by m or more subarrays versus C, the 

ratio of T to the large timber T--500-ft array radius, 2,000-ft 

monitored square................................................ 39 

Probability of detection by m or more subarrays versus C, the 

ratio of T to the large timber T--500-ft array radius, 4,000-ft 

monitored square............................................... 40 

Probability of detection by m or more subarrays versus C, the 

ratio of T to the large timber T--1,000-ft array radius, 

4,000-ft monitored square....................................... 40 

Probability of detection with m or more subarrays versus array 

radius, large timber source (C = 0 db), 4,000-ft monitored 

square.......................................................... 41 

Probability of detecting a miner's signal as a function of depth 

by one or more subarrays in an array of 1,000-ft radius 

monitoring a square area 0.5 mile on a side..................... 43 

Probability of detecting a miner's signal as a function of depth 

by one or more subarrays in an array of 1,000-ft radius 

monitoring a square area 1.0 mile on a side..................... 43 

Probability of detecting a miner's signal as a function of depth 

by five or more subarrays in an array of 1,000-ft radius 

monitoring a square area 0.5 mile on a side..................... 44 

Probability of detecting a miner's signal as a function of depth 

by five or more subarrays in an array of 1,000-ft radius 

monitoring a square area 1.0 mile on a side..................... 44 

Location error contours over area of the mine, Hamilton /I1 array.. 46 

Probability of signal peak (R) exceeding threshold point (R,) as a 

function of the ratio of R, to the noise rms level o~........... 52 

TABLES 

Seismic noise..................................................... 10 

Parameter values used in waveform modeling procedure.............. 16 

Mean values for AM and SDM for the three Kentucky coal mines and 

for the total data set.......................................... 23 

Average value of At for best source and noise amplitude and N and 

T values for Westinghouse 1977 data and 1976 Kentucky mine data. 27 

Signal amplitude of various sources relative to signal amplitude 

of a large timber on a roof..................................... 28 

Range of T values for various sources............................. 30 

Theoretical subarray noise reduction.............................. 34 
Page 

8. Probability of detection for a subarray directly above the source.. 41 

9. Probability of detection with one or more and with five or more 

~ubarrays...................................................... 42 

10. Number of mines with average horizontal error in four ranges....... 45 
EVALUATION OF THE SEISMIC SYSTEM FOR LOCATING 

TRAPPED MINERS 

by 

John Durkin 1 and Roy J. Greenfield 2 

This report discusses the configuration and system deployment for the 

postdisaster surface seismic system for detecting and locating trapped miners. 

It analyzes the results of 15 field tests to define a signal model, background 

noise levels, and subarray performance. A waveform modeling procedure is 

described and compared with observed waveforms. The resulting similarity 

indicates that the major factors affecting the signal amplitude, waveform, and 

spectral character are understood. A nodel is presented which gives the signal amplitude as a function of source type, source depth, and horizontal offset between source and receiver. Using this model a curve is presented which 

gives the range at which a signal will be detected for different signal and 

noise levels. Finally, and most important relative to the mission of the system, the ability of the system to detect signals on one or more subarrays is 

put into a probabilistic framework. For a strong source it is almost certain 

that a subarray directly over the source will detect the signal. After signal 

processing, it is highly likely that signals will he detected on sufficient 

subarrays to locate the trapped miner. Location errors have been found to be 

less than 100 ft in the majority of cases. Techniques have been used that 

can reduce the location errors to this level even when soil layer variation 

between subarrays is severe. 

INTRODUCTION 

Mine disasters continue to be a serious problem in underground mining. 

Disasters are caused by explosions, fires, cave-ins, or floods. Some explosions are so violent and extensive that they kill or suffocate, almost immediately, every man underground. However, if the men are not in the exact 

vicinity of the explosion and do not come in contact with the deadly gases 

following the fire, they may be rescued later. 

- - - - - - - - - -- - - -- -- -- - - - - - - -- 

I Supervisory electrical engineer, Pittsburgh Research Center, Bureau of Mines, 

Pittsburgh, Pa. 

2~rofessor of geophysics, Geoscience Department, Penn State University, 

University Park, Pa. 
Studies (15)3 have shown that the men who barricade themselves to prevent the carbo~monoxide from reaching them stand the best chance of survival. 

However, these men can be regarded as prisoners within the mine. Usual means 

of communication may be destroyed, prohibiting members of the rescue team from 

communicating with the trapped men. Without this communication the rescue 

team knows little about the condition of the men or their location. The last 

factor is the most regrettable, since reliable knowledge on the location of 

the entombed men could lead to prompt arrival of the rescue team and could 

prevent unnecessary deaths. 

In 1970, the National Academy of Engineering (19) reported that a seismic 

system might be capable of detecting and locating trapped miners. They proposed that the miner would strike a part of the mine with any heavy object 

that could be found. The resulting vibrations would then be detected on 

the surface by the use of seismic transducers (seismometers), which will be 

referred to as geophones in this report. The vibrations are converted into 

electrical signals by the geophones and then amplified, filtered, and recorded. 

By comparing arrival times at several different geophone locations, the 

trapped miner could be located. 

In 1971 Westinghouse Electric Co. (26) built and tested such a system. 

From 1972 until the present westinghouse7in cooperation with the Mine Safety 

and Health Administration (MSHA) and the Bureau of Mines, has modified and 

tested the system in a variety of mines. 

The purpose of this Bureau of Mines paper is to describe the present 

seismic system and to define its effectiveness in locating a miner trapped 

underground following a mine disaster. To predict the system's performance 

at a given mine, signal and noise models were formed from field test data, and 

signal detectability statistics were evolved. Results of the study indicated 

that this system should provide an effective means of locating trapped miners. 

ACKNOWLEDGMENTS 

The major portion of the field measurements used in this report were conducted by the Westinghouse Corp.'s Mine Emergency Operations Integrated Logistic Support group. Westinghouse personnel participating in the programs were 

Jim Moore, Ray Rouiller, Jerry Weinsert, Walt De Castro, John Frank, Herold 

Hannah, John Hartman, and Bob Koper. This field program was jointly funded by 

the Bureau of Mines and MSHA. Jeff Kravitz, of MSHA, was continually involved 

in the planning and execution of the field program. 

Richard A. Watson and Wymar Cooper of the Bureau of Mines helped conduct 

the 1976 field tests. 

Pennsylvania State University Department of Geosciences students who 

have made major contributions to the project were Mark Ruths, Jeff Hoffman, 

Pam Justice, Mark Angeleno, and Randy Christian. 

- -- - - - 

3~nderlined numbers in parentheses refer to items in the list of references 

preceding the appendixes. 
FIGURE 1. - Seismic van. 
FIGURE 2. - Ideal array configuration. 

After a site is chosen, the seismic array is 

deployed in a configuration 

that will cover the area to 

be monitored. An ideal 

array configuration is shown 

in figure 2. The array 

geometry is adjusted to the 

geometry of the mine and to 

surface conditions. The 

array consists of 7 subarrays; each subarray is 

composed of either 7 or 

24 geophones configured as 

shown in figure 3. The 

detailed discussions of 

these subarrays are given in 

a later section. While the 

array is being deployed, a 

survey of the subarray locations is made using surveying equipment maintained 

with the seismic system. 

MSHA has a continuing effort to explain to the mining community the operation of the seismic location system. The miner is instructed to do the following in the event he is trapped underground: 

1. When all possible escape is cut off, the miner is to barricade himself for protection from possible toxic gases and wait for a signal from the 

surface, before attempting to signal the seismic system. 

2. As soon as the system is in a state of readiness, the surface crew 

detonates three explosives which can be easily heard underground by the 

trapped miner. 

3. After hearing these 3 shots, the miner is to pound 10 times on a part 

of the mine, preferably the roof or a roof bolt, with any heavy object he can 

find; a heavy timber is best. Figure 4 shows the miner pounding while an 

operator in the seismic van listens for the miner's signal. 

4. Following this the miner is to rest 15 minutes and listen for five 

shots from the surface which will indicate to the miner that his signal has 

been heard and help is on the way. 

5. If the miner hears no shots, he repeats signaling every 15 minutes. 

During the expected signaling period, attempts are made to reduce surface 

activity while the seismic system is in use to optimize the chances of detecting the miner's signal. This system operates continuously, but this quiet 

period should enhance the chances of detection during the expected signaling 

period. 
FIGURE 3. - Subarray configurations of 7 geophones (top) and 24 geophones 

(bottom). 

Once the signal is detected and miner's location has been determined, 

directions are given to the rescue team to guide them in their rescue efforts. 

If a rescue team is unable to reach the trapped men, a drilling rig is positioned over the site of the miner's location and a rescue borehole is drilled 

for his evacuation. 

System Instrumentation -- 

The operation of the system can best be described by referring to the 

system diagram shown in figure 5. The geophone used is the ~eos~ace~ GSC-11D 

model M-3, having a natural undamped frequency of 14 Hz, a coil resistance and 

shunt resistance of 4,000 ohms, and an intrinsic sensitivity of 2.95 V/in/sec. 

At each subarray a preamplifier increases the signal level and sends it to 

the van via cable or radio telemetry. At the van the signals are first each 

passed separately through a tracking digital notch filter. This filter 

removes narrow-band manmade interference such as power line pickup or seismic 

disturbances caused by local machinery by latching onto the fundamental frequency of interference and tracking it if slight variations in frequency 

occur. The filter also removes the harmonics of the interfering noise. This 

initial processing step eliminates interference that would, in some instances, 

limit the system performance. 

An example of the performance of this filter can be seen in figure 6. 

Figure 6A - shows a seismic record heavily contaminated with 60-Hz interference. 

I storage I 

FIGURE 5. - Seismic system block diagram. 

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

endorsement by Bureau of Mines. 
I I I I I I 1 I I 

qal (DCVoCV(D~q - 

OIIII~ 
Figure 6B shows the sane record after passing through the notch filter and 

illustrates how a miner's signal is easily seen after filtering, whereas prior 

to filtering it would be impossible to see the signal. 

After notch filtering the signals are amplified and then recorded on analog tape. The signals are bandpass-filtered 20 to 200 Hz and displayed on an 

oscillograph record for recordkeeping purposes. By visually monitoring the 

oscillograph record, the operator can determine whether a signal has 

occurred. 

When the operator detects a signal, the analog tape containing the event 

is replayed into a PDP 11/34 computer via an analog-digital (A-D) converter. 

The computer performs interactive signal processing on the data and displays 

the results on the CRT terminal. A permanent record can be obtained using the 

hard copy unit. 

One commonly used signal-processing technique is known as stacking. Here 

the pulses from the subarray with the strongest signal are time-alined and 

added. In theory, this leads to an increase of J in amplitude signal to 

noise ratio (SNR), where N is the number of pulses stacked. In practice, this 

Jimprovement is in fact normally obtained. Stacking can thus provide an 

advantage for channels where the pulses cannot be seen to obtain arrival 

times. Using time differences between pulses obtained from the stronger 

channel, stacking can help in detecting the pulses buried in the noise on the 

weaker channels. 

When the processing has been completed, the relative arrival times of the 

signals from each channel are determined. These data, together with information on the location of the subarray and the velocity of seismic waves 

obtained by refraction surveys, are submitted to the computer location program to determine the miner's location. 

The present system relies on the operator's ability to determine when a 

signal has occurred. Manual detection of the signal can be unreliable due to 

the low SNR often encountered and the inability of the operator to maintain 

peak performance over extended periods. At present, efforts are being made to 

automatically detect the miner's signal by computer, thus eliminating possible 

human error. 

SEISMIC NOISE 

Seismic noise can be a major problem when detecting small seismic signals. Since the signal level from a trapped miner can be on the order of a 

few micro-inches per second (pips), normal background noise may mask the signal. Thus, information is needed on the types of noise sources, the amplitude 

ranges, and the amplitude variation with frequency and time. 

Typically, in the field three common noise sources are encountered: 

(1) Natural seismic background noise, (2) man-made seismic noise, and (3) manmade electromagnetic interference (EMI) coupled into the field equipment. 

Narrow-band man-made noise can be eliminated through digital notch filtering 

techniques previously discussed. Thus, in this report we will be mainly 
concerned with natural seismic noise that is not of very narrow bandwidth and 

that cannot be attributed to an obvious manmade noise source. 

Since seismic noise tends to vary widely as a function of time, 

geographic location, and frequency, it is not possible to make precise 

predictions of the noise at the site of some future mine disaster; thus the 

noise can be treated only in statistical terms. For some purposes, however, 

it is sufficient to know the noise characteristics within fairly broad limits. 

Study of the miner-induced seismic signal spectra indicates that most of 

the signal energy can be found in the frequency band between 20 and 200 Hz. 

Therefore, discussions on seismic noise will be for noise found within this 

band. 

The noise data used in this study were from Frantti (9-lo), field studies -- at 12 mines by Westinghouse (24), and a field study by the Bureau of Mines at 

3 different mines. In each orthese studies the noise in the band of interest 

had a roughly l/n frequency dependence. 

The spectra of earth noise in the frequency range 0.2 to 100 Hz were 

measured by Frantti in one-third octaves at a number of locations within the 

United States and at other North American and foreign sites. In the reduction 

of the data, attempts were made to delete records containing obvious manmade 

noise. Frantti gave curves of maximum and minimum values of peak-to-peak 

(P-P) ground velocity up to 100 Hz. These curves generally show a wellbehaved 1/n relationship with frequency. Using this relationship, the 

spectrum was extrapolated to 200 Hz. 

Studies have shown that the amplitude of the envelope of seismic noise is 

often Rayleigh distributed (4). Based upon this assumtion Frantti's data are 

then converted to root mean yquare values (rms) in the manner shown in 

appendix A. The high and low values of seismic noise found by Frantti are 

shown in table 1. 

TABLE 1. - Seismic noise, yips (rms) 

Bureau.................. 1-00 

Frantti................. 

Test data 

Westinghouse............ 

Greenfield.............. I NAP 1 2.551 -37 

NAp Not applicable. 

These results provide information only on the extreme bounds of seismic 

noise. A more meaningful presentation of Frantti's work has been given by 

Greenfield (13). Here seismic noise nns levels are given where these levels 

are exceeded75 pct of the time (low noise) and 25 pct of the time (high 

noise). Greenfield's results are for the frequency range of 25 to 100 Hz. 

Using the fact that the seismic noise varies as l/n in frequency, these 

results are adjusted to include the band 20 to 200 Hz. The resulting high, 

low, and average values found are shown in table 1. 

Low 

0.17 

Average 

1.10 

High 

8.00 
The Bureau of Mines performed field tests at three midwestern coal mines. 

A number of noise samples were taken. The obvious manmade noise was eliminated, and the natural background noise was averaged over a 1-minute period. 

Results are shown in table 1. The spread in this data is much less than the 

spread found in the Frantti data and may be explained by the much smaller data 

base used by the Bureau. However, the average noise level appears to be near 

the midpoint found between the boundary curves of Frantti. 

Westinghouse (24) performed field tests to evaluate the performance of 

the trapped miner seismic system. Tests were performed at 12 mines in the 

Southern Appalachian, Midwestern and Far Western, and mid-Appalachian regions. 

At each mine noise data were taken at various times and locations using seven 

geophones connected in parallel. Results once again are shown in table 1. 

To some degree the Westinghouse noise levels are artificial. These noise 

levels do not represent true natural background noise levels since the sevengeophone subarray used reduces the noise level relative to a single geophone. 

Typical expected values of noise reduction for this subarray are 2 to 8 db 

(5). In the data reduction done by \Jestinghouse, no attempts were made to 

delete manmade noise sources because this data reduction was performed in the 

field by measuring the noise levels from a visicorder display, and no processing capability was available at the time to remove the manmade interference. 

Studies performed on a few tapes indicated the true natural noise levels were 

reduced by 4 to 8 db when the manmade noise was eliminated. To some extent. 

these two opposing influences, subarray noise reduction and manmade contamination, tend to cancel one another, so the levels of noise reported by Westinghouse should approximate natural ground motion on a single geophone. Finally, 

in many instances, the data appeared to be thermal noise limited; thus caution 

is advised in using the minimum level for the Westinghouse data. 

THEORETICAL SEISMIC WAVEFORM MODELING PROCEDURE 

An analysis was performed to understand the factors that affect the seismic signal amplitude, waveshape, and signal spectra. Based on this analysis a 

waveform modeling procedure (WMP) was developed to model seismic signals generated from impacts on the surface of mine openings. The output of the WMP is 

the predicted vertical particle velocity of the surface geophone, denoted by 

V,. This procedure was implemented in a Fortran computer program and is shown 

in figure 7. The computations for each of the boxes are convolved to give a 

final theoretical waveform, which is then compared with forms recorded on 

field tests. 

A major factor that determimes the seismic waveform is the time history 

of the force g(t) that the miner's implement (for example, timber) applies to 

the mine roof or floor. Measurements of this time history are not available, 

so a theory was developed to give g(t). The theory begins by calculating the 

momentum, P, that the implement has at the time it contacts the roof, as shown 

in figure 8. Let a man apply an upward force, F, to the implement of mass, M, 

over a distance, D. From simple physics the velocity of the mass at impact 

will be J 2(~-MG)D/M. The term MG reduces the upward applied force F by the 

gravity force MG, G being the gravitational constant. Thus the momentum is 
Force-time function 

hk 

v 

Force to ground motion 1 

+ 

Cavity effect L 

Geometric spreading 

Anelast ic attenuation 

...:. . :.. ...: Layering and free surface J/ 1 

Seismometer 

Filter, 20-200 

Theoretical waveform 

-+I 10 msec 

FIGURE 7. - Flow chart of waveform modeling procedure. 
Vertical s 

Surface 

eismometer 

FIGURE 8. - Man signaling with timber on roof of mine. 

FOR P = 4 2M (F-MG) D. Note 

that if F >> MG, the momentum is P = -D. which 

m- predicts a roughly t'-% 

dependence for momentum. 

It can be shown based 

on work by Sung (23) that if 

the wavelengths iGolved are 

long compared with a length 

characterization the surface 

I area of the implement that 

4 I is in contact with the surface of the mine opening, 

then the force the implement 

,,, exerts on the surface is 

0 

0 \ proportional to the amount 

\ / the surface is displacing 

\ 0 

\ 0 ~(t); see figure 9. The t --& force is then written as 

g(t) = K ~(t). Here K is 

FIGURE 9. - Surface force-time function. the constant relating the 
surface displacement and the source applied to the surface of the mine opening. If the timber were to remain in contact with the surface it would 

undergo a harmonic motion of the form 

-at T t n(t) = n0e sin - TS/2 

Here T, is the period of the surface force. This form was suggested previously by Quo (21). However, after the first half cycle, which is shown as 

the solid lineTn figure 9, the implement will separate from the surface. In 

physical tenns it will bounce off. The decay constant, a, is small, so only 

a small decay will occur during the first half cycle. Thus, for practical 

purposes g(t) is of the form 

otherwise J 

~,/2 is the dwell time that the implement is in contact with the surface. A 

theory has been developed that relates T, to the elastic constants of the surface and to M. If the contact is a 0.1-m-radius disk, the predicted value for 

T, is less than 1 msec. Results to be discussed below indicate that the 

actual value of T, is much longer, about 10 msec. Thus, it is probable that 

when hitting a roof bolt or floor, a much smaller area than the whole of the 

end of the implement makes contact with the surface; this will give a longer 

T. Therefore, it is not believed that T, can presently be predicted theoretically, and it is treated as an adjustable parameter in the WMP. It would be 

useful to have measurements of T,. 

The value go is obtained from a momentum argument. The upgoing momentum is P, and the implement bounces off with a downward momentum EP, where 

0 < E < 1. Thus the momentum change in the impiement is (1 + E) P and must 

be-equal to the time integral of g(t). 

T t P(l + E) = g(t)dt = go sin - ~~12 dts 

which gives 

T 

go =- (1 + E) J 2 M(F - MG) Do 

T s 

This completes the definition of the force time function. 
Returning to the geometry shown in figure 8, the outgoing P-wave radial 

displacement is next related to the force-time function. White (27) gives the 

radial displacement (good at more than a few wavelengths from thesource) as 

the equation 

cos 0 dR(t) = 4np~Vg g(t - R/Vp), 

where 0 is the angle between the source-to-receiver direction and the vertical, p is the density, R is the source-to-receiver distance, and Vp is the 

P-wave velocity. This expression is for a point source in an infinite medium. 

A blow on the roof is assumed to be an upward force and a floor blow a downward force. To include the effect of the mine tunnel or cavity, the theory 

described by Greenfield (14) is used. The geometric spreading is given for 

the present situation by the 1/R term in equation 5. The effect of an elastic 

attenuation (often called Q-damping) on the wave as it propagates is included 

by using the Futterman (11) operator. The effect of geologic layering and the 

free surface of the earthis included by the method developed by Haskel (16), 

using a modification of the program described by Leblanc (18). The transfer 

function between the ground displacement and the voltage output of the seismic 

sensor was calculated based on the description of a seismometer given by 

Bollinger (2). The seismic system 20- to 200-Hz filter response was obtained 

by recording the impulse response of the filter. 

Figure 10 shows the cavity and geologic model used in computing the seismograms to be described. The mine is included as an 83-diameter horizontal 

cylindrical opening. The diameter was taken to approximate the width of a 

mine opening. The rock P-wave velocity was taken as 3,000 m/sec, which is 

typical of the normal mine overburden. The soil layer P-wave velocity used 

was 1,000 m/sec. The soil thickness is denoted by Ds. 

The waveforms given by the WMP give extremely good fits to records 

observed at the mine field tests. Both the waveshapes and absolute amplitudes 

are well fit. The first example is from the Orient /I6 Mine; figure 11 shows 

the seismograms and figure 12 the spectrum. The parameters used in constructing these and the other theoretical waveforms are given in table 2. The lower 

spectral content of the signal from the Orient /I6 floor blow is due to a 

larger T,, probably caused by soft floor material; also, the higher frequencies generated by the source are shielded by the mine opening. A second 

example, from the King Mine, is shown in figure 13. In figure 14 the signals 

from an event at the Orient /I6 Mine are shown. Also shown are the observed 

amplitudes and the amplitudes predicted by the WMP. Notice that the WMP is 

able to predict the variation of amplitudes between subarrays for this event. 
TABLE 2. - Parameter values used in waveform modeling procedure 

Parameter 

P-wave velocity .................................. m/sec.. 

S-wave velocity.. ................................ m/sec.. 

Density ............ ......................o....aa.g/ cm3.. 

Cavity diameter......................................m.. I 

Source depth ........................................ t I 

Q (Quality factor)............. ......................... NAp Not applicable. 

Rock Soil 

Vertical 

geophone 

r- 1 Tvv;g\i; / ii",7~e,"'~'~80i'f ' b \ ye;' ' A ALWj'ALV'' J.'V'/L'Vl' ~'~'U~~~~~~A~W*\~'/A\ V'/A\ Y~'''~//~~UA\ vl Ak I I 

FIGURE 10. - Geometry and parameters used in waveform modeling procedure. 
k-:+ 'a- 
Amplitude (p-p) = 19~~ips 

Observed 

Theoretical 

Amplitude (p-p) = 25bips 

FlGU RE 13. - Comparison of observed and theoretical seismograms at 1,800-ft depths, King Mine. 

Figure 15 shows the effect on the waveform of soil thickness. For no 

soil, (D, = 0 m) the waveform is a single simple pulse. For a thick soil 

layer (20 m) the waveform is a series of pulses of decreasing amplitude. 

These represent the successive wave bounces between the surfact and the soilrock interface. The time between pulses is the two-way travel time in the 

layer. As the layer thickness decreases, the time between pulses decreases; 

when D, is reduced to 10 m the pulses overlap in time. 

The exact form of the signal is quite dependent on the D,. The signals 

for D, values from 2.5 m to 10 m resemble the actual waveforms from field 

tests, but the single simple pulses do not. This indicates that a soil layer 

was present at the mine sites. This is in agreement with seismic refraction 

results at the mine sites. 

msec 

20 .o 

Amplitude (p-p), 

FIGURE 16. - Effect of force pulse width, r,/2. 
The P-P amplitude of the first cycle or so is not dependent on the soil 

thickness if the soil thickness is great enough for the first pulse to develop 

before the second arrives. 

Finally, the effect on the signal caused by varying T, is shown in figure 16. A soil thickness of 20 m was used for this figure to allow examination of the change in the simple pulse shape. As expected, the pulses appear 

longer for the larger T,. It can also be noticed that the amplitude of the 

pulses increases with decreasing T,. The amplitude dependence is approximately (l/~z). Thus the variation of r, is a major factor that contributes to 

the scatter of amplitudes in the field test data. Since T, decreases as the 

surface being struck becomes more rigid, the signal amplitude should increase 

with increasing surface rigidity. 

SIGNAL AMPLITUDE MODEL DERIVED FROM FIELD TESTS 

The following discussion is divided into two parts. In the first part, 

an extensive set of data taken from three coal mines in Kentucky in 1976 is 

discussed. For these data a large timber on a roof bolt source gave the largest signal, and impacts from this source were used to develop a mathematical 

form for a model of signal strength. In the second part, signal amplitude 

data from 12 field tests conducted in 1977 are analyzed using the form of the 

signal model from the first part. For these data the signals from the best 

application point at each mine were used since at some mines no roof could be 

hit. 

1976 Kentucky Coal Mines Results 

The most extensive data reduction was done on data from 1976 field tests 

at three Kentucky coal mines: Peabody Camp No. 1, Island Creek Hamilton #1, 

and the Freeman-United Orient #6. These data were used to find the best 

form for the representation of the dependence of signal amplitude on the mine 

depth, h, and on the horizontal offset between source and receiver, r 

(fig. 17). 

The data used to develop this model consisted of signals from largetimber blows on roof bolts as measured with the seven-geophone, 15-ft-diameter 

subarrays. Large-timber blows on roof bolts consistently gave larger signals 

than other sources at these mines. The signal amplitude is defined as the P-P 

value of the ground velocity, V,, in units of microinches per second. 

Using theoretical considerations, three forms were initially tested to 

see which fit the data best. They were 

with M= 0, 1, or 2. 
Ve = Peak-to-peak ground veIocity,pips 

Source 

FIGURE 17. - Geometry for signal amplitude model and the form of model for earth velocity, 

ve. 

Each source, or large-timber blow on a roof bolt, is called an event, and 

for each event amplitudes were read on the seven subarrays, Six events for 

Peabody (h = 400 ft), 6 events for Hamilton #1, (h = 600 ft), and 12 events 

for Orient /I6 (h = 800 ft) were used to fit for the average values of AM, 

defined as xM. The iiM values were determined by first computing xjPkpM for 

k th subarray and j th event as 
This then gave the A"j,k,M for each of the three model forms for each geasured 

amplitude. Then a least-squares criterion was used to determine the AM by 

minimizing the sum 

N 

This criterion gives AM as the mean of the Aj, k,~. A form of standard deviation (SD) was computed for the AM by forming 

where Ns is the number of amplitude measurements in the sum. This procedure 

was done separately for the data at each mine and for the total data set from 

all three mines. The results are given in table 3. 

TABLE 3. - Mean values for AM and SDM for the three Kentucky coal mines 

and for the total data set; uips-ft 

75 pct........................... 1 16,000( NAp 123,0001 NAp 131,0001 NAp 

NAp Not applicable. 

Mine 

Orient //6.......................... 

Hamilton bl... ..................... Peab~dy.......................~.... 

Total data set................ 

Cumulative probability for A: 

25 ~~t...ee.............ee~e...~. 

50 pct (median)....... ........... 

Table 3 shows that the values of each of the iM are fairly consistent 

between the three mines. The SDM are approximately one-half to one-third the 

value of the corresponding AM. This gives confidence in adopting a signal 

A1 

28,480 

27,833 

26,597 

27,938 

model that is characteristic'of these three mines. The value used in the 

model was obtained using the whole data set. The M = 1 form wa_s used since 

its total data set results provided the smallest ratio of SDM/AMe 

SDI 

16,835 

19,140 

14,757 

16,838 

34,000 

23,000 

SD 2 

18,291 

18,480 

18,657 

18,462 

A2 

35,990 

41,950 

35,266 

37,143 

NAP 

NAp 

A3 

48,015 

70,341 

48,204 

52,949 

SD3 

27,722 

31,260 

26,465 

29,562 

46,000 

34,000 

NAP 

NAp 

65,000 

76,000 

NAP 

NAp 
Thus the model adopted for the average P-P amplitude of the earth 

velocity, V, (h,r), for a large timber on a roof bolt is 

Xl COS 0 

Ve(h,r) = R (pips) , 

where R is in feet and A1 is the mean constant value for a large timber on a 

roof bolt, in microinches per second foot. A plot of the V, (h,r) predicted 

by this model is shown in figure 18. To give an indication of how this model 

Ve (h,r) fits the data, data from the Hamilton No. 1 Mine (depth = 600 ft) are 

compared with V, (600,r) in figure 19. The location of individual events is 

given by Westinghouse (25). The scatter of roughly 6 db observed on the plot 

is consistent with the of about 1/2 Al. 

HORIZONTAL OFFSET (r), ft 

FIGURE 18. - Surface P-P particle velocity versus horizontal offset for A1 model. 
As a further indication 

of the spread of the data 

values, cumulative probability curves have been plotted 

in figure 20, ,k,M with M = 1 andfir=A~. 

Table 3 gives the 25 pct 

values (25 pct from largest), 50 pct values (median), 

and 75 pct values for 

Aj , k, In all cases the 

median values are close to 

the mean values. The 25- 

pct value is the signal 

amplitude that was exceeded 

25 pct of the time; analogous definitions hold for 

the 50- and 75-pct values. 

Signal Amplitudes From " the 1977 Field Tests 

,0,K26 ,'-I0 , , In 1977, Westinghouse 

v, 

Electric Corp, carried out 

a series of seismic field 

tests at 12 mines (24). 

1 The primary purposeTf these 

0 200 400 800 1,200 17600 27000 tests was to compile data 

HORIZONTAL RANGE (r), ft from as many mines as possible to assess the ability 

FIGURE 19. - Comparison of Al model predictions for signal of the seismic system to 

ampI i tudes with Westinghouse data from the Hamilton 81 Mine. detect underground signals 

from trapped miners. Signals were observed at 11 of the 12 mines; signals were not observed at the Jim 

Walters /I4 mine because the receivers had to be located in close proximity to 

various types of active machinery, and the high noise level caused by this 

machinery prevented detection, 

The data from these tests were reduced by Westinghouse to give signal 

amplitudes for the sources that gave the largest values, For these field 

tests a large timber source gave the largest signal, and signal amplitudes 

were generally similar for application to the floor or to a roof bolt. 

From the Westinghouse values of V,, values of the constant A, were 

derived using the formula 

R A1 = V, - 

cos 0 (11) 

for each measured amplitude, For each mine all signals reported for a 

subarray location were averaged to give an average A1 value for the location. 
A AND A, fii ps 

FIGURE 20. - Cumulative probability of Al coefficient and A2 coefficient for three 

Kentucky mines. 

Then 

value - 

A, va 

the averages for each location were averaged to give an overall average 

of A,, called xl, for the mine; these values are given in table 4. The 

lues from these field tests were generally lower than those from the roof 

bolt blows of the 1976 Kentucky field tests; the difference may be due to calibration problems but could be due to soft roof conditions or to poor roof 

bolt coupling. Nevertheless, an overall average value for Al at the 14 mines 

is given in table 4. 
TABLE 4. - Average value of Al for best source and noise amplitude 

and N and T values for Westinghouse 1977 data 

and 1976 Kentucky mine data 

Mary Lee #1... ........... Concord Mine............. 

Jim Walters /I3 ........... Jim Walters /I4 ........... 

Mine 

1977 tests: 

Independent Salt Co...... 

Bear..................... 

King......... ............ Starpoint................ 

Staufer.................. 

Quarto #4................ 

Hatters.................. 

VP /I1.. ............. ... 1976 tests: 

Orient ~I6................ 

Hamilton #1.............. 

Peabody Camp No. 1.. ..... 

A1 pips-f t 

(mine average) 

Average of 14 mines.. . 1 

9,800 

12,600 

14,300 

No data 

Noise values (N), 

pips, (P-P) 

3.4 

8.4 

6.0 

No data 

- 

Al/N) = T (ft) 

2,882 

1,500 

2,383 

No data 

NAp Not applicable. 

Also given in table 4 are the noise values, N, for the mines that were 

discussed in the first part of this section. From xl and N values the ratio - 

T = A1/~ was formed. This ratio is a distance-independent SNR which is critical to the ability of subarrays to detect the seismic signals. The significance of T is discussed in the section in "Detection Range." 

The data from the 1977 tests were used to get a form of SNR and to examine the relative signal amplitudes from different source types. The 1977 data 

were not included in the calculations of the model for signal strength, which 

was completed before the 1977 tests. Also, there was some question about the 

gain of the amplifiers used in the seismic system during the 1977 tests, 

whereas for the 1976 tests, time was available to check the calibration by 

cross-checking several different seismic systems to assure accurate gains. 

SIGNAL AMPLITUDE MODEL FOR VARIOUS SOURCES 

In this section, signal models are developed which are applicable to 

sources other than the best-source type. This is done by relating the amplitudes from other source types to the amplitude from the best-source type. 

From the data an average difference in decibels between each of the source 

types and the best-source type is determined. This difference is called the 

adopted value. 
In the majority of measurements the best signal was from a large timber applied 

to a roof bolt (denoted by source type, Sl). There were exceptions to this; for 

example, it was noted (24) that at the Staufer Mine a large timber on the roof 

(there were no roof bolts) created weak signals because the roof was high, which 

made it difficult to use the large timber effectively. However, in general, the 

large timber on the roof bolt source amplitude was either the best source or within 

a few decibels of the best source. Thus, for the S1 source, a value of 0 db is 

adopted. This value is entered in table 5. 

TABLE 5. - Signal amplitude of various sources relative to signal amplitude 

of a large timber on a roof 

Source type........ 

Application point.. 

Orient //6 Mine.. db.. 

Peabody Mine...db.. 

Peabody Mine...db.. 

Concord Mine...db.. 

Staufer Mine db.. 

(no roof bolts). 

Source 

S 1 

Large 

timber. 

Roof 

bolt. 

Source 

S2 

Small 

timber. 

Roof 

bolt. 

Source 

S3 

Sledge 

Value adopted db.. 

for cl. 

Al (~k)2. .yips-ft.. 

Roof 

bolt . 

Source I Source I source! source1 Source 

NAp Not applicable. 

0 

317,924 

Rol: 

s4 S5 S7 S8 

Large Small Hard Sledge Rock 

timber. timber. hat. pick. 

Floor Floor Floor Roof 

bolt. bolt. 

-3 

12,689 

ND No data. 

l~~~roximate average difference between amplitude from source type and amplitude 

from large timber hitting roof bolt. 

20btained by reducing the value of xl (Sl) by the C value for each source. 

3~ee table 4. 

For other source types, representative differences between their amplitude 

and that from a large timber applied to a roof bolt are given. From these data 

approximate average differences, C, are formed; these C values are rough estimates 

of the difference in signal amplitude between the best source and others. 

- Based on C values for the source types S2 to SQ, an estimate was made of the 

Al (Sk) constant for each source type. This was obtained by reducing the value of 

Al(S1) = 17,924 yips-ft from table 5 by the C value for each source. With the A1 

(Sk) values of table 5 the signal amplitude model for each source type is given by 

- V, (Sk) = AI(Sk) cos 0 

R . (12) 
DETECTION CRITERION 

In this section the criterion for signal detection is developed. The 

criterion that will be used in this report is that the P-P signal amplitude be 

greater than the P-P noise envelope. 

A reasonable approach is to consider that a threshold is set which will 

be exceeded by the noise once in 100 sec. The normal bandwidth of the system 

is 180 Hz; however, as discussed in the section on seismic noise, the power is 

concentrated in roughly the lower half of this frequency range. Thus, it is 

reasonable to use an equivalent bandwidth of 25 Hz in computing the time 

between independent samples of noise amplitude. Thus in 100 sec, 7,500 independent values of the envelope occur. In the appendix it is shown that if the 

zero-to-peak threshold R, is set to 4.22 oN, the envelope will have a probability of exceeding the threshold of 1/7500, thus giving the desired false 

alarm rate of once every 100 sec. Here is the the rms noise value. 

Therefore a 4.22 an zero-to-peak threshold or a 8.44 on P-P threshold will 

be used. It will be assumed in this report that a signal will be detected if 

its P-P amplitude is above this value. 

It is noted that the assumptions that a signal whose amplitude is above 

the threshold will always be detected and that a signal whose amplitude is 

below the threshold will never be detected are not strictly valid. However, 

detection done manually or by an automatic computer algorithm is a complex 

process. Therefore, it is not felt that a more complex criterion than the one 

adopted is presently justified. Digital analysis of an extensive data set in 

the future could justify a more complex criterion. 

DETECTION RANGE 

The range at which a single geophone or subarray can detect a source 

depends on the signal amplitude and the noise level. In this section universal curves are given that allow an estimation of the maximum horizontal 

range at which a signal of a given strength can be detected under a known 

noise condition. The M = 1 signal model is used. Let A1 be the constant 

for the source under consideration. On the basis of the M = 1 signal model 

the condition for detection is that 

- A1 cos O > N . R (13) 

Define the quantity T = A1/N. Then T is a measure of the size of the generated signal divided by the noise and is independent of the source depth h and 

the horizontal offset between the source and geophone. In table 6, values of 

T are given for large timber sources. These values, which are the individual 

mine averages, range from 1,500 to 5,652 ft. For other source types, the T 

values are adjusted by the factors given in table 6. Using the range of 1,500 

to 5,652 for the large timber on the roof bolt source and the table 5 adopted 
value adjustments, the range of T values expected for various sources is compiled in table 6. 

TABLE 6. - Range of T values for various sources 

Large timber on roof bolt.......... 

Small timber on roof bolt.......... 

Sledge on roof bolt................ 

Large timber on floor.............. 

Small timber on floor.............. 

Hard hat on roof bolt.............. 

Sledge on floor.................... 

Geopick on roof bolt............... 

Feet 

1,500-5,652 

1,062-4,001 

1,062-4,001 

597-2,250 

474-1,787 

267-1,005 

299-1,128 

670-2,525 

Then the condition for detection can be written 

Based on this criterion, curves were calculated (fig. 21) that give the maximum horizontal range for detection, r,, as a function of the source depth, 

h. Note that the maximum value of r, for a given T does not occur for a very 

shallow source. Rather it 

6,0001 I I I 1 occurs for the value of h 

SOURCE DEPTH (h), ft 

FIGURE 21. - Maximum horizontal detection range 

which is half the miximum h 

at which a source can be 

detected. For example, if 

T = 1,500 ft, the maximum 

depth at which a source is 

detectable is 1,500 ft and 

the maximum of r, occurs at 

h = 750 ft. The reason that 

the greatest r, does not 

occur for the most shallow 

sources is that the radiation pattern is such that 

the outgoing signal has a 

cos O = h/r dependence; 

therefore, when h/r is 

small, the signal is small. 

S UBARRAY PERFORMANCE 

The seismic rescue system uses an array composed 

of seven subarrays rather 

than seven individual geophones to receive seismic 

signals because a subarray 

will give a better SNR than 

versus source depth. the single geophone. This 
improvement is achieved principally in three ways. First, noise that is 

uncorrelated between the geophones will be reduced in amplitude by fl by the 

cancellation that occurs by averaging zero mean random numbers. Second, noise 

that is propagating at a slow horizontal velocity will be reduced on the output of the subarray because, if the subarray is thought of as an antenna, 

the noise will be outside of the antenna's main beam. Finally, any adverse 

effects that would result if a single badly planted geophone were used will 

be alleviated by the averaging of all the subarray geophone outputs. 

A subarray output Y(t) is formed by averaging the individual geophone 

inputs, Xi(t), as 

Thus, the formation of the subarray output can be thought of as forming an 

averaging of the individual inputs. xi(t) is composed of two parts: Ni(t), 

the noise; and Si(t), the signal from the trapped miner. In this section the 

SNR gain will give the improvement of a subarray compared to the single geophone. In determining this, both the noise reduction by the subarray and the 

effect of the subarray on the signal amplitude will be considered. 

As mentioned before, two subarray configurations have been developed and 

used extensively. The first is a seven-geophone subarray Westinghouse (24) 

with a 4.5-m diameter having the geophones wired in parallel. The seconris a 

larger 24-geophone subarray with a 24-m diameter. This large subarray uses 

two series-connected strings of 12 geophones with the 2 strings connected in 

parallel (6). The subarrays are shown in figure 3. The electronic configurations of both subarrays are such that the sensitivity of the subarrays is well 

below even low levels of natural seismic noise. Thus, the ability to detect 

and identify signals from an underground miner is determined by the seismic 

noise level. 

The use of a subarray will normally result in some loss of amplitude compared with using a single geophone, in measuring a signal from a miner hitting 

below ground. This signal loss is due to the fact that the signal is not 

exactly the same on each subarray geophone. For a miner directly below the 

subarray the signal is in phase at all geophones and the signal loss will be 

minimal. However, for sources horizontally offset from the subarray there is 

a phase shift (or equivalently an arrival time difference) between the geophones. 

The signal output of the subarray is 
Let 

sur 

ve c 

-h the N elements of the subarray be loca$ed+at the points rl on the earth's 

i (at-r i*k 1 + 

ace. The signal is of the form e where k is the wavenumber 

or. Note I k I = a/VH, where VH = (V/sin 0) is the horizontal phase velocity of the wave. Here V is the wave velocity and 0, the angle of incidence, 

is the angle the ray makes with the vertical. The geometry of this situation 

is shown in figure 17. When the magnitudes of the signals are equal on all 

seismometers, the signal output compared to a single geophone is (in db) 

For a signal th2t is identical and in phase at all geophones (this 

requires VH = rn, so k = 0), G, = 0 db. This would approximately be the case 

for the small seven-geophone subarray where signal loss is not significant. 

The 24-geophone subarray was designed to be as large as possible without causing unacceptable signal loss. For the 24-geophone subarray the loss at frequencies below 50 Hz is negligible. For 100 Hz and angles O of greater than 

35', signal losses are in excess of 3 db compared with a single geophone. 

However, field test results discussed by Durkin and Greenfield (6) indicated 

that very rarely were signal losses above 1 or 2 db for the 24-geophone subarray. One reason that signal amplitude decreases of more than 3 db were rare 

with the 24-element subarray is that for 0's greater than 30' or 40' the signals usually do not have a major portion of their power above 60 or 70 Hi. 

Thus, signal amplitude loss due to the subarray does not appear to be a serious problem. 

The noise reduction for noise that is incoherent between the geophones 

is 20 log N (db). This is a gain of 13.8 db for the 24-geophone subarray and 

8.5 db for the 7-geophone subarray. Seismic noise that is completely incoherent is not the normal situation but occurs during rain. In this situation 

the noise level is high and thus the subarray gain is especially important. 

Field test results have verified that this gain occurs during rain. In areas 

with brush or high grass ground cover the noise generated by the wind may also 

be essentially incoherent between geophones. The larger spacing between geophones of the 24-geophone subarray compared with the 7-geophone subarray 

enhances the possibility that the noise will be incoherent. 

In many situations the seismic noise may be highly coherent between the 

subarray geophones; however, the subarray can still give noise reduction 

because the noise is not in phase between the geophone (3). - 
The source of coherent noise may be wind acting on trees outside of the 

subarray, distant traffic, machinery, or airborne noise. Much seismic noise 

at frequencies of 20 to 200 Hz is of low horizontal phase velocity, VH, since 

it travels at an acoustic velocity (330 m/sec) or at seismic surface wave 

velocities, which are usually below 1,000 msec. 

In practice there could exist many surface noise sources propagating with 

different VH and at different angles of incidence on the subarrays (17). It 

is instructive to study the expected attenuation of these waves by tG subarrays by choosing waves of discrete frequency and velocity within the ranges 

of interest and treating the angle of incidence of the waves on the subarray 

as a random variable. 

The output of a subarray for a horizontally traveling wave is 

+ 

where Y is the normalized amplitude of the noise output and kN is the horizontal wavenumber of the noise. 

The noise reduction is G = 20 log Y db. 

Table 7 gives an indication of the subarray noise rejection for the 24- 

element and 7-element subarrays, as a function of frequency and VHe The horizontal phase velocity of the wave is related to the wavenumber by VH = w/kN. 

The noise reduction depends on the direction as well as VHe The values in 

these tables are the smallest noise reductions (worst case) for any direction. 

These tables were constructed from more extensive tables generated by a computer program based on equation 18. 
TABLE 7. - Theoretical subarray noise reduction, db 

(Minimum in any direction) 

30 Hz 

NMENT S1 

7.6 

15.0 

18.0 

14.0 

17.0 

17.0 

9.7 

3.4 

MENT S1 

11.0 

4.2 

3.4 

2.3 

1.0 

. 5 

. 3 

.1 

uency 

60 Hz 1 90 Hz 1 120 Hz 

The 24-element subarray will suppress most coherent low VH noise for frequencies of 30 Hz and larger quite well. The worst case noise reduction values for coherent noise are generally nearly as large as the incoherent noise 

reduction. Note that the subarray reduction of coherent noise can be above or 

below the reduction of incoherent noise. 

The seven-element subarray does well against coherent noise at horizontal 

wavelengths, VH/f, below approximately 10 m. For the higher velocities and/or 

lower frequencies, the seven-element subarray does not give significant noise 

reduction. 

From the above theoretical considerations of SNR improvement by the 24- 

and 7-geophone subarrays, it is to be expected that the 24-geophone subarray 

would offer a significant SNR gain over the 7-geophone subarray. In an extensive series of field tests this was often the case (6). Typical gains were 

5 db for the 7-geophone subarray and 10 db for the 2x-geophone subarray. 

There were, however, some mines where the SNR of the two subarray types were 

comparable. The 7-geophone subarray, however, may offer practical advantages 

in terms of deployment where a clear area cannot be found to deploy the larger 

24-geophone subarray. 

PROBABILITY OF DETECTION 

It is desirable to determine the probability that a given surface array 

will detect an underground source. In the configuration normally used, seven 
subarrays are placed on the surface to monitor a portion of the subsurface. 

A method has been developed to calculate the probability that m subarrays or 

more, with 1 < m < 7, will detect a miner's signal. The detection of a signal 

by one subarray .may be sufficient to identify the signal as coming from an 

underground miner. However, identification can be more certain if several 

subarrays can detect the signal. To locate, at least three subarray detections are required, and five or more are desirable for accurate location. 

Figure 22 shows a surface array monitoring a volume of the subsurface. 

The criterion for detecting a signal from a given underground location with 

subarray k is 

Rk 

> cos 8, (19) 

Subsurface volume 

being monitored 

FIGURE 22. - Geometry for calculation of detection probability. Triangles indicate 

subarray locations. 
If T is treated as a random variable, then the probability of detecting with 

subarray k is the probability that T > Rk . To apply this detection 

cos Ok 

criterion the probability destribution was developed using the best source 

(large timber) type values for T given in table 4. The 14 values were ordered 

and plotted as a cumulative distribution in figure 23. For convenience this 

observed distribution was fit with the chi-square cumulative probability function (I), P (~216). It was found that using the number of degrees of freedom, 

6 = 6,and X2 = T/550 gave a good fit to the data. In other words, the fit 

chi-square curve, shown in figure 23, states that the probability that T - < To 

is given by 

The notation PL (To) will be used for P (- 1 6), the cumulative distribution 550 

of T, and notation QL (To) = 1 - P (To) will be used as the probability that 

T exceeds To. The probability of hetection with a large timber source is then 

given by QL (cos Rk Ok ) Note that the T data used were average values for 

FIGURE 23. - Chi-square fit to cumulative probability of T. 
individual mines. If the individually measured T values were to be plotted 

as a cumulative distribution, the curve could be expected to be similar to 

the mine averages. 

For a source other than the large timber on a roof bolt, reasonable 

cumulative probability curves for T can be estimated by using Q (To C) 

for the curve. Here C is the factor, which is given in db in table 8, that 

gives the amplitude of a particular source type relative to the large timber 

source S1. 

Let QL (5) where k = 1,2,. . . ,7 be the probability that the k subarray 

will detect the signal from a source at rk. Next calculate the probability of 

m and only m subarrays detecting the signal (8, - pp. 89-96): 

where (m l) are the binomial coefficients, 

The sums in the definition of the S are taken such that if i<j<k<**7, then 

each combination appears once and only once in the sum. The probability of m 

or more subarrays detecting the signal is denoted by Pm(ri) and is given by 

First it is necessary to obtain the average value of Pm for detecting the 

signal from a source which is at some depth h but which can be located with 

equal probability in some horizontal region of the mine. This probability of 

detecting with m or more subarrays is denoted by P, (h) and is given by 

P, (h) = - A th) dx d~ 

A 
Here A(h) isAthe area of the mine at depth (h). To get the overall average A 

probability P, of detecting with m or more subarrays for a source in the volume shown in figure 22, which extends from hl to h2, use 

A A A 

To evaluate P, and P, the integrals are approximated by sums over a 

three-dimensional grid covering the volume of interest. 

In the following three examples the volume considered was a rightrectangular prism with top at hl = 200 ft and bottom at h2 = 1,200 ft. This 

depth range is consistent with the fact that the majority of mines lie in 

this range. 

Figure 24 is the first example of the results of the calculations. The 

plan view shows an array of seven subarrays with a 500-ft radius. The subsurface being monitored is a square having sides of 2,000 ft. For the large timber on a roof bolt source with no subarray SNR improvement, one looks at the 

0-db position on the abscissa to get the probability of m or more subarrays 

detecting. For example, the probability of m = 5 or more detecting is 0.62 

(index base 1.00). From table 5 the signal for a small timber on a roof bolt 

(S2) has C = -3 db. Thus, one looks at the -3 db abscissa value for an S2 

source. Note that for any source type the use of the subarrays gives approximately a +5-db improvement in SNR compared with the single sensor values. 

After a single subarray has detected a signal, the stacking of successive 

blows will also improve the SNR. If 10 blows are stacked a 10 db improvement 

is commonly obtained. Thus, for the case of locating the source using stacked 

traces from the subarrays, the C = +15 db value applies for the large timber 

on the roof bolt. 
FIGURE 24. - Probability of detection by m or more subarrays versus C, the ratio of T to the 

large timber T-500-ft array radius, 2,000-ft monitored square. 

Thus for large timber sources for the figure 24 configuration it is very 

likely that at least one subarray will initially detect the signal; after 

stacking, signals should be seen on the five or more subarrays that are desirable for accurate location. 

Figures 25 and 26 show corresponding results for the monitoring of a 

square having sides of 4,000 ft for array radii of 500 ft and 1,000 ft. Since 

a large area is being monitored, the detection probabilities are lower than 

for the 2,000-ft square. 

For the monitoring of the 4,000-ft square with an array centered at the 

center of the square, the effect on the detection probability of the array 

radius was examined. This was done for the value C = 0 db; that is, for the 

best source with no array gain or stacking. Results are shown in figure 27. 

To obtain a signal from at least one subarray, the use of the larger radius 

arrays is somewhat better. The reason for this is that for the 500-ft-radiusarray points on the boundary of the square will be a minimum of 1,500 ft 

horizontally removed from the nearest subarray. Thus, to have the maximum 

probability of detection, it is suggested that before a signal is found it 

might be best to use a 1,000-ft-radius array when monitoring such a large 

area. If conditions allow, after detection on a single subarray, it would 
FIGURE 25. - Probability of detection by m or more subarrays versus C, the ratio of T to the 

large timber T-500-ft array rod ius, 4,000-ft mon itored square. 

FIGURE 26. - Probability of detection by m or more subarrays versus C, the ratio of T to the 

large timber T- 1,000-ft array radius, 4,000-ft monitored square. 
LL) 

0 .6 

then be desirable to move 

some of the distagt subarrays to the vicinity of 

the detecting subarray and 

signal the trapped miner to 

repeat his signal to allow 

improved location. 

Next the situation 

will be examined where the 

trapped miner is believed to 

be below a particular point. 

One subarray would be set 

directly above that point. 

The probability of detecting 

that miner can be calculated 

by fixing the subsurface 

region to be monitored as a 

very small area directly 

below the central subarray 

of a 1,000-ft-radius array. 

Calculations were made, and 

results are shown in 

table 8. For a source 500 

ft deep even a weak source 

500 1,000 1,500 2,000 with C = -10 db will be 

detected with 0.85 probaARRAY RADIUS, ft bility. Noting that a 24- 

geophone subarray gives a 

FIGURE 27. - Probability of detection with m or more sub- 5- to 10-db SNR improvement, 

arraysversusarray radius, large timber source (C = 0 db), it is expected that a sub4,000-ft monitored square. array would probably detect 

the signal even for sources 

down to 2,000 ft. This high probability of seeing a source directly below a 

subarray is consistent with the fact that in field tests signals from sources 

directly below a subarray were consistently detected. 

TABLE 8. - Probability of detection for a subarray 

directly above the source 

Depth, ft 

500.......... 

l,OOO.......... 

1,500.......... 

2,000.......... 

2,500.......... 

Amplitude of particular source type relative 

to large timber source (C) 

-15db 

0.53 

-13 

.02 

.OO 

.OO 

Odb 

1.00 

1.00 

1.00 

1.00 

.99 

-10db 

0.85 

-65 

.42 

-2 1 

.09 

+5db 

1.00 

1.00 

1.00 

1.00 

1-00 

-8db 

0.93 

.87 

.72 

.49 

.28 

-5db 

0.99 

-99 

96 

887 

-72 
For convenience in considering the probability of detecting a source 

under various situations, table 9 was compiled. For this table it was assumed 

that the postdetection stacking would give a 10-db SNR improvement, which is 

what has been observed. Also, a 5-db gain for subarray use has been included 

for two of the five sources. The table gives the probability of detecting 

with one or more and with five or more subarrays. The one or more case is 

most important in the detection process, and five or more case in the location 

process. 

TABLE 9. - Probability of detection with one or more 

and with five or more subarrays 

It is instructive to observe the variation in the probability of detection as depth is varied. These results are shown in figures 28-31. The probability of detecting a miner's signal was determined when using an array of a 

1,000-ft radius over square areas of 0.5 and 1.0 mile on a side, for varying 

depth. Probabilities were determined for weak and strong sources with and 

without processing. This processing takes the form of stacking. Also considered was whether detection is probable on one or more subarrays (m > 1) - or five or more subarrays (m > 5). - 

Source type 

Large timber (with 

gain).................. 

Large timber............ 

Sledge on roof.......... 

Rock pick on roof ....... Sledge on floor......... 

The detection probabilities discussed have all been based on the use of 

subarrays made of geophones that measure the vertical particle velocity of the 

ground. Geophones that measure the horizontal particle velocity are also manufactured and have been used in a limited number of experiments. The results 

of these experiments indicate that most often the vertical geophones outperform the horizontal geophones. There have been exceptions to this; the cases 

where horizontal geophones gave better performance have occurred where the 

angle 8 (see fig. 17) is fairly large. This result is consistent with the 

radiation patterns of P- and S-type seismic waves. Often in these situations 

it is the S wave on the horizontal that is the largest signal. To employ horizontal geophones two extra channels (one for north-south and one for eastwest polarization) at each subarray location must be employed. When using 

horizontal geophones each geophone must be carefully oriented. The signals 

from horizontal phones are often more difficult to interpret. Therefore, the 

logistics of the operations suggest that for the surface seismic location system the present vertical geophone system should be maintained, rather than a 

mixed vertical and horizontal system. 

Assumed 

subarray 

gain, 

db 

+5 

+O 

+O 

+5 

+O 

Mine area 2,000 by 

2,000 ft, 500-ft 

array radius 

Mine area 4,000 by 

4,000 ft, 1,000-ft 

array radius 

5 or 

more 

with 

stacking 

1.00 

. 99 

.98 

.96 

.25 

1 or 

more 

1.00 

1.00 

.99 

.97 

.38 

1 or 

more 

0.96 

.87 

.80 

.78 

.13 

5 or 

more 

0.92 

.64 

.37 

.30 

.OO 

5 or 

more 

0.35 

.09 

.05 

.02 

.OO 

5 or 

more 

with 

stacking 

0.90 

.68 

.56 

.50 

. 00 
. - 0 t xo us02 

2 r O. .- a 'a- E 

= a-0 

XO X0 

- .ZKZ2 

.- 0 6 0 

d '5 
Strong source with processing 

- m 15 - 

Array rad~us -1,000 ft 

Test area = 0.25 sq mi 

- - 

Strong source and weak 

source with processing 

- - 

Weak source 

1 1 I 

0 500 1,000 1,500 2,000 

DEPTH, ft 

FIGURE 30. - Probability of detecting a miner's signal as 

a function of depth by five or more subarrays 

in an array of 1,000-ft radius monitoring a 

square area 0.5 mile on a side. 

I I 

- 

Array radi

- Test area = 

- 

Strong source and w

source with processi

Weak sour

L I 

0 500 1,000 1

DEPTH, f t 

FIGURE 31. - Probability of detecting a m

a function of depth by five or 

in an array of 1,000-ft rad

square area 1.0 mi le on a si
LOCATION ACCURACY 

To guide the efforts of the rescue team or to determine where to site the 

rescue drill, it is necessary to determine the location of the trapped miner. 

For the rescue team an accuracy of 100 ft or less would appear desirable. For 

positioning the drill an accuracy of a few feet would be desirable. However, 

as discussed below, accuracies of a few feet do not appear feasible. Thus the 

positioning of a rescue drill so as to intersect a mine entry near the 

estimated location of the trapped miner would best be done using a mine map, 

if available. 

The seismic system presently uses the "MINER" program (12) to calculate 

the location from arrival times measured on stacked seismogr~s. This program 

combines the individual subarray arrival times either three or four at a time 

to find a location. The MINER program can use a known depth for the source or 

can fit for the source depth. Alternate methods of location based on the 

least squares principle are more often used in seismic location work; this 

principle is the basis of work done by Ruths (22). - 

Westinghouse (24) compiled estimates of location errors obtained for a 

limited number of lGations at 12 mines. Table 10 gives these results. This 

table indicates that horizontal location errors are usually below 100 ft. 

However, it should be understood that these results are generally for the 

better SNR events and that the majority of the sources were located near the 

center of the array where location accuracy is best. 

TABLE 10. - Number of mines with average horizontal 

error in four ranges 

Error range Number of mines within 

error range 

0-49 ft.................... 

50-99 ft................... 

100-199 ft................. 

Over 200 ft................ 

Two of the mines discussed by Westinghouse had average errors of approximately 150 ft. In addition extensive work by Ruths (22) showed errors of this 

order of magnitude for Island Creek's Hamilton /I1 ~inz The mines at which 

the larger errors occur tend to have topographic relief and geologic conditions that vary with position. Ruth's work indicates that the presence of 

very-low-velocity soil layers that are different between the subarrays is 

among the most serious sources of error. 

A technique to relate location error estimates in a statistical manner to 

estimates of the arrival time "reading errors" was implemented. The method 

used is similar to that described by Crosson and Peters (5) and Peters and 

Crosson (20). In the location of miners the two most sigzificant sources of 

errors areerrors in reading arrival times in low-SNR situations and individual delays at the different subarrays caused by soil and/or water table variations. Both of these types of arrival time errors are uncorrelated between 

subarrays so may be treated as "reading errors." 
In the present computer implementation contours are drawn of the semimajor axis of the 95-pct fiducial confidence ellipse (7). This confidence 

ellipse is the elliptic curve on the floor of the minethat should contain the 

true source location 95 pct of the time. Thus on the average the error will 

be somewhat less than half the semimajor axis fiducial confidence ellipse. 

Figure 32 shows a computer-generated contour plot for the subarray configuration used for the Hamilton 111 Mine test. The mine depth is approximately 

600 ft. In generating figure 32, an rms reading error of 0.008 sec was used. 

X 

FIGURE 32. - Location error contours over area of the mine, Hamilton #l array. 
This rms reading error was used based on soil thickness variations 

measured at the Hamilton #1 Mine by means of a short refraction survey at 

each subarray location. The unsaturated low-velocity soil (1,000 ft/sec 

velocity) ra~ged in thickness from 0 to 20 ft, which gives an unaccounted-for 

variation in arrival times of up to 0.020 sec. Location errors up to 200 ft 

were observed for the test. 

Three techniques have been used to decrease the location error resulting 

from soil layer variations. Results to date with these techniques indicate 

that soil-layer-related errors can be reduced to 100 ft or less. Ruths (22) 

studied the first of these techniques both by compu,t&r simulations and bystudy of data from an earlier Island Creek field test (25). In technique 1, 

called the Reference Correction Method, it is necessaryto get a source to 

within a several hundred feet of the suspected position of the trapped miner. 

This might be impractical in a disaster situation. As an alternative method 

of employing technique 1, a receiver in a drill hole near the level of the 

mine might be used to measure travel times from shots near each subarray. The 

Reference-Correction Method appears to greatly improve the probability that 

location errors will be below 100 ft even in mines with highly variable nearsurface conditions. In technique 2 a short refraction measurement is made at 

each subarray and used to make an arrival time correction. In technique 3 an 

arrival time is measured at each subarray from a blast at a known position 

outside the seismic array. Recent work at the Hamilton /!1 Mine (March 1980) 

gives an indication that the errors from soil layer variations can be greatly 

decreased by use of technique 2 or 3. 

SUMMARY 

A system based upon seismic techniques, as envisioned by the National 

Academy of Engineering in 1970, has proven to be an effective means for 

detecting and locating miners trapped underground following a mine disaster. 

Expected signals from miners pounding on the roof of a mine are of sufficient strength to enable detection over a large area of the mine. Estimations 

of the location of the trapped miner are of sufficient accuracy to aid the 

rescue team or the position of the rescue drill. 

The seismic system, as discussed in this report, is presently operational 

and in a state of readiness in the event of a mine disaster. It should prove 

to be an invaluable aid to future postdisaster rescue efforts. 
REFERENCES 

Abramowitz, M., and I. A. Stegum. Handbook of Mathematical Functions. 

NBS, 1964, p. 941. 

Bollinger, G. Blast Vibration Analysis. Southern Illinois Press, 

Carbondale, Ill. 1971, pp. 37-45. 

Capon, J., R. J. Greenfield, R. J. Kolker, and R. T. Lacoss. ShortPeriod Signal Processing Results for the Large Aperature Seismic Array. 

Geophysics, v. 33, 1968, pp. 452-472. 

Capon, J., R. J. Greenfield, and R. T. Lacoss. Long-Period Signal 

Processing Results for the Large Aperature Seismic Array. Geophysics, 

v. 34, 1969, pp. 305-329. 

Crosson, S., and D. C. Peters. Estimates of Miner Location Accuracy: 

Error Analysis in Seismic Location Procedures for Trapped Miners. 

Part 3 in Survey of Electromagnetic and Seismic Noise Related to Mine 

Rescue Communications. Volume 11. Seismic Detection and Location of 

Isolated Miners (USBM Contract HO 122026), by L. Lagace, J. J. Ginty, 

M. Fa Roetter, R. Ha Spencer, and Consultants. BuMines Open File 

Rept. 38 (2)-74, 1974, pp. 3.1-3.36; available for consultation at the 

Bureau of Mines libraries in Pittsburgh, Pa., Denver, Colo., Spokane, 

Wash., Twin Cities, Minn., and Morgantown, W. Va.; at the Central 

Library, U.S. Department of the Interior, Washington, D.C.; and from 

the National Technical Information Service, Springfield, Va., 

PB 235 070/AS. 

Durkin, J., and R. J. Greenfield. Study of Possible Modifications to the 

Trapped Miner Seismic Location System. Pittsburgh Mining and Safety 

Research Center, Pittsburgh, Pa., Interim Report BuMines 4268, May 15, 

1979, 95 pp. 

Evernden, J., Jr. Precision of Epicenter Obtained by Small Number Worldwide Stations. Bull. Seis. Soc. America, v. 59, 1969, pp. 1365-1398. 

Feller, W. An Introduction to Probability Theory and Its Applications. 

John Wiley & Sons, Inc., New York, v. 1, 1950, 461 pp. 

Frantti, G. E. Investigation of Short-Period Seismic Noise in Major 

Physiographic Environments of Continental United States. Prepared for 

the U.S. Air Force under Contract AF 19 (628-200), Task No. 865204, 

June 1965; available from National Technical Information Service, 

Springfield, Va., AD 617122. 

. The Nature of High Frequency Noise Spectra. Geophysics, v. 28, 

1963, pp. 547-563. 

Futterman, W. I. Dispersive Body Waves. J. Geophys. Res., v. 67, 1962, 

pp. 5279-5291. 
12. George, D. C., and R. Fa Linfield. Seismic Subsystem Location 

Calculation: Software Concepts and Interpretation. Sec. in Trapped 

Miner Location and Communication System Development Program. V. 1. 

Development and Testing of an Electromagnetic Location System 

(USBM Contract HO 220073), by A. J. Farstad, C. Fisher, Jr., R. Fa Linfield, R. 0. Maes, and B. Lindeman. BuMines Open File Rept. 41 (1)- 

74, 1973, pp. Gal-G.23; available for consultation at the Bureau of 

Mines libraries in Pittsburgh, Pa., Denver, Colo., Spokane, Wash., Twin 

Cities, Minn., and Morgantown, W. Va.; at the Central Library, U.S. 

Department of the Interior, Washington, D.C.; and from the National 

Technical Information Service, Springfield, Va., PB 235 604. 

13. Greenfield, R. Detection Range and Arrival Time Estimates. Part 3 in 

Survey of Electromagnetic and Seismic Noise Related to Mine Rescue 

Communications. V. 11. Seismic Detection and Location of Isolated 

Miners (USBM Contract HO 122026), by R. L. Lagace, J. J. Ginty, 

M. F. Roetter, R. H. Spencer, and Consultants. BuMines Open File 

Rept. 38 (2)-74, 1974, pp. 2.1-2.30; available for consultation at the 

Bureau of Mines libraries in Pittsburgh, Pa., Denver, Colo., Spokane, 

Wash., Twin Cities, Minn., and Morgantown, W. Va.; at the Central 

Library, U.S. Department of the Interior, Washington, D.C.; and from 

the National Technical Information Service, Springfield, Va., 

PB 235 070/AS. 

14. Greenfield, R. J. Seismic Radiation From a Point Source on the Surface 

of a Cylindrical Cavity. Geophysics, v. 43, 1978, pp. 1071-1082 

15. Harrington, D., and W. J. Fene. Barricading as a Life-Saving Measure 

Following Mine Fires and Explosions. BuMines, Miners Circ. 42, 1948, 

80 PP. 

16. Haskell, N. A. Critical Reflection of P and SV Waves. J. Geophys. Res., 

v. 67, 1962, pp. 4751-4767. 

17. LaCoss, R. T., E. J. Kelly, and Ma N. Toksoz. Estimation of Seismic 

Noise Using Arrays. Geophysics, v. 34, 1969, pp. 21-38. 

18. Leblanc, G. Truncated Crustal Transfer Function and Fine Crustal 

Structures Determination. Bull. Seis. Soc. America, v. 57, 1967, 

pp. 07 19-0734. 

19. National Academy of Engineering, Committee on Mine Rescue and Survival 

Techniques, Mine Rescue and Survival. 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., Johnstown, 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. 
20. Peters, D. C., and Crosson, R. S. Application of Prediction Analysis to 

Hypocenter Determination Using a Local Array. Bull. Seis. Soc. America, 

v. 62, 1972, pp. 775-788. 

21. Quo, J. T. Theoretical Seismic Signal Source and Transmission Characteristics. Part 7 in Survey of Electromagnetic and Seismic Noise Related 

to Mine Rescue Communications. V I. Seismic Detection and Location of Isolated Miners (USBM Contract HO 122026), by R. L. Lagace, 

J. J. Ginty, M. F. Roetter, R. H. Spencer, and Consultants. BuMines 

Open File Rept. 38 (2)-74, 1974, pp. 7.1-7.33; available for consultation at the Bureau of Mines libraries in Pittsburgh, Pa., Denver, 

Colo., Spokane, Wash., Twin Cities, Minn., and Morgantown, W. Va.; at 

the Central Library, U.S. Department of the Interior, Washington, D.C.; 

and from the National Technical Information Service, Springfield, Va., 

PB 235 070/AS. 

22. Ruths, M. A. The Reference-Correction Method for Improving Accuracy in 

the Seismic location of Trapped Coal Miners. M.S. Thesis, Pa. State 

Univ., Coll. of Earth and Mineral Sciences, University Park, Pa., 

November 1977, 141 pp. 

23. Sung, T. Y. Vibrations in Semi-Infinite Solids Due to Periodic Surface 

Loading in Symposium on Dynamic Testing of Soils. American Society for 

Testing and Materials, Philadelphia, Pa., 1953, pp. 35-63. 

24. Westinghouse Corp. Mine Emergency Operations Program Seismic Location 

Field Test Program. Report for MESA Contract 50277500, AprilSeptember, 1977; available for consultation at Pittsburgh Research 

Center, Bureau of Mines, Pittsburgh, Pa. 

25. . Mine Emergency Operations Group, Field Tests--Seismic Location 

System. Final Report for MESA Contract 52775001, 403 pp., MarchOctober 1976; available for consultation at Pittsburgh Research Center, 

Bureau of Mines, Pittsburgh, Pa. 

26. Westinghouse Electric Corp. Coal Mine Rescue and Survival. V. 2: 

Communications Location Subsystem (USBM Contract HO 101 262). BuMines 

Open File Rept. 9(2)-72, 1971, 258 pp.; available for consultation at 

Bureau of Mines libraries at Pittsburgh, Pa., Denver, Colo., Twin 

Cities, Minn., and Spokane, Wash.; at the Central Library, U.S. 

Department of the Interior, Washington, D.C.; and from the National 

Technical Information Service, Springfield, Va. PB 208 267. 

27. White, J. E. Seismic Waves: Radiation, Transmission, and Attenuation. 

McGraw-Hill Book Co., Inc., New York, 302 pp. 
APPENDIX Am--RELATION OF THE AMPLITUDE DISTRIBUTION OF A NARROW-BAND 

NOISE ENVELOPE TO RMS LEVEL 

The zero-to-peak amplitude R of the envelope of narrow-band noise is 

given by the Rayleigh distribution: 

R P(R) = ;ji~ exp (-~~/2o$) 

where ON is the noise rms. 

With noise alone, the probability that a single measurement of the envelope 

amplitude R will exceed some value R, is 

P[R > R,] = exp (-R,~/~o~) . (A-2) 

The equation is plotted in figure A-1. Frantti (9) gave results in terms of 

the P-P amplitude of the envelope. If it is assumed that the envelope value 

he recorded was the R, which has a probability of being exceeded of 1/7500, 

the ON may be estimated from his data using the value 

read from figure A-1. 

Note that the RJaN value used is quite insensitive to large changes in 

probability of R exceeding R,. For example, the value of 4.22 adopted for a 

probability of 1.33 x only changes to 4.7 if a probability of 1 x 

is used. If a probability of has been used, the RdaN value would have 

been 3.7. 
9 CUO 

0 cu ti 

=d- 
APPENDIX B . --NOMENCLATURE 

area of mine at depth h 

coefficient for amplitude model M 

difference, in decibels 

distance implement moves before contact 

thickness of soil layer 

decay constant 

radial displacement time history 

electromagnetic interference 

force applied to accelerate implement 

frequency 

force of gravity per unit mass 

SNR gain of subarray 

constant in force time history 

force time history of implement 

mine depth 

event number 

subarray number 

wavenumber vector 

horizontal wavenumber of noise 

mass of implement 

model number and power of cos O dependence 

noise particle velocity 

number of pulses stacked 

number of seismometers in a subarray 

number of amplitude measurements 
P-P 

rms 

SNR 

v~ 

vP 

VOL 

WMP 

implement momentum at contact 

peak to peak 

cumulative distribution functions 

probabilities 

quality factor for seismic wave attenuation 

source-to-receiver distance 

zero to peak detection threshold 

root mean square 

denotes type of source 

standard deviation 

signal-to-noise ratio 

signal OM ith geophone 

squared error for Mth model 

signal output of a subarray 

A,/N, amplitude coefficient divided by noise level 

t ime 

wave velocity 

ground particle velocity 

horizontal phase velocity 

compressional wave seismic velocity 

volume of mine 

waveform modeling procedure 

angular frequency 

ith geophone output 

seismometer location vector 

subarray output 
degrees of freedom 

rebound coefficient 

constant in displacement time history 

displacement time history of implement, into mine surface 

angle, at source, between upward vertical and receiver 

microinches per second (unit of ground particle velocity) 

rock density 

noise root mean square 

horizontal offset between source and receiver 

time implement dwells in contact with surface 

chi squared, statistical variable 

aU.S. GOVERNMENT PRINTING OFFICE: 1981-703-002182