DETECTION OF TRAPPED MINER ELECTROMAGNETIC 

SIGNALS ABOVE COAL MINES 

Robert L. Lagace, Project Leader 

James M. Dobbie, Thomas E. Doerfler, 

William S. Hawes, Richard H. Spencer 

prepared for 

UNITED STATES DEPARTMENT OF THE INTERIOR 

BUREAU OF MINES 

ARTHUR Dm LITTLE, INC. 

Cambridge, Massachusetts 

FINAL REPORT ON 

CONTRACT NO. J0 188037 

Technical Support of Throygh-the-Earth 

EM Transmission Measurement Program 

Arthur D Little, Inc 
REPORT DOCUMENTATION PAGE 

4. Title and Subtitle 

DETECTION OF TRAPPED MINER ELECTROMAGNETIC SIGNALS I 5. Report Date 

July 1980 

1. Report N;. 3. Recipient's Accession No. 

ABOVE COAL MINES I " 

2. 

7- Author(s) Robert L. Lagace, James M. Dobbie, Thomas E. Doerfler, 

William S. Hawes, Richard H. Spencer I 8. Performing Organization Report No. 

AD L-81978 

9. Performing Organization Name and Address 1 LO. Project/Tuk/Work Unit No. I 

Department of the Interior 

Washington, D.C. 20241 

Arthur D. Little, Inc. 

15 Acorn Park 

Cambridge, Massachusetts 021 40 

12. Sponsoring Organization Name and Address 

Office of the Assistant Director - Mining 

Bureau of Mines 

1 15. Supplementary Notes 

11. Contract or Grant No. 

JO 188037 

13. Type of Report 

FINAL 

May 1978 - July 1980 

16. Abstract 

This report assesses the expected detectability, on the surface above mines, of electromagnetic signals produced in the 

frequency band of 630 to 3030 Hz by a rescue transmitter activated by miners trapped underground. This assessment 

is based on a statistical analysis of experimental signal and noise data taken at a representative sample of coal mine sites 

well distributed over the United States underground coal fields. 

Regression analyses are performed to characterize the signal transmission behavior of overburdens as a function of depth 

and frequency. The predicted signal behavior is then combined with experimentally based distributions of the background 

noise, and aural detection characteristics of signals in noise, to generate curves of the expected probability of detection for 

trapped miner signals versus overburden depth and operating frequency. The implications of these results, and associated 

recommendations, are presented regarding the detectabil ity of trapped miners, sensitivity analyses and confirmatory tests, 

and operational utilization considerations for the trapped miners and the search and rescue team on the surface. 

17. Originator's Key Words 

Trapped Miner Location; Communications-Mine, Coal Mines; 

Through the Earth Communications-Electromagnetic; 

Electromagnetic Propagation-Conducting Media; Signal Detection; 

Probability of Detection; Statistical Sampling; 

Statistical Analysis 

18. Availability Statement 

I 

19. U.S. Security Classif. of the Report . 

Unclassified 

1 

20. U.S. Security Clusif. of Tbis Page 

Unclassified 

21. No. of Pages 

288 

22. Price 
USBM J0188037 

DETECTION OF TRAPPED MINER 

ELECTROMAGNETIC SIGNALS ABOVE COAL MINES 

Robert L. Lagace, Project Leader 

James M. Dobbie, Thomas E. Doerfler, 

Wllliam S. Hawes, Richard H. Spencer 

ARTHUR D. LITTLE, INC. 

Cambridge, Massachusetts 02140 

C-81978 

The views and conclusions contained in this document are those of 

the authors and should not be interpreted as necessarily 

representing the official policies or recommendations of the 

Interior Department ' s Bureau of Mines 

or of the United States Government 

FINAL REPORT 

USBM CONTRACT NO. J0188037 

July 1980 

United States 

Department of the Interior 

Bureau of Mines 

Arthur D Little, Inc 
FOREWORD 

This report was prepared by Arthur D. Little, Inc., 

Cambridge, Massachusetts, under USBM Contract No. J0188037. The 

contract was initiated under the Coal Mine Health and Safety 

Program. It was administered under the technical direction of the 

Pittsburgh Mining and Safety Research Center with Mr. John Durkin 

acting as the technical project officer. Mr. William McCarty was 

the contract administrator for the Bureau of Mines. 

This report is a summary of the work recently completed as 

part of this contract during the period May 1978 to July 1980, and 

Contract H0346045, Task Order No. 3, Task B, during the period 

March 1976 to October 1977. This report was submitted by the 

authors in July 1980. 

No inventions or patents were developed, and no applications 

for inventions or patents are pending. 

The authors wish to thank John Durkin, Harry Dobroski, 

Wymar Cooper and Carl Ganoe, of the United States Bureau of 

Mines, Pittsburgh Mining and Safety Research Center, for their 

encouragement and assistance in this work ; Howard E. Parkinson, 

presently of the United States Department of Energy, Carbondale 

Energy Technology Center, for the initial support of this work; 

A. Farstad and D. Kalvels of the Westinghouse Geophysical Instrumentation Systems measurement team for their cooperation and 

perseverance; and all the United States coal mining companies who 

contributed to the success of this program by providing the 

measurement team access to their mines and the cooperation 

required. 

Arthur D Little, Inc 
TABLE OF CONTENTS 

List of Tables 

List of Figures 

I . SUMMARY 

A. OVERVIEW 

B. OBJECTIVES 

C. APPROACH 

D . RESULTS 

E. ORGANIZATION OF REPORT 

11. THE NEED 

ZIT. THE EXPERIMENT 

A. PHILOSOPHY OF TESTS 

B. MINE SELECTION 

1. The Statistical Mine Sample 

2. The Final Mine Sample 

C. CONDUCT OF TESTS 

1. Uplink Measurements 

2 . Downlink Measurements 

3 Bureau of Mines Surface Noise Measurements 42 

4. Additional Supporting Information 

IV. DATA COMPILATION AND VERIFICATION 

A. APPROACH 

B. DESCRIPTIVE STATISTICS 

1. Signal Verification and Purging Process 44 

2. Tabulation of Magnetic Moments and 50 

Screened Signal Data 

3 . Conclusions Related to Other Variables 67 

C. THE FINAL UPLINK DATA BASE 69 

D. SURFACE NOISE DATA BASE 75 

1 . Verification and Assessment Process 75 

2. The Final Surface Noise Data Base 81 

3. Relationship to Reported Atmospheric 83 

Noise Data 

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V. CHARACTERIZATION OF OVERBURDEN TRANSMISSION 87 

MODEL 

A. RATIONALE 87 

B. REGRESSION ANALYSIS OF SURFACE SIGNAL DATA 89 

1. Surface Signal Strength vs. Log Depth 90 

Model for the Final (Expanded) Data Base 

a. Methodology 90 

b. Results 

2 . Other Models 

a. Log Depth Model for the 

Purged Data Base 

b. The D-~ Exponential Model 

C. THE RECOMMENDED MODEL AND ITS APPLICABILITY 114 

VI. SIGNAL ESTIMATES FOR THE GENERAL INSTRUMENTS 117 

TRANSMITTER 

VI I. CHARACTERIZATION OF SURFACE NOISE ABOVE MINES 121 

VI 11. ESTIMATES OF SIGNAL-TO-NOISE RATIO 

ON THE SURFACE 

IX. AURAL DETECTION OF PULSED CW TONES IN NOISE 145 

EFFECT OF LISTENING FREQUENCY 

EFFECT OF PULSE LENGTH 

C. EFFECT OF BANDWIDTH 149 

D . EFFECT OF PULSE REPETITION RATE 152 

E. PROBABILITY OF DETECTION VS. S/N RATIO 152 

X. PROBABILITY OF DETECTION ESTIMATES ON THE 159 

SURFACE ABOVE MINES 

A. METHODOLOGY 159 

B. ILLUSTRATIVE EXAMPLE 162 

C. FINAL DETECTABILITY RESULTS 164 

XI. IMPLICATIONS OF RESULTS AND RECOMMENDAT IONS 167 

A. DETECTABILITY VS. DEPTH AND ALTITUDE 167 

B. SENSITIVITY ANALYSES 169 

C. CONFIRMATORY TESTS 171 

D. OPERATIONAL UTILIZATION OF THE DETECTION 173 

SYSTEM 

1. In-Mine Transmitters 173 

2. Surface Detection Receivers 174 

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XI I. REFERENCES 177 

APPENDICES 

INFORMATION ON STATISTICALLY SELECTED MINES 179 

PLANNED FOR FIELD MEASUREMENT PROGRAM 

INFORMATION ON ACTUAL MINES VISITED DURING 195 

FIELD MEASUREMENT PROGRAM 

DERIVATION OF THE FUNDAMENTAL CURRENT AND 205 

MAGNETIC MOMENT FOR THE IN-MINE TRANSMIT LOOP 

ANTENNA 

COMPREHENSIVE TABULATIONS OF DATA BASES, 217 

DERIVED PARAMETERS AND EVALUATION INDICES 

COMPLETE COMPUTER OUTPUT OF REGRESSION ANALYSES 247 

FOR SIGNAL VERSUS LOG DEPTH MODELS 

AT EACH OF FOUR FREQUENCIES 

PROBABILITY OF DETECTION BASED ON PROBIT ANALYSIS 265 

OF SUCCESS/FAIL FIELD TEST DATA 

APPLICATION OF SEARCH THEORY TO THE 

DETECTION OF TRAPPED MINERS 

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LIST OF TABLES 

Sampling Fractions by Depth Intervals 

In-Mine Collins Transmitter RMS Magnetic 

Moment (MMFUND) at Fundamental Operating 

Frequency vs. Frequency and Depth 

Surface Transmitter RMS Magnetic Moment (MMDN) 

at Fundamental Operating Frequency 

vs. Frequency and Depth 

Surface Vertical Magnetic Field Signal Levels 

vs. Overburden Depth Measured by Westinghouse 

In-Mine Magnetic Field (Mainly Vertical ) 

Signal Levels (MEMF vs. Overburden Depth 

Measured by Westinghouse 

Final Screened Surface Signal Data with 

Substitutions and Replacements - Vertical 

Magnetic Field Levels vs . Overburden Depth 

Surface Vertical Magnetic Field Noise Levels 

Measured by Westing house with Collins Receiver 

Surface Vertical Magnetic Field Noise Levels 

Derived from Bureau of Mines Tape Recordings 

Regression Results for Surface Signal in dB 

vs. Log Depth Model, Using Expanded 

Uplink Data Base 

Regression Results for Surface Signal in dB 

vs. Log Depth Model Using Purged 

Uplink Data Base 

Least Squares Estimate 

Loop Impedances and Magnetic Moments for the 

General Instruments Transmitter 

Illustrative Example for Calculating Plot 

Points for Analysis of Noise Data 

Estimated Parameters Characterizing Signal 

and Noise Distributions Above Coal Mines 

Probability of Achieving Signal-to-Noise Ratios 

of Interest Above Coal Mines Using GI Transmitter 

Probability of Signal Detection versus 

Signal-to-Noise Ratio 

Listing of Specific Mines Selected for 

Field Measurements in U.S. Fields 

Listing of Actual Test Site Locations in U.S. 

Coal Fields and Selected Test Site Information 

Arthur D Little, Inc 
Key to Field Evaluation Reports and Mine Tests 203 

Tabulation of In-Mine Transit Loop 209 

Dimensions, Areas, Number of Turns, Wire Size 

Resistance, Inductance, and Time Constant for 

Total Transmitter Circuit 

Comprehensive Tabulations of Screened but 218 

Undeleted Surface and In-Mine Signal Strengths, 

Key Indices, and Variables (ranked by depth) 

Comprehensive Tabulations of Surface and In-Mine 227 

Data Bases with Key Indices and Variables 

(Rank Ordered by Depth) 

Summary Table of Statistics for Selected 

Variables by Frequency 

Summary Table of Statistics for Set of Key Variables 238 

by Frequency and Depth Interval 

Statistical Analysis of Uplink Data 248 

Summary of Test Outcomes - Failure to Detect 267 

Uplink Signals 

Summary of Specific Failure to Detect and Test 268 

Uplink Test Results 

Exact Probit Solutions 270 

II 

Arthur D Little, Inc 
LIST OF FIGURES 

Predicted Probability of Signal Detection vs. 

Overburden Depth by Frequency 

Illustration of Electromagnetic (EM) Trapped 

Miner Signalling and Detection System 

Geographical Distribution of Mines Sampled by 

County in U.S. Coal Fields 

Distribution of Mines Selected by Maximum 

Overburden Depth 

Uplink Transmit/Receive Measurement Equipment 

Surface Searcher Using Rescue Receiver Hardware 

Comparison of Westinghouse and Bureau of Mines 

Measured Noise Levels at 630 Hz 

Comparison of Westinghouse and Bureau of Mines 

Measured Noise Levels at 1050 Hz 

Comparison of Westinghouse and Bureau of Mines 

Measured Noise Levels at 1950 Hz 

Comparison of Westinghouse and Bureau of Mines 

Measured Noise Levels at 3030 Hz 

Two Terminal Pair Network Analogy for 

Characterization of Overburden Signal 

Transmission Response 

Uplink Normalized Overburden Signal Response 

Data and Linear Regression Log Model at 630 Hz 

Uplink Normalized Overburden Signal Response 

Data and Linear Regression Log Model at 1050 Hz 

Uplink Normalized Overburden Signal Response 

Data and Linear Regression Log Model at 1950 Hz 

Uplink Normalized Overburden Signal Response 

Data and Linear Regression Log Model at 3030 Hz 

Uplink Regression Results for 630 Hz 

Uplink Regression Results for 1050 Hz 

Uplink Regression Results for 1950 Hz 

Uplink Regression Results for 3030 Hz 

Normalized Overburden Response Curves - Uplink Regression Results, Average Surface 

Vertical Signal Strength HZ, vs. Overburden 

Depth by Frequency 

Arthur D Little, lnc 
VII 1-7 

Normalized Surface Vertical Magnetic Field HZ vs. 109 

Frequency with Depth as a Parameter 

Predicted Uplink Response Curves for General 118 

Instruments Transmitter - Average Surface 

Vertical Magnetic Field Signal Strength HZ vs. 

Depth by Frequency 

Statistical Distribution of RMS Surface Noise 124 

at 630 Hz 

Statistical Distribution of RMS Surface Noise 125 

at 1050 Hz 

Statistical Distribution of RMS Surface Noise 126 

at 1950 Hz 

Statistical Distribution of RMS Surface Noise 127 

at 3030 Hz 

Comparison of Distributions of Westinghouse and 

Bureau of Mines Noise Data at 630 Hz 

Determination of Distribution of Signal-toNoise Ratio Above Coal Mines 

Cumulative Probability Distribution of S/N 

Ratios Expected Above U .S. Underground 

Coal Mines at 630 Hz 

Cumulative Probability Distribution of S/N 

Ratios Expected Above U .S. Underground 

Coal Mines at 1050 Hz 

Cumulative Probability Distribution of S/N 

Ratios Expected Above U. S. Underground 

Coal Mines at 1950 Hz 

Cumulative Probability Distribution of S/N 

Ratios Expected Above U .S. Underground 

Coal Mines at 3030 Hz 

Probability that Mean RMS Signal is Greater 

Than or Equal to RMS Noise +gdB for the G.I. 

Transmitter 

Probability that Mean RMS Signal is Greater 

Than or Equal to RMS Noise for the G.I. 

Transmitter 

Relationship of Signal/Noise Ratio vs. Depth 

for Frequency = 630 Hz for the G. I. Transmitter 

Measured Values of the Critical Bandwidth 

of the Ear 

Recognition Differential for Sinusoidal Pulses 

in Broadband Noise Reduced to 1-Hz Bands 

L 

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Diagram Illustrating Recognition of an Echo of 150 

Constant Frequency and Rather Long Duration 

When the Noise Leve1,is Great Enough to Cause 

Masking Limited Conditions for all Bandwidths 

The Effect of Repetition Rate of Short Tones 

on the Masked Threshold 

Probability of Recognition of a Pure Tone in 155 

a Background of a Noise at a Constant RMS Level 

of 12 dB 

Aural Probability of Detection vs. RMS Signal- 156 

to-Noise Ratio for Trapped Miner Pulsed CW 

Signals in Background Gaussian Noise 

Predicted Probability of Signal Detection vs.. 

Overburden Depth by Frequency for the G.I. 

Transmitter 

Equivalent Circuit of EM Transmitter and 206 

Loop Antenna Configuration for Computing IFUND 

Results of Probit Analysis 27 1 

Estimated Uplink Probability of Successful 

Detection vs. Overburden Depth (based on. 

Success/Fail Data from 94 Mine Field Tests) 

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Arthur D Little Inc 
I. SUMMARY 

A. OVERVIEW 

In response to the Coal Mine Health and Safety Act of 1969, 

the Bureau of Mines of the United States Department of the Interior 

embarked upon a program to perform research and development 

aimed at increasing the survivability of miners trapped underground after a coal mine disaster. A principal ingredient of this 

program was the development of practical and effective means to 

detect, locate, and communicate with miners trapped within extensive mine workings. 

This report assesses the expected detectability, on the 

surface above mines, of electromagnetic signals produced by a 

rescue transmitter activated by miners trapped underground. This 

assessment is based cn a statistical analysis of experimental 

signal and noise data taken at a representative sample of coal 

mine sites well distributed cver the United States underground coal 

fields. 

B. OBJECTIVES 

This study had two main objectives. The first was to characterize the electromagnetic signal transmission behavior of overburdens above the coal mines. The second was to estimate the 

likelihood of successfully detecting electromagnetic signals transmitted by miners trapped beneath these overburdens. A secondary 

objective was to formulate an approach, based on search theory, 

for the allocation of post-disaster search efforts aimed at detecting 

the largest number of miners capable of being rescued per unit of 

search effort. 

Arthur D Little, Inc 
C. APPROACH 

A theoretical approach to the characterization of overburden 

signal transmission behavior was impractical, because of the 

variability and complexity of the overburden material of coal 

mines. Therefore, an approach based on measured signal data 

taken at mines well distributed throughout the U.S. coal fields was 

chosen. To make inferences concerning signal transmission characteristics over the entire population of U.S. underground coal 

mines, we adopted a statistical approach at the outset. We selected 

a representative sample of mines and performed regression analyses 

to characterize the signal transmission behavior of overburdens as 

a function of depth and frequency. The predicted signal behavior 

was then combined with experimentally based distributions of the 

background noise, and aural detection characteristics of signals in 

noise. These were used to generate curves of the e.xpected 

probability of detection for trapped miner signals versus overburden depth and operating frequency. 

The overall program objectives were accomplished through a 

collaborative effort which took advantage of the skills and 

resources of three parties; namely: Arthur D. Little, Inc., as the 

experiment design and data analysis team; Westinghouse Geophysical Instrumentation Systems as the measurement team; and the 

United States Bureau of Mines, Pittsburgh Mining and Zafety 

Research Center, as the overall coordination and support team. 

D. RESULTS 

The final results in the form of expected probabilities of 

detection are plotted in Figure 1-1. These plots represent the likelihood, on the average, of trapped miner signals being detected on 

the surface above U.S. coal mines having the indicated overburden 

Arthur D Little, Im- 
- 

- 

- 

- FREQUENCY (Hz) 

- 

- El---.4 3030 

- - 1050 

- O----4 630 

L 

- 

- 

- DATA SOURCES 

- - SIGNAL (WESTINGHOUSE) 

- - NOISE (BUREAU OF MINES) 

- 

7 

- 

- 

- - 

,1111 11111111 111 11 11 11 11 11111- 

0 250 500 750 1000 1250 1500 

OVERBURDEN DEPTH (FEET) 

FIGURE 1-1 PREDICTED PROBABILITY OF SIGNAL DETECTION VERSUS 

OVERBURDEN DEPTH BY FREQUENCY FOR THE GENERAL 

INSTRUMENTS TRANSMIlTER 
depths. The plots apply for the General Instruments transmitter 

and aural detection by a searcher using a Collins receiver 

equipped with a headset. 

At any particular mine site and given overburden depth, 

trapped miner signals can either be detected or not be detected 

during a search exercise. If such a detection experiment is 

repeated at several mines having the same overburden depth, the 

predicted expected percentage of experiments that will achieve 

signal detection at each operating frequency is as shown in 

Figure 1-1. For example, if the device were tested at many 

locations having a 750-foot overburden, it is expected that the 

transmitted signal would be detected at about 68 percent of the 

locations for the operating frequency of 1950 Hz, and at about 

43 percent of the locations for 630 Hz. The curves also indicate 

that the chances of being detected are higher for signals in the 

upper part of the 630 to 3030 Hz frequency band. 

Detailed discussion of some implications of these results is 

presented in Sections X and XI. The discussion centers on four 

areas : 

detectability related to overburden depth profiles, 

diurnal/seasonal noise variations, and miner distribution ; 

sensitivity analyses and experiments; 

desirability of confirmatory tests; and 

cperational utilization considerations from two points of 

view -- use of the in-mine transmitters by the trapped 

miners, and use of the surface detection equipment by the 

search and rescue team. 

L Arthur D Little, Inc 
E. ORGANIZATION OF REPORT 

Section 11 describes the events and circumstances which led 

to this comprehensive program involving the measurement and 

analysis of data from many coal mines. In Section 111, the overall 

philosophy of the tests, the mine selection process, and the 

specific measurements performed at each mine are discussed. 

Section IV describes the process of compiling and verifying the 

extensive set of data taken at 94 mine sites to produce a final 

data base for both signal and noise. Section V presents the linear 

regression analyses of the signal data and the derived regression 

models describing the signal transmission behavior of U. S. coal 

mine overburdens as a function of depth and frequency. Section VI 

presents, using the transmission model of Section V, the signal 

strength expected on the surface for the planned General Instruments transmitter. Section VII characterizes the statistical distribution of the expected background noise on the surface. In 

Section VIII, probability distributions are generated for the 

signal-to-noise ratio expected on the surface at each frequency. 

Section IX describes the aural detection of pulsed CW tones in 

noise and presents signal-to-noise requirements for detection. In 

Section X, the results of the previous sections are combined to 

generate the final curves describing the expected probabilities of 

detection for trapped miner signals as a function of overburden 

depth and frequency. Section XI discusses the implications of these 

results and recommendations. 

Arthur D Little Inc 
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Arthur D Little, Inc. 
11. THE NEED 

In response to the Coal Mine Health and Safety Act of 1969, 

the Bureau of Mines of the United States Department of the Interior 

embarked on a program to perform research and development aimed 

at increasing the survivability of miners trapped underground 

during coal mine disasters. A principal ingredient of this program 

was the development of practical and effective means to detect, 

locate, and communicate with miners trapped within the extensive 

mine workings. The sooner such miners can be found at a mine 

disaster site, the greater will be their chances of surviving. This 

benefit will accrue because of the more efficient and effective 

allocation of the limited mine rescue resources generally available 

at disaster sites to help rescue miners before they succumb to 

injuries or noxious mine environments. 

Two means were conceived and developed to provide trapped 

miners with this location and communication capability: an electromagnetic (EM) signaling system, and a seismic signaling system. 

This report examines the potential effectiveness of the electromagnetic signaling system and is particularly concerned with the 

statistical analysis of experimental magnetic field strength data 

taken at 94 coal mine sites well distributed over the United States 

coal fields. The objective is to obtain an experience-based assessment of the probable effectiveness of this electromagnetic signaling 

system prior to initiating the formulation and promulgation of new 

regulations bearing on the use of such a system. 

The need to conduct this specific, comprehensive program 

involving field measurements and analysis of data from a large 

number of coal mine sites became apparent in 1975-76. At that 

time, the Bureau of Mines had completed development of electromagnetic trapped-miner signaling and receiving hardware. This 

hardware was based on intrinsic safety requirements and on 

Arthur D Little, lnc. 
available geological information regarding the anticipated severity 

of overburden signal attenuation characteristics. Namely, the 

average effective electrical conductivity of the overburden was 

considered to be approximately 0.01 mho/m. Performance estimates 

based on this value of conductivity predicted effective signal 

detections for an overburden depth of 1,000 feet using an intrinsically safe transmitter design utilizing the miner's cap lamp 

battery as a primary source of power. 

Figure 11-1 illustrates the principle of operation of the EM 

trapped-miner signaling device and associated detection/receiving 

hardware on the surface. The figure also depicts the sedimentary 

nature of both a coal seam and the numerous layers of different 

materials comprising the overburden above a coal seam. The EM 

signaling transmitter shown in Figure 11-2 was developed by 

Collins Radio based on the above requirements and ,assumptions. 

This transmitter was tested at several deep mines in the Appalachian coal fields having overburden depths between 500 and 

1,000 feet, and the results were successful as anticipated. 

However, this equipment was also tested at mines shallower than 

500 feet; the results were unsatisfactory and unanticipated. 

Namely, some or all of the frequencies tested in the 630 to 3030 Hz 

band did not penetrate the overburden with significant strength to 

be detected on the surface at these shallow mine sites. Furthermore, the reasons for the lack of successful detections above the 

shallow overburdens were not apparent. 

These unanticipated, negative results precipitated the need to 

establish a way to characterize the signal transmission behavior of 

overburdens above United States coal mines, and to assess the 

impact of this behavior on the expected detectability of trapped 

miner EM signals. Such a characterization and assessment is 

required before the promulgation of new regulations. This requirement led to the establishment of the extensive measurement and 

data analysis program whose results are presented in this report. 

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Source: U.S. Bureau of Mines 

FIGURE 11-2 COLLINS RADIO EM TRAPPED MINER 

TRANSMITTER MOUNTED ON MINER'S 

CAP LAMP BATTERY 

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111. THE EXPERIMENT 

A. PHILOSOPHY OF TESTS 

The objective of this study 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 United States coal fields; and 

second, to use this data base to predict the likelihood of successful performance of the EM trapped-miner signaling system. A transmission measurement program was required, because the limited 

information on, and the inherent variability and complexity of, 

overburden electrical characteristics above U.S. coal mines made a 

theoretical approach infeasible. Furthermore, we concluded that, in 

order to obtain results that would account for this variability, the 

measurement program should consist of simple measurements made at 

a large number of mines throughout the United States coal fields, 

instead of a comprehensive set of measurements made at only a few 

selected mines. 

We also concluded that a representative sample of mines 

should be selected from the population of all coal mines on the 

basis of both the overburden depth and the number of miners 

employed at the mine. Namely, the sample should reflect proper 

concern both for the physical dependence of signal penetration on 

overburden depth and the number of miners exposed to potential 

disasters within each depth interval. Since this program would 

require the cooperation and participation of approximately one 

hundred mines, it was also important to design the tests to not 

interfere with mine production activities and to require a. minimum 

time within the mine. 

These criteria were satisfied by designing the experiments so 

that the in-mine test crew required only two people, who could 

Arthur D Little, Inc 
conveniently hand-carry a minimum of equipment to one predesignated non-interfering location within the mine, set up and 

complete all tests, and leave the mine, all within a single working 

shift. This minimum interference with mine production operations 

was accomplished through the efficient design of the measurement 

procedures and the pre-test arrangements made with mine personnel 

prior to entering the mine. 

It was further decided to accomplish the overall program 

0bjective.s through a collaborative effort to take advantage of the 

available skills and resources of three parties, namely: Westinghouse Geophysical Instrumentation Systems, as the measurement 

team; Arthur D. Little, Inc., as the experiment design and 

analysis team; and United States Bureau of Mines Pittsburgh 

Mining and Safety Research Center (PMSRC), as the support team 

that provided vital staff resources and coordination to both the 

field measurement and the data analysis activities of this program. 

The remainder of this section briefly describes the mine selection 

and field measurement activities. 

B. MINE SELECTION 

To make meaningful inferences about the overall performance 

of the candidate EM detection system throughout the U.S. coal 

fields, it was necessary to conduct tests at a sufficient number of 

mines. Since experimental results were intended to be representative of a large number of active mines, each with unique 

physical and operational characteristics, it was necessary to 

utilize some type of sampling process to determine specific test 

locations for the program. By invoking statistical sampling theory 

in the selection process, it was possible to: 

(1) assure the validity of estimated performance measures 

subsequently derived from test results; 

P 

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(2) increase the precison of these estimates; and 

(3) reduce or eliminate the possibility of built-in biases in 

interpreting test results. 

It was decided at the outset of the program that test results 

from approximately one hundred different mine locations would be 

sufficient for estimating the transmission characteristics of the 

overburden above coal mines, and necessary to provide an 

adequate data base for estimating overall probability of successful 

signal detection on the surface in a meaningful quantitative sense. 

1. The Statistical Mine Sample 

Although a simple random sample of 100 mines could have 

been selected from the total mine population (in which case each 

mine would have an equal probability of being selected), it was 

reasoned that the sampling plan should reflect two additional 

important considerations; namely: (1) since the performance of the 

device was likely to be depth-dependent , the distribution of mines 

selected should take into account the greater variability in test 

results anticipated at greater depths than at lesser depths; and 

(2) since most mines are relatively small in terms of number of 

miners employed, the probability of mine selection within a depth 

interval should be based on the number of workers to be protected 

at the mine, thereby giving large mines a justifiably greater 

chance of being selected than smaller mines. By utilizing these two 

concepts in designing a sampling plan, it was felt that the 

analysis of test results would yield more meaningful and precise 

estimates of transmission behavior relative to - all mines and miners 

eventually employing the device. 

The population considered was identified from a computer 

listing of 1,222 active coal mines in the United States obtained 

from PMSRC. This computer listing was constructed by PMSRC from 

two independent computer data bases, one from MSHA that contained 

Arthur D Little, Inc 
data on the number of miners at each mine, and one from the 

Bureau of Mines Eastern Field Operations Center that contained 

data on the maximum overburden depth at each mine. This listing 

included the mine name, address, maximum overburden depth, 

number of miners employed, and MSHA identification number. All 

mines were subsequently stratified according to maximum mine overburden depth values into 15 different depth intervals. Total miners 

employed at all mines contained within each depth interval were 

also tabulated. Although the sample could have been allocated 

proportional to the size of the strata (that is, the ratio of the 

number of mines sampled to the total number of mines would be 

constant within each interval), it was decided to vary the 

sampling fraction based on consideration (1) above. 

To determine actual sampling fractions, a technique known as 

optimum allocation(2) was used, which is based on the principle 

that larger samples are required in strata that exhibit greater 

variability. This principle can be expressed as follows: 

where 

"h = sample size for the h-th stratum; 

Nh = total number of mines in the h-th stratum; 

= variance of the characteristic being measured in the Sh h-th stratum (e.g ., the estimated probability of 

successful transmission at a specified frequency); and 

= total sample size (approximately 100 mines). 

- 

Arthur D Little, Inc 
By estimating the relative variability Sh, it was determined 

that: 

4 percent of the mines would be sampled in each of three 

strata less than 400 feet deep; 

10 percent of the mines would be sampled in each of six 

strata between 400 and 1,000 feet deep; and 

15 percent of the mines would be sampled in each of six 

strata greater than 1,000 feet. 

These results are illustrated in Table 111-1. 

As stated in (2) above, the sample selection process within 

each depth interval was based on the number of miners employed 

at each mine. This technique, known as sampling with probability 

proportional to size, can be illustrated by the following simple 

example for five mines in a given depth interval: 

Probability of 

Mine -- Number of Miners Being Selected 

The important features of the sampling procedure used in this 

program are summarized below: 

Each mine had a chance of being selected for this test. 

The chance (i.e., the probability of selection) was known 

beforehand and was based on the relative size of the mine 

in terms of miners employed. 

Arthur D Little, Inc 
Table 111-1 

Sampling Fractions by Depth Intervals 

TI- --- 

I Maximum I Total number Sample 

-r 

I Total Number 

1 I I 

I 

1 Mine Depth I of Active Mines Size Sampling 

(nh) Fraction 

of Miners 

(all mines) 

I Total I 1222 102 100,619 

- 

Source: Arthur D. Little, Inc. 

and United States Bureau of Mines Composite 

Computer File based on MSHA and Bureau of Mines 

Mine Data Files as of 1975. 

Arthur D Little, Inc - 
The selection process was random. 

All depth intervals were represented. 

Test results could be used to make valid inferences about 

all mines. 

The sample of 102 mines selected in this manner for this 

program is given in Table A-1 of Appendix A, in which the 

selected mines are ordered by increasing depth intervals and by 

increasing number of miners per mine within each depth interval. 

Examination of this listing also reveals that the mines are well 

distributed among the major and minor underground coal-producing 

states in the United States coal fields. 

2. The Final Mine Sample 

The statistically selected mine sample described above and 

listed in Appendix A provided a guide for the organization and 

implementation of the field measurement program. Although a reasonable attempt was made to visit the specific mines selected, 

necessity, mine availability and practical travel schedule constraints introduced deviations from the originally selected sample 

of mines. However, we believe these deviations do not significantly 

affect or bias the results derived from the data obtained from this 

measurement program. 

The following is a brief listing of reasons for deviation from 

the original mine selection plan, with respect to the specific mine, 

the anticipated overburden depth, or the number of miners employed at the mine: 

Arthur D Little, Inc 
Delays in the availability of mine population information 

required that a number of mines already tested replace 

selected mines having similar characteristics; 

a Some mines selected from the 1975 mine information data 

base no longer existed as operating mines at the time of 

the test program; 

In some cases, the data base information regarding 

maximum overburden depth and number of miners was 

found to be erroneous on arrival at the mine, requiring 

that the measurement team settle for a test site with a 

shallower overburden depth than planned; 

Some mines were not able to accommodate the measurement 

teams within the time frame of the planned field trip 

schedules ; 

Occasionally, mines which can best be classified as 

"targets of opportunity" were visited on some of the field 

trips, because of their ready availability within the geographical region visited and/or favorable selection 

characteristics. 

Care was taken to adhere to the spirit and form of the 

original selection list while coping with the realities imposed on 

the practical implementation of such an extensive field measurement program over a period of 24 months, from September 1977 to 

September 1979. 

At the completion of the test program, measurements had been 

performed at 94 mine sites well distributed within the U.S. coal 

fields. The specific 94 mine sites sampled in this program are 

listed in Table B-1 of Appendix B, together with selected mine and 

test information about each mine site. The mines in Table B-1 are 

ordered by state within major coal-producing regions, and by 

county in each state, scanning from west to east and then southward within each state. Included in the table is the following 

information about each mine: its location, the seam, mine test 

number, Westinghouse field report number, seam thickness, number 

of miners, overburden depth, horizontal offsets between transmitter 

II 

Arthur D Little, Inc 
and receiver for both uplink and downlink transmission tests, the 

month and year of test, and mines with Bureau of Mines tape 

recorded data. A listing of mine test numbers associated with each 

field report has been included as Table B-2 for convenient 

reference. 

Figure I 11-1 depicts the geographical distribution of actual 

mines tested by county within the U.S. coal fields. Examination of 

this map reveals that the counties tested are well distributed within the U.S. coal fields. Figure 111-2 depicts the actual vs. 

planned distribution of selected mines vs. overburden depth 

intervals. Examination of Figure 111-2 reveals that, for the 

practical reasons cited above, the actual distribution of mine sites 

reflects a substantial over-sampling of mines less than 300 feet 

deep and a corresponding under-sampling of mines with overburden 

greater than 700 feet deep. This means that the final mine sample 

was somewhat inefficient, in that it over-sampled shallow mines 

having a high anticipated probability of signal detection; namely, 

near unity. Furthermore, this occurred at the sacrifice of data 

needed for the deeper mines which wzre expected to exhibit much 

greater variability among test results. Attempts were made to 

provide mid-program corrections to this skewing of the sampling 

distribution of depth intervals. This corrective action was only 

partially successful for a number of reasons, the most important of 

which being the relative scarcity of mines having deep overburdens. 

C. CONDUCT OF TESTS 

The tests were designed to be as simple and straightforward 

as possible, not only to minimize the inconvenience to mine 

operators, but also to maximize the likelihood of obtaining usable 

data from measurements taken in demanding and hazardous environments. The primary objective was to measure uplink signal transmission through the overburden directly above a trapped-miner EM 

transmitter connected to a single turn loop of wire wrapped around 

33 

Arthur Ll Little Inc 
Arthur D Little, Inc. 
0 

0 300 500 700 1000 1200 >I200 

DEPTH INTERVALS IN FEET 

I I I I I 1 I I I I I I 1 

ACTUAL I 

34 (94) 

- 

22 

- 

- 9% 

I I 

0 

0 300 500 700 1000 1200 >I200 

DEPTH INTERVALS IN FEET 

I I I I I 1 I I 1 I I 1 I I 1 

PLANNED 

( 102) 

- - 

25 25 

FIGURE 111-2 DISTRIBUTION OF MINES SELECTED BY 

MAXIMUM OVERBURDEN DEPTH 

9% 

I 

- 

9 

- 

. 

4% 

h I I 

- 

21 

6% 

I 

7% 

I 

- 

- 6 6 - - 

5 

3% 1 0% 6% 

I I I I I 

1 0% 

I 

22 

1 0% 

I I 

- 16 

8 

14% 

I 

- 20% 

I I 
a coal pillar, depicted in Figure 11-1. Note that the plane of the 

surface receive loop antenna must be oriented horizontally, not 

vertically, to detect the vertical component of magnetic field. In 

the vicinity of the point directly above the trapped-miner transmitter, the vertical component of the magnetic field will be 

significantly stronger than the horizontal. Therefore, the vertical 

component is the primary one used to detect trapped miners. The 

horizontal component, which experiences a null directly above the 

transmit antenna, is used to get a more precise location of the 

miner. 

The small and lightweight Collins Radio trapped-miner 

transmit and receive equipment was used to gather the field 

strength data. This provided direct experience and results on the 

ability of signals from these devices to be successfully detected 

above coal mines in the presence of ambient noise, as well as 

providing the desired signal strength data. However, since the 

limited-power trapped miner transmitters might not be detectable 

above some deep or highly lossy overburdens, downlink transmission tests were also made. This was accomplished by using a 

significantly stronger transmitter on the surface, where it was 

possible to use heavy, bulky, high-power equipment. The goal was 

to utilize appropriately normalized downlink results, in the 

absence of valid uplink data, by applying the principle of reciprocity. A detailed description of equipment configurations and 

procedures used in the field measurement program is given in 

Reference 1. The following brief description is included to give the 

reader a sense of the measurements and procedures. 

1. Uplink Measurements 

The vertical component of signal magnetic field penetrating 

the overburden, and the corresponding vertical component of 

Arthur D Little, lnc - 
ambient noise magnetic field, were measured. Arrangements were 

made with the mine operator to choose a transmit location at the 

desired overburden depth that allowed the surface team to set up 

its equipment at an easily identified and accessible location 

directly above the mine transmit location. Most of the time, the 

measurement team was able to obtain the desired transmitheceive 

geometry, and sometimes this occurred at the sacrifice cf some overburden depth. At other times, achieving this objective required 

considerable initiative, perseverance, and courage by the surface 

crew to reach, set up, and perform the measurements on narrow 

benches cut into steep mountainsides in the Appalachian coal fields. 

Attempts were also made to select in-mine and surface 

measurement sites away from conducting cables, pipes, and other 

long conductors. In some instances, inductive coupling to these 

conductors might accidentally provide either an alternative lowerloss conducting path between the mine and the surface EM 

equipment, or perhaps a more favorable long-wire antenna effect. 

In many cases, tests had to be conducted in the presence of such 

structures, because it was not always possible to avoid them. This 

did not seriously impede the analysis of the associated data or the 

corresponding results, because in most cases the presence of the 

conductors did not appear to produce a significant discernible 

effect or trend in the data. 

Figure 111-3 is a block diagram of the mine subsurface EM 

transmitter equipment and the surface equipment used to detect and 

measure the strength of the received signal and noise. Figure 11-2 

is a photograph of the Collins EM transmitter attached to a 

miner's cap lamp battery. A one-turn loop of #12 wire was 

connected to the terminals at the top of the transmitter and 

wrapped around one (or sometimes two) coal pillars, as depicted in 

Figure 11-1. The 0.1-ohm precision resistor in series with the loop 

was used with a portable Tektronix oscilloscope to monitor the 

shape, and measure the peak-to-peak value, of the loop current 

waveform for use in magnetic moment calculations. 

37 

Arthur D Little, Jnc 
I 

HP 2OBA 

SIGNAL 

GENERATOR 

L -,---, ,J 

CALIBRATION BOX 

SURFACE EQUIPMENT SUBSURFACE EQUIPMENT 

. 4 

MANPACK 

LOCATION 

TRANSMITTER 

I 

(Receive) (Transmit) 

o.ln TU

Source: Westinghouse, Ref. 1 

FIGURE 111-3 UPLINK TRANSMIT/RECEIVE MEASUREMENT EQUIPM

AN

i 

I 

r*- 

LO

% 

TEKTRONIX 2 1 1 

OSCl LLOSCOPE 

, 
The surface measurement equipment consisted of the Collins 

EM receiver and 500-turn, 15-inch diameter loop antenna, as portrayed in Figure 111-4. In this program, the plane of the receive 

loop was oriented horizontally, usually by laying it on the 

ground. The calibration box, attenuator, and portable HewlettPackard signal generator, shown in Figure 111-3, allowed the use 

of a highly reliable substitution method to measure the absolute 

value of the magnetic field with the uncalibrated temperaturesensitive Collins receiver. The method ( ) consisted of recording 

the signal generator voltage required to produce the same meter 

deflection on the EM receiver as that produced by the measured 

signal or noise magnetic field. 

Four representative channels used by the trapped miner 

equipment were selected to assess performance variation with 

frequency across the band of interest. The channel frequencies 

chosen were 630, 1050, 1950, and 3030 Hz, each of which are 

located halfway between harmonics of the 60 Hz power grid 

frequency. 

The measurements were performed according to the following 

prearranged schedule to compensate for the lack of communication 

between the in-mine and surface teams. A preset amount of time 

was allowed for both surface and in-mine measurement teams to get, 

into place and set up their equipment before the test. Test 

commencement time was typically set at 10:OO a.m. The hour was 

divided into four 15-minute segments, each allocated to a series of 

uplink and downlink signal and noise measurements at one of the 

four frequencies. The test sequence was initiated by 630 Hz 

downlink transmissions, using the equipment described below, for 

the first seven and a half minutes of the first &minute segment. 

The second seven-and-a-half minutes of the &minute segment 

consisted of uplink transmissions at 630 Hz. This sequence of 

operations was repeated during the following three 15-minute 

Arthur D Little, Inc. 
Arthur D Little, Inc. -. 
segments for the frequencies of 1050, 1950, and 3030 Hz, respectively. Afterward, the first &minute sequence was usually 

repeated, in case either the surface or the in-mine team was unable to meet the test initiation schedule. In many cases, the 

complete one-hour test sequence was repeated. Finally, when 

possible, noise readings were taken at the beginning or end of the 

seven-and-a-half minute segments, to provide an approximate 

comparison between measured signal levels and ambient noise levels 

measured a short time before or after the signal. However, it was 

not always possible to accomplish this during the measurement 

sequence,in which case the noise measurements were taken after 

the signal tests were completed. 

2 . Downlink Measurements 

The downlink measurements utilized the same 'receive equipment configuration in the mine as used on the surface for uplink 

measurements. However, the downlink transmitter on the surface 

consisted of an audio frequency signal generator, a pulse interrupter, and a high-fidelity, high-power amplifier driving a 

one-turn, 500-foot periphery loop antenna deployed on the surface 

of the ground. This equipment was capable of transmitting both 

pulsed CW tones and voice transmissions into the overburden. It 

was also capable of generating CW RMS magnetic moments of up to 

2 20,000 Amp-m , independent of frequency, to provide improved 

penetration capability in deep and/or high-loss overburdens. 

Transmit moments generated in the mine ranged between about 300 

and 1,500 ~m~-m~ depending on loop size and frequency. In mines 

with relatively shallow overburdens, less than approximately 700 

feet deep, voice transmission was attempted to gather information 

related to the more difficult problem of successfully transmitting 

voice through the overburden. 

Arthur D Little, Inc 
3 Bureau of Mines Surface Noise Measurements 

During the last half of the field measurement program, the 

Bureau of Mines' Pittsburgh Mining and Safety Research Center 

conducted an independent series of surface noise measurements at 

27 of the mine sites. These measurements were made during the 

uplink/downlink measurements conducted by the Westinghouse field 

measurement team. The Bureau of Mines equipment consisted of the 

Collins 500-turn, 15-inch diameter receive loop antenna fed through 

an appropriate preamplifier into a wideband instrumentation tape 

recorder. The recordings were later analyzed by PMSRC, using 

digital FFT (Fast Fourier Transform) analysis equipment to 

generate RMS noise level information in selected narrow bandwidths 

centered on each of the four channel frequencies of 630, 1050, 

1950, and 3030 Hz. Detailed descriptions(3) of this equipment and 

the FFT analysis can be obtained from the Bureau. of Mines 

Technical Project Officer. 

4. Additional Supporting Information 

To assist the overall assessment of the signal transmission 

data, the measurement team obtained a wide range of additional 

supporting information on each mine and its environment. This 

information included mine size, age, power usage, type of mining 

and haulage, number of miners, overburden thickness, seam mined, 

seam thickness, a geologic log of the overburden strata near the 

specific test site, approximate analysis of the coal, general 

descriptions of the in-mine and surface test sites and environmental conditions, and a mine map showing the part of the mine 

where the test site was located. These maps depicted the location 

of the rails, belts, power lines, water lines, gas lines, bore 

holes, and other objects and surface features that might have some 

bearing on the measured field data. 

I* 

Arthur D Little, Inc 
IV. DATA COMPILATION AND VERIFICATION 

A. APPROACH 

The painstaking task of compiling and verifying the extensive 

data taken by the Westinghouse measurement team at 94 mine sites, 

prior to detailed statistical analysis by Arthur D. Little, Inc., was 

undertaken as a collaborative effort between Arthur D. Little, Inc., 

and the U.S. Bureau of Mines, Pittsburgh Mining and Safety 

Research Center. PMSRC performed the initial tasks of gathering, 

verifying, and coding measured and supporting data from the 

Westinghouse field reports as they were received. They then 

assembled an easily accessible computer data file, consisting of the 

original data and derived parameters, on a mine-by-mine basis. 

This process included checks for completeness and consistency in the 

data obtained from the field reports and the clarification of questionable issues with the Westinghouse measurement team. 

When the computer data file had been assembled for all 

94 mine sites, it was sent in a compatible computer tape format to 

Arthur D. Little, Inc., for final verification and extensive 

analysis. This phase of the work was a laborious one, for the 

following two reasons: First, it was necessary to produce a final, 

verified, and complete data base of both signal and noise data 

obtained from an extensive and specialized field measurement 

program, conducted over an extended period of time, by different 

field crews, under widely varying and difficult environmental and 

operational conditions. Second, it was necessary to assess the 

relevance to the determination of depth and frequency relationships, 

of a large number of observed, and possibly important, experimental conditions existing at each test site, such as distance from 

conductors, transmittedreceiver horizontal offset, overburden 

Arthur D Little, Inc 
composition, environmental conditions, etc. Any such measurement 

program is prone to the generation of some erroneous data, inconsistencies, and secondary variables of questionable importance. 

These had to be ferreted out, assessed, and resolved by a 

specially tailored, iterative purging process to arrive at a final 

data base that could be used with confidence. 

This section is devoted to describing the principal elements 

of the purging process, and the results in terms of preliminary 

and final data bases for signal and noise. This phase of the work 

also involved a considerable amount of successful collaboration 

between ADL and PMSRC technical staff as we sought to resolve 

questions regarding signal and noise data and experiment configurations within the mines and on the surface. 

In addition, data taken by a Bureau of Mines PMSRC measurement team was analyzed and eventually chosen to serve as the 

final surface noise data base. During the second half of the 

measurement program, the PMSRC team made independent surface 

noise recordings at 27 mine sites. The noise levels on these recordings were found to be at variance with many of the Westinghouse 

readings taken with the trapped-miner surface receiver. These 

discrepancies led to a comparative analysis of the Bureau and 

Westinghouse noise data by ADL and Bureau technical staff, resulting in the decision to use the Bureau of Mines noise data. 

B. DESCRIPTIVE STATISTICS 

1. Signal Verification and Purging Process 

A number of initial listings, cross-tabulations, and preliminary analyses were performed in order to discern trends and 

relationships, and to formulate methods to identify "outliers" in 

the data that appeared to deviate from the sample averages. For 

L.. 

Arthur D Little, Inc 
example, several key quantities were rank ordered by depth for 

each of the four frequencies to examine any obvious trends. These 

variables were the surface magnetic field as measured, the surface 

magnetic field normalized for a nominal in-mine magnetic moment 

2 of 750 Amp-m , the in-mine magnetic field as measured, the in-mine 

magnetic field normalized for a nominal magnetic moment of 

2 7,500 Amp-m , both the uplink transmission loss (TLU) in dB, and 

the downlink transmission loss (TLD) in dB, defined below, A TL, 

defined as the difference between uplink and downlink transmission 

losses (TLU - TLD) in dB, the in-mine moment (Mm = N I A ), and 

mmm 

the surface magnetic moment (M = N I A 1. N, 1, and A are the 

S SSS 

transmit loop number of turns, current in amperes, and area in 

square meters, respectively. The transmission loss is defined as the 

amount by which the presence of the overburden decreases the 

magnetic field signal strength below the field strength produced by 

an infinitesimal static magnetic dipole of the same strength. Namely, 

TLU and TLD are defined as follows: 

where SEMF and MEMF are surface and in-mine vertical components 

of magnetic field strength in dB re 1 pA/m, respectively; Mm and 

Ms are the in-mine and surface transmit magnetic moments in 3 

~mp-mL, respectively; and D is the overburden depth in meters. 

The above quantities were then cross-tabulated by depth and 

frequency and aggregated in eight depth intervals to give means, 

standard deviations, maximum and minimum values, and number of 

mines within each depth interval. The data aggregated by depth 

interval were also subjected to initial linear regression analyses, 

the most useful being the regression between field strength and the 

logarithm of depth at each measured frequency. Tabulations and 

regression results showed a strong relationship of decreasing 

signal strength vs. log of depth, indicating a power law type of 

Arthur D httle, Inc 
behavior. A weaker relationship was found between decreasing 

signal strength with increasing frequency. These results indicated 

the general nature of the relationships expected, but did not 

explain significant variations from this behavior on a mine-bymine basis. 

An attempt was made to identify mines exhibiting systematic 

deviant behavior as a function of proximity to long conductors in 

the mine or on the surface, or large horizontal offset. of the transmit and receive antennas. To assist in this endeavor, an attempt 

was made to identify and classify so-called "average" transrvission 

loss behavior vs. frequency within each of the eight depth intervals. This classification exercise proved to be fruitless, because 

of the completely unsystematic behavior displayed by the 

aggregated transmission loss versus both frequency .and depth. 

Namely, it did not increase monotonically with increasing 

frequency, nor did it increase monotonically with increasing depth 

interval. This completely unsystematic behavior of the aggregated 

transmission loss, together with its wide variability about the 

average, led to the conclusion that the magnetic field strength 

itself, instead of the derived transmission loss originally intended, 

should be the primary variable of interest to characterize the 

transmission characteristics of mine overburdens of the U. S. coal 

fields. However, we did conclude that both transmission losses 

(TLU and TLD) and the quantity ATL would, in conjunction with 

other key identifiers, be highly useful for tagging so-called 

"outlier" readings demanding closer scrutiny on a mine-by-mine 

basis. 

Comprehensive screening, verification, and purging processes 

were initiated on the uplink and downlink data to identify those 

data points requiring closer examination. This was accomplished 

principally through the generation of a screening chart constructed 

with the mines rank ordered by depth, and characterized in terms 

of four key indices of potential problem behavior. The four key 

indices were: 46 C 

Arthur D Little, Inc 
Transmission loss negative or suspiciously deviant. A 

negative transmission loss indicates a field strength 

reading greater than that obtainable from an equivalent 

infinitesimal dipole moment in free space i.. , in the 

absence of the overburden). This could indicate a grossly 

erroneous reading, or the presence of a lower loss 

propagation path between the surface and the mine, likely 

caused by nearby electrical conductors. 

A TL outliers greater than or equal to 10 dB. This would 

indicate a large unexpected difference in the uplink and 

downlink transmission characteristics. 

Outlier values of the normalized surface magnetic field 

greater than or equal to 10 dB from corresponding preliminary regression estimates based on the unpurged data 

base. All surface magnetic field values were adjusted to 

those for a nominal transmit moment of 750 ~m~-m~ for 

this calculation. 

Receivedtransmitter loop horizontal offset tangents greater 

than 0.1, where the offset tangent is defined as the ratio 

of the horizontal offset between centers of transmit and 

receive loops to the overburden depth. 

The following columns were also added to the chart to aid the 

screening process : mine number, indication of no test performed, 

indication of missing signal levels, indication of questionable noise 

readings, and the values of the ratio of transmit loop radius to 

the overburden depth for those mines with offset tangents greater 

than 0.1. Any mine data scoring on one or more of the four key 

indices described above on any frequency were examined in detail, 

down to the field report and final report level, to determine 

Arthur D Little, lnc 
(a) whether the tabulated magnetic field strength levels were 

correctly transcribed into the computer data base, and (b) if 

correctly transcribed, whether they should be retained as valid 

readings or be excluded as defective data or as data falling into 

a special restrictive category. 

The final judgments regarding exclusion of data were always 

conservative, in the sense that data were retained unless the 

weight of evidence against them was clearly strong. As a result, 

very few data points were excluded, and only for the following 

reasons: 

Defective receiver equipment, or suspected defective equipment coupled with highly deviant readings (as determined 

from the Westinghouse field reports and/or final report); 

Negative transmission losses greater than or equal to 

1-4 1 dB; negative transmission losses less than 1-4 I dB 

were allowed because sample calculations indicated that 

overburden depth reporting errors on the order of 10 to 

20 percent (a rare but real possibility at some mines in 

this program) could produce errors on the order of 2 to 

5 dB in the calculated transmission loss. These infrequent 

errors stemmed from the absence of accurate information 

on site depth or absolute horizontal location of the 

in-mine and surface measurement sites. 

Signal levels based on the use of the temperature 

calibration chart, not on the signal injection method. 

These chart-based levels are less reliable, because they 

are based on laboratory-prepared charts of receiver 

response versus receiver temperature in degrees Farenheit, 

which depend cn estimating the physical receiver temperature in the test environment. This comparatively 

unreliable method was used as a fallback when the signal 

substitution method was unavailable. 

48 I 

Arthur D Little, Inc. 
Very large horizontal offset tangents; i.e., greater than 

0.45 in conjunction with deep overburdens. Only two mines 

fell into this category, having not only a large tangent 

but a numerically large horizontal offset, which placed 

the antennas significantly far apart horizontally. 

A fifth category was also used in a few instances to delete some 

data; namely: 

a Signal levels judged to be less reliable than corresponding levels derived from Bureau of Mines surface tape 

recordings. These levels were subsequently replaced by 

the Bureau of Mines values. 

The initial screening, verification, and purging (deleting) 

of the data were performed in this manner. The transmission losses 

(TLU, TLD) were calculated based on the originally recorded information on loop antenna areas, dimensions, currents, and numbers 

of turns, used at the 94 mine sites, as recorded by the Westinghouse measurement team for both uplink and downlink transmission 

tests. The loop currents in the surface antennas were true 

sinusoids, and measured with an RMS meter; therefore, the derived 

antenna magnetic moments were the required RMS values for the 

fundamental frequency of the transmitter. However, the in-mine 

currents were exponential, periodic ac waveforms, not sinusoids, 

and the recorded approximate "RMS currents" were derived from the 

peak-to-peak values recorded with the portable oscilloscope on the 

basis of a sinusoidal waveform assumption. These current values 

did not represent the required true RMS values for the loop current 

component at the fundamental frequency of the in-mine transmitter. 

Therefore, we obtained a more accurate and dependable estimate of 

the in-mine RMS fundamental current and also of the uplink transmission loss, TLU, in order to allow a more accurate and reliable 

Arthur D Little, Inc 
screening and purging of data, and subsequent data analysis 

based on all magnetic field readings normalized to a unit strength 

2 of M = 1 Amp-m . This was accomplished by the method described 

in Appendix C. 

2. Tabulation of Magnetic Moments and Screened Signal Data 

The RMS values of in-mine fundamental loop current, 

computed by the method of Appendix C, were used to generate the 

required fundamental magnetic moments for the in-mine loop 

antennas tabulated in Table 1V-1. The corresponding RMS values of 

fundamental magnetic moment for the surface loop antennas are 

tabulated in Table IV-2. 

The RMS values of the fundamental in-mine magnetic moment 

(MFUND) listed in Table IV-1 were used to regenerate the key 

evaluation indices of TLU and ATL for a revised screening and 

verification chart to make the final data purge. This final assessment resulted in the purging of only one additional uplink data 

point. Table IV-3 presents a complete tabulation of the RMS 

values, at the transmitter fundamental frequency, of all the uplink 

vertical magnetic field strengths measured on the surface above 

mines, appropriately annotated to indicate the specific nature of 

missing data and to indicate which data points were selected for 

deletion, and the specific reason for each deletion. Table IV-4 

presents the corresponding results for the RMS values, at the transmitter fundamental frequency, of all the downlink vertical magnetic 

field strengths measured in the mines, appropriately annotated as 

in Table IV-3. 

Table D-1 of Appendix D presents a more comprehensive 

tabulation of the screened, but undeleted, values of surface and 

in-mine vertical magnetic field strengths, rank ordered by mine 

Arthur D Little, Inc ' 
Table IV-l 

In-Mine Collins Transmitter RMS Magnetic Moment ( MMFund) 

At Fundamental Operating Frequency 

Versus Frequency and Depth at 94 Coal Mine Sites 

RMS Moment in Amp-m 2 

Frequency (Hz) 

Mine No. State Depth (ft.) - 630 - 1050 - 1950 - 3030 

N = No test measurement performed. 

Source: Arthur D Little, Inc., Westinghouse (194), and U. S. Bureau 

i5 of Mines . 

Arthur D Little, lnc 
Table IV-l(Continued) 

Mine No. State Depth (ft.) - 630 

Frequency 

1050 1950 

(Hz 

3030 

I 

Arthur D Little, Inc 
Table IV-1 (Continued) 

Mine No. State Depth (ft. ) 

Frequency 

1050 1950 - 

(Hz) 

3030 

Arthur D Little, Inc 
-- Table IV-1 (Continued) 

Mine No. State 

wv 

TN 

UT 

KY 

wv 

TN 

UT 

VA 

UT 

wv 

KY 

CO 

AL 

Depth (ft. ) 

915 

945 

loco 

1010 

1050 

1191 

1197 

1200 

120c 

1342 

1397 

1401 

1551 

Frequency (Hz) 

1050 1950 3030 

Arthur D Little, Inc - 
Table IV-2 

Mine No. State 

Surface Transmitter RMS 

Magnetic Moment (MMDN) at 

Fundamental Operating Frequency 

versus Frequency and Depth at 

94 Coal Mine Sites 

RMS Moment in Amp-m 2 

Frequency (Hz) 

Depth (ft.) 

69 

190 

200 

210 

216 

230 

233 

239 

239 

250 

254 

256 

260 

262 

262 

262 

264 

264 

270 

279 

N = No test measurement performed. 

Source: Arthur D. Little, (L4.J (5) Inc., Westinghouse, nd U.S. Bureau of Mines. 

55 

Arthur D Little, Inc 
-- Table IV-2 (continued) 

Fre~uencv (Hz) 

Mine No. State 

IL 

AL 

IL 

PA 

KY 

wv 

KY 

wv 

PA 

PA 

PA 

wv 

wv 

AL 

KY 

wv 

KY 

KY 

KY 

wv 

wv 

VA 

wv 

PA 

wv 

IL 

AL 

OH 

PA 

KY 

Depth (ft.) 

U 

Arthur D Little, lnc 
Table IV-2 (continued) 

Mine No. 

74 

72 

41 

63 

86 

80 

39 

28 

7 

83 

84 

22 

29 

58 

1 

15 

81 

31 

73 

53 

89 

75 

6 

62 

16 

26 

27 

50 

38 

4 

61 

State 

Frequency ( Hz) 

Depth (ft.) - 630 - 1050 - 1950 - 3030 

Arthur D Little, Inc 
Table IV - 2 (continued) 

Mine No. State 

Frequency ( Hz 

Depth (ft. - 630 - 1050 1950 3030 

II 

Arthur D Little, Inc 
Table IV-3 

Surface Vertical Magnetic Field 

Signal Levels vs. Overburden Depth 

Measured by Westinghouse 

at 94 Coal Mine Sites 

Using Collins ULF Transmitter 

RMS Signal Level in dB re 1 p.A/m 

Symbols : 

N = No test measurement performed 

F = Failure to detect transmitted signal 

D = Outlier reading deleted from initial regressions 

S = Received, but value not recorded 

Frequency (Hz) 

Mine No. State Depth (ft.) - 630 1050 - 1950 - 3030 

(1,4) Source: Arthur D. Little, Inc., Westinghouse and U.S. Bureau of Mines. (5) 

Arthur D Little, Inc 
Table IV-3 (continued) 

Mine No. - State Depth (ft. ) 

289 

295 

308 

325 

325 

325 

328 

331 

34 1 

34 1 

348 

351 

354 

358 

380 

387 

400 

403 

403 

420 

423 

426 

430 

446 

449 

459 

469 

469 

479 

479 

Frequency (Hz) 

- 1050 - 1950 3030 

m 

Arthur D Little, lm 
~ableIV-3 (continued) 

Freq uencv ( Hz ) 

Mine No. State 

PA 

PA 

AL 

wv 

KY 

OH 

wv 

VA 

VA 

OH 

OH 

wv 

VA 

wv 

KY 

PA 

OH 

V A 

PA 

IL 

AL 

PA 

KY 

wv 

PA 

V A 

VA 

IL 

wv 

IL 

wv 

Depth (ft. ) 

479 

482 

485 

485 

499 

500 

508 

518 

520 

541 

561 

569 

58 1 

58 1 

600 

600 

600 

620 

626 

649 

649 

658 

674 

686 

689 

689 

689 

745 

781 

800 

846 

Arthur D Little, Inc 
TableIV-3 (continued) 

Mine No. State 

wv 

TN 

UT 

KY 

wv 

TN 

UT 

V A 

UT 

wv 

KY 

CO 

AL 

Depth (ft. ) 

Frequency (Hz) 

Defective surface receiver 

' Reading based on temperature calibration chart, not on 

signal injection method 

Very large horizontal offset between surface receiver and 

in-mine transmitter 

Transmission loss, TLUI > -4 1 dB; 

i. e. : SEMF 2 free space field + 4 dB 

Substituted field value from Bureau of Mines tape recordings 

judged to be more reliable than Westinghouse readings 

I 

Arthur D Little, lnc 
Table IV-4 

In-Mine Magnetic Field (Mainly Vertical ) 

Signal Levels (MEMF) vs. Overburden Depth 

Measured by Westinghouse 

at 94 Coal Mine Sites 

RMS Signal Level in dB re 1 pA/m 

Y- S mbols: 

N = No test measurement performed 

F = Failure to detect transmitted signal 

D = Outlier reading deleted from initial regressions 

S = Received, but value not recorded 

Frequency (Hz ) 

Mine No. State Depth (ft. ) - 630 - 1050 - 1950 - 3030 

68-00 

51.00 

N 

60.00 

64.00 

42,. 50 

70. OOD 

51.00 

60.00 

56.47 

50.90 

40.00 

54.00 

50.00 

49.00 

-16.00~' 

60.10 

35.60 

55.00 

65.00 

Source : Arthur D. Little, Inc. , westinghouse ! '&h)d U, S. Bureau of Mines. (5) 

Arthur D Little Inc 
Mine No. State 

-- Table IV-4(continued) 

Freauencv (Hz ) 

Depth (ft. ) 

289 

295 

308 

325 

325 

325 

328 

331 

34 1 

34 1 

348 

351 

354 

358 

380 

387 

400 

403 

403 

420 

423 

426 

430 

446 

449 

459 

469 

469 

479 

479 

I" 

Arthur D Little, Inc 
-- 

Table 1- 4 (continued) 

Frequency (Hz) 

Mine No. State Depth (ft.) 630 - 1050 - 1950 - 3030 

65 

Arthur D Little, Inc 
Table IV- 4 (continued) 

Mine No. State Depth (ft.) 

Frequency (Hz) 

- 630 - 1050 - 1950 - 3030 

l Defective surface receiver 

Reading based cn temperature calibration chart, not 

on signal injection method 

Very large horizontal offset between surface receiver 

and in-mine transmitter 

Transmission loss, TLU~~ -4 1d~; 

i.e. : SEMF 2 free space field +4 dB 

Substituted field value from Bureau of Mines tape 

recordings judged to be more reliable than Westinghouse 

readings 

- 

Arthur D Little, Inc 
depth, together with the key indices of uplink transmission loss 

(TLU) , downlink transmission loss (TLD) , and A TL. Also included 

are the mine number, the in-mine antenna area, the mine fundamental current (IFUND), the mine fundamental magnetic moment 

(MMFUND), the Westinghouse tabulated in-mine current (IWEST), 

and 'EST, IDEL, IDIFF, and IDIFFY which are comparative 

estimates of loop current and current differences explained in 

Appendix D. 

3 Conclusions Related to Other Variables 

The above screening, verification, and purging process 

included not only data analysis, but the detailed examination of 

mine maps and both quantitative and subjective information from 

the Westinghouse field reports and final report. As a result, we 

came to a number of other conclusions regarding the likely 

relevance of several test conditions and variables for characterizing the primary overburden transmission characteristics from 

the data set. These conclusions are listed below: 

a The presence of long electrical conductors, such as power 

lines, phone lines, pipes, rails, etc., located near the 

transmit and/or receive antennas, did not appear to 

produce consistent, recurring or systematic, deviant 

behavior in the measured signal strength, either on the 

surface or in the mine. Although there were a few mines 

in which significantly large deviations of an enhancing 

nature were observed, and likely caused by coupling to 

electrical conductors, such large deviations were the 

exception rather than the rule in the presence of conductors. As a result, the few very large deviant points 

were classified as exceptional "outliers1' and deleted from 

the data base. Most of the other deviant points were 

Arthur D Little, lnc 
retained without being given any special attention, 

because their negative transmission losses were not 

greater than I -4 I dB. 

Corrections to the field strength readings to account for 

the finite size of the transmit antenna relative to the 

overburden depth as compared to that for an infinitesimal 

magnetic dipole antenna were not warranted. The objective 

was to determine the magnetic field strength relationship 

with overburden depth for the kind and size of loop 

antennas to be used under disaster conditions, not what 

might occur if one were to use an infinitesimal ideal 

magnetic dipole. 

Corrections to the measured magnetic field strengths, 

based on homogeneous earth theoretical propagation 

models, to account for horizontal offsets from the point 

directly above or below the transmitters were not justifiable on a mine-by-mine basis. Reasons for this 

conclusion include (a) the approximate nature of the 

model itself; (b) the errors incurred in depth estimation 

as a result of horizontal positioning errors and/or lack of 

precise overburden depth information at some mines; 

(c) the absolute sizes of the horizontal offsets compared 

to the finite but similar sizes of the transmit and receive 

antennas, and to the overburden depth; and (dl the 

relatively small corrections predicted for the near overhead conditions at most mine sites. Namely, we believe 

that these factors, taken together, are likely to lead to 

corrections that are not meaningful. As in the case with 

nearby conductors, there were a few mines with extremely 

large offsets, and the data from these were deleted as 

non-representative on the initial data screening. 

Arthur D Little, Inc - 
Therefore, all magnetic field strength data retained in the 

data base for subsequent statistical analysis should be considered 

representative of behavior observed at or near "ground zero," for 

all practical purposes; namely, directly above or below (i . e. , 

coaxial with) the appropriate transmitters. This also implies, of 

course, that the data and results should also apply to configurations having horizontal offsets of up to several hundred feet, 

particularly at deep mines. This is not surprising, because the 

vertical component of magnetic field exhibits the slowly varying 

cosine-type dependence with horizontal offset in the vicinity of the 

transmit loop vertical axis. For large offsets, on the order of the 

overburden depth, the horizontal magnetic field component should 

start to predominate at about a level more than 10 dB below the 

peak vertical field strength directly above the transmitter. In 

addition, the results should apply even in the presence of 

electrical conductors; except, for example, in rare pathological 

cases where the conductor provides a direct alternative signal path 

(up a borehole, for example) to the surface receiver. Although it 

was judged unnecessary and impractical for the purposes of this 

study to devote additional effort to the extraction of perhaps 

marginal relationships on the influence of nearby conductors and 

horizontal offsets from the data base, some scientific benefits may 

be obtainable from more detailed analyses of the data base by 

others in the future. 

C. THE FINAL UPLINK SIGNAL DATA BASE 

The final "expanded" surface signal data base used for the 

final statistical analyses is presented in Table 1V-5. This data 

base was created by replacing, where possible, both missing and 

deleted data with appropriately adjusted downlink in-mine field 

strength values, or by readmitting data points previously deleted 

Arthur D Little, Inc 
Final Screened Surface Signal Data with 

Substitutions and Replacements -- 

Vertical Magnetic Field Levels vs. Overburden Depth 

from 94 Coal Mine Sites 

RMS Signal Level (SEMF) in dB re 1 pA/m 

Symbols : 

N = No test measurement performed 

F = Failure to detect transmitted signal 

a = Substituted in-mine value adjusted for difference between 

in-mine and surface transmit moments; 

SEMFA = MEMF - 20 log (MMDN/MMFUND) 

b = Readmitted surface value originally deleted during first purge 

Frea uencv ( Hz ) 

Mine No. State 

KY 

KY 

KY 

PA 

wv 

wv 

wv 

PA 

PA 

wv 

OH 

wv 

KY 

AL 

KY 

Depth (ft.) 

69 

190 

200 

210 

216 

230 

233 

239 

239 

250 

254 

256 

260 

262 

262 

(1,4) (5 Source: Arthur D. Little, Inc., Westinghouse, and U.S. Bureau of Mines. 

70 

Arthur D Little, lm I* 
 able IV-5 (continued) 

Mine No. State 

I L 

AL 

IL 

PA 

KY 

wv 

KY 

wv 

PA 

PA 

PA 

wv 

wv 

AL 

KY 

wv 

KY 

KY 

KY 

wv 

wv 

VA 

wv 

PA 

wv 

IL 

AL 

OH 

PA 

KY 

Frequency (Hz) 

Depth (ft.) - 630 - 1050 - 1950 

Arthur D Little, Inc 
TableIV-5 (continued) 

Frequency (Hz) 

Mine No. State 

PA 

PA 

AL 

wv 

KY 

OH 

wv 

VA 

V A 

OH 

OH 

wv 

VA 

wv 

KY 

PA 

OH 

V A 

PA 

IL 

AL 

PA 

KY 

wv 

PA 

V A 

V A 

IL 

wv 

IL 

wv 

Depth (ft. ) - 630 - 1050 - 1950 

Arthur D Little, Inc - 
~ableI~-5 (continued) 

Freauencv ( Hz ) 

Mine No. - State Depth (ft.) 

Arthur D Little, Jnc 
in the initial screening and purging process which resulted in 

Table IV-3. These substituted or readmitted values are indicated 

by the letter symbols a and b, respectively, beside each such 

data point represented in Table IV-5. 

As indicated in Table IV-5, the substituted in-mine value 

has been adjusted in magnitude to reflect the value that would 

have been measured had the downlink transmitter been equal in 

strength to the uplink transmitter. The readmitted values designated by b were of three types. The most prevalent type was calibration chart readings for which corresponding in-mine measured 

values were missing and not available for substitution. In one 

case, the downlink value was a calibration chart reading judged 

less appropriate than the surface one. We concluded that a less 

precise calibration chart reading was better than no reading at 

all, 

The second category of readmitted data was a single mine, 

No, 45, having a very large offset, but a reasonable transmission 

loss, so it was readmitted. Finally, a single data point from one 

mine having a borderline deleted transmission loss of -4.45 dB was 

readmitted, since this borderline value was more consistent with 

the other surface readings than the available downlink reading. 

The data base of Table IV-5 is the one used in Section V, in 

conjunction with the in-mine magnetic moment data base of 

Table IV-1, to generate final normalized surface field strength 

values for each mine site for a reference transmitter having a 

2 magnetic moment of M = 1 Amp-m . Linear regression analyses were 

applied to these values to determine the expected transmission 

response characteristics of overburdens above mines in the U,S, 

coal fields, 

Table D-2 of Appendix D presents a complete printout of the 

signal data bases of Tables IV-4 and 1V-5 for both uplink and 

Arthur DLittle,lnc - 
downlink magnetic field strengths on the surface and in the mine, 

rank ordered by depth, together with the following key variables: 

a the in-mine fundamental magnetic moment, 

a the in-mine fundamental current, 

a the downlink surface transmitter magnetic moment, 

the in-mine magnetic moment as computed from the 

originally tabulated Westinghouse data, 

a the three key indices, transmission loss up (TLU), 

transmission loss down (TLD) and A TL, 

a the mine number, and 

two current comparison indices, IDI FF and ID IFF^' 

Table D-3 presents a summary table of statistics for selected 

variables vs. frequency, averaged over all depth intervals. 

Table D-4 presents a tabulation of statistics for another set of key 

variables averaged within each of the eight depth intervals for 

each frequency. These more comprehensive tabulations of computer 

output of our cross-tabulations and other descriptive statistics 

have been included in Appendix D for convenient reference. 

D. SURFACE NOISE DATA BASE 

1. Verification and Assessment Process 

As the measurement program progressed and noise data from 

a number of field measurements became available, a number of 

questions emerged regarding the quality and reliability of the 

surface noise data taken by the Westinghouse field measurement 

team. During the second half of the measurement program, a 

Bureau of Mines PMSRC team accompanied the Westinghouse team 

and made independent noise measurements at 27 mine sites using 

an entirely different method of data gathering. As previously 

described, the Westinghouse team used the Collins receiver with its 

Arthur D Little, Inc 
loop antenna and the signal substitution method to record vertical 

magnetic field noise levels on the surface at each frequency. The 

Bureau PSMRC team used the same kind of loop antenna together 

with a wideband instrumentation-grade tape recorder to record raw 

vertical magnetic field strengths on the surface that were later 

processed and analyzed in the laboratory at PMSRC. 

The data from the two measurement techniques were compared, 

and substantial differences were discovered between them. At 

several mines, the measurement team readings were significantly 

below the intrinsic self noise limits of the Collins receiver, 

indicating some conventional data acquisition errors. Even more 

serious, however, were the more systematic and substantial 

differences noticed at the two higher frequencies of 1950 and 

3030 Hz. At these frequencies, the measurement team data were 

10 to 20 dB higher than the Bureau data, while the data for the 

two lower frequencies, at least on average, were in good agreement. Furthermore, the frequency behavior of the Bureau cf Mines 

data was more compatible with that of atmospheric noise data 

reported in the literature by other investigators. 

To investigate these differences, corresponding noise levels 

for the 27 common mine sites were verified, and the values from 

both sources were tabulated in Tables IV-6 and IV-7. Then the 

common data pairs were plotted for each frequency, as indicated in 

Figures IV-1 through 1V-4. Ideally, all data points should cluster 

about the °ree line shown on each graph. Although the 

Westinghouse individual meter readings should be expected to 

exhibit greater variability than the Bureau's readings derived 

from fast Fourier transform (FFT) analysis of tape recorded noise 

segments because of the FFT RMS "averaging" process, the two data 

sets should agree on the average. Furthermore, we would also 

expect an equal number of Westinghouse values greater than, as 

well as less than, corresponding Bureau values, since each 

Arthur D Little, lnc C 
Mine No. 

93 

9 1 

71 

85 

92 

55 

88 

Surface Vertical Magnetic Field Noise Levels 

Measured by Westinghouse 

with Collins Rescue Receiver 

at 27 Coal Mines 

"Average" Noise Levels in dB re 1 pA/rn/v30 Hz 

for the 30 Hz Bandwidth Collins Receiver 

State 

KY 

KY 

PA 

KY 

KY 

IL 

KY 

Depth (ft. ) 

69 

190 

239 

Frequency (Hz) 

- 630 1050 - 1950 3030 

+ 4 - 3 -17 - 9 

+ 0 -20 D D 

+35 +36 +18 +2O 

-11 -11 -20 D 

-10 -10 -15 -10 

+30 +30 +30 +32 

-20 -19 -30 D 

D = Deleted, erroneous reading below intrinsic receiver noise. 

N = No test measurement performed. 

(3) Source: Arthur D. Little, Inc. , westinghouse(,' *Ad U. S. Bureau of Mines. 

77 

Arthur D Little, Inc 
Table 

Equivalent RMS Noise Levels in dB re 1 pA/m/v30 Hz 

for a 30 Hz Bandwidth Surface Receiver 

Surface Vertical Magnetic Field Noise Levels 

Derived from Bureau of Mines Tape Recordings 

at 27 Coal Mines 

Mine No. 

Source : 

State 

KY 

KY 

PA 

KY 

KY 

IL 

KY 

KY 

wv 

wv 

IL 

OH 

PA 

PA 

KY 

OH 

OH 

OH 

OH 

PA 

IL 

AL 

PA 

wv 

UT 

UT 

AL 

Depth (ft. ) 

Frequency (Hz) 

- 1050 1950 - - 3030 

Arthur D. Little, Inc., and U. S. Bureau of Mines. (3) 

- 

Arthur D Little, Inc 
BOM NOISE LEVELS (dB) 

FIGURE IV-1 COMPARISON OF WESTINGHOUSE 

AND BUREAU OF MINES MEASURED 

NOISE LEVELS (dBre la~lrnl~ 

FOR 27 MINES AT 630 Hz 

BOM NOISE LEVELS (dB) 

FIGURE IV-2 COMPARISON OF WESTINGHOUSE 

AND BUREAU OF MINES MEASURED 

NOISE LEVELS (dB@ lp~/rnV~ 

FOR 27 MINES ~f 1050 Hz 
FIGURE IV-3 
observation taken at each mine site can be considered as a random 

variable selected from the same underlying distribution of noise 

values. Thus, even under extreme variability conditions, points 

should exhibit a random departure above and below the line. 

Inspection of Figures 1V-1 to IV-4 suggests that the two lower 

frequency plots generally exhibit this property and are in 

reasonable agreement. However, the noise values at 1950 Hz and 

3030 Hz clearly do not. The Westinghouse readings are consistently 

higher than the corresponding Bureau ones, which is indicative of 

some form of bias in one of the data sets. 

Similar plots of pairs of signal and noise readings taken 

with the Collins receiver at each mine site were constructed to 

determine the presence of any correlations between the measured 

signal and noise data. No statistically significant correlations 

were found between signal and noise data. 

2. The Final Surface Noise Data Base 

The procedures and equipment used to obtain noise data for 

both Westinghouse and Bureau of Mines measurement techniques 

were carefully reviewed to discover the sources of error and to 

assess the quality of the data. This review included detailed 

diagnostic measurements on the equipment in question. As a result 

of this review, it was decided to use only the Bureau of Mines 

noise data from 27 mine sites tabulated in Table IV-7 to represent 

the noise conditions above mines for the purpose of estimating 

probabilities of trapped-miner signal detection. These noise levels 

are the ambient background, believed to be broadband levels of 

atmospheric, not man-made, origin that are present between the 

high amplitude discrete harmonics of the ac power line frequency 

of 60 Hz. The principal reasons for the decision to use the Bureau 

of Mines data were: 

Arthur D Little, Inc 
The Westinghouse measurement team used a modified 

version of the Collins surface receiver in which the frontend bandpass filter had been removed. This filter 

provided protection from interference by inputs below the 

receiver operating band. Without this filter, the receiver 

is susceptible to intermodulation between the frequently 

occurring large 60 Hz component of ac power line interference fields and the other interference components and 

noise being measured. As a result, this intermodulation 

caused the addition of significant interference power at 

the 1950 and 3030 Hz frequencies being measured. 

Noise readings below the Collins receiver intrinsic noise 

levelL3)of -21, -26, -31, -35 dB/1 Ct~/rn/vz at 630, 

1050, 1950, and 3030 Hz, respectively, were reported by 

the measurement team at 19 mine sites. 

The frequency behavior of the Bureau data was consistent 

with the behavior of atmospheric noise data reported in 

the literature. (6,7,8) 

The Bureau data and Westinghouse data are in good agreement on the average at 630 and 1050 Hz for the 27 common 

mine sites. Furthermore, as shown in Section VII, the noise 

distribution plot at 630 Hz on normal probability paper 

comparing the Bureau noise values at 27 mines with the 

Westinghouse values measured at all 94 mine sites reveals 

excellent agreement between the two sets of data. 

The 27 Bureau mine sites were well distributed geographically among the 94 mine sites sampled throughout the 

U.S. coal fields for this measurement program. 

Arthur D Little, Inc 
3. Relationship to Reported Atmospheric Noise Data 

It must also be noted, however, that the Bureau noise 

measurements were taken during the daylight morning hours 

(generally the time of day having low atmospheric noise activity) 

and during the months of May to September (the months having 

high atmospheric noise activity), and that atmospheric noise levels 

generally exhibit pronounced diurnal and seasonal variations. A 

comprehensive study and analysis of magnetic field noise above 

mines was not the objective of this contract. However, the question 

of the potential effect of this noise variability on the adequacy of 

the Bureau of Mines noise sample for making detectability estimates 

was briefly addressed. 

Unlike the frequency band between 10 kHz and 32 MHz, only 

relatively few reported atmospheric noise measurements have been 

made below 10 kHz. In addition, even these meager noise data 

generally concern themselves with the vertical electric field 

strength and the horizontal magnetic field strength, and not with 

the 12 to 20 dB lower values of vertical magnetic field strength of 

greatest interest to trapped-miner detection. The general concern of 

the literature with the vertical electric and horizontal magnetic 

noise fields arises because of its applicability to surface-based, 

long-range radio communications. The behavior of the horizontal 

magnetic field noise is also important to the final localization of 

trapped miners which utilizes the null behavior of the horizontal 

signal magnetic field directly above the miner's transmit loop. 

Our brief examination of the literature (6,7,8,9) on atmospheric noise reveals the following behavior characteristics for the 

vertical electric field and horizontal magnetic field ~oise components normally measured: 

Arthur D Little, Inc 
a Between approximately 500 and 5,000 Hz, the earth ionosphere waveguide exhibits a maximum in attenuation rate 

which significantly attenuates atmospheric noise contributions from distant thunderstorm activity. This 

attenuation rate behavior produces a pronounced minimum, 

or trough, in atmospheric noise levels between 1 and 

3 kHz; 

a For a particular geographical location, the highest noise 

levels usually occur during the nighttime hours of 

8:00 pm and 4:00 am and in the local summer months, and 

the lowest levels usually occur during the morning hours 

of 8:00 am to 12:OO noon and in the local winter months; 

Regions having very little thunderstorm activity produce 

very small changes, on the order of 2 dB, in RMS noise 

levels on the average between the quiet morning periods 

and the noisy nighttime periods. Areas with high thunderstorm activity, on the other hand, may experience changes 

in noise level from 10 to 20 and sometimes as high as 

30 dB between the daily quiet and noisy time periods. 

a Regions with relatively low thunderstorm activity tend to 

display drops in noise level versus increasing frequency 

on the order of 20 dB from 600 Hz to 3,000 Hz (at the 

bottom of the noise trough), whereas areas with higher 

thunderstorm activity exhibit decreases on the order of 

10 to 12 dB from 600 Hz to 2 kHz (at the bottom of the 

noise trough). 

a Locations which experience significant diurnal changes in 

thunderstorm activity will generally exhibit larger 

increases in noise level in the 500 to 5,000 Hz band than 

experienced above and below this band, as a result of 

the high attenuation characteristics in this band. 

84 

Arthur D Little, 111~. - 
We then compared the above atmospheric noise characteristics 

with those of the statistical noise distributions based on the 

Bureau of Mines noise data (&?hat are derived and presented in 

Section VII of this report. If we further make the plausible assumption that the vertical magnetic field levels are at least proportional to the horizontal noise components, and exhibit roughly the 

same frequency, diurnal, and seasonal variations, we can make 

the following comparative observations: 

The average RMS value of the Bureau of Mines noise 

decreases by 20 dB from 630 Hz to 3030 Hz, similar to the 

behavior reported for atmospheric noise in areas of low 

thunderstorm activity ; 

The Bureau of Mines levels are not inconsistent with those 

reported when adjusted for bandwidth and field component; 

The U.S. coal fields lie within the temperate zone, and 

could probably be classified as moderate to low-moderate 

regions of thunderstorm activity. 

In addition, the normal distribution of the RMS values of the 

Bureau of Mines data taken at 630 Hz over the months from May to 

September are in excellent agreement with the normal distribution 

of the Westinghouse data taken over the months from February 

through November. These data were also typically taken during the 

same time period of 8:00 am to 12:OO noon, and over the same widespread geographical coal field areas as the Bureau of Mines data. 

Consequently, the noise distributions derived in Section VII 

of this report, based on the Bureau of Mines noise data, can 

probably be considered representative of noise conditions expected 

Arthur D Little, Inc 
over coal mines during daytime mine rescue search operations. In 

winter, levels may be about 10 dB lower, whereas in summer, 

during late afternoon or evening, high local thunderstorm activity, 

the levels may increase by perhaps 10 or even 20 dB in the 

vicinity of the 2,000 to 3,000 Hz noise trough. However, search 

operations are likely to be conducted during daylight hours, and 

for all practical purposes suspended during periods of abnormally 

high noise activity. Therefore, the Bureau of Mines noise data 

have been used in subsequent chapters as the basis for predicting 

the expected probabilities of detection of trapped-miner signals 

above U.S. coal mines. As a further check on the general applicability of this conclusion, a more thorough comparison of the 

Bureau of Mines noise behavior with additional reported atmospheric noise behavior may be warranted. 

I 

Arthur D Little, Inc. 
V. CHARACTERIZATION OF OVERBURDEN TRANSMISSION MODEL 

A . RATIONALE 

The objective is to characterize the overburdens above mines 

in the U.S. coal fields with respect to their response to trapped 

miner electromagnetic signals as a function of overburden depth 

and operating frequency. The overburdens above coal mines are 

sedimentary in nature. They consist of a large number of nearly 

horizontal layers of different materials and thicknesses, which in 

turn have differing electrical conducting properties as a result of 

variations in salts, water content, porosity, and a number of other 

factors. Therefore, for any given overburden depth, we can expect 

the signal transmission characteristics to vary significantly from 

location to location within the coal fields. Consequently, we 

adopted a statistical approach of sampling a representative number 

of mines within each of the depth intervals of interest in order to 

characterize the average transmission characteristics of overburdens, and their corresponding variability about the average, as 

a function of depth and operating frequency. 

To accomplish this characterization, we found it helpful to 

think of the overburden above U.S. coal mines as a two-terminal 

pair electrical network having an unknown and randomly varying 

transfer function from mine to mine which must be determined 

experimentally. In particular, we wish to characterize the 

transfer function between the output surface magnetic field 

strength, HZ (corresponding to open circuit output voltage), and 

the input magnetic moment (corresponding to the input current) 

for the overburden network portrayed in Figure V-1. In circuit 

theory terms, we wish to define the output response to a unit 

input stimulus, which in this case is a magnetic moment 

2 M = 1 Amp-m . Once this is known, the output response can be 

Arthur D Little, Inc 
FIGURE V-1 TWO TERMINAL PAIR NETWORK ANALOGY FOR 

CHARACTERIZATION OF OVERBURDEN SIGNAL 

TRANSMISSION RESPONSE 

M, 

I 

Arthur D Little, Inc 

NETWORK OF COAL 

MINE OVERBURDENS a + 
predicted for any input magnetic moment stimulus within the 

limits of operating frequency and loop geometry characterized. 

To derive the transmission response function of coal field 

overburdens, it is necessary to normalize all the valid uplink 

field strength readings obtained on the surface at mine sites to 

the readings that would have been measured (in a noiseless 

environment) for a transmitter having a unity magnetic moment, 

2 M = 1 Amp-m . The magnetic moment of interest here is the RMS 

value of the magnetic moment at the fundamental operating 

frequency of the transmitter; namely, that portion of the transmitted signal which is capable of being detected by the narrowband rescue receiver on the surface. Therefore, each measured 

value of magnetic field on the surface listed in Table IV- 5 was 

reduced by its corresponding value of transmitter fundamental 

2 magnetic moment, expressed in dB re 1 Ampm , prior to being 

subjected to the statistical analyses described in this section. 

The field values in Table IV- 5 also include adjusted field 

strengths derived from downlink transmission data in those cases 

where we judged it necessary and justifiable to replace an 

unreliable or unavailable uplink reading with one based on an 

acceptable downlink measurement. All analyses have been 

performed on the surface magnetic field strength signal data 

expressed in dB relative to 1 Amp/m normalized to a transmit 

2 magnetic moment of 1 Ampm . 

B. REGRESSION ANALYSIS OF SURFACE SIGNAL DATA 

As described above, uplink and downlink signal strength 

data were normalized prior to statistical analysis. In this section, 

the regression analytical methods considered are described in some 

detail, and the results and conclusions pertaining to the expected 

behavior of surface signal strength as a function of overburden 

depth and frequency are presented. 

Arthur D Little, Inc 
1. Surface Signal Strength vs. Log Depth Model for the 

Final (Expanded) Data Base 

a. Methodology 

In formulating the problem for this stage of the analysis, 

signal strength is assumed to be related to depth in an unknown 

mathematical/statistical/physical form. Up to 94 data points were 

obtained as a result of field tests conducted at each of four 

frequency levels. Each data point can generally 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 at 

which tests were performed. Thus, each surface measurement Sij 

taken in this program can be considered as a single observation of 

signal strength at a pre-determined frequency and overburden 

depth level at a particular mine. Specific values Sij can be 

expected to vary in some unknown way; that is, the readings can 

be expected to differ if more than one measurement was taken at 

different times at the same mine location, or at the same depth at 

some other location within the mine, or at the same depth at a 

different mine. 

The use of statistical regression theory requires an assumption that the observed values of Sij represent a random sample 

from a normal distribution with mean dependent upon j (depth) and 

variance the same over all depths (that is, independent of j). 

Furthermore, if the relationship of the mean value of Sij to depth 

can be expressed in linear terms, probability statements can be 

inferred from the derived regression model. The statistically-based, 

random mine selection process described in Section 111 was used to 

increase the reasonableness of the required assumption that all 

oberservations S can be described by a common normal proba- i j 

bility law. Although necessity and practicality dictated some 

deviation from the originally selected list of mines, we believe 

that the final mine sample provides a good enough approximation 

to the assumption to warrant the valid use of regression theory. 

Arthur D Little,Inc. - 
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 Sij is 

linearly related to the logarithm of overburden depth, as shown in 

Equation ( 4 1. 

'ij = i 

+ pi log DEPTH. + cij, I 

where : 

Sij is the normalized vertical magnetic field signal strength 

th (expressed in dB re 1 pA/m) for the i- frequency level and 

2. depth j, for a transmit moment of M = 1 Amp-m , 

and Pi are parameters to be estimated from the data; 

depth is known and measured in meters; and 

c represents a random variable that is normally i j 2 distributed with expected value zero and variance oij , which is the same for all values of j. 

Equation (4 ) corresponds to a power law relationship, H = c 

(~e~th)" for the surface magnetic field expressed in rationalized 

MKS units of Amp/m. Regression analysis of the S data was i j 

subsequently performed in crder to address the following four basic 

concerns : 

Does the postulated linear relationship explain the data? 

If so, what are the best estimates of the parameters ai 

and pi? 

Arthur D Little, Inc 
a Does the inverse cubic relationship suggested by simple dc 

magnetostatic theory apply; that is, does Pi - 

-60 (n = -3) for each frequency? 

a Can regression results be used to make reliable predictions 

about the behavior of signal strength? 

Four separate regression lines were subsequently derived 

using the log DEPTH model, one for each frequency. To make 

maximum use of the available field test data, and to provide 

additional data points at depths exceeding 700 feet, where several 

uplink readings were missing, the "expanded" version of the 

original uplink signal data base described in Section IV-C was 

used. This "expanded" data base includes the replacement of 

missing and/or unreliable surface readings with appropriately 

adjusted downlink in-mine values taken at the same site as 

described in Section IV-C. A statistical regression routine (the GLM 

procedure) published by SAS Institute, Inc., (lo) was used for this 

analysis. This routine performs a standard least-squares fit to the 

A A data, determining the parameters oi and pi that uniquely minimize 

the following expression (for each i): 

2 A A = (Sij - a - pi log DEPTH.) 

2 

i 

j J 

Summary statistics useful for interpreting regression results are 

also provided by the routine. 

b. Results 

The derived regression lines for each of the four frequencies 

are plotted in FiguresV-2throughV-5 , which are also seen to include 

the actual observations (normalized) taken at each mine test site. 

Although it is readily apparent from inspecting the plots that a 

log-linear relationship is an appropriate one, a more formal and 
LOG(DEPTH IN METERS) 

20 

10 

0 

-10 

-20 

-30 

-40 

-!a 

-60 

-70. 

FIGURE V-2 UPLINK NORMALIZED OVERBURDEN SIGNAL RESPONSE DATA AND 

LINEAR REGRESSION LOG(DEPTH) MODEL AT 630 Hz 

1111 l~l~l~l~ I I I~IIII~ Illljllr 

- SURFACE VERTICAL MAGNETIC FIELD, Hz, VERSUS LOG (DEPTH) FOR - 

- o A,TRANSMIT MOMENT M=1 ~rn~-rn~ - 

- - 

- - 

- REGRESSION LlNE AMOUNT OF 

, VARIABILITY NOT - 20 LOG S, = 99.83 - 6 1.97 LOG D 

- R2 = 83% - 

- - 

AMOUNT OF 

- VARlABl LlTY - 

- "EXPLAINED" - 

BY THE LlNE 

- - 

MEAN OF OBSERVED VALUES - -- - - - - 

- - 

- o - OBSERVED DATA VALUES o - 

- - 

- 

DATA SOURCE: WESTINGHOUSE 

- DEPTH(FEET) 

- 

I 

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 
NORMALIZED SURFACE FIELD STRENGTH 

Hz, dBrelpA/m 
30aj~~~~~~,1 1111111 11 111 11 1111(1 

- 

- 

SURFACE VERTICAL MAGNETIC FIELD, Hz, VERSUS LOG (DEPTH) FOR - 

A TRANSMIT MOMENT M=l Amp-m2 10 - - 

- 

0 - - C 

- 

-10 - - 

- - 

- 

- - 

-40 - - o - OBSERVED DATA VALUES 

- - 

-50 - 

- 

-60 - 

L DEPTH(FEET) 

-70 - 200 300 400 500 

- 

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 

LOG(DEPTH IN METERS) 

FIGURE V-4 UPLINK NORMALIZED OVERBURDEN SIGNAL RESPONSE DATA AND 

LINEAR REGRESSION LOG(DEPTH) MODEL AT 1950 Hz 
LOG(DEPTH IN METERS) 

FIGURE V-5 UPLINK NORMALIZED OVERBURDEN SIGNAL RESPONSE DATA AND 

LINEAR REGRESSION LOG(DEPTH) MODEL AT 3030 Hz 
objective procedure is required to answer the four basic questions 

outlined earlier in this section. The methods for doing this will be 

described in some detail for the regression analysis of the 630 Hz 

data, the first one presented. 

As is usually the case in the statistical treatment of data, 

the question of the existence of linearity can be stated in the form 

of a hypothesis to be tested; namely, do the data provide evidence 

of a "real" linear relationship of normalized signal strength to log 

depth? Expressed another way, it is clear that normalized signal 

strengths vary considerably, ranging from -70.8 dB re 1 pA/m to 

+11.3 dB re 1 pA/m over the 90 measurements taken at 630 Hz. Can 

some of this variability be explained or accounted for by a linear 

model, and, if so, to what extent? 

A summary statistic used to quantify this statement is the 

2 coefficient of determination (R ), which is defined as follows: 

where SEST is the linear (regression) estimate, SOBS is the 

observed signal value, and 7 is the average signal taken over all 

observations. The quantities are summed over all j observations, 

with 90 such terms used in the calculation for 630 Hz data. A 

graphical depiction of the elements of this expression is given in 

2 Figure V-2. For the case of 630 Hz, R equals 83 percent. It 

should also be noted that the standard linear correlation 

coefficient, R = ,/T, equals 0.91 for 630 Hz data, indicating a 

very high degree of linearity. The actual statistical test for 

linearity is somewhat involved, in that it requires knowledge of 

distribution theory, and therefore will not be presented here. 

Detailed explanations are given in most statistical methods texts, 

such as Reference 11. Suffice it to say that the test statistics are 

such that the hypothesis of no true linear relationship between 

Arthur D Little, Inc 
normalized signal strength and log depth can be rejected with less 

than a one percent chance of being wrong for each of the four 

regression lines presented in this section. Therefore, it has been 

established that the postulated linear relationship does indeed 

explain the data, and the estimating equation is as follows: 

SEST = 99.83 - 61.97 log DEPTH at 630 Hz. 

The third question concerns the applicability of the inverse 

cubic relationship over the range of data obtained in this measurement program. Again, this can be expressed as a hypothesis to be 

tested; that is, with the above formulation, does the slope of the 

regression line appear to be -60 (i.e. for n = -31, since S = i j 

20 log H in dB. Again, the necessary input to perform this test is 

provided by the regression routine. For the 630 Hz case, the test 

statistic is not significant, and we therefore conclude that the 

inverse cubic law is an appropriate one for these data. Another . 

way to arrive at the same conclusion is to construct an interval 

estimate of the slope, rather than a point estimate. For the 630 Hz 

case, we are 95 percent certain that the true (unknown) slope is 

included in the interval (-2.8 to -3.41, which is seen to 

include -3.0, the hypothesized value. 

The interval estimate depends on another important summary 

A statistic, the standard error of estimate a , which is defined as 

follows : 

where N is the number of observations. The standard error is used 

in determining the reliability, or predictive capability, of the 

estimating equation and, as a result, addresses the final question 

of concern stated earlier. The smaller the standard error, the more 

reliable the predictions based on the equation are likely to be. 

- 

Arthur D Little, lnc 
Regression results are summarized for all four frequencies in 

Table V-1 , in addition to the earlier plots in Figures V-2 to V-5, 

Inspection of Table V-1 reveals the following: 

2 

(i) The linear relationship applies in each case; R values 

are high at each frequency, implying that the model 

adequately explains the data. 

(ii) The best estimates derived from the data reveal that 

the intercepts increase and slopes become more 

pronounced as frequency increases; however, there 

appears to be very little difference between 1050 Hz 

and 1950 Hz results, 

(iii) The inverse cubic relationship applies only at the 

lowest frequency considered ; estimated slopes differ 

significantly from -60 at each of the other frequencies. 

(iv) Reasonably reliable predictions can be made from all 

regression models; standard errors are between 

6 and 9 dB; for example, the theoretical average 

normalized signal strength expected from many tests at 

approximately 139 meters (450 feet) is estimated to be 

-33 - + 1.4 dB at 630 Hz, where the +1.4 dB is calculated - 

from the formula to estimate confidence limits; i.e,, 

+t a /@, where t is a statistical value based on - 

sampling distribution theory. 

It is evident that if this test program were replicated, and 

another sample of 94 different mine sites were selected, the 

analytical results would not be identical. However, the strength cf 

each relationship derived in this study is such that we would 

expect linearity between signal strength and log depth, even 

though the estimated slope and intercept would change. The 

Arthur D Little, Inc 
Table V-1 

Regression Results 

For Surface Signal in dB versus Log Depth Model 

Using Expanded Uplink Data Base 

I 33% 

1 I confidence Correlation Standard 

FrequencyNo. of Estimated Estimated interval for coefficient error 

(Hz) i obs. intercept slope = slope/20 (R) R~ (c ) I 

Source: Arthur D. Little, Tnc. 

C 

Arthur D Little, Inc 
magnitude of the change is expressed in terms of interval estimates 

that are based on the sample data at hand. 

Two types of intervals have been estimated from the data. 

The smallest is referred to as a confidence interval, which is 

defined as a range of values computed from the sample that can be 

expected to include the true (but unknown) mean value with a 

known probability. Figures V-6 to V-9 display 95% confidence 

intervals with dashed lines. To illustrate this concept using 

Figure V-6, it follows from this field experiment that the probability is 0.95 that the interval from -6 dB to -12 dB includes the 

true mean normalized signal strength for a transmitter of magnetic 

2 moment M = 1 Amp-m at 630 Hz and an overburden depth of 

190 feet. 

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 we reasonably expect if we 

were to conduct one more test at a predetermined frequency and 

overburden depth? This situation is depicted by prediction intervals also plotted in Figures V-6 to V-9. To illustrate this concept, 

again using FigureV-6, the probability is 0.95 that another test 

performed at 630 Hz at a depth of 500 feet would yield a signal 

strength between -49 dB and -22 dB. 

Also plotted in Figures V-6 to V-9 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 material. For 

the depths and frequencies in question, this free space field does 

not vary with frequency. This field strength is computed from the 

simple equation: 

Arthur D Little, Inc 
-100 

1 00 1 50 200 250 300 500 700 1000 1500 

OVERBURDEN DEPTH(FEET) 

I I i I I I I I I I I I(1III 

NORMALIZED TO TRANSMIT MOMENT OF M=l Amp-m2 - 

95% PREDICTION INTERVAL - 

- REGRESSION LINE 

- 

FREE SPACE CURVE 

- - 

- - 

- 95% PREDICTION 

INTERVAL 

- 

- 

95% CONFIDENCE INTERVAL f 

- 

- - 

- - 

I I 1 I I Ill I i I I I Ill, 

FIGURE V-6 UPLINK REGRESSION RESULTS FOR 630 HZ-NORMALIZED 

VERTICAL SIGNAL STRENGTH, Hz, VERSUS DEPTH 

Arthur D Little, Inc" 
I I I I I Ill I I I I]IIII 

NORMALIZED TO TRANSMIT MOMENT OF M=l ~mp-rn2 - 

95% PREDICTION INTERVAL 

- 

REGRESSION LINE 

- 

FREE SPACE CURVE 

- 

- - 

95% PREDICTION 

- INTERVAL - 

- 

95% CONFIDENCE INTERVAL - 

- 

- 

- - 

I I I 1 I 111 I I I I I I Ill. 

OVERBURDEN DEPTH(FEET) 

FIGURE V-7 UPLINK REGRESSION RESULTS FOR 1050 HZ-NORMALIZED 

VERTICAL SIGNAL STRENGTH, Hz, VERSUS DEPTH 

Arthur D Little, Inc 
I I I I I 111 I I I I I I Ill* 

NORMALIZED TO TRANSMIT MOMENT OF M=l Amp-m2 - 

95% PREDICTION INTERVAL 

- 

- 

REGRESSION LINE 

- 

- 

- - 

- 95% PREDICTION INTERVA 

- 

- 

- 

95%CONFlDENCElNTERVAL -J 

- 

- 

- - 

I I I I I Ill I I I I 11111 

OVERBURDEN DEPTH(FEET) 

FIGURE V-8 UPLINK REGRESSION RESULTS FOR 1950 HZ-NORMALIZED 

VERTICAL SIGNAL STRENGTH, Hz, VERSUS DEPTH 

Arthur D Little, Inc" 
I I I I I Ill 1 I I I / 1111 

NORMALIZED TO TRANSMIT MOMENT OF M=l ~rn~-rn~ - 

- 

95% PREDICTION INTERVAL 

9 

REGRESSION LINE 

- 

- FREE SPACE CU'RVE 

- - 

- - 

- - 

95% PREDICTION 

INTERVAL - 

- 

95% CONFIDENCE INTERVAL 

- 

7 

- 

I I I I I Ill I I I I IIIII, -100 

100 150 200 250 300 500 700 1 000 1500 

OVERBURDEN DEPTH(FEET) 

FIGURE V-9 UPLINK REGRESSION RESULTS FOR 3030 HZ-NORMALIZED 

VERTICAL SIGNAL STRENGTH, Hz, VERSUS DEPTH 

Arthur D Little, Im; 
where M is the transmitter magnetic moment set equal to 1 Amp-m 2 

and D is the depth in meters. 

Examination of Figures V-6 to V-9 reveals that the 95% 

prediction interval extends above the free space field values. This 

is not surprising, for there are several ways in which the 

normalized data can, under certain circumstances, exceed the free 

space values as discussed in Section IV. The ways include: 

a) depth estimation errors which can cause a data point to be 

plotted at a depth greater than the actual depth, b) the enhancing 

effects of nearby metal conductors creating more favorable transmission paths to the surface receiver, c) meter reading errors 

during data recording in the field, and d) errors introduced in 

the normalizing process caused by uncertainties in the accuracy of 

the values of the fundamental component of the in-mine transmit 

magnetic moments (MMFUND). In most cases, these discrepancies 

were less than 4 to 5 dB greater than the free space field and the 

data values were retained, as discussed in Section IV. The few 

data values that deviated grossly above the free space values were 

almost always associated with equipment malfunctions or suspected 

very strong cqupling to nearby conductors. Therefore, these were 

deleted from the original data base as invalid data and replaced 

by more reliable, adjusted downlink in-mine field strength values 

when possible. 

Figure V-10 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. The most 

useful part of the graph is to the right of the intersection of the 

regression lines; namely, between depths of 250 and 1500 feet. 

Examination of this plot reveals that the 630 Hz regression line 

Arthur DLittle,lnc. -' 
r I I I I I 'I I I I I1 1 I IIIIIII 

- -, 

NORMALIZED TO TRANSMIT MOMENT OF M = 1 Amp-m2 - 

- 

- - 

\-FREE SPACE CURVE 

- - 

- - 

- - 

- - 

630 

- 1050 , 

1950 

3030 

- FREQUENCY(Hz)- 

- - 

I I I I 111 I I I I I I I I I IIIII 

50 200 250 300 400 500 700 1 000 1500 2000 

OVERBURDEN DEPTH (FEET) 

FIGURE V-10 NORMALIZED OVERBURDEN RESPONSE CURVES-UPLINK 

REGRESSION RESULTS, AVERAGE SURFACE VERTICAL 

SIGNAL STRENGTH. Hz. VERSUS OVERBURDEN DEPTH BY 

FREQUENCY 
runs nearly parallel to, and about 7-9 dB below, the free space 

curve. The 3030 Hz line dips more steeply and varies from about 

7 dB below the free space curve at 250 feet to about 20 dB below 

at 1500 feet. The 1050 and 1950 Hz lines fall approximately 

halfway between the 630 and 3030 Hz curves. 

Figure V-11 summarizes the frequency dependence across the 

630 to 3030 Hz band over the 250 to 1500 feet overburden depth 

range of interest. This figure allows one to extrapolate 

performance to other frequencies in the 630 to 3030 Hz band of 

interest. It also shows that the frequency dependence of signal 

strength is ;elatively insignificant for depths less than about 

500 feet, and that the change across the band is only about 10 dB 

even at the maximum depth of 1500 feet. 

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 

3030 Hz band. The utilization of the results, properties, and 

predictive capabilities of these regression models is described in 

Section VIII of this report. Actual computer output produced by the 

SAS regression routine is given in Appendix D for each frequency. 

2. Other Models 

For the sake of completeness, it should also be mentioned 

that several other models were examined as possible candidates for 

representing the data. Furthermore, these models, as well as the 

log depth regression model presented in the previous section, were 

also considered for the uplink data base purged of all questionable signal measurements , without replacements according to the 

Arthur D Little, Inc - 
FREQUENCY IN Hz 

0 

E -10 \ 

4, 

F 

al L 

m 

u 

-30 

I 

4 

ILI - 

LL 

0 E -5O 

z 

(3 

a 

2 

W 2 -70 

LL 

a 

3 

V) 

-90 

FIGURE V-11 NORMALIZED SURFACE VERTICAL MAGNETIC FIELD, Hz, VS 

FREQUENCY WITH DEPTH AS A PARAMETER 

I I I I I I I I I I 1 I 

- 

- 

- DEPTH - 

- - 0 250 FT. - 

0 4 .2 

- w 

- 

- 

- 

- 

m 

C 0 + /. - 0 500 FT.- 

- 

- d 

- - 

- 0 

- n - 

- 

- 

4 1000 FT. 

- 

- 

- h 

d 

- 

- 1500 FT. ' 

- 4 

d 

- t 4 4 

630 10 0 1950 3030 - I I I 11 I I I I I 1 I I I I 

600 1 000 2000 3000 
process described in Section IV. These results will be discussed 

briefly in this section, since they were not used in subsequent 

steps necessary to calculate detection probabilities. 

a. Log Depth Model for the Purged Data Base 

In Table V-2, summary statistics similar to Table V-1 are 

given for the purged uplink data base measurements only. Not 

surprisingly, the models are very similar for the two data sets 

and lead to the same conclusions as stated in the previous section. 

There is no evidence that the utilization of the downlink signal 

data to augment the validated uplink signal measurements introduced bias into the results. The only effect in using the expanded 

data base appears to be a slight loss in precision in making 

estimates at the two higher transmission frequencies, as indicated 

by slightly higher standard errors. 

b. The D-~ Exponential Model 

In addition to the simple statistical model used to interpret 

the data, a modified version was also studied. The purpose of this 

approach was to acknowledge and make use of an approximate 

physical relationship that expresses signal strength as a function 

of a magnetostatic power law factor D-~ and an exponential attenuation factor e -bD to account for resistive losses in the overburden. The underlying model initially considered in this analysis 

was the following: 

where H is the measured signal strength in A/m, D is the 

overburden depth in meters, and a and b are parameters to be 

estimated from the (H,D) data pairs. The factor e -bD was introduced as an alternative to the arbitrary power law by depth model 

3 to account for the known lack of agreement when using (1/D ) only. 

.D 

Arthur D Little, lnc 
Table V-2 

Regression Results 

For Surface Signal in dB versus Log Depth Model 

Using Purged Uplink Data Base 

Source: Arthur D. Little, Inc. 

r 

Frequency 

(Hz) 

630 

1050 

1950 

3030 

Arthur D Little, Inc. 

95% 

confidence Correlation 

No. of Estimated Estimated interval for coefficient Standard 

(R) R~ error obs. intercept slope q= slope/20 tS) 

78 98.59 -61.41 -2.7 to -3.4 0.91 0.82 6.66 

78 109.01 -66.57 -3.0 to -3.7 0.92 0.85 6.50 

78 110.00 -67.39 -3.0 to -3.7 0.92 0.84 6.74 

75 121.72 -73.33 -3.2 to -4.1 0.89 0.80 8.60 
In order to take advantage of model fitting properties and 

summary statistics provided by computer routines, the above model 

was further modified as follows: 

With this formulation, normalized signal strength, SN, expressed 

in dB re 1 pA/m units, assumes a linear form (in the sense that 

it is linear in terms of the parameters to be estimated); namely: 

20 [log a - 3 log D - (c - 3) log D - bD log el. 

The problem then reduces to deriving a least-squares estimate 

of the three parameters a, b, and c, which minimizes the sum 

of squares of differences between observed signal strengths and 

values estimated by the derived model. Furthermore, it is possible 

to determine which of the two parameters, b or c (or factors 

depending on them) is more effective in representing the observed 

deviation from the inverse depth cubed form. Regression estimates 

are given in Table V-3. 

Inspection of goodness-of-fit statistics revealed a result similar 

to the simple log depth linear regression case at 630 Hz, in that 

neither term involving the parameters b and c contributed any 

explanatory capability. Although a significant contribution was 

apparent for the 1050 Hz and 1950 Hz frequency levels, the adjustment factor involving b, and/or the exponent of depth term involving 

c, were equally adequate, and there is no evidence as to which 

is preferable. However, there is rather strong evidence that the 

modified exponent of depth term involving c better explains the data 

taken at 3030 Hz than the exponential adjustment term involving b. 

Arthur D Little, Inc " 
Table V-3 

Least-Squares Estimate 

(Depth Cubed Model) 

(Using Expanded Uplink Data Base) 

Source: Arthur D. Little, Inc. 

Arthur D Little, Inc 

b 

.. 

Frequency 

(Hz) 

630 

1050 

1950 

3030 

r 

1 

Estimated parameters No. of Standard 

observations 20 log a c b error 

90 87.21 2.73 0.0023 6.66 

90 89.96 2.76 0.0037 6.46 

9 1 102.90 3.15 0.0016 7.11 

90 130.26 3.89 -0 0003 8.97 
Equation (11 ) can also be viewed as an oversimplified 

approximate relationship for the magnetic field above a small 

horizontal loop transmitter immersed in a homogeneous overburden 

of uniform conductivity. Although this model may appear to be 

more satisfying at first glance, because of its allusion to the 

physics of propagation in homogeneous conducting media, it does 

not provide as good and complete a representation of the data 

as the log depth power law model, and in some respects can even 

be misleading in the sense that it overly constrains the conductivity to be constant and independent of depth. 

C. THE RECOMMENDED MODEL AND ITS APPLICABILITY 

The signal strength(in dB)vs. log depth power law model 

of Section V-B1 is the most representative and practical regression 

model for predicting the detectability performance of trapped miner 

transmitters in the U.S. coal fields. The rationale for characterizing the relationship of signal strength to depth with a 

mathematical or statistical model is to permit the estimation of 

detection probabilities under actual trapped miner conditions. Many 

extraneous and uncontrollable factors can be expected to influence 

the detection system performance in any given real situation. 

However, by using the data obtained in this experimental program, 

we can in fact make probability statements about the strength 

of a signal reaching the surface when it is transmitted from 

relevant overburden depths in the frequency band of interest. 

It is well known that statistical regression theory is a sound 

and useful tool for making inferences and probability statements 

about the behavior of one variable (signal strength) when another 

variable (depth) is known. Furthermore, the theory is simple and 

straightforward and has wide-ranging applicability in scientific 

and engineering studies. It is particularly appropriate in this 

n Arthur D Little, Inc 
case, since the model explicitly takes into account random 

fluctuations known to exist that influence the signal strength 

levels ultimately received at the surface from a transmitter located 

at identical overburden depths. 

It has already been shown that a simple regression model 

describes the observed data from the sampled mine locations 

remarkably well. Since mines were randomly chosen, the regression 

relationships derived from sample results should be representative 

of all signal transmission conditions for similar overburden 

depths. The statistical model clearly describes the data, has a 

sound analytical framework, and allows for the straightforward 

quantification of probability estimates. Since no bias appears to 

have been introduced by augmenting uplink transmission data with 

downlink data when the former were unattainable, the simple 

regression model with estimated parameters given in. Table V-1 

is used in the subsequent analyses required to estimate detection 

probabilities. 

Arthur D Little Inc 
(THIS PAGE INTENTIONALLY LEFT BLANK) 

I 

Arthur D Little Inc 
VI. SIGNAL ESTIMATES FOR THE GENERAL INSTRUMENTS TRANSMITTER 

Having derived the overburden transmission response model 

presented in Section V-B1, it becomes a straightforward matter to 

estimate the expected overburden signal strength response as a 

function of overburden depth and frequency for the newly developed General Instruments rescue transmitter for trapped miner applications. 

The GI transmitter signal strengths on the surface can be 

obtained by first computing the expected magnetic moment at each 

of the operating frequencies, and then translating each of the 

overburden response curves of Figure V-10 upward by an amount 

equal to the value of the magnetic moment expressed in dB rel2 ative to 1 Amp-m . Figure VI-1 depicts the results of this translation for the General Instruments transmitter. 

The indicated values of GI transmitter magnetic moments 

shown in Figure VI-1 were computed by the same method used to 

compute the fundamental RMS magnetic moment for each of the 

measurement program in-mine loop configurations described in 

Appendix C. The circuit configuration for this calculation is the 

same as that shown in Figure C-1, but without the 0.1-ohm 

precision reference resistor used in the field to measure loop 

current. The GI transmitter characteristics of V and RS are 

S 

identical to those used for the Collins tran~mitter'~). The GI loop 

antenna consists of 300 feet of number 18 wire, arranged in the 

shape of a square. This loop configuration was chosen because it 

best represents the practical implementation of the strategy that 

the miners will be instructed to follow in the event that they are 

required to utilize the trapped miner transmitter. Namely, the 

miner will be instructed to deploy the complete length of wire 

around a coal pillar in such a manner as to create the largest 

Arthur D Little,Inc 
-40 

150 200 250 300 400 500 700 1000 1500 2000 

OVERBURDEN DEPTH (FEET) 

I I 1 I I I I I I I I I I I I Ill1 ' 

- MAGNETIC MOMENT OF GI TRANSMITTER - 

- f M~ I - 

(Hz) (A-m2 ) (dB11 A-m2 ) 

- 

- 

- -. 

- - 

- - 

- FREQUENCY 

- 

- 

- - 

I I I I 1 I I I I I I 11 11 1111 

FIGURE VI-1 PREDICTED UPLINK RESPONSE CURVES FOR GENERAL 

lNSTRUMENTS TRANSMITTER-AVERAGE SURFACE 

VERTICAL MAGNETIC FIELD SIGNAL STRENGTH, Hz, 

VS DEPTH BY FREQUENCY 
loop antenna area with the available wire. Table VI-1 presents 

the loop impedance, current, and magnetic moment values calculated on the basis of this standard configuration for the GI 

transmitter. Although in some mines slightly larger or smaller 

loop areas, and thus magnetic moments, will be deployed, the 

tabulated values represent the most practical and realistic ones 

on which to base expected probabilities of signal detection on the 

surface. 

Arthur D Little, IK 
Table VI-1 

Loop Impedances and Magnetic Moments 

for the General Instruments Transmitter 

Vs zk3.45 volts: (0-p square wave), R = 0.312 ohm 

S 

. 

Frequency 

(Hz) 

630 

1050 

1950 

3030 

2 

/MI ~~~d = NA 111 ~~~d , where N = 1, A = 523 m2 (in a square) 

RMS RMS 

Source: Arthur D. Little, Inc., and U.S. Bureau of Mines 

Loop Impedance -- 

R~ *L 

(Ohms ) (Ohms ) 

for 300 ft. fcr L = 

#18 wire 136 h 

l.92 0.737 

1.92 1.229 

1.92 2.282 

1.92 3.545 

I 

Arthur D Little, Inc. 

--- 

Transmitter Current/Moment - 

111 Fund 'MI Fund Ih" Fund 

RMS RMS RMS 

2 (dB re 

(Amps) (Amp-m ) 1 Amp-m 

1.272 665 56.5 

1.180 617 55.8 

0.953 498 54.0 

0.732 383 51.7 

4 

v 
VI I. CHARACTERIZAT ION OF SURFACE NOISE ABOVE MINES 

As discussed in Section IV-D, two independent sets of 

surface magnetic field noise measurements were obtained during the 

course cf the measurement program. The Bureau cf Mines tape 

recorded noise measurements, although far from comprehensive, 

were found to be more reliable, as well as representative, for the 

purpose of estimating signal-to-noise distributions on the surface 

and the corresponding probabilities of trapped miner signal 

detection. In this section we present the approach used to 

establish an appropriate probability distribution to characterize 

the noise data, together with the derived results. 

As discussed in Section IV, atmospheric broadband noise, 

not discrete frequency man-made noise, will provide the main . 

impediment to the detection of trapped miner signals. For the 

purpose of estimating signal detectability during a typical miner 

rescue operation, the RMS values of the vertical component of this 

atmospheric noise under non-extraordinary atmospheric noise conditions are the values of most interest. In practice, mine rescue 

signal detection efforts can be temporarily suspended during 

periods of severe local noise conditions. Furthermore, short instantaneous impulsive bursts of noise can be ignored without significant detection penalties during normal search and detection 

activities. 

To investigate the behavior of the Bureau of Mines noise 

data, the convenient plotting technique described in Reference 12 

was used. This procedure is computationally very simple and 

utilizes special probability graph paper that provides a convenient 

method of examining various theoretical probability distributions 

that might describe the data of interest. The procedure requires 

first ranking the data from lowest to highest value, assigning the 

Arthur D Little, Inc 
lowest value the rank n (where n is the total number of observations), and then calculating H(x), where 

where K(x) equals the number of observations greater than or 

equal to x, the observed noise measurement. 

As an illustration, some of the BOM noise data taken at 

630 Hz yield the quantities given in Table VII-1. The cumulative 

conditional probability function H( x) is related to a probability 

law F(x), which is defined to be the probability of observing a 

noise value less than or equal to x. The theoretical properties are 

such that F(x) and H(x) are related as follows: 

for *any distributional form F(x). Probability paper is available for 

several different distributional forms ; namely, the exponential, 

Weibull, normal, lognormal, and extreme value distributions. The 

paper is constructed so that the observed cumulative distribution 

values F(x) will tend to plot as a straight line if the underlying 

distribution form is appropriate. 

For the BOM noise data, normal probability paper gave 

satisfactory results at each frequency. These plots of the RMS 

noise distribution are given in Figures VII-1 to V11-4. The mean 

value for each RMS noise distribution is located at the 50% point 

and is displayed on each graph. Examination of the graphs 

reveals that the RMS values decrease monotonically with increasing 

frequency by 20 dB over the 630 to 3030 Hz band. This behavior is 

consistent with that observed for atmospheric noise in this 

frequency band by other investigators,(6ds discussed in Section IV-Do 

111 

Arthur D Little, Inc 
Table VII-1 

Illustrative Example for Calculating 

Plot Points for Analysis of Noise Data 

Noise Rank Cumulative Cumulative 

(dB ( inverse conditional distribution 

(re 1 pA/m/ 30Hz) order) probability function 

function 

x K(x) H(x) F(x) 

-15.2 27 0.0370 0.036 

-8.2 26 0.0755 0.073 

-7.2 25 C. 1155 0. 109 

. . . 

. . . . 

. . . . 

+29.8 2 2.8915 0 . 945 

37.8 1 3.8915 0.980 

v 

Source: Arthur D. Little, Inc. 

Arthur D Little, Inc 
I I 1 Ill Ill11 Ill I 1 It 1 

- FOR 30 Hz RECEIVER BANDWIDTH a 

- 

- - 

- 

- 

- 

- - 

MEAN = 6.5 .------I,- - 

- - 

- - 

- I DATA SOURCE: BUREAU OF MINES - 

- - 

I I 

1 .O 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99.5 99.9 

CUMULATIVE NORMAL PROBABILITY (%) 

FIGURE VII-1 STATISTICAL DISTRIBUTION OF RMS SURFACE NOISE AT 630 HZ 
Arthur D Little, Inc 
- 

Arthur D Little, Inc 
I I I I11 I IIII Ill I 111 I 

- 

- FOR 30 Hz RECEIVER BANDWIDTH 

- - 

- - 

- - 

- 

- - 

- - 

- 

- - 

- 

- 

- 

1 .O 2 5 10 20 30 40 5060 70 80 90 95 98 99 99.5 99.9 

CUMULATIVE NORMAL PROBABI LlTY (%) 

FIGURE Vll-4 STATISTICAL DISTRIBUTION OF RMS SURFACE NOISE AT 3030 HZ 
Figures IV-1 to IV-4 of Section IV-D indicate that the 

Westinghouse and Bureau of Mines noise data taken at the 27 

mines jointly visited tend to agree on the average at the lower 

two frequencies, 630 and 1050 Hz, but depart significantly from 

each other at the upper two frequencies, 1950 and 3030 Hz. 

Westinghouse values consistently exceed BOM values at 1950 and 

3030 Hz because of Collins receiver hardware problems. Figure 

VII-5 is a distribution plot at 630 Hz on normal probability paper 

comparing the BOM values at 27 mines with the 94 Westinghouse 

values measured at all mines. The excellent agreement between 

these two distributions at 630 Hz, together with the frequency 

(6) dependence consistent with that of other investigators , lends 

added credence to using the Bureau of Mines data from 27 mines 

as descriptive cf the expected surface noise to be found at mines 

in the U.S. coal fields. 

The applicability of normal theory exhibited by the noise 

readings, coupled with the regression results which characterized 

signal strength in normal theory terms as well, permits a convenient analytical rather than empirical ~,olution to the problem 

of characterizing signal-to-noise ratios on the surface. The 

approach and solution to estimating the behavior of signal-tonoise ratio at the surface as a function of overburden depth and 

frequency are described in the next section. 

I 

Arthur D Little, Inc. 
3'"o mEm -3a 

pk a, gs< a k 

86s 

2 3 w 

00~ 

p5g 

aZW 

g 5 g ow- osr 

Arthur D Little, ;nc 
- 

Arthur D Little Inc. 
VIII. ESTIMATES OF SIGNAL-TO-NOISE RATIO ON THE SURFACE 

In the three previous sections, the behavior of signal data 

and noise data obtained in this study have been characterized by 

statistical relationships. In particular, explanatory models have 

been derived from experimental data that portray the overburden 

signal transmission response as a linear function of log depth. It 

has been observed that the relationship differs somewhat over a 

range of four discrete frequencies considered in the test. The 

linear model actually expresses an average, or expected, signal 

strength that would be likely to occur if a very large number of 

tests were conducted at the same overburden depth level for widely 

varying nine sites and conditions in the U.S. coal fields. The 

variability about these average values is measured by the 

standard error of estimate, which is used to calculate confidence 

intervals and prediction intervals as described in Section V. 

Furthermore, probability distributions have been established for 

representing surface noise data. These noise distributions are 

independent of both transmitter signal strength and overburden 

depth. 

The basic input for the derivation of RMS signal-to-noise 

ratio estimates on the surface is summarized in Table VIII-1, in 

which six overburden depth values are selected at 250-foot 

intervals for illustrative purposes. Mean RMS signal strength 

values at each frequency have been adjusted accordingly to 

pertain to the General Instruments transmitter, as discussed in 

Section VI and plotted in Figure V1-1. The objective is to obtain 

probability distributions of the RMS signal-to-noise ratio at each 

frequency above mines. These distributions can then be combined 

with probability of detection versus signal-to-noise ratio results 

for pulsed CW trapped miner signals, so that estimates of the 

probability of detecting trapped miner signals on the surface can 

be computed. 

131 

Arthur D Little, Inc 
Table VZII-1 

Estimated Parameters Characterizing Signal 

and Noise Distributions Above Coal Mines 

Estimated Mean Signal in dB re 1 pA/m for GI Transmitter 

Estimated Mean Noise in dB re 1 p~/rn/iK 

Overburden 

depth 

(ft.1 

250 

500 

750 

1000 

1250 

1500 

Standard 

Deviation 

630 Hz 1050 Hz 1950 Hz 3030 Hz 

39.71 39 77 37.28 35 83 

21.05 19.57 16.71 12.74 

10.14 7.75 4.68 -0.77 

2.40 -0.64 -3.85 -10.36 

-3.60 -7.14 -10.47 -17.79 

-8.51 -12.45 -15.88 -23.86 

6.65 6.52 7.08 8.92 

Source: Arthur D. Little, Inc. 

1 

- 

Arthur D Little, Inc 

All 

Depths 

Standard 

Deviation 

I! 4 

T 

630 Hz 1050 Hz 1950 Hz 3030 Hz 

6.5 -0.5 -8.5 -13.5 

13.5 11.5 12.5 12.5 

i 
The independence of signal and noise distributions, in 

addition to the property of normality exhibited by each distribution, permit straightforward combination of the two distributions 

to generate signal-to-noise probability estimates. This is due to 

the fact that the sum (or difference) of two normally and 

independently distributed variables is also normally distributed, 

with the mean equal to the sum (or difference) of the individual 

means, and the variance equal to the sum of the individual 

variances. This property is illustrated by the example portrayed 

in Figure VIII-1 for the expected performance of the GI transmitter 

at 1,000 feet and 3030 Hz. For the sake of completeness, it should 

be mentioned that the standard deviation given for signal strength 

(9.20 dB) in the figure is slightly higher than the tabular value 

given in Table VIII-1, since the actual 95% prediction interval 

width was used in the calculation to estimate signal strength 

variability. 

The signal-to-noise distribution appearing in Figure V11I-1 is 

more conveniently plotted using normal probability paper. This 

probability paper is designed so that only the two parameters 

needed to specify the normal curve (the mean and standard 

deviation) are required. Since one axis represents the cumulative 

probability under the normal curve, the mean is plotted at the 

50 percentile point and the mean plus or minus one standard 

deviation is plotted at the 84 or 16 percentile point respectively. 

These points are then connected by a line which can be used to 

determine any percentile point for the specified normal curve. Such 

normal probability plots derived from the data in Table VIII-1 in 

the manner illustrated in Figure VIII-1 are given in Figures 

V111-2 tc VI 11-5 for five different overburden depth configurations 

at each of the four frequencies. To illustrate the plotting technique, it can be seen in Figure VIII-5, at 1,000 feet, that the 

mean of 3.1 dB is found at the 50% point on the vertical axis, and 

3.1 - + 15.5 = -12.4 and +18.6 are found at the 16% and 84% points, 

respectively. 

Arthur D httle, Inc 
I'l~l'l'l~l~l'l'll~I~" 

- 

- 

= MEAN = -10.36 - - - 

o = STD. DEV. =9.20 

- - 

- 

IIIII 

a) NORMAL DISTRIBUTION CURVE, x = LOG SIGNAL (dB) 

l'l~l'l'l'~'l'l~l'~'~' 

- 

- 

= MEAN = -13.5 

o = STD. DEV.= 12.5 - 

IIIIII 

b) NORMAL DISTRIBUTION CURVE, x = LOG NOISE (d~) 

c) NORMAL DISTRIBUTION CURVE, x = LOG(SIGNAL/ 

NOISE)(dB) 

FIGURE VIII-1 DETERMINATION OF DISTRIBUTION OF SIGNAL-TONOISE RATIO ABOVE COAL M INES(lllustrative Example 

for 1000 Feet, 3030 Hz) 

LI 

Arthur D Little, Irws. 
-20 -10 0 10 20 30 

Ro = SIN RATIO IN (dB) 

FIGURE Vlll-2 CUMULATIVE PROBABILITY DISTRIBUTION OF SIN 

RATIOS EXPECTED ABOVE U.S. UNDERGROUND COAL 

MINES AT 630 Hz 

Arthur D Little, Inc 
-20 -1 0 0 10 20 30 

Ro = SIN RATIO IN (dB) 

FIGURE Vlll-3 CUMULATIVE PROBABILITY DISTRIBUTION OF SIN 

RATIOS EXPECTED ABOVE U.S. UNDERGROUND COAL 

MINES AT 1050 Hz 

II 

Arthur D Little, Inc 
CUMULATIVE NORMAL PROBABILITY (%) 

Pr (S/N < Ro dB) 
-20-15 -10 -5 0 5 10 15 20 25 30 

Ro = SIN RATIO IN (dB) 

FIGURE Vlll-5 CUMULATIVE PROBABILITY DISTRIBUTIONS OF S/N 

RATIOS EXPECTED ABOVE U.S. UNDERGROUND COAL 

MINES AT 3030 Hz 

.L. 

Arthur D Little, lnc 
These four figures provide a simple method for determining 

estimates of achieving various signal-to-noise ratios in actual 

practice. Since the vertical axis represents the area under the 

normal curve from minus infinity to some signal-to-noise ratio Ro 

(measured in dB units) specified by the horizontal axis, this 

percentage is defined as the probability of achieving a signal-tonoise ratio less than or equal to R . By subtracting cumulative 

0 

probabilities corresponding to two different ratios R1 and R2, these 

plots also yield direct probability estimates of observing signalto-noise ratios in the interval represented by R to R2. 1 

Some probability estimates for signal-to-noise ratios of 

interest have been read directly from the plots given in Figures 

VIII-2 to VIII-5 and are tabulated in Table VIII-2. These probabilities are subsequently used with the aural detection results of 

Section IX to derive signal detection probability estimates according to the method presented in Section X. 

Prior to describing the analytical procedure used to 

determine overall signal detection probabilities over mines, it is 

also recognized that the data given in Table VIII-2 can be 

displayed in various ways. For example, it is possible to illustrate and compare the behavior of probability estimates associated 

with exceeding specified signal-to-noise ratio as a function of overburden depth and frequency. Two examples are given to illustrate 

such behavior; namely, Figure VIII-6 gives the probability of RMS 

signal being at least 9 dB greater than RMS noise, while Figure 

VIII-7 illustrates the probability of RMS signal simply exceeding 

RMS noise, as a function of overburden depth. The relative effect 

of frequency is also apparent in these figures. The figures reveal 

a relatively weak frequency dependence, and the somewhat surprising result of best predicted performance occurring in the upper 

part of the frequency band, and worst performance at the bottom 

of the band. This occurs because the measured RMS noise levels 

Arthur D Little, Inc 
Table VIII-2 

Probability of Achieving Signal-to-Noise Ratios of Interest 

Above Coal Mines Using GI Transmitter 

-- Source: Arthur D. Little, Inc. 

Signal-toNoise 

Ratio 

(dB) 

<O 

0 to 3 

3 to 6 

6 to 9 

9 to 12 

> 12 

<O 

0 to 3 

3 to 6 

6 to 9 

9 to 12 

'12 

li 

Arthur D Little, IK 

? 

Frequency 

(Hz) 

630 Hz 

1050 Hz 

250 ft. 

0.015 

0.009 

0.013 

0.018 

0.025 

0.920 

{o.ol 1 

0.008 

0.982 

1950 Hz 

<O 

3 to 6 

6 to 9 

9 to 12 

>I2 0.99 

eO 

Overburden 

500 ft. 

0.170 

0.053 

0.055 

0.077 

0.078 

0.567 

0.065 

0.035 

0.044 

0.056 

0.070 

0.730 

3 to 6 

6 to 9 

9 to 12 

>I2 0.99 

0 . 039 

0.021 

0.030 

0.039 

0.050 

0.821 

0.045 

Depth (ft. ) 

1000 ft. 

0.605 

0.075 

0.067 

0.060 

0.050 

0.143 

0.500 

0.090 

0.087 

0.075 

0.068 

0.180 

0.023 

0.030 

0 037 

0.045 

0-820 

1500 ft. 

0.836 

0.046 

0.034 

0.026 

0.020 

0.038 

0.834 

0.051 

0 . 037 

0.028 

0.020 

0.030 

0 374 

0.081 

0 . 088 

0.082 

0.075 

0 . 305 

0.420 

0.692 

0.058 

0.060 

0.050 

0.039 

0.091 

0.745 

0.075 

0.075 

0.076 

0.069 

0.285 

I 0.056 r 

0.049 

0.051 

0.031 

0.078 

3030 Hz 
- 

- - 

- FHEUUENCY (Hz) - 

- .om-- 1950 - 

- 43 3030 3 

- 1050 - 

- 0---0 630 - 

- - 

- - 

- 

- 

- 

- 

- 

DATA SOURCES: 

- - SIGNAL (WESTINGHOUSE) 

- - NOISE (BUREAU OF MINES) 

- 

- 

- 

OVERBURDEN DEPTH (FEET) 

FIGURE Vlll-6 PROBABILITY THAT MEAN RMS SIGNAL IS GREATER THAN OR EQUAL TO 

RMS NOISE + 9dB FOR THE GENERAL INSTRUMENTS TRANSMITTER 
A Am 

WW 

mz 

:s 

ILL 

UO 

53 

+a 

mu zg5 

OYm al3aw 

0252 

**o 

azz 

tl l 

0 

I 

Arthur D Little, Inc 
decrease faster with frequency than the mean RMS signal levels. A 

somewhat different method of presenting the same signal-to-noise 

data is shown in Figure VIII-8 for a frequency of 630 Hz. This 

figure illustrates the nature and approximate boundaries of the 

normal distributional characteristics of signal-to-noise ratio as a 

function of overburden depth. 

Arthur D Little, Inc 
WWW 

K>W 

Arthur D Little, Inc 
IX. AURAL DETECTION OF PULSED CW TONES IN NOISE 

Trapped miner rescue operations based on the use of minercarried ULF rescue transmitters will rely primarily on a surface 

search team to detect (and then locate the source of) signals 

generated by miners trapped underground. The pulsed CW signals 

generated by the transmitters will be detected by searchers 

carrying rescue receivers equipped with a hand-held loop antenna, 

headsets, and a meter indication as depicted in Figure 111-4. Thus, 

the primary mode of detection will be aural, based on the headset 

signals perceived by the ear and brain. The objective of this 

section is to establish the signal-to-noise ratios required to 

achieve probabilities of aural signal detection in the broadband 

noise described in Section VII. 

There is a wide body of theory and experimental data 

treating the ability of persons to detect audio frequency signals in 

background noise. Several parameters affect this ability to detect 

audio frequency tones in noise. They are: 

the listening frequency ; 

the pulse length; 

the bandwidth of the noise; and 

the pulse repetition rate. 

We have made use of this well-developed body of material 

from the literature to establish how each of these parameters 

affects pulse detection capability. We then combined the known 

results for each parameter to generate a probability of detection 

curve as a function of the RMS signal-to-noise ratio. This detection 

curve can then be applied to the signal-to-noise distributions of 

Section VIII to estimate probabilities of detecting trapped miner 

signals as a function of overburden depth. 

Arthur D Little. Inc 
A. EFFECT OF LISTENING FREQUENCY 

The present trapped-miner rescue receivers are designed so 

that all listening is done at 978 Hz, independent of the transmitted 

frequency. Namely, all receiver frequencies are heterodyned by the 

receiver to this relatively favorable frequency for aural detection. 

Figure IX-1 (I3) illustrates the auditory response to tones masked 

by broadband noise as a function of the frequency. This figure 

depicts the capability of the auditory response process to act as a 

filter to tune out competing background noise. In effect, the 

response can be considered as a relatively narrow bandpass filter 

centered at the listening frequency and of the bandwidth found on 

the plot, called the critical bandwidth. From this plot as a 

function of frequency, we find that the effective bandwidth, or the 

critical bandwidth, is approximately 60 Hz at the 978 Hz listening 

frequency of the rescue receivers. 

B. EFFECT OF PULSE LENGTH 

The effect of pulse length on aural detection capability is 

illustrated in Figure IX-2. (I3) Psychoacoustic data taken by a 

number of investigators are combined in this figure to show the 

"recognition differential" required vs. pulse length for a 

50 percent probability of detection. The recognition differential is 

the amount in dB by which the signal level needs to exceed the 

measured noise spectrum level within the listening bandwidth to 

provide a 50 percent probability of detection. The body of data 

comes from the investigators' psychoacoustic experiments on a 

number of subjects made under laboratory controlled conditions. 

The rescue transmitters have a fixed pulse duration (length) 

of 100 ms. Therefore, this fixes the operating point of interest in 

Figure IX-2. The 100-ms pulse length prescribes a recognition 

L 

Arthur D Little, Inc 
100 1,000 

Frequency, HZ 

o NDRC Surnrn. ~ekh. Rept. 9, Fig. 17, p. 35, Ref. 33 

I + 

SOURCE: R.J. URICK, "PRINCIPLES OF UNDERWATER SOUND FOR ENGINEERS," 

McGRAW HILL - 1967, FIG. 12.10, REF. 13. 

+ Schafer et al., Ref. 29 

- 

Hawkins and Stevens, Ref. 37 

A Zwicker, Flottorp, and Stevens, Ref. 30 

- 

x Swets, Green, and Tanner, Ref. 32 

Green, Birds01 I, and Tanner, Ref. 34 

- - Eye average of values other than 

- those of Zwicker, Flottorp, and 

Stevens 

1 , AA fk 

FIGURE IX-1 MEASURED VALUES OF THE CRITICAL BANDWIDTH OF THE EAR 

A e/ 

A 

/ 

/ 

/ 

A 4 

+$I0 

/ '0 

A,/ 

\ 

4 A -p 

-- 

1 I 11 1111 

/ 

/ 

0 

I '\ + 

\- 0 

-- 

0 

O 0 0 

1 1 .I 11 111 1 1 1 11 Ill 

differential of 23 dB to achieve a 50 percent probability of 

detection. This is a fundamental number to the development of the 

detection capability that follows, and simply means that for a 

50 percent probability of detection, the signal power level of a 

single tone burst needs to be 23 dB above the noise spectrum level 

in the listening bandwidth. 

C. EFFECT OF BANDWIDTH 

To determine the significance of the 23 dB recognition 

differential in terms of required signal-to-noise ratio, a bandwidth 

must be associated with the noise spectrum level. The electronic 

bandwidth used in the rescue receivers is 30 Hz, one-half the 

critical bandwidth of the ear at the receiver listening frequency. 

The effect of this reduced bandwidth can be estimated by using the 

data presented in Figure 1x4. (14) Figure IX-3 illustrates how the 

noise, N, and the required signal level, E, vary for a relatively 

long pulse when a 50 percent probability of detection is desired. 

The effect of the aural detection bandwidth, Wf, is clearly shown. 

As the electronic bandwidth is increased beyond Wf, the output 

noise level increases, while the signal level required remains 

fixed. It is as if a fixed bandpass filter were used; and indeed, 

the aural detection process works just that way with an effective 

filter bandwidth of Wf. Below the critical bandwidth, the signal 

level required remains constant with decreasing bandwidth until 

the bandwidth is reduced to less than about one-half of the 

critical bandwidth Wf. 

The impact of this behavior on signal-to-noise ratio 

required for the trapped-miner detection hardware is as follows: 

The receiver has an electronic bandwidth of 30 Hz -- not small 

enough to provide any reduction from the signal level required for 

the 60 Hz critical bandwidth. Thus, from a detection standpoint, 

Arthur D Little, Inc 
BAND WIDTH,W,CYCLES 

10 100 1000 L v 1 1' 

SPECTRUM LEVEL CONSTANT 

"1" m 

i I I I, 

I 

SOURCE: PRINCIPLES AND APPLICATIONS OF UNDERWATER SOUND - 

SUMMARY TECHNICAL REPORT OF DIVISION 6, NDRC, VOL. 7, 

WASHINGTON, D.C., 1946 (REISSUED 19681, CHAP. 9, FIG. 7A., 

REF. 14. 

FIGURE IX-3 DIAGRAM ILLUSTRATING RECOGNITION OF AN ECHO 

OF CONSTANT FREQUENCY AND RATHER LONG 

DURATION, WHEN THE NOISE LEVEL IS GREAT ENOUGH 

TO CAUSE MASKING LIMITED CONDITIONS FOR ALL 

BANDWIDTHS 

- 

Arthur D Little, Inc 
the system will behave as one having a noise bandwidth of 60 Hz 

and requiring a recognition differential of 23 dB. Therefore, a 

signal-to-noise ratio of 23 - 10 log 60 = 23 - 18 = 5 dB is needed 

for -the 60Hz critical bandwidth to yield a 50 percent probability of 

detection. 

The signal-to-noise ratios developed in Section VIII of this 

report have been based on the real 30 Hz electronic bandwidth of 

the receiver. Since we must account for the 60 Hz critical bandwidth effect of Figure 1X-3, we have adopted the simple artifice 

of merely adding 3 dB to the 60 Hz 5 dB required signal-to-noise 

ratio criterion when using the signal-to-noise levels computed on 

the basis of the 30 Hz electronic bandwidth of the receiver. Thus, 

a 50 percent probability of detection will occur for the electronically-based signal-to-noise ratio of 8 dB. Alternatively, we could 

have chosen to reduce all of the computed electronically-based 

signal-to-noise ratios by 3 dB. We chose the easier path of altering 

the signal-to-noise criterion for 50 percent probability of detection 

to allow the use of the electronically-based signal-to-noise ratios. 

The following quote, from Reference 14, page 197, describing 

some of the subjective effects of reduced bandwidth on the detection process, is also included for completeness: 

"When the bandwidth is less than Wf, echo and noise are 

heard as a single blended sound and recognition is 

caused almost entirely by a noticeable increase in loudness when the echo comes in. When the bandwidth is 

greater than W echo and noise are heard as two 

distinct, thougA9 simultaneous, sounds, and the operator 

feels able to ignore the noise and concentrate on the 

echo. To a very considerable extent, this feeling is not 

an illusion. " 

Arthur D Little, Inc 
EFFECT OF PULSE REPETITION RATE 

One more factor must be considered before arriving at a 

final value for the signal-to-noise ratio required to yield a 

50 percent probability of detection. That factor is the continuously repeating nature of the transmitted signal. The data used 

above to arrive at the required signal-to-noise ratio are all based 

on the detection of a single tone burst in noise. Others (15,161 

provide some data on continuously repeating tone bursts that 

enable us to take this repetition effect into account in setting the 

signal-to-noise 50 percent detection criterion. Figure IX-4 illustrates Garner ' s findings. (I5) It shows that as the repetition rate 

of a 50 ms pulse is changed from one in four seconds to one per 

second, 2 dB less signal-to-noise ratio is required. From the 

nature of the Garner data, an even greater improvement might be 

expected, but the lack of data at repetition rates less than one 

per four seconds precludes a guarantee of this. Therefore, we use 

the 2 dB improvement value as a conservative estimate, and 

establish a 50 percent probability of detection signal-to-noise ratio 

criterion of (8-2) dB, or 6 dB. 

We believe that a more reliable measure of detectability 

attainable through the use of repetitive pulse trains is still 

required. M. Ristenbatt of the University of Michigan is currently 

conducting laboratory experimental tests for the Bureau of Mines on 

this matter over a wide range of pulse repetition rates and observation intervals. The results of these tests should provide the 

information desired. 

PROBABILITY OF DETECTION VS. S/N RATIO 

Having established a basis for identifying the signal-tonoise ratio required for a 50 percent detection probability, we 

need a means for quantitively extending the signal-to-noise ratio 

I 

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NOTE: 

SOURCE: 

% 1 2 5 10 15202535 50 75 100 

REPETITION RATE (TONES/SECOND) 

EACH CURVE IS FOR A DIFFERENT TONAL DURATION. 

THE MASKING NOISE WAS FILTERED WlTH A 5000 Hz 

LOW PASS FILTER, AND SIGNAL-TO-NOISE RATIOS ARE 

WlTH RESPECT TO THE TOTAL NOISE ENERGY. THE 

INTENSITY OF THE MASKING NOISE WAS APPROXIMATELY 

90 dB re 0.0002 dyne/cm2. FREQUENCY IS 1000 Hz. 

W.R. GARNER "AUDITORY THRESHOLDS OF SHORT TONES 

AS A FUNCTION OF REPETITION RATES", JASA VOL. 19, 

NO. 4, JULY 1947, PP. 600-608, FIG. 4, REF. 15. 

FIGURE IX-4 THE EFFECT OF REPETITION RATE OF SHORT TONES ON THE MASKED THRESHOLD 
criterion to include higher and lower detection probabilities. We 

choose to stay with experimentally determined aural detection 

(14) results for tones in noise such as that shown in Figure IX-5 . Although this figure is strictly applicable to pure tones in noise, 

we believe that the shape of the response about the 50 percent 

probability value should be representative of the behavior expected 

for detecting pulsed CW tones in the field. Therefore, the probability of detection vs. signal-to-noise ratio curve for 100 ms 

repetitive CW audio pulses of Figure 1X-6 has been constructed by 

relabeling the horizontal axis of Figure 1X-5 so that the 50 

percent probability of detection condition occurs for the signal-tonoise ratio of 6 dB derived above. This plot is used with the 

results of Section VIII to compute the trapped miner signal probability of detection estimates in Section X. 

In conclusion, we make the following additional comments on 

the aural detection of pulsed tones noise: 

Alerted vs. non-alerted detection. The probability of 

detection vs. signal-to-noise ratio is the product of 

psychoacoustic testing. These tests can readily be biased 

by alerting the listeners by such instructions as "Make 

sure you don't miss a signal," or "Be very sure you 

have a signal." Such instructions will alter the detection 

curve. We chose to use the non-alerted characteristic as 

being applicable to the trapped-miner detection problem. 

Modern treatments of detection disregard the recognition 

differential and adopt the detection index as a means of 

including false detections. We do not regard false detections as a problem. If a surface-based searcher thinks 

he has a detection while he is searching an area, he 

will stop and listen carefully. If he can't verify the 

ILI 

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SIGNAL LEVEL, DB . * 17 I8 19 

SOURCE: PRINCIPLES AND APPLICATIONS OF UNDERWATER SOUND - 

SUMMARY TECHNICAL REPORT OF DIVISION 6, NDRC, VOL. 7, 

WASHINGTON, D.C., 1946 (REISSUED 19681, CHAP. 14, FIG. 5, 

REF. 14. 

FIGURE IX-5 PROBABILITY OF RECOGNITION OF A PURE TONE IN A 

BACKGROUND OF A NOISE AT A CONSTANT RMS LEVEL 

OF 12 dB 

Arthur D Little, Inc 
mz 

p I- s:: 

0-I1.5 2.5 3.5 4.5 5.5 1 6.5 7.5 8.5 9.5 10.5 

6.0 dB @ 50% PROBABI LITY 

SIGNAL TO NOISE RATIO (dB) 

NOTE: FOR 100 MILLISECOND PULSES, 1 PER SECOND REPETITION RATE, 

957 Hz LISTENING FREQUENCY, AND 30 Hz RECEIVER BANDWIDTH. 

SOURCE: ARTHUR D. LITTLE, INC., AND REFS. 13, 14, 15. 

FIGURE IX-6 AURAL PROBABILITY OF DETECTION VERSUS RMS 

SIGNAL-TO-NOISE RATIO FOR TRAPPED MINER 

PULSED CW SIGNALS IN BACKGROUND GAUSSIAN 

NOISE 
detection, he will merely move on. Thus, we chose to use 

the recognition differential as a valid tool in the 

development of detection characteristics such as presented 

above. 

a Additional detectability experiments should be performed, 

perhaps in con junction with Ristenbatt ' s pulse repetition 

rate aural detection experiments, as a further check on 

the accuracy and applicability of the derived detection 

curve of Figure IX-6. 

Arthur D Little, Jnc 
(THIS PAGE INTENTIONALLY LEFT BLANK) 

L 

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X. PROBABILITY OF DETECTION ESTIMATES 

ON THE SURFACE ABOVE MINES 

A. METHODOLOGY 

In an actual mine emergency situation, the signal transmitted 

from a mine cannot always be expected to be detected at the surface. Several factors will influence the reception, detection and 

recognition of a true signal. As discussed throughout this report, 

the signal strength itself is known to vary, primarily as a function of overburden depth and transmitter frequency, but also 

according to overburden composition and other unknown and 

uncontrollable ancillary factors. The presence of these factors 

influencing the strength of signals transmitted through-the-earth 

has been acknowledged in this test program and is implicitly represented by the regression models derived from test data obtained by 

Westinghouse from the 94 mine sites. The noise level for any given 

emergency situation is also a random phenomenon, rather than a 

deterministic one, and has been characterized by a normal, or 

Gaussian, probability law from additional experimental data 

collected by the Bureau of Mines at 27 of the 94 mine sites. 

Furthermore, for a known signal strength/background noise 

level combination, the actual detection of the signal by an 

observer at or above the surface cannot be treated deterministically; that is, signal detection must be considered a random 

event, the occurrence of which follows some probability law. In its 

simplest form, this law can be expressed in terms of signal-tonoise ratio. At extremely low ratios the chance of signal detection 

would be essentially zero, while at extremely high ratios detection 

would be close to certainty. At intermediate levels, the chance of 

detection would be expected to increase monotonically with increasing signal-to-noise ratio. Various studies have been conducted on 

Arthur D Little, Inc 
hearing and aural detection of tones in noise to investigate 

properties of this relationship. Figure IX-6 of the previous section 

presents empirically derived probability of detection results that 

have been adapted for application to the trapped-miner detection 

problem. 

The probability of detection curve in Figure 1X-6 actually 

represents conditional probabilities ; that is, the likelihood that 

detection will occur given the presence of a fixed, observable RMS 

signal-to-noise ratio. As a consequence, the chance of detecting a 

signal transmitted through the earth can be calculated according 

to the fundamental multiplication rule for probabilities: 

P D and Rk I 

where P ( D and Rk represents the probability of achieving a I 

signal-to-noise ratio of size R and also detecting the signal k 

embedded in this noise; P [ Rk ) is the probability of the occurrence of a signal-to-noise ratio of size R k' and P (D I Rkt is the 

conditional probability of detecting a signal, given a signal-tonoise ratio of size R k' 

Probability distributions have been derived and presented in 

previous sections of this report for both factors on the right-hand 

side of the above equation. As mentioned above, Figure 1X-6 gives 

P ( D I Rk) ; certain integral values of R and their associated k 

probabilities of detection are also tabulated in Table X-1. Signalto-noise probability distributions P { Rk 1 are given in Figures 

VIII-2 to VIII-5. These figures emphasize the fact that these 

probabilities also depend on frequency and depth. Using additional 

subscripts to account for these dependencies, the probability of 

achieving a signal-to-noise ratio of size Rk (measured in dB) and 

detecting the signal transmitted from a depth i, at frequency j, 

can be denoted as follows: 

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- - 

inc 

- - - 

1 
TABLE X-1 

PROBABILITY OF SIGNAL DETECTION 

VERSUS SIGNAL-TO-NOISE RAT I0 

Signal-to-Noise 

Ratio (dB) 

Probability of 

Detection 

Source: Arthur D. Little, Inc. (Figure IX-6) 

Arthur D Little, Inc 
'iPj,k ( D and Rk = Pi,j ('k}' ('I'kt (16) 

This is the probability associated with a specific Rk value. The 

analytical result that is of interest here is not simply P but 

i, j,k, Pi {Dl, the expected probability of detecting a signal transmitted at a specified overburden depth i,for a known transmission 

signal frequency j ,summed over all possible R 's. Since signal-to- k 

noise ratio can take on any value R and these values are k' 

mutually exclusive, the addition rule for probabilities applies; 

that is, 

where the summation over all possible signal-to-noise ratios R is k 

actually an approximation to the continuous integral over all Rk. 

B. ILLUSTRATIVE EXAMPLE 

These probability formulas and concepts can best be illustrated by a numerical example. For a transmission frequency of 

3030 Hz at an overburden depth of 1,000 feet, the data from 

Table VIII-2 are as follows: 

Sign al-to-Noise Probability of Achieving 

Ratio ( Interval) - Signal-to-Noise Ratio in Interval 

(For depth of 1,000 feet at 3030 Hz) 

less than 0 dB 0.420 

0 to 3 dB 0.075 

3 to 6 dB 0.075 

6 to 9 dB 0.076 

9 to 12 dB 0.070 

greater than 12 dB 0.285 

Arthur D Little, Inc 
It should be noted that the probabilities in this table sum to 

unity, since the table includes all possible signal-to-noise values. 

(Interval size could be made successively smaller to give closer 

approximations to the probability of detection integral actually 

being evaluated. ) 

Detection probabilities corresponding to the above signalto-noise ratios can be obtained from Figure 1X-6 using the 

midpoint of each interval, and these values are as follows: 

Signal-to-Noise Interval 

Ratio ( Interval) Midpoint 

Probability of 

Detection at Midpoint 

less than 0 dB less than 0 dB 0 

0 to 3 dB 1.5 dB 0.01 

3 to 6 dB 4.5 dB 0.15 

6 to 9 dB 7.5 dB 0.85 

9 to 12 dB 10.5 dB 0.99 

greater than 12 dB greater than 12 dB 1.00 

Applying the summation formula, Eq. 17 , the expected probability 

of detection at 1,000 feet and 3030 Hz, is estimated to be: 

The interpretation of this quantity is that, based on the results of 

this experimental program, a signal transmitted at 3030 Hz through 

an overburden depth of 1,000 feet can be expected to have a 

43 percent chance of being detected by an observer at the surface. 

Arthur D Little, Inc 
C. FINAL DETECTABILITY RESULTS 

Similar calculations were made for several other depth/- 

frequency combinations spanning the 630 Hz to 3030 Hz band and 

overburden depths down to 1,500 feet presently of interest to the 

detection of trapped miners. All data relevant to these calculations 

appear in Figures VIII-2 to VIII-5 and in Table VIII-2 of SectionVIII, and Figure 1X-6 of Section IX. Final results representing 

the expected probabilities of detection are plotted in Figure X-1. 

These plots represent the likelihood, on the average, of trapped 

miner signals being detected on the surface above U.S. coal mines 

having the indicated overburden depths. The plots apply for the 

General Instruments transmitter and aural detection by a searcher 

using a Collins receiver and headset. 

At any particular mine site with a given overburden depth, 

trapped-miner signals will either be detected or not detected. If 

such a detection experiment is repeated at several mines having 

the same overburden depth in the U.S. coal fields, the curves of 

Figure X-1 predict the expected percentage of experiments that will 

achieve signal detection at the indicated overburden depth and 

operating frequency. For example, if the device were tested at 

many locations having a 750-foot overburden, it is expected that 

the transmitted signal would be detected at about 68 percent of the 

locations for the operating frequency of 1950 Hz and at about 

43 percent of the locations for 630 Hz. 

Like the signal-to-noise ratio plots in Figures Vll-6 and 

VIII-7 of Section VIII, the curves of Figure X-1 reveal that the 

chances for successful detection are significantly higher in the 

upper portion of the transmitter operating frequency band. This 

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Arthur D Little, Inc 
occurs because, as shown in Section IV and Section VII, the background electromagnetic noise is lower and decreases faster than the 

signal, in this part of the band. Section IV-D also indicates that 

we can also expect somewhat worse signal detection conditions for 

certain geographical regions and times of day that have higher 

local thunderstorm activity. Under these conditions, the better 

detection results predicted at the higher frequencies will likely 

move downward towards the poorer results expected at the lower 

frequencies. As mentioned in Sections IV and VIT, an acceptable 

solution for these situations may be the suspension of search 

activities until a more favorable time of day, such as the daylight 

morning hours. 

I 

Arthur D Little, Inc 
XI. IMPLICATIONS OF RESULTS AND RECOMMENDATIONS 

Quantitative results have been obtained related to the 

expected detectability of trapped miner signals above U.S. coal 

mines. This section is concerned with the need of the U.S. Bureau 

of Mines to assess the impact of these results on the trapped miner 

location program. The discussion centers on four areas: detectability vs. depth and altitude, sensitivity analyses, confirmatory 

tests, and cperational utilization of the system. 

A. DETECTABILITY VS. DEPTH AND ALTITUDE 

The probability of detection vs. overburden depth curves of 

Section X depict a substantial departure from the intended performance goal for the equipment, namely to 1,000 feet. Even at the 

most favorable operating frequencies in the upper portion of the 

operating band, the expected probability of detection decreases 

from a highly satisfactory value of 90% for a 500 foot overburden 

to a value of about 45% for a 1,000 foot overburden. At the bottom 

of the operating frequency band these values decrease to about 70% 

at 500 feet and 35% at 1,000 feet, again a reduction by about a 

factor of two. These values of detection probability refer to the 

long-run, or limiting, frequency of occurrence of signal detection 

at mine sites throughout the U.S. coal fields having the indicated 

overburden depths. 

However, this shortfall of the performance goal does not 

negate the value of the trapped miner transmitter and its potential 

to save lives. Several other factors need to be considered, 

including the distribution of miners throughout the U.S. coal fields 

vs. overburden depth, and the variability of overburden depth 

above each coal mine. For example, the device will provide very 

Arthur D Little Inc 
good protection to miners working in mines having cverburdens 

shallower than 500 to 600 feet. In addition, consideration must be 

given to the fact that many mines, particularly in the Appalachian 

coal fields, will experience wide variations in overburden depth in 

different sections of the mine workings. Thus, many "deeper" mines 

will have areas with overburdens shallower than 500 to 600 feet. 

Therefore, the overall potential of the transmitter to save lives 

might be much more favorable than the raw detectability curves 

indicate at first glance when compared to the original performance 

goal. 

On the other hand, the results of Section X apply to rescue 

teams searching on foot with hand-carried detection receivers. To 

speed up the search effort, helicopter-based detection receivers are 

desirable. To estimate how the detectability performance will 

behave as a function of altitude, compared with that experienced 

on the surface, requires that the behavior of both signal and 

noise be determined as a function of altitude above the surface. In 

addition, the results of Section X strictly apply only within horizontal distances of about several hundred feet from the point on 

the surface directly above the in-mine transmitter. Therefore, to 

obtain detectability estimates for greater horizontal ranges, the 

signal strength behavior as a function of horizontal offset must 

also be estimated both on the surface and as a function of altitude. 

A convenient approximate method for extrapolating the overhead vertical signal strength results to off-axis and above the 

surface locations based on the homogeneous-earth radio propagation 

models developed by J. R. waH has been described in Reference 18 . To use these models, values of effective earth conductivity must be chosen. Two approaches have been suggested; one 

based on estimating overburden conductivities on a mine-by-mine 

basis from the individual field strength readings at each mine, 

and a second based on estimating an average overburden conductivity as a function of overburden depth from the transmission 

I 

Arthur D Little, Inc 
response regression lines derived from the normalized field strength 

data taken from all mines. We believe that the second approach 

based on the regression results may yield the most representative 

conductivity estimates and field strength extrapolations in the most 

systematic manner. These average extrapolated signal strength 

values can then be used with the Section VII surface noise distributions (assuming them to be independent of altitude to first 

approximation) to generate plots of approximate expected probabilities of detection as a function of altitude and horizontal offset. 

The specific applicability of these results to the development of 

practical search strategies needs to be assessed. 

B. SENSITIVITY ANALYSES 

A primary objective of this study was to quantify the likelihood, or chance, of detecting trapped miners over a wide range of 

actual operating conditions. Detection probability curves have been 

empirically derived from various transmit frequency/overburden 

depth combinations. These curves also depend on probability 

distributions which have been used to characterize the conditional 

behavior of signal strength, background noise, and aural detection 

levels. Although the analyses described in this report support the 

applicability of these distributions, some consideration should be 

given to investigating the effects of variations in their underlying 

form. For example, analytical studies can be performed to examine 

the effect of varying parameters, such as the following: 

estimated RMS signal strength mean 

estimated RMS signal strength variance 

estimated RMS noise mean 

estimated RMS noise variance 

Variations can be considered independently or in combination. 

Since the relative behavior of the dependent variable (i.e., the 

Arthur D Little, Inc 
probability of detection) is of primary interest, this type of study 

is generally referred to as a sensitivity analysis. 

In addition to variations in the specific parameters, it might 

be of interest to consider deviations from normality as well. Other 

distributional forms could be assumed for characterizing RMS signal 

strength and noise; for example, a lognormal or exponential distribution might be more appropriate for characterizing transmitted 

signal strength at certain depths beyond, say, 1,500 feet. 

Furthermore, the detectability results of Section X apply for 

basic aural detection, by a human operator with a headset, of the 

simple, pulsed CW signals produced by the General Instruments 

transmitter in the presence of background noise. Based on the 

literature, we estimate that a human cperator requires about a 

6 dB signal-to-noise ratio to achieve a 50% probability of detection 

for this type of signal in random background noise. Additional 

experimental work needs to be conducted to check the validity of 

this 6 dB estimate, assess its sensitivity to pulse length and 

repetition rate, and to check the shape of the chosen detectability 

vs. signal-to-noise ratio curve above and below the 50% value. 

These experiments should also compare results obtained using 

random noise with those obtained using noise with characteristics 

similar to that recorded by the Bureau of Mines on the surface 

above mines. Finally, the Bureau of Mines noise recordings should 

be subjected to a more thorough analysis and comparison with 

other available results on atmospheric and cultural noise, to more 

firmly establish the characteristics and origin of this recorded 

noise. 

To complement this experimental work, a parallel effort 

should be undertaken to analytically assess the sensitivity of the 

final probability of detection results to both the signal-to-noise 

ratio at the 50% detectability point and the shape of the probability of detection vs. signal-to-noise ratio curve, in addition to 

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the variations in noise and signal levels recommended in the 

previous paragraph. The results of these sensitivity analyses 

should provide a means for deciding whether more sophisticated 

signalling and receiving systems are worth pursuing. 

It may also be instructive, in light of the well-behaved 

regression models developed in Section V, to devote some additional 

effort to the possible extraction of quantitative, although perhaps 

weak, relationships between measured signal strengths on the 

surface and the distance to nearby electrical conductors, or the 

distance to receivers with large horizontal offsets, particularly for 

those situations that appear to represent pathological cases. 

Similarly, it may be instructive to better quantify the sensitivity 

of the regression results to random errors in reported parameter 

values such as overburden depth, transmit antenna dimensions, etc. 

C. CONFIRMATORY TESTS 

The program has yielded probability statements about the 

expected values of trapped miner signal strengths on the surface 

and their detectability as a function of overburden depth and 

frequency. Therefore, the results of several additional tests with 

pre-selected depth/frequency combinations at mine sites chosen at 

random from the U.S. coal field population would be expected to 

agree, on the average, with the results presented in this report. 

Oscar Kempthorne, in the introductory chapter of his classic 

text (19 on experiment design, emphasizes the circular nature of 

the experimental process; namely, that observations lead to the 

development of theory, which in turn leads to the prediction of 

new events, which then suggests the taking of new experimental 

observations, etc. Furthermore, it is well recognized as good scientific practice to experimentally verify deduced findings whenever 

possible. 

Arthur D Little, Inc 
The verification process assumes particular importance for 

this experimentally-based program with its potential regulatory 

implications. More specifically, we cite the following reasons for 

recommending verification tests: 

The experimental findings are important; it is clearly 

worth knowing with a high degree of certainty just how 

well the trapped miner detection system can be expected 

to perform under actual use conditions; 

The predicted performance is such that detection probability declines rather abruptly beyond overburden depths 

of 500 feet; 

There is a paucity of actual test data at mine sites 

having overburdens deeper than 700 feet;. namely, only 

15 tests were actually conducted at depths greater than 

700 feet, although 43 were planned; 

a The overburden and its transmission characteristics are 

known to be complex and variable between mine locations 

and between specific sites within the same mine. 

Although there are many aspects to be considered during the 

actual planning of confirmatory tests, not the least of which is the 

need itself, we recommend for the sake of completeness that some 

additional testing be considered. For example, hypotheses could be 

tested, with relatively few additional test measurements, that 

address the validity of the probability estimates beyond certain 

overburden depths such as 700 feet. It is always possible that 

"unusual" site conditions could lead to unexpected outcomes. It is 

also recognized that agreement, based on a few additional tests, 

would not "prove" the theoretical relationships established by this 

n 

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study. Nevertheless, some additional results from tests designed on 

the basis of the models developed to date would increase our 

knowledge about the performance of the device, no matter what the 

outcomes might be. 

D. OPERATIONAL UTILIZATION OF THE DETECTION SYSTEM 

Given that a trapped miner detection system of specified 

performance is available, the question of its most effective utilization under mine emergency conditions needs to be addressed. 

This can be examined from two points of view; namely, the use of 

the in-mine transmitters by the trapped miners and the use of the 

detection equipment on the surface by the mine search and rescue 

team. 

1 . In-Mine Transmitters 

The in-mine transmitters are presently designed to be carried 

on the miner's belt for use if the miner is unable to exit the mine 

during a mine emergency. In view of the above detectability 

findings and search strategy considerations discussed below, consideration should be given to the training of miners in the use of 

their transmitters. Namely, attention should be given to a number 

of psychological, operational and signal transmission factors that 

will tend to optimize the miner's probability of being detected and 

rescued. For example, if at all practical, provisions should be 

made to enable the miner to set up his transmitter and antenna at 

locations having signal transmission advantages, such as close to 

mine electrical conductors like power and communication cables, 

rails, etc., and in mine areas having shallower overburdens. 

Locations adjacent to mine conductors will also extend signal transmission ranges within the mine workings and increase the chances 

Arthur D Little. Inc 
of being detected by the in-mine rescue crew. Underground areas 

having shallower overburdens could even be designated by colorcoded signs to inform miners of locations having the most favorable 

transmission characteristics and, therefore, locations to which 

surface search teams will attach higher priorities. Practical 

operational procedures should also be developed to increase the 

chances that the in-mine transmitter's limited energy source will 

not be prematurely expended before at least the initial search 

efforts are substantially complete. 

Consideration should also be given to another possible implementation of the rescue transmitter that has the advantages of 

being both more economical and more conveniently tested on a 

routine basis. This can be achieved by building the rescue transmitters into the mine pager phones located Gn each working section 

and at other strategic locations along mine haulageways and 

escapeways. Thus, during a mine disaster, miners could simply 

take one of the pager phones and carry it with them for use if 

they were not able to exit the mine. This would allow the use of a 

longer life energy source such as the pager phone lantern battery, 

provide routine inspection and testing during pager phone maintenance cycles, and not require the miner to carry another piece 

of equipment. 

2. Surface Detection Receivers 

Even more important consideration needs to be given to the 

problem of devising effective search plans and procedures for 

maximizing the number of rescuable miners detected per unit of 

search effort at a mine disaster site. Namely, how should the mine 

search and rescue team allocate its effort and resources to best 

accomplish the objective of finding and rescuing all trapped miners 

within the limited time constraints? This problem has been 

- 

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addressed in a preliminary manner in Appendix G, where we have 

formulated the search problem specifically for a rapid helicopterbased search effort backed up by man-carried surface-based 

receivers for pinpointing the underground transmitter locations. 

These plans and procedures can be modified accordingly to accommodate the situation in which the search must be conducted 

entirely by a large number of search team members carrying rescue 

receivers on the surface. 

The appendix presents a methodology and mathematical representation to describe the important parameters, constraints, 

relationships and quantities to be optimized, together with key 

input information that must be obtained or estimated before "good," 

if not optimum, search patterns can be formulated and their effectiveness assessed. This key input information includes several 

important time intervals involved in post-disaster search and 

rescue operations, such as: 

The life expectancy of the trapped-miner transmitter as a 

function of the residual energy in the miner's cap lamp 

battery at the time of transmitter activation, 

The expected survival times of trapped miners for different mine disaster environmental conditions, 

Expected times required to rescue miners after detection 

for typical mine disaster conditions and mine configurations, 

Expected arrival and set-up times of ground and airborne 

search and rescue teams after a disaster has occurred. 

The lengths of these times and their relationships to each cther 

will not only influence search and rescue team strategies, but may 

also have an impact on the training of miners regarding procedures for the activation and prolonged operation of their transmitters. 

Arthur D Little, lnc 
Another important input parameter will be the effective sweep 

width for the detection equipment used on the surface or in the 

air. The sweep width, Wf, (typically defined in terms of the horizontal offset for 50% signal detectability) will be a function of the 

mine overburden depth, altitude of the receive antenna above the 

surface, ambient noise conditions, and the actual signal detection 

process (i.e., aural or other). At mines with relatively flat 

surface topography, as in Illinois and Ohio, a constant sweep 

width can be assumed for the whole mine. In relatively mountainous areas such as West Virginia and eastern Kentucky, several 

sweep widths may be required to properly characterize different 

regions of a widely dispersed mine. The rescue team should take 

advantage of available topographic information in a practical 

manner that will minimize the number of different sweep widths 

required and simplify search operations and procedures as much as 

possible. 

The signal detectabilityhweep width information can be 

combined with mine map and operational information on the likely 

distribution and movement of miners in the mine. This combined 

information will enable the rescue team to quickly identify, in 

gross terms, high priority areas of the mine that have the highest 

likelihoods of both trapped miner presence and detectability, and 

those with proportionally smaller likelihoods. These priorities will 

then allow the efficient and systematic allocation of scarce search 

and rescue resources so as to increase the probable number of 

miners detected and rescued per unit of search effort. 

The methodology and mathematical representations developed 

in Appendix G need to be refined and applied to several typical 

mine disaster operational scenarios for specific practical values of 

the key parameters. This should result in the formulation and 

assessment of a number of search strategies and lead to a better 

understanding of their practical application to real mine disaster 

situations. 

Arthur D Little, Inc 
XI1 . REFERENCES 

Kehrman, R. F., A. J. Farstad, D. Kalvels. "Reliability 

and Effectiveness Analysis of the USBM Electromagnetic 

Location System for Coal Mines." Westinghouse Electric 

Corporation, Geophysical Instrumentation Systems, Final 

Report, December 1978. (U.S. Bureau of Mines Contract 

J0166060) 

Cochran, W. G. Sampling Techniques, John Wiley and Sons, 

New York, 1953- 

Durkin, J., U. S. Bureau of Mines Pittsburgh Mining and 

Safety Research Center, personal communication. 

"Field Evaluation of USBM Coal Mine EM Location System," 

First Through Eighteenth. Westinghouse Electric Corporation, 

Geophysical Instrumentation Systems, Field Reports, October 

1976 to October 1978 (U.S. Bureau of Mines Contract No. 

J0166060). 

Durkin, J. and L. Cooper. "Final Computer Tabulation 

of Surface Field Strengths and In-Mine Transmitter Parameters," May 12, 1980, and "Computer Tabulation of 

Recorded Numerical Data by Westinghouse Measurement 

Team," November 20, 1979, U.S. Bureau of Mines, Pittsburgh 

Mining and Safety Research Center. 

Maxwell, E.L. "Atmospheric Noise from 20 Hz to 30 kHz." 

Radio Science, 2 (New Series) (6): 637-644, June 1967. 

Maxwell, E. L., and D. L. Stone. "Natural Noise Fields 

from 1 cps to 100 kc." IEEE Trans. Antennas and Propagations, AP-11(3): 339-343, May 1963. 

Watt, A.D. "Atmospheric Radio Noise Fields." VLF Radio 

Engineering, Chapter 5. Pergamon Press, Oxford, 1967. 

C. C. I. R. "World Distribution and Characteristics of Atmospheric Radio Noise," Report 322, Documents of the Xth 

Planary Assembly, Geneva, 1963, International Telecommunications Union, Geneva 1964. 

Barr, A., J. Goodnight, J. Sail, and J. Helwig. "A User's 

Guide to SAS 76," SAS Institute, Inc., Cary, NC, pp. 

127-144. 

Snedecor, G. W. and W. G. Cochran. Statistical Methods. 

6th Edition, Iowa State University Press, 1974. 

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Nelson, W. "Theory and Application of Hazard Plotting 

for Censored Failure Data ." Technometrics November 1972. 

Urick, R.J. "Detection of Signals in Noise and Reverber- - 

ation : Detection Threshold. " Principles of Underwater Sound 

for Engineers. Chapter 12, McGraw-Hill, 1967. 

Principles and Applications of Underwater Sound. Summary 

Technical Report of Division 6, NDRC, Vol. 7, Washington 

DC, pp. 184-189, pp . 258-265, 1946 ( Reissued 1968) . 

Garner, W. R. , "Auditory Thresholds of Short Tones as 

a Function of Repetition Rates," JASA 9(4): 600-608, 

July 1947. 

"Noise Masking of Echoes." Recognition of Underwater - Sounds. Chapter 8, Summary Technical Report of Division 6, 

NDRC, Vol. 9, Washington DC, p. 204, 1946. 

Wait, J. R. and K.D. Spies. "Subsurface Electromagnetic 

Fields of a Circular Loop of Current Located Above Ground," 

IEEE Trans. on Antennas and Propagation, pp. 520-522, 

July 1972. 

Durkin, J. "Earth Conductivity Measurements Using Subsurface Electromagnetic Fields of a Circular Loop of Current 

Located on the Surface," U.S. Bureau of Mines, Pittsburgh 

Mining and Safety Research Center, Technical Report, 

1980. 

Kempthorne, 0. The Design and Analysis of Experiments. 

John Wiley and Sons, New York, 1952. 

C 

Arthur D Little, Inc 
APPENDIX A 

INFORMAT ION ON STAT ISTICALLY 

SELECTED MINES PLANNED 

FOR FIELD MEASUREMENT PROGRAM 

This information was generated by the statistically based 

mine selection method described in Section IIIB. This method was 

applied to a consolidated Bureau of Mines computer data base of 

coal mines obtained by the merging of an MSHA mine data file 

containing the number of miners at each mine and a Bureau cf 

Mines Eastern Field Operations Center data file containing the 

maximum overburden depth at each mine. 

Arthur D Little. Inc 
TABLE A1 

LISTING OF SPECIFIC MINES SELECTED FOR FIELD MEASUREMENTS 

IN U.S. FIELDS (ORDERED BY DEPTH INTERVAL, DEPTH, AND 

* - NUMBER OF MINERS WITHIN EACH DEPTH INTERVAL) 

J & J Mining Co. 

#2 Mine 

Sewickley 

Route 8, Box 292C 

Morgantown, W.V. 26505 

Peabody Coal Co. 

Baldwin Mine ill 

No. 6, P.O. Box 67 

Marissa, IL 62257 

Consolidation Coal Co. 

Humphrey #7 UG 

Pittsburgh 

P.O. Box 100 

Osage, WV 26543 

Peggs Run Coal Co. Inc. 

Peggs Run /I2 

Upper Fr eepor t 

P.O. Box 184 

Shippingport, PA 15077 

Amherst Coal Co. 111 

MacGregor ij8 UG, Coalburg 

Lundale, WV 25631 

Martin County Coal Corp. 103 

jI1-S UG 

Stockton 

Route 40, Box 82A 

Inez, KY 41224 

Max. KO. 9ep th 

MESA ID Depth --. Men -. Interval 

Peabody Coal Co. 0250 110 200-299 

Sinclair !I1 UG 

Kentucky No. 9 

301 No. Memorial Dr. 

St. Louis, MO 63102 

180 Ih 

ppppppp---- 

Arthur D Little, Inc 
Name/Location MESA ID 

Consl. Coal-Cen. Div. 036 3301065 

Franklin Highwall UG 

Pittsburgh (No. 8) 

Georgetown General Office 

Cadiz, OH 43907 

Republic Steel Corp. 036 3600973 

Banning /I4 

Pittsburgh 

617 Fayette National Bank Bldg. 

Uniontown, PA 15401 

Ranger Fuel Corp. 167 4603446 

H Mine UG 

Peer less 

P. 0. Box 966 

Beckley, WV 25801 

Union Carbide Corp. 

Ferralloys 

#7C UG 

No. 5 Block 

Route 2, Box 224 

Clendenin, WV 25045 

Shamrock Coal Company 135 1502502 

Shamrock /I18 

Hazard No. 4 

Box 36A 

Beverly, KY 40913 

Badger Coal Co. Inc. 076 4601254 

Badger No. 14 UG 

Upper Kittanning 

P. 0. Box 472 

Clarksburg, WV 26301 

Bethlehem Mines Corp. 074 3600852 

/I38 UG 

Lower Freeport 

Box 29 

Ebensburg, PA 15931 

Max. No. Depth 

Depth - Men Interval 

Arthur D Little, Inc 
Island Creek Coal Co. 484 

Fies Mine 

Kentucky No. 11 

444 South Main Street 

Madisonville, KY 42431 

Peabody Coal Co. 

Alston 114 Mine UG 

Kentucky No. 9 

301 No. Memorial Dr. 

St. Louis, MO 63102 

Peabody Coal Co. 

1/10 Mine 

No. 6 

P. 0. Box H 

Pawnee, IL 62558 

Indian Ridge Coal Co. 216 

Indian Ridge #4 UG 

Gilbert 

Ottaway Trent 

Hanover, WV 24839 

Southeast Coal Co. 

11402 UG 

Hazard No. 4 

Route 2, Box 60 

Whitesburg, KY 41858 

Jumacris Mining Inc. 

115 Mine UG 

Lower Cedar Grove 

P. 0. Drawer D 

Gilbert, WV 25621 

Omar Mining Co. 

Chesterfield #1 UG 

Stockton 

P. 0. Box 338 

Madison, WV 25130 

MESA ID 

1502018 

Max. No. Depth 

Depth - Men Interval 

- 

Arthur D Little, Inc 
Max. No. Depth 

Depth - Men Name/ Location MESA Interval ID 

Hawley Coal Mining Corp. 

Bottom Ck. /I1 Mine 

Pocahontas No. 12 

Drawer J 

Keystone, WV 24852 

United States Steel Corp. 036 

Mt. Braddock - Frick Coal 

Dist. 

Pittsburgh 

Fayette Bank Bldg. 

Uniontown, PA 15401 

Westmoreland Coal Co. 

Prescott /I2 Mine UG 

Imboden 

Osaka Star Route 

Appalachia, VA 24216 

ARMCO Steel Corp. 

Robin Hood No. 8 UG 

Dorothy 

Montcoal, WV 25135 

National Mines Corp. 

Isabella 

Pittsburgh 

P. 0. Box 431 

Isabella, PA 15447 

Republic Steel Corp. 

Republic UG & Prep Plant 

Lower Elkhorn 

Route 1, Box 306 

Elkhorn City, KY 41522 

Republic Steel Corp. 

Newf ield 

Double Freeport 

617 Fayette National Bank 

Bldg . Uniontown, PA 15401 

Arthur D Little, Inc 
Name/Location MESA ID 

Island Creek Coal/West 489 1502156 

KY Div. 

Providence /I1 

Kentucky No. 9 

Drawer N 

Madisonville, KY 42431 

Alabama By-products Corp. 229 0100340 

Gorgas Mine /I7 

America 

P. 0. Box 158 

Goodsprings, AL 35560 

United States Steel Corp. 036 3600909 

Robena /I1 - Frick Coal Dist. 

Pittsburgh 

Fayette Bank Bldg. 

Uniontown, PA 15401 

Jones & Laughlin Steel 036 3600907 

Corp. 

Shannopin UG 

Pittsburgh 

Box 608 

California, PA 15419 

Gateway Coal Co. 036 3600906 

Gateway Mine 

Pittsburgh 

P. 0. Box 608 

California, PA 15419 

Nacco Mining Co. 

Powhatan /I6 UG 

Pittsburgh (No. 8) 

Powhatan PT, OH 43942 

Bill Branch Coal Co. Inc. 177 4404134 

/I2 UG 

Blair 

Box 556 

Vansant, VA 24656 

Max. No. Depth 

Depth Men - Interval 

I 

Arthur D Little, Inc 
Max. No. Depth 

MESA ID Depth - Men Interval 

Betty B Coal Co. 

Mine 113 

Upper Banner 

Box 340 

Clintwood, VA 24228 

White Peter Coal Mining 

Corp. 

War Eagle /I1 Hawley Coal 

Lower War Eagle 

Gen. Delivery 

Isaban, WV 24846 

Bethlehem Mines Corp. 

Solomon Run 1/73 UG 

Upper Kittanning 

Box 29 

Edensburg, PA 15931 

Southern Appalachian Coal 168 

Co . Bull Creek 112 

No. 2 Gas 

217 94th Street 

Mannet, WV 25315 

Bethlehem Mines Corp. 

11108 UG 

Redstone 

P. 0. Box360 

Bridgeport, WV 26330 

Webster City Coal Corp. 

Retiki Mine 

Kentucky No. 9 

P. 0. Box 45 

Henderson, KY 42420 

Pocahontas Fuel Co. 

#7 UG 

Pocahontas No. 3 

Horsepen, VA 24619 

Arthur D Little, Inc 
Name/Location MESA ID 

North Amer. Coal Corp. 084 3600928 

East. Div. Comemaugh /I1 UG 

Lower Kittanning 

Seward, PA 15954 

Sewell Coal Co. 

Meadow River ill UG 

Sewell 

Lookout, WV 25863 

Consl. Coal-Cen. Division 074 3301158 

Oak Park 117 UG 

Lower Freeport (No. 6A) 

Georgetown General Office 

Cadiz, OH 43907 

North American Coal Corp. 036 3300937 

Ohio Division 

Powhatan /I5 UG 

Pittsburgh (No. 8) 

Powhatan PT, OH 43942 

Republic Steel Corp. 227 0100759 

North River /I1 UG 

Prat t 

P. 0. Box 268 

Berry, AL 35546 

Alabama By-products Corp. 279 0100347 

Segco /I1 UG 

Mary Lee 

P. 0. Box 127 

Goodsprings, AL 35560 

Hatter Coal Co. 

Middle Split Slope 

Manmoth (Top Split) 

Hegins, PA 17938 

Calvert Coal Co. 

117 UG 

Pocahontas No. 3 

110 Harvey Street 

Beckley, WV 25801 

Max. No. Depth 

Depth Men Interval 

I 

Arthur D Little, Inc 
Johnson Coal Co. 

/I11 UG 

Hazard No. 4 

Box 888 

Martin, KY 41649 

Youngs Branch Coal Co. 

i'14 UG 

Widow Kennedy 

Box 653 

Vansant, VA 24656 

Barnes & Tucker Co. 

Lancashire i'24 B UG 

Lower Kittanning 

1912 Chestnut Avenue 

Barnesboro, PA 15714 

Affinity Mining Co. 

Keystone /I5 UG 

Pocahontas No. 3 

P. 0. Box 948 

Sophia, WV 25921 

Youghiogheny & Ohio 

Coal Co. 

Nelms /I2 UG 

Lower Freeport (No. 6A) 

Hopedale, OH 43976 

Greenwich Collieries/PA 

Mines 

Greenwich Collieries 1'12 

Lower Freeport 

P. 0. Box 367 

Ebensburg, PA 15931 

Consolidation Coal Co. 484 

Hillsboro Mine/Midwes tern 

Reg. 

No. 6 

P. 0. Box 218 

Pinckneyville, IL 62274 

MESA ID 

1507092 

Max. No. Depth 

Depth - Men Interval 

Arthur D Little, Inc 
MESA ID 

Peabody Coal Co. 

Camp i12 

Kentucky No. 9 

RR #5, Box 46-A 

Morganfield, KY 42437 

Peabody Coal Co. 489 1502709 

Camp ill 

Kentucky No. 9 

Morganfield, KY 42437 

Standard Sign & Signal Co. 154 1502424 

May Mine UG 

Elkhorn #2 

Box 801 

Pikeville, KY 41501 

Sewell Coal Co. 

Sewell ill UG 

Sewell 

Nettie, WV 26681 

National Coal Mining Co. 151 4601450 

#25 UG 

Cedar Grove 

Box 461 

Holden, WV 25625 

Kaiser Steel Corp. 

York Canyon ill UG 

York Canyon 

P. 0. Box 281 

Raton, NM 87740 

Beth-Elkhorn Corp. 154 1502092 

Pike il26 UG & Prep Plant 

Elkhorn #2 

Jenkins, KY 41537 

Max. No. Depth 

Depth - Men Interval 

I 

Arthur D Little, lnc 
U. S. Steel Corp. 

/I9 Mine UG 

Pocahontas No. 3 

Gary, WV 24836 

MESA ID 

344 4601418 

Southern Ohio Coal Co. 084 4603805 

Martinka #1 UG 

Lower Kittanning 

P. 0. Box 552 

Fairmont, WV 26554 

Valley Camp Coal Co. 036 4601483 

VC /I1 Mine 

Pittsburgh 

2971 E Dupont Avenue 

Shrewsbury, WV 25184 

Amigo Smokeless Coal Co. 344 4604216 

Amiga #2 UG 

Pocahontas No. 3 

Box 966 

Beckley, WV 25801 

Eastern Associated Coal 168 4601270 

Corp. 

Harris j'2 UG 

Campbells Creek 

Star Route 2 

Bald Knob, WV 25010 

Eastern Associated Coal 344 4601535 

Corp. 

Keystone /I2 UG 

Pocahontas No. 3 

Herndon, VA 24726 

Blue Diamond Mining Inc. 111 1502082 

Leatherwood 

Lea therwood 

Box 298 

Leatherwood, KY 41756 

Max. 

Depth 

No. Depth 

- Men Interval 

Arthur D Little, Inc 
P. 0. Box 599 

Fairfield, AL 35064 

Consolidation Coal Co. 174 4601986 0900 

Rowland /I3 Mine/ 

S. Appalachia 

Upper Eagle 

Route 1, Box 169 

Beckley, WV 25801 

Carbon Fuel Co. 

/I36 UG 

Eagle 

Carbon, WV 25037 

Clinchfield Coal Co. 

Moss /I3 Portal D 

Tiller 

Dante, VA 24237 

II 

Arthur D Little Inc 
Name/Locat ion MESA ID 

Allied Chemical Corp.-Semet 176 4601288 

Sol 

Harewood UG 

Eagle 

Box 791 

Montgomery, WV 25136 

Slab Fork Coal Co. 

//lo UG 

Pocahontas No. 4 

Slab Fork, WV 25920 

Valley Camp Coal Co. 036 4601482 

VC /I3 Mine 

Pittsburgh 

2971 E. Dupont Avenue 

Shrewsbury, WV 25184 

Volunteer Mining Corp. 134 4000255 

i/1 UG 

Dean 

Box 512 

Lake City, TN 37769 

Eagle Coal & Dock Inc. 168 4604578 

i/7-A UG 

No. 2 Gas 

P. 0. Box 38 

Stickney, WV 25188 

Ranger Fuel Corp. 

F Mine UG 

War Eagle 

P. 0. Box 966 

Beckley, WV 25801 

Eastern Associated Coal 176 4601271 

Corp. 

Harris ill UG, Eagle 

Max. No. Depth 

Depth - Men I Interval 

Star Route 2 

Baid Knob, WV 25010 

Arthur D Little, Inc 
Name/Location MESA ID 

Consolidation Coal Co. 036 4601968 

Blacksville 112 UG 

Pittsburgh 

Box 24 

Wana, WV 26590 

Eastern Associated Coal 036 4601456 

Corp. 

Federal 112 UG 

Pittsburgh 

Miracle Run 

Fairview, WV 26570 

Bethlehem Mines Corp. 1.76 4601496 

11116 UG 

Eagle 

P. 0. Box 4337 

Charleston, WV 25304 

Jewel1 Ridge Coal Corp. 285 4402253 

Big Creek Seaboard 111 UG 

Lower Seaboard 

Jewell Valley, VA 24623 

Bethlehem Mines Corp. 170 4601268 

#I31 UG 

Powell ton 

P. 0. Box 4337 

Charleston, WV 25304 

U. S. Steel Corp. 

i12 UG 

Pocahontas No. 4 

Gary, WV 24836 

CF & I Steel Corp. 

Allen Mine UG 

Allen 

P. 0. Box 155 

Weston, CO 81091 

Max. No. Depth 

Depth - Men Interval 

C 

Arthur D Little, Inc 
Max. No. Depth 

Depth - Men MESA Interval ID 

Consolidation Coal Co. 4601436 

Shoemaker UG 

Pittsburgh 

P. 0. Drawer L 

Moundsville, WV 26041 

Clinchfield Coal Co. 

Chaney Creek /I2 UG 

Jawbone 

Dante, VA 24237 

Youngstown Mines Corp. 

Dehue UG 

Eagle 

P. 0. Box 900 

Dehue, WV 25618 

U. S. Steel Corp. 

Pinnacle Creek /I50 UG 

Pocahontas No. 3 

Gary, WV 24836 

United States Fuel Co. 

King Mine 

Hiawatha A&B 

Box A 

Hiawatha, UT 84527 

Pocahontas Fuel Co. 

Matthews Mine 

Jellico 

P. 0. Box 460 

Middlesboro, KY 40965 

Westmoreland Coal Co. 

Stonega D 

Osaka /I2 Mine UG 

Inboden 

Osaka Star Route 

Appalachia, VA 24216 

Arthur D Little, Inc 
Peabody Coal Co. 

Deer Creek UG 

Blind Canyon 

P. 0. Box 588 

Huntington, UT 84528 

MESA ID 

855 4200121 

Eeatrice Pocahoetas Co. 344 4400238 

Beatrice UG 

Pocahontas No. 3 

Box F 

Keen Mountain, VA 24624 

Island Creek Coal Co. 344 4402134 

VA Pocahontas /I4 

Pocahontas No. 3 

Keen Mountain, VA 24624 

Max. No. Depth 

Depth - Men Interval . - 

LL 

Arthur D Little, Inc 
APPENDIX B 

INFORMATION ON ACTUAL MINES VISITED 

DURING FIELD MEASUREMENT PROGRAM 

Source : Westinghouse (1,4) 

Arthur D Little, lnc 
Gateway Coal Co. - Gateway Mine 

Clarksville, Greene County, PA 

Pittsburgh 

U.S. Steel Corp. - Robena Mine 

Greensboro, Greene County, PA 

Pittsburgh 

Buckeye Coal Co. - Nemacolin Mine 

Nemacolin, Greene County, PA 

Pittsburgh 

rri 

cn 

I Duquesene Light - Warwich No. 2 

Greensboro, Greene County, PA 

Pittsburgh 

Duquesne Light - Warwich No. 3 

Greensboro, Greene County, PA 

Se wick le y 

Eastern Associated Coal - Delmont Mine 

Hunker, Westmoreland County, PA 

Upper Freeport 

North Amer. Coal Co. - Conemaugh No. 1 

Seward, Westmoreland County, PA 

N. E. Mains B 

Republic Steel - Newf ield Mine 

New Kensington, Westmoreland County, PA 

Upper & Lower Freeport 

Republic Steel - Banning No. 4 

W. Newton, Westmoreland County, PA 

Pittsburgh 

4 

< $8 3 h)4 d 4 2 00 0 0 Q) 0 P bin P P 

Helen Mining Co. - Homer City Mine 

Homer City, Indiana County, PA 

Upper Freeport 

- rri 

D 0 

Greenwich Collieries - Mine No. 2 

Spangler, Cambria County, PA 

Lower Freeport 

Eastern Associated Coal - Colver Mine 

Colver, Cambria County, PA 

Lower Kittanning 

Barnes & Tucker Coal - Lancashire No. 20 

Bainsboro, Cambria County, PA 

Lower Kittanning 

A w Barnes & Tucker Coal - Lancashire 25D $ gg 'P 'W in ID Q) ~1 P Bainsboro, Cambria County, PA 4 Lower Freeport 

w Barnes & Tucker Coal - Lanceshire 24D ? 4% h)Q) z inb 2 gn 0 P ; Bainsboro, Cambria County, PA 

Lower Freeport 
F 

373 8 3 3 u, ii' 

H 

-r A 

in io 

-r P 

inb 

G c 

-. m bo io 

-. P 

in io 

.; 

-r & 

in io 

-. & 

inb 

? P u a 

W 

b to 

z g 

-r & 

in io 

-. m 2 in 

-rP 

b tn 

Mining Co., Mine Name, 

Town, County, State, 

Seam Name 

Consol - Oak Park No. 7 

Cadiz, Harrison County, OH 

Lower Freeport 6A 

Youghiogheny & Ohio Coal - Nelm's 2 

Hopedale, Harrison County, OH 

Lower Free~ort 

N. American Coal - Powhatan No. 1 

Powhatan Point, Belmont County, OH 

Pittsburgh No. 8 

N. American Coal - Powhatan No. 3 

Powhatan Point, Belmont County, OH 

Pittsburgh No. 8 

Youghiogheny & Ohio Coal - Allison 

Beallsville, Belmont County, OH 

Pittsburgh No. 8 I 

Southern Ohio Coal Co. - Meigr No. 2 

Athens, Meigs County, OH 

Clarion 4A 

Southern Ohio Coal Co. - Meigs No. 2 

Athens, Meigs County, OH 

Clarion 4A 

Valley Camp Coal Co. - Mine No. 1 

Short Creek, Ohio County, WV 

Pittsburgh 

Consolidation Coal - Eastern Reg. (Shoemaker Mine) 

Moundsville, Marshall County, WV 

Pittsburgh 

Southern Ohio Coal Co. - Martinka No. 1 

Fairmont, Marion County, WV 

Lower Kittanning 

Consolidation Coal - Loveridge Mine 

Fairview, Marion County, WV 

Pittsburgh 

Badger Coal Co., Inc. - Mine No. 14 

Philippi, Barbour County, WV 

Kittanning 

Bethlehem Mines Corp., No. 108 

Century, Barbour County, WV 

Redstone 

Sewell Coal Company - Mine No. 1 

Nettie, Nicholas County, WV 

SeweN 
2 -h 

Z"5 

2% 

q-c 

rn 2 -. 

3 

x Mining Co., Mine Name, 

Town, County, State, 

Seam Name 

e uu Central Appalachian Coal - Five Block 1 

=j bb o o Mermet, Kanawha County, WV 

Lower Kittanning 

ul 

\ =g N -a VI Sewell Coal Company - Meadow No. 1 

2 00 o o 03w ul into d CD Lookout, Fayette County, WV 

Se well 

- d Allied Chemical Corp. - Harewood 

03 o w 8 Boomer, Fayette County, WV 

Eagle 

ul 

\ P h) 

0 y.;: d 

Armco Coal Co. - Robinhood No. 8 

2 00 o o g 2 o d % Twilight, Boone County, WV 

Dorothy 

Q, P -. A ;& 8 gg d UJ Bethlehem Steel - Mine 131 

2 00 w b 03 cn o N w Van, Boone County, WV 

Po wellton 

h) -a d 

Omar Mining Company - Omar No. 4 

00 P3 o i, i, N Madison, Boone County, WV 

Stock ton 

h) %$ g cg d Bethlehem Steel (downlink) - Mine 116 

do wcn N 2 Eunice, Boone & Raleigh County, WV 

Eagle 

s 

m ,r 

M Bethlehem Steel (uplink) - Mine 116 0 " 

"k s cg 8 8cn o 8 Eunice, Boone & Raleigh County, WV ,c 

01 5 

Eagle sl o 

d l " z, h) w8 4, Eagle Coal & Dock - Hope No. 10 '"3 J 

w b 03 o cn ; 81 Stickney, Boons & Raleigh County, WV h) c; CI Stockton Lewiston z D A M Q 

w o h) -w Slab Fork Coal Co. - Mine 10 h)cn 3 '-.b d VI Q 

o o o o d u Slab Fork, Raleigh County, WV 5 D 

Pocahontas No. 3 n r E B 

-w Ranger Fuel - Mine F ,Z 0 

0 cn o o u o to biD 8 Bolt, Raleigh County, WV w -0 D z - 

Eagle D 

2 

h) d 

4 h) 4 d 

Amherst Mining Co. - MacGregor No. 8 

o o u u N 8 Lundale, Logan County, WV 

Coa lburg 

- 

2 ;52 " M 2% Eastern Associated Coal - Keystone 

bb in i, in to i$ x a Herndon, Wyoming County, WV ' 

Pocahontas No, 3 

d A 

WO &a Jumacris Mining Inc. - Mine No. 4 

u P Q, o IQ UJ 2 Gilbert, Mingo County, WV h) gg u Lower Cedar Grove 

N 5 5: uw w Hawley Mining Corp. - Bottom Creek No. 1 to 

4 0 0 o -w UJ 8 Keystone, McDowell County, WV 

Pocahontas No. 12 

A 

Q, h) 

\ - P 4 -a d 

Petter White Coal Co. - Brushy No. 2 

2 00 2 c u o o "o i, w Isaban, McDowell County, WV w cn 

Lower War Eagle 

P ( P 8 -w U.S. Steel - Gary No. 9 

2 cnb o bio 8 Filbert, McDowell County, WV 

hcahontas No. 3 

Q, U.S. Steel - Gary No. 2 2 00 0 0 to cn d 4 w 0 Wilcoe, McDowell County, WV 

Pocahontas No. 4 
3 3 Mine Co., Mine Name, 

Town, County,State, 

Seam Name 

N co N .J 0, 

2 40 p" % 8 -a Island Creek - Virginia Pocahontas No. 3 

=f bio 04 to8 ol b b " Keen Mtn., Buchanan County. VA 

Harlan 

d 

'L 

\ G 2 N Eastover Mining Co. - Virginia City .J 00 Q, o o a N 8 g Virginia city, wise county, VA 

Jaw Bone 

0 0 (0 'L 

-Q) -ul Jewell Ridge Coal Corp. - Seaboard No. 2 2 ?g bb 8% * hb, 4 " Tazewell County. VA --- - 

Lower Seaboard , @ 

N .J = 0 

8 3 'a Clinchfield Coal Co. - Moss No. 2 = c 4 o cn " Dante, Russell County, VA 

Tiller E s 

Drn - e d Clinchfield Coal Co. - Moss No. 4 = .J gg o " Dante, Russell County, VA Z .J 

Tiller D 

N D .J Q,& NO A Westmoreland Coal - Prescott No. 2, Test 1 D 

3 y'C gz .J G 8 rn in b % Big Stone Gap, Wise County, VA D 

r lmboden D N 0 

2 8; pg 38 ; -e Westmoreland Coal - Prescott No. 2, Ten 2 1 P~I o o m in b " 2 Big Stone Gap, Wise County, VA - 

lmboden D 

2 d 

.J g% ;h Westmoreland Coal Co. - Bullitt Mine 3 fly .J b in 0 Q, e " % Big Stone Gap, Wise County, VA 

Dorchester 

Volunteer Mining Corp. - No. 2 Mine ' 2 40 ' ' -A ' u '.J OD @ & Devonia, Anderson County, TN 4 

Dean Big Mary Z 2 

P 'L 59 0 'L -(D aw r -* Consolidation Coal Co - Mathews 

3 Ul N o .J o in io @ & Arco, Claiborne County, TN 

I 

m 

m Jellico 
Mining Co., Mine Name, 

Town, County, State 

Seam Name 

Peter Cave - Mine No. 1 

Lovely, Martin County, KY 

War field 

Pontika - No. 1 

Lovely, Martin County, KY 

hnd Creek 

Standard Sign & Signal - No. 1 Mine 

Pikeville, Pike County, KY 

Elkhorn 

Republic Steel Co. - Republic 

Elkhorn City, Pike County, KY 

Lower Elkhorn 

South East Coal Co. - Mine No. 402 E 2 

Irvine, Knott County, KY 1 p Hazard No. 4 ml 

OD 

Beth-Elkhorn Corp. - Pike No. 26 5; CI 

Shelby Gap, Pike County, KY gz 6 

Elkhorn No. 3 2 g. 

Beth-Elkhorn Corp. - Pike No. 25 

r: % 

2- 5. 

Shelby Gap, Pike County, KY ID 

Hazard No. 4 g r s 

Eastover Mining Co. - Highsplint (Harlan) 

Highsplint, Harlan County, KY - 

Harlan D 

2 

~astovir Mining Co. - Highsplint (Darby) 

Highsplint, Harlan County, KY 

Darby 

Path Fork Harlan Coal Co. - FEE 

Alva, Harlan County, KY 

Upper Harlan 

Eastover Mining Co. - Highsplint 4 

Highsplint, Harlan County, KY 

Harlan No. 4 

Cal Glo - No. 21 

Siler, Knox County, KY 

Blue Gem 
0 

i 

Mining Co., Mine Name 

-. Town, County, State, 

d 

-. Island Creek - Hamilton No. 1 

Morganfield, Union County, KY 

No. 9 

(D -.a -. 

PP 68 VI Peabody Coal Co. - Camp No. 1, Site No. 1 '3 y: b -. w o o ' N Morganfield, Union County, KY 0 kz m No. 9 

Peabody Coal Co. - Camp No. 1, Site No. 2 

Morganfield, Union County, KY 2 

No. 9 V, 

-I 

rn 

Pyro Mining Co. - Pyro Slope 6 3 

z 

Sturgis, Union County, KY 1C 

No. 6 rn 

z 

-I 

Peabody Coal Co. - Alston No. 4 C 

0 Centertown, Ohio,County, KY 1C 

No. 9 -I 

Peabody Coal Co. - Sinclair No. 2 

6 0 r 

Drakesboro, Butler County, KY rn rn 

No. 9 Z 2 

-I = 

a bJ 

Owl Creek Corp. - SueJan Coal Co. 

St. Charles, Hopkins County, KY D g. 

No. 6 i 

- 

Amax Coal Co. - Wabash Mine 

Kennsburg, Wabash County, I L 

Harrisburg No. 5 

VI h) h) Freeman United - Orient No. 4 

00 ES !2 ix s 2 Marion, Williamson County, IL 

Herrin No. 6 

VI (D Zeigler Coal Co. - Mine No. 4 

< 2 wb wb 00 s8g gg s Johnston City, Williamson County, I L 

Herrin No. 6 

(D N 03 Freeman United - Orient No. 6 \ $ 00 o o P o P Waltonville, Jefferson County, IL PO g E; 

Illinois No. 6 

VI Old Ben Coal Co. - Old Ben No. 26 

y s Sesser, Franklin County, lL 

Herrin No. 6 

VIM (D h) g h)m Monterey Coal Co. - Monterey No. 1 

( 2 (~b b mw 00 ,, ; s Carlinville, Macoupin County, IL 

Herrin No. 6 

ul 0 Peabody Coal Co. - Mine No. 10 \ 2 00 ; $ P 00 a, '-.b (DWg 8 s Pawnee, Christan County, I L 

Herrin No. 6 
Mining Co., Mine Name 

Town, County, State, 

Seam Name 

Alabania By-Products - Segco No. 1 

a 6 Goodsprings, Walker County, AL 

Mary Lee 

Alabama By-Products - Gorgas No. 7 a 6 Goodsprings, Walker County, AL 

Mary Lee 

Alabama By-Products, Corp-Mary Lee No. 1 

% Goodsprings, Walker County, AL 

firy Lee 

Jim Walter Resources - Blue Creek No. 3 E $ Adger, Jefferson County, AL Cll C 

Blue Creek g4 

PS A 

The Mead Corp. - Mulga Mine 

a % Mulga, Jefferson County, AL 

Pra tt 

Republic Steel Corp. - North River 

a 5 Berry, Jefferson County, AL 

Pratt 

Jim Walker Resources, Inc. - Bessie 

a $ Birmingham, Jefferson County, AL 

Mary Lee 

c11 w N Kaiser Steel - Sunnyside No.1 

c 2 00 o o tn o $I 2 Sunnyside, Carbon Coonty, UT m 0 

Lower Sunn yside 

d - 03 d Kaiser Steel - Sunnyside No. 3 2 00 o o ' tn o ' o UI Sunnyside, Carbon County, UT 

Lower Sunn yside 

d V) 

03 % 8 Plateau Mining Co. - Star Point No. 2 -I 

c 2 00 o o Q) o $I 2 Wattis, Carbon County, UT (seam 3) 

3rd 

A A 

03 PP d Western Slope Carbon-Hawk's Next 3 0 

- tn(0 W Atn 2 4(0 N 0 o o 4 o $ 3 Somerset, Gunnison County, CO 

E % 
TABLE B-2 

KEY TO FIELD EVALUATION REPORTS AND MINE TESTS 

Field Report Mine Test Number - 

* Reports consolidating results of two consecutive 

field trips. 

Arthur D Little Inc 
(THIS PAGE INTENTIONALLY LEFT BLANK) 

- 

Arthur D Little Inc 
APPENDIX C 

DERIVATION OF FUNDAMENTAL CURRENT 

AND hllAGNETIC MOMENT FOR THE IN-MINE 

TRANSMIT LOOP ANTENNA 

The fundamental component of in-mine loop current (I FUND) 

was calculated in a straightforward manner from a knowledge of 

the loop configuration and dimensions used at each mine, and the 

measured transmitter characteristics. Based on laboratory measurements by PMSRC, both the Collins Radio and the new General 

Instruments transmitters were shown to behave as square wave 

voltage sources having a peak-to-peak voltage swing of 6.9 volts 

(+3.45 volts) and a series source resistance of 0.312 ohms. The - 

equivalent circuit of the transmitter and the associated loop 

antenna encircling one or two pillars is shown in Figure C-1. The 

0.1-ohm precision resistor is the means used to monitor the loop 

current with the oscilloscope at each mine. 

The values of loop resistance RL and inductance LL were 

calculated based on the loop dimensions and number of turns 

(usually one turn) for each mine, using the following equations: 

RL = N p p ohms, (1) 

where N is the number of turns, p is the perimeter in feet, and 

p is the wire resistivity in ohms per foot; and the inductance .'a 

formula for a rectangular loop of wire 

Grover, F. W. Inductance Calculations - Working Formulas and 

Tables, Dover Publications, Inc., New York., p. 60, 1962. 

Arthur D Little, fnc 
I 

I 

Vs = 6.9 Volt p-p Square Wave* (f3.45 v) 

Rs = 0.312 Ohm* 

Rr = 0.1 Ohm Reference Resistor 

RL and LL depend on loop configuration used in 

each mine test 

"Derived from BOM PMSRC Laboratory Measurements 

FIGURE C-1 EQUIVALENT CIRCUIT OF EM TRANSMITTER AND LOOP 

ANTENNA CONFIGURATION FOR COMPUTING IFUND 

-> 

Arthur D Little, lx 
where N is the number of turns, r is the wire radius in feet, and 

a and b are length and width, respectively, in feet. For the #12 

and #19 wire used, p and r are: 

ohm/ft 

feet 

The fundamental component of the loop current is simply the 

steady-state ac current flowing in the series R-L circuit of 

Figure C-1. The magnitude of its RMS value is siven by 

Equation 3, from which can be calculated the fundamental component of magnetic moment, M~~~~' qiven by Equation 4: 

M~~~~ = NA1~~~~ 

RMS RMS 

IFUND = 4 

RMS 427~ 

The area and linear dimensions of the loop antennas for each 

mine were obtained by PMSRC and ADL staff from the Westinghouse 

vs 

RS+O. l+RL+juLL 

field reports, mine maps, and original data sheets. All areas were 

based on the geometrical shape (usually rectangular) described by 

the antenna deployed in the mine. The resistance, RL, was based 

on the perimeter of the loop, as in Equation 1. The inductance, 

LL, was based on the formula of Equation 2 for a rectangularshaped loop. In the small number of cases where the loop was 

actually deployed in a trapezoidal, rhombic., L-shaped, or some 

other shape, an equivalent rectangle was selected for the purposes 

Arthur D Little, Inc 
of estimating the inductance. Table C-1 provides a complete list of 

these in-mine loop dimensions, areas, number of turns, and wire 

size (usually #12). The data in this table were used to generate 

the RMS values of the in-mine fundamental loop currents and the 

corresponding magnetic moments listed in Table IV-1 in the body of 

this report for all mines at all frequencies. 

I, 

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213 Arthur D Little, lnc 
EXPLANATION OF NOTES 

The in-mine antenna area for each mine test was recorded in the 

Westinghouse Field Reports prepared for each field trip. These reported areas 

were used unless, as for Mine Site 57, an obvious arithmetic error was made, 

or there were discrepancies between the reports and the original data sheets. 

The antenna lengths and widths, for the most part, had to be obtained or 

derived from information in the original data sheets. Whenever discrepancies 

occurred in the reocrded data that were not easily resolved, they were subjected 

to joint examination and consultation by Bureau of Mines (PMSRC) and Arthur 

D. Little, Inc., technical staff, to arrive at final agreed-upon values for 

length, width, perimeter, and area for the mines in question. The specific 

note explanations are listed below. 

1. Antenna perimeter and area were given by Westinghouse in the field 

reports. The length and width dimensions of the antenna have been 

derived to agree with the given perimeter and area data, and to be 

consistent with the dimensional constraints of deployment around the 

coal pillar(s1 used in the mine (as shown on either a mine map or 

hand drawing supplied in the field report or in the original data sheets 

from which the reports were prepared). 

2. Length and width dimensions of the antenna were given by Westinghouse 

in the original data sheets. These values resulted in the same areas 

reported in the field reports. 

3. Only antenna area was reported by Westinghouse. Length and width 

dimensions have been derived from this area information and the probable 

antenna shape as estimated from the mine map supplied. For example: 

Mine 20 Square indicated, and side dimensions chosen to give 2 the recorded area of 377 m . 2 a Mine 21 Rectangle indicated, with a recorded area of 199 m . The rectangle aspect ratio of about 1.3-to-1 computed 

from the mine map was used to estimate the length 

and width dimensions of 54 ft. by 40 ft. tabulated. 
4. Similar to Note (I), except the antenna perimeter was recorded by 

Westinghouse in the original data instead of in the field report. 

5. Discrepancies in reported data. Antenna length, width, perimeter, and 

area tabulated are those resolved by telephone consultation between 

Arthur D. Little, Inc., and PMSRC staff on April 22, 1980. 

6. The antenna was deployed in an irregular shape. For the purpose of 

estimating loop inductance, an "equivalent" rectangular shape was 

chosen to obtain the tabulated values for length and width. 
(THIS PAGE INTENTIONALLY LEFT BLANK) 

L 

Arthur D Little Inc 
APPENDIX D. 

Comprehensive Tabulations of Data Bases, 

Derived Parameters and Evaluation Indices 

Arthur D Little, lnc 
Table D-1 

Comprehensive tabulations of screened but undeleted 

surface and in-mine signal strengths, key indices, 

and variables (ranked by depth) 

Symbol Legend 

MINE = Mine Number 

ANTMIN = In-Mine Transit Antenna Area in Square Meters 

IWEST = In-Mine "RMS" Transmit Loop Current in Amperes 

Recorded by Westinghouse (peak-to-peak value/ 

2 42) 

SEMF = Surface Vertical Component of Magnetic Field 

Strength in dB re 1 pA/m 

MEMF = In-Mine Vertical Component of Magnetic Field 

Strength in dB re 1 pA/m 

DEPTHFT = Overburden Depth in Feet 

MMFUND = In-Mine RMS Fundamental Compcyent of Transmitter 

Magnetic Moment in Amp -turn-m 

I FUND = In-Mine RMS Fundamental Component of Transmit 

Loop Current in Amperes 

I EST = In-Mine "RMS" Value of Total Periodic Exponential 

Current in Transmit Loop in Amperes (peak-to-peak 

value/2 d2) Based on Theoretical Calculation for 

Circuit of Figure C-1. 

IDIFF = 20 Log (IFUND/IWEST) in dB 

IDEL = IEST - IWEST in Amperes 

IDIFF2 = 20 log (IEST/IWEST) in dB 

TLU 3 = Transmission Loss Uplink = -20 Log (2nD /Mm) 

- SEMF + 120 in dB 

TLD 3 = Transmission Loss Downlink = 20 log (2 n D /MS) 

- MEMF + 120 in dB 

DELTATL = TLU - TLD in dB 

I 

Arthur D Little, lrm 
LISTING OF SELECTED VARIARLES 

--------o----~-L--------o--~----o-~-----------~------~---.--- FRE 

HIrdE ANTHIN IWEST SFHF MEMF DfiPTHFT MMFUNO IFUND IEST IUIFF IOEL IDIFFZ TLU TLD DELTATL 
w-u L 1 W N -r rr Nrr yy c 

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W W W -N Wl - I I nl Owm--PulW CPm-0 4CP tw CW Wfom--oE4m N4PWW .......................................... 

(P 

W NO-W00@0 W-m4 9- 4fDN4ulO@S O4ND WU W4 9@@m--NO--Jo -*EEP 

3 WoDQDoFm Wwm- 3lQ ul9 QNSmmNNo9e 044WC 

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mu- cn 4NW @ WPW a 
LISTING OF SELECTED VARIABLES 13:42 WEDNESDAY* MAY 149 1980 3 

MINE ANTMlh IWEST SEHF HEMF OtPTHFT MMFUNO !FUND IEST IOIFF IOEL IDIFF2 TLU TLD OELT AIL 
LlSTING OF SELECTED VARIA~LES 13842 WEDNESDAY, MAY 

MINE ANTMIN IUEST SEMF MEMF DEPTHFT MMFUND IFUhD TEST IDIFF IDEL IDIFF2 TLu TLD 
LISTING OF SELECTED VARIARL.ES 13:42 WEDNESDAY* MAY 14- 1980 5 

MINE ANTWIN IWEST SEMF MEMF OEPTHFT 

IN OROER OF INCREASING DEPTH 

MMFUND IFUNO IEST IDIFF IDEL IDIFF2 TLU TLD DELTATL 

86.887 

415.236 

670 m698 

500m719 

651 m033 

124.572 

501 m478 

586 757 

562.851 

467.820 

467.820 

501 m478 

565m41H 

492.507 

378.814 

657 m992 

467 . 820 

405.263 

338.168 

409.683 

703.739 

370.027 

500m568 

427 28 1 

608.033 

657 . 992 

176.073 

562.944 

608.073 

sso ,072 

324.31 3 

540 -495 

549.7R7 

451 112 

322.938 

467 820 

565.618 

370 027 

37Om027 

701 0299 

465.796 

590 898 

608.732 

634.695 

467.820 

471m3P9 

558.143 

513.34H 

703.739 

500.504 

657 932 

481 0758 
LISTING OF StLEC7ED VARIABLkiS 13:42 WEDNESDAY, MAY 14, l9RO 6 

IWEST SEHF MEW oEPTHFT 

IN ORDER OF lNCREASING DEFTn 

MMFUNO IFUND IEST IDIFF lDEL IDIFFZ TLU TLO OELT ATL 
Arthur 11 L.ittle, Inc-, 
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Arthur D Little, Inc. 
Table D-2 

Comprehensive tabulations of surface and in-mine data bases 

with key indices and variables 

(rank ordered by depth) 

Symbol Legend 

MINE = Mine Number 

SEMF = Surface Vertical Component of Magnetic Field 

Strength in dB re 1 pA/m 

MEMF = In-Mine Vertical Component of Magnetic Field 

Strength in dB re 1 pA/m 

DEPTHFT = Overburden Depth in Feet 

MMFUND = In-Mine RMS Fundamental Compyent of Transmitter 

Magnetic Moment in Amp-turn-m 

IFUND = In-Mine RMS Fundamental Component of Transmit 

Loop Current in Amperes 

IDIFF = 20 Log (IFUND/IWEST) in dB 

IDIFF2 = 20 log (IEST/IWEST) in dB 

MMDN = Surface RMS Fundamental Component of 

Transmit Magnetic Moment in Amp-Turn-m 2 

MMUP = In-Mine "RMS" Transmit Magnetic Moment 

in ~m~-~urn-m~ Based on IWEST 

TLU 3 = Transmission Loss Uplink = -20 Log (2rD /Mm) 

- SEMF + 120 in dB 

TLD 3 = Transmission Loss Downlink = 20 log (2 r D /M ) 

- MEMF + 120 in dB S 

DELTATL = TLU - TLD in dB 

Arthur D Little, Inc 
L 

Arthur D Little Inc. 
SCREENED DATA YIlH OUTLIERS FLAGGED 13842 UEDNESDAYI HAY 141 1980 17 

MINE SEMF MEMF DEPT~FT MMFU~D IFUND IDIFF IDIFFZ IrcMOh MMUP TLU TLD OELTATL 
SCREENED DATA WITH OUTLIERS FLAGGED 13:42 WEONESOAYI MAY 141 1980 18 

IN ORDER OF INCREASING DEPTH 

MINE SEMF HEMF OEPTHFT MMFUNU IFUND IDIFF 

68.880 

l09.?40 

200.0t)o 

209. 920 

21604PO 

229.600 

P~~.QRO 

239.440 

239.440 

249.q36 

253oR72 

255.A40 

260w104 

262.400 

262.400 

262.480 

264 040 

264.040 

269 944 

278.900 

288.540 

295.200 

308.320 

324.720 

324 720 

324.720 

328. an0 

331 0280 

341 130 

341.126 

347.6RO 

350 960 

354.740 

357.520 

380 480 

387.040 

400.160 

403.440 

403.440 

419.940 

423.120 

4?6.400 

429.6P.O 

446.0R0 

449.360 

459.200 

469.040 

469.040 

478.9P0 

479 RPO 

473.8R0 

4n>. 160 

I DIFFZ MMON MMUP TLU fL0 OELf AT L 
SCREENED DATA WITH OUTLIERS Fl-h6GE.D 13:42 WEDNESDAY, MAY 14r 1980 19 

IN ORDER OF INCREASING DEPTH 

MINE SEMF MEMF OEP THF T HMFUND IFUNO IOIFF IDIFF2 HMDK HMUP TLU TLD DELTATL 
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Arthur D Little, Inc 
Table D-3 

Summary table of statistics for 

selected variables by frequency 

(for final data base of Table D-2) 

Symbol Legend 

I FUND = In-Mine RMS Fundamental Component of Transmit 

Loop Current in Amperes 

IWEST = In-Mine "RMS" Transmit Loop Current in Amperes 

Recorded by Westinghouse (peak-to-peak value/ 

2 d2) 

IDIFF = 20 Log ( IFUND/IWEST) in dB 

IDIFF2 = 20 log (IEST/IWEST) in dB 

IDEL = IEST - IWEST in Amperes 

MMUP = In-Mine "RMS" Sransmit Magnetic Moment 

in Amp-Turn-m Based on IWEST 

MMDN = Surface RMS Fundamental Component of 

Transmit Magnetic Moment in Amp-Turn-m 2 

FREQ = Frequency 

N = Number of data values 

MEAN = ( ZXi)/N 

STANDARD - 2 

DEVIATION 

VARIANCE = (STD. DEV.) 2 

MINIMUM 

VAlUE = Min. Data Value 

MAXIMUM 

VALUE = Max. Data Value 

lli 

Arthur D Little, Inc 
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Arthur D Little, Inc. 
Table D-4 

Summary table of statistics for set of key variables 

by frequency and depth interval 

(For final data base of Table D-2) 

Symbol Legend 

DEPTHFT 

MMFUND 

MMDN 

SEMF 

MEMF 

TLU 

TLD 

DELTATL 

FREQ 

DEPTHINT 

= Depth in feet 

= In-Mine RMS Fundamental Compyent of Transmitter 

Magnetic Moment in A/p-turn-m 

= Surface RMS Fundamental Component of 

Transmit Magnetic Moment in Amp-Turn-m 2 

= Surface Vertical Component of Magnetic Field 

Strength in dB re 1 pA/m 

= In-Mine Vertical Component of Magnetic Field 

Strength in dB re 1 rA/m 

3 = Transmission Loss Uplink = -20 Log (2nD /Mm) 

- SEMF + 120 in dB 

3 = Transmission Loss Downlink = 20 log (2 n D /MS) 

- MEMF + 120 in dB 

= TLU - TLD in dB 

= Frequency in Hz 

= Depth Interval in Feet (8 total) 

1 = less than 300 

2 = 300-399 

3 = 400-499 

4 = 500-599 

5 = 600-699 

6 = 700-999 

7 = 1000-1199 

8 = 1200 or more 

C 

Arthur D Little, Inc 
ST4TISTIcS FOR DEPTH INTERVALS 

FREO=630 DEPTHINT=l 

i3:42 WEDNESDAYI MAY 14

V AR I ABLE t : MEAN ST ANOARD MINIMUM MAX IYUM 

DEVIATION VALUE VAL !JE 

OEPTHFT 

YHF IJN!, 

YPIDN 

SEF'F 

YEMF 

TLLl 

f LO 

DELTATL 

OEPTHFT 14 

VHFI;NI) 14 

YUCK 13 

SFMF 14 

VEMF 13 

1 LU 14 

TLD 13 

DELTATL 13 

DEPTHFT 19 45 lo94947368 

MMFUNI) 19 1047093@415?9 

MCnh 17 569b.84117647 

SEYF 13 2d~88111111 

YE r4F lit 41 051428571 

TLU It 6.86936201 

TL D 1s 60386FJ6006 

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STATISTICS FOR DEPTH INTERVALS 

FREQt630 LbEPTH INT=6 

13:42 WEDNESDAY, MAY 14, 1980 10 

VA~I AWE tl ME AN ST PNDARD MINIMUM MAXIMUM 

DEVIATION VALUE VALUE 

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(THIS PAGE INTENTIONALLY LEFT BLANK) 

IC 

Arthur D Little Inc 
APPENDIX E 

COMPLETE COMPUTER OUTPUT 

OF REGRESSION ANALYSES FOR 

SIGNAL VERSUS LOG DEPTH MODELS 

AT EACH OF FOUR FREQUENCIES 

Standard output of regression analyses produced by SAS 

sub-routine GLM (General Linear Models) Procedure is given. Computational details and definition of terms are given in "A User's 

Guide to SAS 76", SAS Institute, Inc., Cary, North Carolina, 

pages 127 to 144. 

Observation number refers to mine position in listing when 

ranked by increasing depth. All signal field strength values 

SEMFNORM are expressed in dB re 1 uA/m. SEMFNORM = Surface Vertical Component of Magnetic Field Strength for a Transmit Magnetic 

2 Moment of 1 A-m . 

Arthur D Little, Inc 
Table E-1 

Statistical Analysis of Uplink Data 

ANALYSIS OF UPLINK DATA 

Fk?€[J=630 

10:30 WEDNESDAY* MAY 169 1980 6 

DEPENDENT VAPIAHLE INFORMA~ION 

NUM8ER OF' OBSEWVAT IONS IN BY GR('!JP = 94 

NOTE: ALL DEPEhCEhT VPRIABLES AEF CONSISTE!-1 UITH RFSPECT TO Thf Pf?€SFbCE OW AL~SENCE OF MTSSING VAL~JFSI HOWEVERI ONLY 90 

OBSERVATIOkS IN RY GROUP C!.N BE USED IN THIS ANALYSIS. 
ANALYSIS OF UPLINK DATA 

f REO=630 

10:30 YEDNESDAYI MAY 141 1980 7 

GENERAL L INEAP #ODELS PHOCEOIIRE 

DEPENOtkT VARIABLE: SfMFNORM 

SOURCE DF 

MODEL I 

ERROR 8 8 

CORRECT~O TOTAL 89 

SOURCE C F 

INTERCE pl 99.82861848 

LOGDEP TH -61.967409?9 

9esEavEn 

VPLUE 

MEAh SQIbARE F VALUE 

19592.77611750 1142 89 

44.2387?114 

PC) > F R-SQUARE ce Ve 

o.onni o 834240 20 1692 

Sf0 OEV SEWNORM MEAN 

TYPk 1 SS F VALUE PR > f Of TYPE IV 55 F VALUE PR > F 

T f:.~ Ho: PR > IT1 ST0 EUdOR CF 

PAkAp kTkk=O EST iqATL 

UPPER 95% CL 

INDIVIDUAL 
u EP 4 m"m 

9 0 + ceo rcdit 

rC.NS Lnd9 mN4 

... 

ee* 

NNN 

Ill 

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099 IUdfi 

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0.. 

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Ill 

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Nit@ a4Q 

0.. 

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IIa 

- 

Arthur D Little, lnc. 
ANALYSIS OF UPLIM OAT4 

FFiE0=630 

GENERAL LINEAR MODELS PROCEPIIRE 

OEPENoEhT VARIABLE: SEMFNORM 

OBSERVED PREDICTED 

VALUE VALUE 

* O~SEHVATION MAS NOT USED IN TPIS ANALYSIS 

SUM OF RESIDUALS 

SUM OF SOUARtO RESlnUACS 

SUM Of SQUARED WESIO~JALS - ERROk SS 

PRESS STATISTIC 

FIRST OWNR AUTOCORRELPTION 

OURBIN-kATSOh 0 

RESIDUAL LOWER 9591 CL 

INOIVID~~AL 

10830 YEDNESDAY, MAY 14, 1980 9 

UPPER 95% CL 

INDIVIOUAL 
GENERAL LINEAR MODELS PROCEDU?E 

DEPtNDENT VARIABLE INFORHAT l~~h( 

10:30 wEDNESDAk* MAY 149 1980 10 

NUMBER OF OBSERVATIONS IN BY GROUP s 94 

NOTE: ALL DEPENDENT VARTAYLES ARE CONSISTEhl WITH RESPtCT TO THE PRESFNCE OR ABSENCE OF HISSING VALUES. HOWEVERI ONLY 90 

OBSERVATIONS IN BY GROUP CAN BE USED IN THIS ANhLYSIS. 
~SN~dOUfbbXO~Nbd~NSNc?NN~+NJI~~~ 

111 1 I IIN I II II 

Arthur D Little, Inc. 
m - F, 

e r- d - om dm 

UIQ ?c= 

am 

(UN 

I I 

rnCN 

C @ r- om4 

NGomm drnN mu0 

: $? +it0 

NNN 

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- 

Arthur D Little, Inc. 
ANALYSIS OF UPLIhK OAlA 

FREQ= 1050 

GENERAL LINEAR HOOELS PROCEDURE 

OEPENOkNT VARIABLE: SEMFkOWM 

OBSERVATION OBSERVE0 PREDICTED RESIOUAL LOWER 95% CL 

VALUE VALUE INDIVIOUAL 

SUM GF HtSIDIIALS 

SUM OF SUUARFO RESIDIJALS 

SUM OF SQUARED RESInrlALS - ERROR SS 

PRESS STATISTIC 

FIRST OHDER I\UTOCORRFLATION 

DUReIN-bATSoN D 

10130 UEONESOAY* HAY 14- 1900 13 

UPPER 95% CL 

INOIVIDUAL 
ANALYSIS CF UPLINK DATA 

FRFQ= 1950 

GENERAL LINEAU MODELS PROCEDURE 

DEPENDENT VARIABLE INFORMAIION 

NUMbER OF OBSERVATIONS IN BY GROUP r 94 

10130 WEDNESDAY* MAY 149 1980 14 

NOTE: ALL DEPENDENT VARIABLES AQE COYSISTC~!! WITH RESPECT TO THE PRESENCE OR ABSENCE OF MISSING VALUES. HOWEVERI ONLY 91 

08SERVATIONS 114 BY GROllP CPN BE USE[> IN THIS ANALYSIS. 
0.m 

90 

u 0 

(0 9 

CI 44 d 

00 

aD 1 

. . 

inn, 

-00' 

n40 

NN+ 

00'9 rcbd 

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c ~e L? ~~~~~o+c~~~rc~u-u~~~+u~\~c

a aia w e~aaafimc~~~m~v'~~m~v'~~1eemrc

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- arc Nad&9G-T9b99U04dd9mULFIhLnnat4dGCJ C ~CJ UA QL9~~0itO-~~~OUNInU~~C0~9a'NLnit(o~

m mu cmc~~a~~~+~~~nrca~~~u~a~'.t

U ?? a> ~9meb0c9C+00uu99mmauu9Q~+rtdc~ 3 h~dU+QO~CQnIOoO~~UdC(\rQO~~&~Q.ObC d5 ...................~~~~

~~~~4a'.tv'~~~0~~~~mommp+rcrnrne

@ I dddAI I-4ddadmd@dddddNddNC?C\,dm(?- 111 llIlI#l 1l1118811Il111l 

Arthur D Little, Inc. 
- 

Arthur D Little, Inc. 
ANALYSIS OF UPLIt4K OATA 

FREQ= 1950 

GCNERAL LINEAR MODELS PROCCDURE 

DEPENDENT VARIABLE: SEMFNOPM 

O~SEHVATION OBSERVED PWDICTEO RESIOUAL LOWER 95% CL 

VALUE VALUE INDIVIDUAL 

SUM OF KES1I)UALS 

SUM OF SUUARED RESIDUALS 

SUM OF SCUARED RES1DCALS - EkHOk SS 

PRESS STATISTIC 

FIRST OHDER AUTOCORRELATION 

DURRIN-*ATSON o 

lor30 WEDNESDIYI MAY 14, 1980 17 
Arthur D Little, Inc 
ANALYSIS Of UPLINK DATA 

F REO-3030 

10830 UEDNESDAY, MAY 14, 1980 19 

GENERAL LINEAR MODELS PROCEDURE 

DEPENDENT VARIABLE8 SEMFNORM 

SOURCE OF 

MODEL 1 

ERROR 8 8 

CORRECTtD TOTAL 8 Y 

SUM OF SQUARES MEAN SOUARF F VALUE 

360.01 

R-SQUARE 

0 803575 

C.V. 

25 1365 

SEWNORM MEAN 

-35.46918468 

0 . 000 1 

ST0 DEv 

8.91570335 

SOURCE 

LOGDEPTH 

F VALUE PR > F 

360.01 Om0001 

TYPE I SS f V4LM PR > F Df TYPE IV SS 

28617.01524838 

STD ERROR OF 

EST IMAT € ESTIMATE 

INT ERCWT 

LOGDEPTH 

OBSERVED 

VALUE 

PREDICTED Rf SIDUAL LOWER 95% CL 

VALUE INDIVIDUAL 

UPPER 95% CL 

INDIVIDU~L 
ANALYSIS Of UPLINK DATA 

f REO=3030 

lot30 WEDNESDAY^ MAY 14, 1980 20 

GENERAL LIkEPH MODELS PROCEDURE 

DEPENDENT VARIABLE: SEMFNORM 

08SERVAl ION OBSERVED 

VPLUE 

PREDICTED RESIDU4L LOWER 95% CL 

VALUE INDIVIOU~L 

UPPER 95% CL 

INOIVIDU4L 
GEYERAL LINEAR MODELS PROCEDURE 

DEPENDENT VARIABLE: SEMFNORW 

PHEOICTED 

VALUE 

* OBSEHVATIOk WAS hOT USED IN THIS ANALYSIS 

sur OF HLSIDUALS 

SUM OF SQUARED RESInUALS 

SUM OF SQUARED RESIDUALS - EWOu SS 

PRESS SlATISTIC 

FIRST OhLER AClTOCORRFLATION 

DURBIN- ATS SO^ D 

RESIDUAL LOWER 95% CL 

INDIVIDUAL 

10:30 WEDNESDAY, MAY 14, 1980 21 

UPPER 95% CL 

INDIVIOUAL 
(THIS PAGE INTENTIONALLY LEFT BLANK) 

- 

Arthur D Little Inc 
APPENDIX F 

PROBABILITY OF DETECTION BASED ON 

PROBIT ANALYSIS OF SUCCESS/FAIL FIELD TEST DATA 

In the most fundamental sense, the outcome of each transmission test conducted at a mine site could be described in terms 

of whether the signal transmitted from the in-mine transmitter was 

actually detected (success) or not detected (failure) on the 

surface. It should be recognized that the experiment was conducted 

under "ideal" rather than "real" conditions, i. e. : 

the observer knew that a signal was being sent, when it 

had been sent, and approximately where it had been 

sent from, 

the observer functioned in a more favorable "alerted" 

state of mind and static measurement conditions, 

the Collins transmit moments were generally stronger 

than the GI operational ones because of the larger loop 

areas used in the deep mines and the larger #12 wire 

size that would not be permissible under emergency mine 

conditions. 

Nevertheless, it is of interest to analyze test results according to 

this most fundamental success/failure property. The purpose of this 

Appendix is to present the results of a statistical technique which 

expresses the likelihood of successful signal detection as a 

function of depth under the exact, but optimistic and impractical, 

transmitter and test conditions experienced in this field test 

program. 

Arthur D Little, Inc 
The basic data for this analysis are given in Table F-1. 

Although a total of 94 tests was conducted, equipment malfunctions 

and other circumstances resulted in a few inadmissible data points 

for this analysis. All remaining "valid" tests (i.e., those in which 

a signal could have been received at the surface) were recorded 

as a success if the signal was actually observed, and a failure if 

it was not. The specific "failure" and "no-test" results are 

summarized by mine in Table F-2. Test outcomes at each frequency 

are given in Table F-1 for various depth intervals, pre-chosen to 

include a sufficient number of data points within each interval. 

A statistical analysis of these data began by formulating 

the following three hypotheses of interest: 

Hypothesis 1: There is no difference in the probability of 

failure to detect signals among the four 

frequency levels tested. 

Hypothesis 2: There is no difference in the probability of 

failure to detect signals at the various 

depths tested. 

Hypothesis 3: There is no frequency/depth interaction; 

i .e., the probability of failure to detect does 

not vary with depth differently, depending 

on which frequency is used. 

The underlying theory and computational details required to test 

the hypotheses stated above are described in Reference F-1, 

Chapter 16, and will not be repeated here. 

The results indicate that the data in Table F-1 lead to 

rejection of Hypothesis 2 only. Thus, there appears to be a direct 

relationship between failure to detect and depth. On the other 

Arthur D Little, lnc 
Arthur D httle, Inc 
TABLE F-2 

SUMMARY OF SPECIFIC FAILURE TO 

DETECT AND TEST UPLINK TEST RESULTS 

Y- S mbols: 

N = No valid test measurement performed 

F = Failure to detect transmitted signal 

T = Valid test performed 

Mine Depth 

No. County/State (ft. > - 630 1050 1950 

Kanawha, WV 250 

McDowell, WV 430 

McDowell , WV 449 

efferson, AL G 469 

estmoreland, PA 479 

Belmont, OH 500 

Westmoreland, PA 626 

Jefferson, IL 800 

Boone & Raleigh, WV 846 

McDowell , WV 915 

Carbon, UT 1000 

Claiborne, TN 1191 

Carbon, UT 1197 

Buchanon, WV 1200 

Marion, WV 1342 

Harlan, KY 1397 

Garrison, CO 1401 

5N 4N 5N 

TOTALS 6F 6F 9F 

89T 90T 89T 

Notes: 

1. Defective surface receiver 

2. Based on fail to detect, even on more sensitive BOM tape 

recording 

3. Receiver not set up in time to detect valid transmission 

4. Uplink tests not performed 

5. Based on BOM tape data, Westinghouse data judged not valid 

6. Based on original receive loop, signal level data based on 

tuned receive loop 

Source: Arthur D. Little, Inc. 

I 

Arthur D Little, Inc 
hand, there is no evidence - from this experiment that the probability of a successful signal detection differs among the four 

frequencies used in this test program. Therefore, the outcomes were 

combined over all four frequencies prior to conducting the next 

stage of the analysis. 

Since failure to detect was observed to be related in some 

way to depth, the next step involved the attempt to quantify this 

relationship. A technique frequently used in the analysis of proportions, known as Probit Analysis, was then used for this 

purpose. This technique, described in Reference F-2, Chapter 10, 

regards the probability of failure p as a normally distributed 

j variable across the depth interval classifications. The Exact Probit 

Solution technique described in detail in Reference 2 is an 

iterative one and takes into account the different sample sizes 

within depth intervals. The relevant calculations are summarized 

in Table F-3, and the resulting Probit regression equation is 

plotted in Figure F-1. 

The interpretation of Figure F-1 is that if the linear 

relationship as derived from experimental data is truly representative, then it is possible to determine the probability of 

successful signal detection at the surface as a function of depth. 

The expression should apply for all mine locations and conditions; 

however, it is crucial to recognize that the estimated probabilities 

are quite optimistic in terms of real trapped miner scenarios, due 

to the nature of the experimental test, as described in the initial 

paragraph. 

Although the details will not be presented here, a test for 

linearity was conducted for these data. The results indicated that 

the probit regression model, as derived, fits or "explains" the 

data extremely well, and therefore can be used for inferential 

purposes. Consequently, the results are re-plotted on a more 

Arthur D Little, lnc 
TABLE F-3 

EXACT PROBIT SOLUTIONS 

(Second Iteration) 

Y = -4.935 + 3.085 log x 

1 = Averaged over all four frequencies. 

Expected Weighting Working 

Probit 2 Factor Probit 2 

(Y) (W) (Y) 

2.47 0.047 2.12 

2.90 0.110 2.49 

3.24 0.191 3.96 

3.52 0.276 3.00 

Avg . Log (depth 

Depth (log x) 

(>o 

250 2.40 

350 2.54 

450 2.65 

550 2.74 

= Value of a normally distributed variate with 

mean of zero and unit variance (with 5 units 

added). 

No. of Proportion 

Tests of Failures 1 

(n 1 (P) 

2 1 0 

14 0 

17.5 0.100 

8.75 0 

Source: Arthur D. Little, Inc. 

650 2.81 

800 2.90 

1100 3.04 

11350 3.13 

D 

Arthur D LittloInc 

13 0.077 3.73 0.346 

5 0.250 0.442 

4 0.250 

6 0.375 0.61756 
- 

UPPER 95% CONFIDENCE LIMIT 

- 

- 

- 

- 

- 

PROBIT REGRESSION .EQUATION 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

9 

- 

- m 

- 

- LOWER 95% CONFIDENCE LIMITg 

- 

- 

250 300 400 500 600 700 800 1000 1200 1500 2000 

OVERBURDEN DEPTH (FEET) 

FIGURE F-1 RESULTS OF PROBIT ANALYSIS 

Arthur D Little, Inc 
convenient scale in Figure F-2. This figure illustrates the behavior 

of the uplink probability of successful detection with increasing 

depth, and the corresponding expansion of the interval estimates 

expressed in terms of upper and lower bounds. For example, at 

1,200 feet, the figure indicates that we are 95 percent confident 

that the interval (0.34 to 0.90) includes the true (unknown) 

probability that a signal will be detected uplink for this type of 

experiment. In other words, it is highly unlikely that the chance 

of detection is lower than 0.34 or higher than 0.90, if repeated 

tests had been carried out at this depth. The graph also indicates 

that a signal detection could be expected to occur about two-thirds 

of the time at this depth. 

It is interesting to note that the optimum allocation formulas 

mentioned in Section 111-B of this report, which were used to determine sampling fractions, made use of assumed probabilities of 

successful detection, as follows : 

- Depth Interval Assumed Probability of Success - 

< 400 ft. 

400 - 1000 ft. 

> 1000 ft. 

The comparison to the observed outcome as illustrated in Figure 

F-2 reveals a remarkable, fortuitous agreement between the two 

independent measures. 

References 

(F-1)Statistical Methods, G. W. Snedecor and W.G. Cochran, Iowa 

State University Press, 6th Edition (1974). 

(.F-2) Experimental Statistics, M .G. Natrella, National Bureau of 

Standards Handbook 51, August 1, 1963. 

IArthur D Little, Jnc 
- - CONFIDENCE 

- FOR COLLINS TRANSMITTER 

CONFIGURATIONS USED IN 

- FIELD MEASUREMENTS 

PROGRAM 

- 

APPLICABLE LOWER 95% \ 

- FREQUENCY BAND: CONFIDENCE \ - 

630 TO 3030 Hz \ LIMIT \ 

- \ - 

\ 

- " '. - 

- - 

I I I 1 I I I I I I I I I I I A 0 

0 200 400 600 800 1000 1200 1400 1600 

OVERBURDEN DEPTH IN FEET 

FIGURE F-2 ESTIMATED UPLINK PROBABILITY OF SUCCESSFUL 

DETECTION VS OVERBURDEN DEPTH (BASED ON 

SUCCESS/FAI L DATA FROM 94 MINE Fl ELD TESTS) 
(THIS PAGE INTENTIONALLY LEFT BLANK) 

1 

Arthur D Little Inc 
APPENDIX G 

APPLICATION OF SEARCH THEORY TO 

THE DETECTION OF TRAPPED MINERS 

A. INTRODUCTION 

This Appendix applies the principles of search theory to the 

problem of devising effective and practical search plans and 

procedures for maximizing the number of rescuable miners detected 

per unit of search effort at a mine disaster site. Given that a 

mine disaster has occured, and that one or more miners may have 

survived and activated their EM rescue transmitters somewhere 

within the mine, how should the mine search and rescue team 

allocate its effort and resources to best accomplish the objective of 

finding and rescuing these miners? The question is obviously 

important, because the amount of time available to rescue live 

miners is unknown but finite, and the roughly circular area of 

signal detectability above a trapped miner is quite small, 

compared to the extensive area of the mine workings. Since time is 

a critical factor, whenever trapped miner signals can be detected 

from the air, a helicopter-carried receiver will most likely be used 

to rapidly survey the large areas involved. Therefore, we have 

formulated the search problem specifically for a helicopter-based 

rapid survey effort, backed up by surface-based receivers for pinpointing, or localizing, the underground transmitters. The problem 

and associated search plan and procedures can be modified to 

accomodate the situation in which the search must be conducted by 

a large number of search team members carrying rescue receivers 

on the surface. 

Arthur D Little, Inc 
B. SEARCH OBJECTIVES 

The objective of the helicopter search is to "detect" signals 

from any transmitters that have been put into operation by the 

trapped miners, and to report their approximate locations to 

searchers on the surface. Hence, in laying out a search plan for 

the helicopter pilot, consideration should be given to the areas in 

which detectable signals are likely to be present at the time of 

the search, and the likelihood that the signals can be detected. 

Consideration also should be given to the likelihood that miners at 

the source of a detected signal can be rescued before they 

succumb, and to the number of miners involved. 

The expected number of miners that can be rescued alive 

after their presence has been detected and their approximate 

location has been ascertained by the helicopter search, is one 

measure of search plan effectiveness that takes these factors into 

account. We assume for the purpose of this initial study that the 

objective of the helicopter search is to maximize the expected 

number of rescuable miners who have been found by the searching 

effort available from the helicopter. Some of the parameters on 

which the search plan is based will not be known accurately. The 

search plan that we seek is the plan that is "best," given the 

information available. 

C. ESTIMATION OF PARAMETERS 

With the EM receiver antenna suspended below the helicopter, 

the pilot will fly over the region covered by the underground 

mine, and use landmarks with known locations relative to the mine 

map to locate and orient his search. The search plan consists of 

instructions to the pilot as to where and how to search, in what 

sequence, and how to change the search procedure when a detection is made. 

L 

Arthur D Little, Inc 
If nothing is known or can be estimated about the locations 

and survival probabilities of the trapped miners, or of the effectiveness of the EM receivers in detecting EM signals from various 

parts of the mine, the best that can be done is to instruct the 

helicopter pilot to fly "at random" over the mine. The pilot would 

then attempt to "cover" the entire region of the mine while taking 

care to stay within its boundaries. If we have an estimate of the 

horizontal range from the helicopter at which the EM signal from 

an underground transmitter can be detected versus helicopter 

altitude, a "regular" pattern, such as parallel sweeps, will be an 

improvement over a random search. Estimates of the probable 

locations of trapped miners can also be used to concentrate the 

searching effort in particular regions, rather than spreading the 

effort uniformly over the entire mine. In addition, estimates of 

survival times and rescue times for miners in various parts of the 

mine can be used to determine the sequence for searching various 

areas above the mine and for modifying the search plan with time. 

We therefore construct a procedure for finding a "good" 

search plan in the general case. We assume that the expected 

numbers of trapped miners, and the conditions that affect the 

search and rescue operations, vary sufficiently from one region of 

the mine to another to justify different concentrations of effort 

from region to region. For this purpose, we divide the mine into a 

number of regions. The division lines are somewhat arbitrary, but 

should take into account the extent and structure of the mine, the 

work schedule for the day, and other factors. The regions need not 

have the same size or shape. They should be large enough that 

the helicopter pilot can achieve a desired distribution of search 

effort within his accuracy limitations in location and navigation. 

On the other hand, the regions should be small enough to permit 

significant differences in numbers and conditions to be specified. 

th For the i- region, i = 1, 2, . . . ,k, the following quantities 

are estimated: 

Arthur D Little, Inc 
th = expected number of trapped miners in the iregion ; 

th = area of the i- region; 

= sweep width of the helicopter receiver in 

th detecting a signal in the i region; 

psi ( t ) = the probability that a signal is being transth mitted from the i- region at time t after the 

disaster ; 

th 

pri(t) = probability that a miner in the i- region will 

survive until rescued, given a helicopter 

detection at time t. 

The sweep width, Wi, is the equivalent width of a strip in the 

horizontal plane that is "swept" by the helicopter. If pi(x) is the 

probability of detecting a signal at horizontal distance x from the 

helicopter path, then 

assuming the same function on both sides of the path. A simpler 

estimate than Eq. (1) is twice the distance at which the probability of detection is 0.5. This estimate is sufficient, since the 

distribution of searching effort depends primarily on the ratios of 

the sweep widths rather than the absolute values. Furthermore, 0.5 

provides a practical balance between the overly conservative 

narrow lane widths and overlapping areas of detectability imposed 

by a high probability such as 0.9, and the wider lanes but higher 

chances of not detecting valid signals offered by a lower probability such as 0.3. 

-. 

Arthur D Little, Inc 
It is unlikely that psi(t) and pri(t) can be estimated with 

precision. Perhaps the only estimates available will be the 

expected times, as follows: 

s = expected duration of a detectable signal transmission i t h from the i- region; 

v 

t h = expected survival time for a miner trapped in the i- i 

region ; 

r th 

i = expected time required to rescue a miner from the iregion. 

To a first approximation, si is proportional to the expected number 

th 

n of miners trapped in the i- region, on the assumption that i 

they are in one group and can pool their batteries to power one 

transmitter. 

If we can estimate only the expected times, we will use an 

assumed shape for the functions p (t) and pri(t), with the si 

expected times as parameters. For example, let v. and ri be the 

1 

times at which the survival and rescue probabilities change 

abruptly from 1 to 0. This results in the following uniform distribution for pri ( t ) : 

A second example is the case of an exponential distribution. If vi 

and ri are the expected survival and rescue times used in 

exponential functions, then 

Arthur D Little, IK 
as will be shown later. In (3), the exponential factor is the 

probability that a miner will survive to time t, while the factor 

vi/(vi + ri) is the probability that he will survive until rescued, 

given that he has survived to time t. 

D. OPTIMIZATION PROBLEM 

We want to construct a search plan that maximizes the 

expected number of miners rescued alive with a given amount of 

searching effort. We will measure the amount of searching effort in 

time t by the length L(t) of the horizontal component of the helicopter flight path while searching over the regions of the mine. 

th Let Li(t) = length of path flown over the i- region by time tThen 

th The probability Pi(t) that a signal has been detected in the iregion by time t, with a random distribution of effort in the 

region, is 

t - - 

Pi(t) = 1 - exp , -c(Wi/Ai) / pSi(x) +)dx , I 

where X .(t) is the search rate (miles of search track per hour) 

td in the i- region at time t: 

The derivation of (5) is given below. 

- 

.---. 

" -. 

LArthur D Little, Inc 
The probability that a signal will be detected in the interval 

(t, t + dt), given that a detectable signal is present at time t, is 

c(Wi/Ai) li(t)dt, where c is a constant that depends on the 

efficiency of the helicopter searcher in scanning the frequency 

bands and becoming aware of a signal indication on his receiver. 

For an efficient searcher, c = 1. Let 

Then r 

I 

Qi(t + dt) = Qi(t) il - p .(t)c(Wi/Ai) ii(t)dt 1 S1 

Equation (8) is obtained by elementary arguments, as follows: The 

probability Qi(t + dt) that no signal will be detected by time t + 

dt is equal to the probability Qi(t) of failure by time t multiplied by the probability that no signal will be detected in the 

interval (t, t + dt). The latter probability is the quantity in 

brackets in Equation (8). The solution of Equation (8) with the 

condition Qi(0) = 1 yields Equation (5), when (7) is used. 

From Equation (6) and the condition that Li(0) = 0, we have 

+ 

The condition expressed by Equation (4) then becomes 

in terms of the search rates. 

The overall search plan will consist of a sequence of search 

plans for various time intervals called stages. Stage 1 extends 

from the start of search to the first detection, Stage 2 extends 

Arthur D Little. Inc 
from the first detection to the second detection, etc. The optimal 

search in Stage 2 will be contingent upon the time t at which the 1 

first detection occurred, the region in which it occurred, and the 

search policy concerning further helicopter search in a region in 

which a detection has been made. If it is reasonable to expect 

that all the miners in the region in question are in one group, or 

are separated but are likely to be found by a rescue team, further 

helicopter search in that region may not be justified. In that 

case, the helicopter search in the region is terminated and the 

surface searchers take over to pinpoint the source of the signal 

detected by the helicopter. 

If the search policy is to include the possibility of search in 

the region in question in later stages, an estimate of the expected 

number nl' of miners not at the location of the detected transmission is needed for Stage 2. Then the optimization problem for 

Stage 2 is essentially the same problem as that for Stage 1, except 

for the change in the expected number of trapped miners in the 

region in which the detection was made. Thus, we proceed from 

stage to stage. The search plan in each stage is contingent on the 

previous detections -- their times, regions, and revised estimates 

of the expected number of trapped miners remaining. 

E. OPTIMIZATION IN THE FIRST STAGE 

We limit further consideration of the optimal problem to the 

first stage. The solution for that stage can be modified easily to 

apply to the later stages. The time tl of the first detection will 

not be known in advance, of course. Our objective in the first 

stage is to construct a search plan that is optimal, if possible, 

whatever the value of tl. If this can't be done, then we must use 

a compromise plan. For this reason, we referred earlier to the 

desired plan as a "good" plan, rather than an optimal plan. 

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Arthur D Little, Inc 
We construct the search plan under the condition that the 

first detection occurs at t = t even though the value of tl will 1 ' 

not be known until the first detection occurs. Hence, we replace 

the detection probability Pi(t) from Equation (5) by the conditional 

detection probability Pi(tl I first detection at t = . For the first 

th detection to occur in the i- region at time t = tl, a detectable 

signal must be present at t = t and detection must be made, 1; 

given that a signal is present. Hence 

Pi(tl I first detection at t = tl) = 

where 

The expected number of miners rescued alive, given that the first 

th detection occurs in the i- region at t = tl, is n.p (tl). Hence, 1 ri 

the expected number N1 of miners rescued alive as the result of 

the search in the first stage is 

k 

We want to maximize N1, subject to condition of Equation (4) 

for t = tl, and the conditions 

First, we find the solution without using conditions of Equation 

(14). By elementary calculus, the solution is 

f k 1 i 

Arthur D Little, Inc 
where 

and Lo is an arbitrary unit of length, say, one mile, that has 

been inserted to make the bracketed quantity in Equation (173 

dimensionless instead of appearing to have dimension of (l/length). 

In computations, we can put Lo = 1. 

The distribution given by Li(tl) in Equation (15) is the 

optimal solution for any value of t for which conditions of 1 

Equation (14) are satisfied. If some of the Li(tl) in Equation (15) 

are negative, a modification is required. We want to find the 

"largest" subset {J} of the set 1 2, .. ., k} for which ~*(t > 0 

j 1 

for j {J} when computed from Equations (151, (161, and (17) by 

limiting the summations in Equation (15) and (16) to the subset {J} . The desired subset can usually be obtained by starting 

with the index il for which hi is maximum, and adding indices in 

1 the order of decreasing values of hi until a negative value of 

Li(tl) is obtained for the index last added; then dropping the last * 

index and putting L.(t ) = 0 for the dropped index and the 

3 1 

remaining indices. Or we can proceed by dropping indices that 

produce negative values when the entire set is used, recompute 

with summations over the reduced set, and continue to drop indices 

that produce negative values until a set (J} is obtained for which 

If the optimal values ~q(t~) of Li(tl) found in this way are 

monotonic nondecreasing functions of t it is possible -- at least 1' 

in theory -- to construct a search plan that is optimal for all 

t1 > 0. In fact, we can proceed step by step in arbitrary 

,111 

Arthur D Little, Inc 
increments of time, optimizing in each step, and the overall * distribution will be optimal. If at least one of the Li(tl) is not 

monotonic nondecreasing, the optimal solution cannot be attained 

for all tl. If we proceed step by step, the distribution obtained 

may be optimal for small values of tl, but not for large values of 

5' 

F. SOLUTlON FOR EXPONENTIAL PROBABILITY FUNCTIONS 

If si is the expected duration of a detectable signal transth mission from the i- region, the corresponding exponential function 

for p (t) is si 

where to is the time after the disaster occurred at which signal 

transmissions start. For t < to, psi( t) = 0. The expected duration 

in the exponential function can be obtained from an estimate of the 

50% value by the equation 

expected value = (50% value)/ln2 . 

If to<<si, we use the approximation 

0, t < to; 

psi(') = ( 

exp (-t/si) , t 2 to. 

To derive Equation (3), we suppress the index i and let 

v and r be the expected survival and rescue times, respectively. 

For exponential functions, the probability that a miner will 

survive no longer than time t is 1 - exp (-tv/v), and the density v 

function f(t ) of the survival time tv is 

v 

Arthur D Little, Inc 
The probability that the rescue time tr does not exceed x is 

For a given survival time t and helicopter detection time t, the 

v 

probability of making a live rescue is zero if tv s t, and is 

P { tr 5 tv - t } if tv > t. Hence, the probability pr ( tv, t) of 

making a live rescue, given t and t, is 

v 

The probability pr(t) of making a live rescue, given that a helicopter detection occurs at time t, is 

Restoring the index i, we obtain 

as stated earlier in Equation (3). 

We now use Equations (18) and (25) in Equation (15). 

Assuming that the total distance L(tl) is 

where u is the effective helicopter speed over the ground in the 

horizontal plane while searching, Li(tl) in (15) becomes the linear 

functions 

1 

Li(tl) = (bi/cB) aibi - aiBl+ Bpi -zbigi , (27) 

i=l 

L 

Arthur I9 Little, lm=. 
where 

and F 7 

If the coefficients of ti in (27) are non-negative for all i, 

the optimal solution can be attained, or closely approximated, by 

the step-by-step procedure described earlier. If some ,of the 

coefficients are negative, the optimal solution may be impossible to 

attain if the first detection occurs late. 

G. COMPARISON WITH THE CLASSICAL SEARCH PROBLEM 

The optimization problem described above differs in several 

respects from the classical search problem associated with detecting 

a submerged submarine first formulated and solved by 

Koopman (G-1,2p?)~t differs in the following ways: 

1) Koopman assumes there is one and only one "target"; 

hence, search stops when the target is found. In the 

search for miners there are multiple "targets," and 

search continues after a detection is made. The searching 

conditions after a detection are not the same as the conditions that are applied before the detection. Hence, 

after detections have been made, the additional search is 

conditional on the detections that have been made. 

2) Koopman assumes that the "visibility" of the target 

remains constant throughout the search. In our problem, 

the signal that is the object of the search may disappear 

at any time; namely, the transmitter may cease to 

operate. 

Arthur D Lrttle Inc 
3) Koopman assumes that the objective of the operation is 

detection. In the search-and-rescue operation for trapped 

miners, a helicopter detection is a first step only; our 

overall objective is to rescue as many live miners as 

possible. 

These differences make the mine search-and-rescue problem more 

difficult than the classical search problem. 

References 

(G-1) Koopman, B.O., Search and Screening, OEG Report No. 56, CNO 

Navy ~e~artmentr~ashin~ton DC, 1946. 

(G-2) Koopman, B.O., "Search and Its Optimization ," American Mathematical Monthly, Vol. 86, August-September, 1979, pp. 527-540. 

(G-3) Koopman, B.O., Search and Screening, 2nd ed., Pergamon 

Press, Elmsford, NY, April 1980. 

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