USBM H0346045 

TECHNICAL SERVICES FOR MINE 

COMMUNICATIONS RESEARCH 

MODELLING AND DATA ANALYSIS OF 

50 to 5000 kHz 

RADIO WAVE PROPAGATION IN 

COAL MINES 

SUPPLEMENT TO FINAL REPORT 

Robef) L. Lagace - Task Leader 

Alfred G. Emslie, Michael A. Grossman 

UNITED STATES 

DEPARTMENT OF THE INTERIOR 

BUREAU OF MINES 

USBM CONTRACT H0346045 

Task Order No. 4 

FEBRUARY 1980 

ARTHUR D. LITTLE, INC. 

Cambridge, Massachusetts 
The view and conclusions contained in this document are thou, 

of the authors and should not be interpreted as necessarily 

representing the official policies or recomm~atiom of the 

Interior Depahent's Bureau of Mines or of the U.S. Government. 
TECHNICAL SERVICES FOR MINE 

COMMUNICATIONS RESEARCH 

MODELLING AND DATA ANALYSIS OF 

50 to 5000 kHz RADIO WAVE PROPAGATION 

IN COAL MINES 

SUPPLEMENT TO FINAL REPORT 

Robert L. Lagace, Task Leader 

Alfred G. Emslie, Michael A. Grossman 

ARTHUR D. LITTLE, INC. 

CAMBRIDGE, MASSACHUSETTS 02140 

C-78453 

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 U. S. Government. 

USBM CONTRACT H0346045 

TASK ORDER NO. 4 

FEBRUARY 1980 

UNITED STATES DEPARTMENT OF Ti INTERIOR 

BUREAU OF MINES 

Arthur D Littlelnc 
PREFACE 

This supplement to the final report is a collection of interim and 

monthly reports and working memoranda prepared during the course of this 

program to document the progress, methods and results of the work. The 

supplement is divided into the self-contained sections briefly described 

below. 

I. SELECTED MONTHLY TECHNICAL LETTER REPORTS - This section is a collection of selected monthly technical letter reports that briefly summarizes 

the chronological development of the analyses and results, including the 

different concepts, theoretical approaches, and methods of data reduction 

and analysis explored, and the discoveries, insights and findings made 

along the way. More detailed treatments of the key developments and 

results are presented in the interim reports and working memoranda 

reproduced in subsequent sections of this supplementary report, and in 

the separately published final report. 

II. BACKGROUND THEORY FOR MEAS~NT PROGRAM ON MEDIUM AND HIGH FREQUENCY 

RADIO TRANSMISSION IN COAL SEAMS - Working Memorandum - This working 

memorandum gives the initial background theory needed to guide the planned 

measurements and data analyses of this program to describe the propagation 

of radio waves in coal seams for the frequency range of 50 to 5000 kHz. 

111. MODELLING AND DATA ANALYSIS OF IN-MINE ELECTROMAGNETIC WAVE PROPAGATION - 

Interim Report - This interim report presents detailed treatments of the 

data analysis and modelling techniques used, and the associated results 

obtained from conductor-free area propagation data measured by T. Cory 

in the first set of six coal mines. The mines were located in three highcoal seams; the Pittsburgh seam in northern West Virginia, the Pocahontas 

No. 3 seam in Virginia, and the Herrin No. 6 seam in Illinois. 

IV. ANALYSIS OF MF PROPAGATION DATA FROM MARGARET NO. 11, NANTY GLO, 

EHRENFELD, AND ADRIAN COAL MINES - Interim Report - This interim report 

presents detailed treatments of several improved data analysis and modelling methods applied to, and results obtained from, conductor-free area 

propagation data measured by T. Cory in the second set of four coal mines. 

These mines were located in three low-coal seams; the Upper Freeport seam 

in Pennsylvania and West Virginia and the Lower Freeport and Lower Kittaning 

seams in Pennsylvania. In addition, this report contains a reprint of two 

papers presented at a Bureau of Mines sponsored EM Guided Waves in Mine 

Environments Workshop held in Boulder Colorado. One paper describes the 

three-layer theoretical model and its application to the conductor-free 

data from the first six mines, while the second paper describes the theory 

developed for the coupling of loop antennas to a cable in a mine tunnel 

in a coal seam, and the model's application to data in the vicinity of 

cables taken at the Margaret No. 11 mine. 

Arthur D Little, lnc 
V. A METHOD FOR NONINTRUSIVE, IN-SITU MEASUREMENT OF COAL AND ROCK 

CONDUCTIVITIES IN A COAL MINE TUNNEL - Working Memorandum - This working 

memorandum briefly describes a possible direct method, and its potential 

advantages and shortcomings, for performing in-situ measurements of coal 

and rock conductivities. 

VI. MODELLING AND DATA ANALYSIS OF IN-MINE ELECTROMAGNETIC WAVE PROPAGATION 

FROM 50 to 5000 kHz - Interim Report - This interim report presents a 

summary comparison of theoretical and experimental results for conductorfree areas in eleven coal mines located in seven coal seams. It also 

summarizes the findings and their implications for intrinsically-saie, 

portable radio communications between roving miners. 

iii 

Arthur D Little.lnc 
TABLE OF CONTENTS 

I. SELECTED MONTHLY TECHNICAL LETTER REPORTS 

11. BACKGROUND THEORY FOR MEASUREMENT PROGRAM ON MEDIUM AND HIGH 

FREQUENCY RADIO TRANSMISSION IN COAL SEAMS - Working Memorandum, 

August 1976. 

111. MODELLING AND DATA ANALYSIS OF IN-MINE ELECTROMAGNETIC WAVE 

PROPAGATION - Interim Report, May 1978. 

IV. ANALYSIS OF MF PROPAGATION DATA FROM MARGARET NO. 11, NANTY GLO, 

EHRENFELD, AND ADRIAN COAL MINES - Interim Report, May 1978. 

V. A METHOD FOR NONINTRUSIVE, IN-SITU MEASUREMENT OF COAL AND ROCK 

CONDUCTIVITIES IN A COAL MINE TUNNEL - Working Memorandum, June 1978. 

VI. MODELLING AND DATA ANALYSIS OF IN-MINE ELECTROMAGNETIC WAVE 

PROPAGATION FROM 50 to 5000 kHz - Interim Report, December 1979. 

Arthur D Little Inc 
I. SELECTED MONTHLY TECHNICAL LETTER REPORTS 

Arthur D L~rrle inc 
COVERING PERIOD FROM 

4 OCTOBER TO 31 OCTOBER 1976 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

During this reporting period the following accomplishments were made in each of 

the individual task areas of Task Order No. 4. 

Technical Support on the In-Mine Electromagnetic Wave 

Propagation Measurement Program 

During this period we received the Spectra Associates field report prepared by 

Terry Cory describing the set of measurements and data taken on the field trip to 

Consol's Ireland mine, and we began analyzing the data taken in the quasi-conductorfree area. We plotted families of theoretical curves of H vs r with the phase constant, P, 

as a parameter for several expected values of the attenuation rate a, in the hope that 

estimates of both a and @ could be obtained by noting which curves best matched the 

data. From a and (3, a, (rock), u, (coak), and K, (coal) are easily calculated. However, 

the curves were found to be not discriminating enough to determine @ from the available 

data. Replotting the H vs r curves with a as a parameter for several values of P, allowed 

more convenient estimates of a to be made, but again not of 8. Therefore, attempts to 

estimate @ were'abandoned and attention was focused on a only. Though the procedure 

is somewhat more involved, u; and or estimates can. be obtained. This method requires 

the use of an assumed value of the coal relative dielectric constant, K,, and a systematic 

search for the combination of or and u, values that produce a good fit' ofthe theory to the 

data. 

Preliminary analysis of the Ireland mine data in this manner revealed an attenuation rate a even lower than the very low one previously measured at Ireland in another 

area. In addition, the data at several frequencies did not behave in accordance with the 

theoretical model for a conductor-free area, particularly at extended ranges in the 

vicinity gf 1000 ft from the transmitter. Something appeared to be preventing the signal 

level from decreasing at the attenuation rate expected. Examination of the mine map 

revealed the presence of a 7200 VAC cable on the floor in the adjacent entry. An 

approximate coupling analysis indicates that such a cable, even in an adjacent entry, is 

apparently capable of providing a lower loss alternate transmission path from the 

transmitter to a receiver located at an extended range in a mine such as this one in 

which the conductivity of the coal is low. This behavior will prove valuable for extending communication ranges in some mines. The coupling analysis took into consideration 

the effects of cable images in the roof and floor. Thus, to obtain accurate estimates of or 

and a,, only data at positions closer to the source (where the data are less likely to be 

contaminated by the presence of the cable) will be usable. Preliminary examination of 

this close-in data reveals an attenuation rate and coal conductivity that is slightly 

higher than that found during the previous visit to Ireland. The analysis of these data 

should be completed during the next reporting period. 

In addition, we remained in close contact with Terry Cory regarding the Ireland 

data reduction and regarding preparations and subsequent measurements made at the 

Inland Steel mine No. 1 in Sesser, Illinois. A simple substitution calibration measurement for determining the value of the transmit moment~of the South Gfricanradios-was _ . _- 

Arthur D Littlelnc 
recommended. A discrepancy in the behavior of the Ireland mine field strength levels 

with changing frequency was noted, which has since been traced to a simple calibration 

error at two of the frequencies. A simplified model geometry for examining the propagation behavior of MF radio waves along longwall coal faces was formulated for subsequent analysis by J. Wait of NOAA. Finally, we recommended two mines for the next 

Spectra Associates field trip, Consol's Robinson Run mine and Eastern Associated 

Coal's Federal No. 2 mine, both in the Pittsburgh seam in West Virginia, but south of 

Pittsburgh in contrast to the Ireland mine which is located west of Pittsburgh in the 

West Virginia panhandle. 

During the next reporting period we plan to: continue our close communication 

with Terry Cory and PMSRC, analyze the Inland Steel mine data as well as complete 

the Ireland mine data analysis, perhaps start analyzing the Robinson Run and Federal 

mine data, and in the process try to devise better and simpler means of applying 

theoretical model results to explain the observed behavior of the data. 
SEVENTH MONTHLY TECHNICAL LETTER REPORT 

COVERING PERIOD FROM 

1 NOVEMBER TO 28 NOVEMBER 1976 

CONTRACT NO. H0346045 

TASK OREER NO. 4 

C-78453 

Technical Support on the 1n-~ine' Electromagnetic 

Wave Propagation Measurement Program 

During the November reporting period, major effort was 

devoted to analyzing the electromagnetic propagation data 

taken at the Inland Steel No. 1 mine in the Herrin No. 6 

coal seam near Sesser, Illinois, and to a lesser extent the 

data taken at Consol's Ireland mine in the Pittsburgh coal 

seam near Moundsville, West Virginia. The analyses showed 

that the signal attenuation rates are about three times more 

severe (and the coal conductivities about ten times higher) 

in the Inland No. 1 mine than in the Ireland mine, thereby 

supporting the need to examine the propagation characteristics 

of mines in both different and similar coal seams and mining 

districts. Data from both mines required more analysis than 

originally anticipated; the Ireland mine data because they 

were contaminated by the presence of a cable in an adjacent 

entry, and the Inland No. 1 mine data because at frequencies 

above about 1 MHz they departed from the behavior expected 

from a simple three-layer model having frequency independent 

material characteristics. 

The Inland mine data in particular were analyzed by a 

straight-forward method that provides a separate estimate of 

attenuation rate and coal/rock conductivities at each frequency 

based on the measured values of field strength versus distance in a conductor-free area of the mine. The analysis 

entails: removing the 1/& cylindrical spreading factor from 

the data, replotting the modified data in the form dB/lpa/m 

versus meters on linear graph paper, fitting each set of 

replotted field strength versus distance data by a straight 

line having a slope a (attenuation rate) and a reference 

field strength level H, at a mid-range distance, computing 

pairs of conductivity values (ac, ar) that satisfy a transmission-line-based attenuation rate equation a = f(ac, ar) 

for the graphically determined value of a, calculating field 

strengths by substituting these conductivity pairs into the 

theoretical field strength equation for the three-layer propagation model, and finally identifying that pair of conductivity values (ac, ar) for which the calculated theoretical field strength matches the data derived reference level 

at the prescribed mid-range distance. 

Arthur D Little.lnc 
Using this method of analysis it was shown that the 

Inland No. 1 mine can be well represented up to about 1 MHz 

by a simple three-layer model having % = 10-3 Mho/m and 

a, = 0.2 Mho/m. However, above 2 MHz the data exhibit 

increases in attenuation rate far in excess of that predicted 

by a model having the conductivities derived from the data 

below 1 MHz. In fact, further investigation revealed that 

the measured behavior can be closely approximated by a threelayer model having constant conductivity rock, but coal whose 

actual, apparent, or effective conductivity increases above 

1 MHz, changing from about Mho/m below 1 MHz to 

1.8 x 10-3 Mho/m at 2 MHz and 3.5 x 10-3 Mho/m at 4.5 MHz. 

Several possible causes for this behavior, which does not 

allow all the data to be fit with a single pair of constant 

conductivities, were hypothesized and analyzed in search of 

an explanation. Several standard references on the measured 

frequency dependence of the dielectric and conducting characteristics of materials did not include coal. Therefore 

we plan to contact potential sources of new or unpublished 

data on coal. Sensitivity analyses showed that even moderateto-large errors in the values of "assumed" or "known" values 

of coal dielectric constant Kc, seam height h, and transmitter 

moment M would not account for the discrepancies. Potential 

resonance effects caused by coal pillars of dimensions in the 

vicinity of X/2 and X were considered and discounted. The 

source coupling factor was modified to include the dielectric 

constant of the rock Kr, to no avail. The scattering loss 

produced by the air/coal interfaces at crosscuts was also 

estimated and found to range from < 1 dB to about a maximum 

of 3 dB per crosscut instead of the approximately 10 dB per 

crosscut required at 4.5 MHz. The leaky waveguide mode of 

propagation (which predominates at UHF) was considered, but 

found to give excessively high attenuation rates. A periodic 

structure propagating mode was also postulated for the layout 

of parallel tunnels typically found along the mains and submains in the coal seam, but was not extensively pursued at 

this time because of its anticipated low potential benefit 

to required effort ratio. 

At present we do not yet fully understand the reason 

for the large increases in the signal attenuation rate and 

the apparent conductivity of the coal at frequencies above 

about 2 MHz in the Inland No. 1 mine. However, we believe 

that further detailed investigation of this behavior is of 

low priority at this time. Though scientifically interesting, 

it may not be of critical importance to the Bureau's present 

mine wireless communication program, because this behavior 

has not yet been encountered in more than one mine, and 

Arthur D Littlelnc. 
perhaps more importantly, even if it were understood, such 

a high attenuation rate at frequencies above 2-3 MHz would 

make these frequencies unsuitable for the intended application. 

The more limited analysis of the Ireland data during 

this period was concentrated mainly on the 493 kHz and 1988 

kHz data, and some 335 kHz SAR data, and was hampered by the 

presence of cables in the adjacent entry. The 1988 kHz data 

and 335 kHz SAR data allowed a good fit for the slopes (a) 

but not for the absolute levels. At 493 kHz, a fit for the 

slope and level was possible only for the three data points 

closest to the transmitter where the cable influence was 

negligible. The findings to date indicate that the coal conductivity oc is about lom4 Mho/m at Ireland, as found before, 

but that the rock conductivity may be considerably lower than 

the 1 Mho/m estimated from previous data. 

A telephone conference meeting was held between the 

Cory/Spectra/Collins team and PMSRC and ADL staff prior to 

the measurement team's visit to Consol's Robinson Run mine 

and Eastern's Federal No. 1 mine. Agreement was reached on 

the following points. Conductor free area data has the 

highest priority. Data will be,taken down to 50 kHz and up 

to 4.5 MHz if possible, and at closer distance spacings if 

the attenuation rates are as high as at the Inland mine. 

The coplanar antenna orientation is the most important, perpendicular orientations the least, with some data samples 

of 40° rotations (about the vertical and horizontal axes) 

from coplanar desirable. If possible, coal samples will be 

taken, and measurements made through a large block of coal. 

A sequence of measurements parallel to an isolated cable 

for several systematically varied transmitter and receiver 

separations from each other and the cable will be performed 

if possible. Discussion of the Robinson Run mine measurements and data was also conducted between T. Cory and 

R. Lagace of ADL via telephone during the week of the above 

mentioned field trip. 

During the December reporting period, we plan to complete 

the analysis of the data from the Ireland and Inland mines, 

and to receive and analyze the data from the Robinson Run 

and Federal No. 1 mines, in preparation for a results presentation and program review meeting scheduled for mid-December. 

We also plan to continue to look for simpler and better ways 

to analyze and explain the behavior of the data, and to 

continue close collaboration with T. Cory and PMSRC staff. 

Arthur D Little. Inc 
EIGHTH AND NINTH MONTHLY TECHNICAL LETTER REPORTS 

COVERING PERIODS FROM 

29 NOVEMBER TO 31 DECEMBER 1976 

AND 

1 JANUARY TO 30 JANUARY 1977 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

Technical Support on the In-Mine Electromagnetic 

Wave Propagation Measurement Program 

During the December and January reporting periods, substantial 

progress was made in analyzing the mine propagation data, in 

devising improved and simpler methods of analysis, and in 

documenting the results of this work. Analysis Of the quasiconductor-free area propagation data from both the Consolidation Coal Ireland mine and the Inland Steel No. 1 mine was 

completed. In addition, similar data were received and 

analyzed for Consolidation Coal's No. 95 mine (Robinson Run) 

and Eastern Associated Coal's Federal No. 1 mine. Both these 

latter mines are located in Northern West Virginia in the 

Pittsburgh coal seam. It was found that the signal propagation behavior in the second pair of mines was similar to the 

behavior in the Ireland mine which is also in the Pittsburgh 

seam. Namely, signal attenuation rates in the Pittsburgh 

seam mines were found to be lower by a factor of about three 

than the rates found in the Inland No. 1 mine in the Herrin 

No. 6 seam over the frequency range from about lOOk~z to 

2MHz. It now appears that plots of the attenuation rate, 

a , versus frequency may be one of the most easily obtainable 

and useful means of classifying and comparing the propagation 

characteristics of different mines and seams. 

Tabulated below is a summary of the coal and rock conductivity 

estimates for each of the mines analyzed to date. Using 

these values of conductivity, corresponding estimates of 

magnetic field strength versus range can be computed, at 

frequencies of interest, from the three-layer model theoretical equations. 

Arthr~r n l ittlp lnr 
Conductivity Estimates 

Mine 

Seam 

Thickness Coal Rock 

Seam h (m) - 

ac (Mho/M) or (Mho/m) 

Robinson Run(#95) Pittsburgh 1.5 0.3x10-~ 0.085 

Federal No. 1 2 0.26~10'~ 0.084 

Ireland (11) 2 1. 0x10-~ 0.054 

Ireland (I) 2 1.4x10-~ 0.3 1 

2. 0x10-~ 1.09 

Inland No. 1 Herrin No. 6 3 10x10-~ 0.22 

Ireland I and I1 refer to measurements taken in two different 

parts of the Ireland mine on two different occasions, the 

I1 data representing the most recent measurements. It should 

also be noted that sedimentary rock and coal typically exhibit 

anisotropic electrical properties; therefore in the strict 

sense, oc represents the vertical or transverse coal conductivity, whereas or represents the horizontal or longitudinal 

rock conductivity. In general, longitudinal values for a 

material are higher than its transverse values. 

As was the case for the first two mines analyzed, it was 

necessary to devise still another method to analyze the data 

from the latter two mines. The previous method (described 

in our November monthly report) using the data-derived attenuation rate, cr , in concert with a reference field strength, 

Ho (rO), was found to be too restrictive to be successfully 

applied to these new data. Thus, we replaced this method 

with another one which is not only simpler but appears to be 

more universally applicable to the analysis of mine propagation 

data. 

This new data analysis method relies mainly on the behavior 

of the data-derived attenuation rate, a , a quantity that 

can be reliably obtained from the field strength versus 

distance data taken in conductor-free areas, and which is 

not dependent on the source/mode coupling factor. The 

attenuation rate a at each frequency is obtained as in the 

previous method, and a family of "constant a" curves are 

then plotted in the form or versus oc. Each data-derived 

value of a is used to generate a or versus oC curve from 

the transmission line attenuation rate equation a = F(or,oc,f) 

A point (8r,cc)representing a kind of "center of gravity" 

of the intersections of the family of curves is then chosen 

by visual inspection of the plot. This point (er,Gc) defines 

the experimentally determined values of rock and coal conductivity for that mine. This method is applicable to mines in 
which the rock and coal conductivities can be treated as 

frequency independent quantities over the frequency range of 

interest. Theoretically, the family of constant a curves 

should intersect at a common point (er,ac) representing the 

unknown conductivities of the coal and rock. In practice, 

variations from the model, experimental errors, and graphical 

analysis errors smear this point into an intersection "region". 

Using these values ($r,?c), the magnitude of the magnetic field 

strength versus range can then be computed at each frequency 

of interest. Comparison of theoretical and experimental field 

strength results for the Robinson Run and Federal #1 mines 

reveal a generally favorable overall agreement with regard to 

form and relative variations, with some differences in absolute 

level yet to be resolved. 

The experimentally determined set of conductivities (6c,2r) 

can also be substituted back into the attenuation rate equation 

a = F (ar, oc, f ) to generate an "average" a versus f curve 

representing the attenuation rate variation with frequency for 

that mine. Comparison of such curves with the corresponding 

data-derived values of a at each measurement frequency in the 

Robinson Run and Federal No. 1 mines reveals these curves to 

be very reasonable "best fit" curves to the a data points, 

as it should be. 

This good agreement provides yet a third method of estimating 

the rock and coal conductivities; namely, finding the pair of 

(or,oc) values (by a constrained trial and error substitution 

procedure) that gives a reasonable "best fit" theoretical 

a = F(or,oc,f) versus f curve to the data-derived values of a. 

This third method was used with success on the Ireland mine and 

Inland No. 1 mine data, data which did not produce a definitive 

intersection region in the method that uses the family of 

"constant a", ar vs oc curves. 

All of these results and methods of analysis were presented at 

the scheduled program status review and planning meeting held 

at PMSRC, Bruceton, PA in mid-December. In attendance were 

R. Lagace and A. Emslie of ADL, T. Cory of Spectra Associates, 

W. Laubengayer and L. Wilson of Collins Radio, and H. Dobroski 

of PMSRC. A twenty-five page handout of results consisting 

of twenty-two graphs and three summary sheets was distributed 

to the attendees by ADL and discussed. Priorities were also 

established for the measurements at the next two mines. Namely, 

the primary objective will be to perform measurements in socalled "quasi-conductor-free" areas, and the secondary objective 

will be to perform measurements along selected paths parallel 

to simple-geometry mine conductor systems. Preference will 

be given to locations adjacent to or through large coal blocks 

in the quasi-conductor-free areas when possible. Section signal 

mapping measurements will not be performed at these mines. 

3 

Arthur D Little, lnc 
As a result of discussions at this meeting and afterwards, 

the selection criteria for the next two mines were established 

and several candidates were identified. One mine will be 

selected in the Herrin No. 6 seam from candidates in several 

high production counties north of the county in which the 

Inland mine is located, to check the applicability of the Inland 

results to another mine in the Herrin No. 6 seam. The other 

mine (the first of the two to be visited) was selected from 

candidates in several high production counties in the Southern 

West Virginia - Eastern Virginia area,in a completely different 

seam, to obtain another sample of the propagation variability 

expected in different coal seams. The mine selected is the 

Island Creek VP #1 mine, in the Pocahontas #3 coal seam, in 

Buchanan County, Virginia and measurements were conducted there 

by the Spectra Associates/Collins Radio measurement team in 

mid-January. 

During the rest of this reporting period our efforts were 

devoted mainly to documenting the theory, analysis techniques 

and results to date in the form of a draft interim report that 

will eventually be incorporated as part of the final report 

for this task. As part of this effort, we also derived a more 

general and complete theoretical expression for the source/mode 

coupling factor, and proved that the accuracy of the transmission line approximation to the wave mode solution is within 0.3% even at the lowest frequency of 57Wlz. We expect 

the draft of the interim report to be completed in February. 

This report will also include plots showing the expected 

variations of signal strength with frequency at two communication ranges of present interest by the Bureau, 400m(1312ft) 

and 200m( 656ft), for several values of rock and coal conductivity that span the values found in mines to date. Such 

plots, when compared with similar curves of receiver and mine 

noise levels versus frequency, will reveal which frequencies 

offer the most favorable performance at each range in mines 

having different propagation and noise characteristics, and 

the source strength required to achieve a specified level of 

performance at these frequencies. 

Finally, summary notes from R. Decker of Spectra Associates 

describing results of his three-layer and five-layer model 

computer analyses of the mine data were also received and 

briefly reviewed during this period. A second set of summary 

notes was received at the end of this reporting period. 

During the February reporting period we plan to complete the 

draft interim report on the first four mines, receive and 

analyze the data from the Island Creek VP #1 mine, and to 

continue close collaboration with T. Cory of Spectra 

Associates and H. Dobroski of PMSRC. 
TENTH THROUGH SEVENTEENTH COMPOSITE MONTHLY 

TECHNICAL LETTER REPORT 

COVERING PERIOD FROM 

31 JANUARY TO 30 SEPTEMBER 1977 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

Technical Support on the In-Mine Electromagnetic 

Wave Propagation Measurement Program 

During the reporting period substantial progress was made both in 

the analysis of the in-mine EM wave propagation data and in the preparation of an interim summary report. The data from the remaining two 

mines were analyzed, and the consolidated results from all six highcoal mines have been plotted up in over 60 graphs which are being 

incorporated into an interim summary report which is near completion. 

During February, the effort was concentrated mainly on: analysis 

of the in-mine data taken by Spectra Associates at the Island Creek Coal 

VP //I mine in the Pocahontas No. 3 coal seam in Buchanan County, 

~ir~inia; collaboration with T. Cory of Spectra Associates regarding 

the data taken at the VP /il mine and previous mines; and preparation of 

theoretical curves indicating the variation of field strength as a 

function of frequency with distance and coal/rock conductivities as 

parameters. 

The VP #l data indicated that the Pocahontas No. 3 seam has a lower 

signal attenuation rate than the Herrin No. 6 seam, but a higher attenuation rate than the Pittsburgh seam. Analysis showed that this 

occurred in spite of a coal conductivity less than that of the Pittsburgh 

seam, because the rock conductivity was also significantly lower than 

that of the Pittsburgh seam, thereby allowing more energy to escape 

from the coal seam waveguide. Generally favorable overall agreement 

was found between the theoretical and experimental magnetic field 

strength versus distance curves, both with regard to form and relative 

variation with frequency. However, there remain some discrepancies 

between theoretical and experimental absolute values over some frequency 

ranges, the theory generally predicting somewhat higher values than 

those measured, as was observed during the analysis of the Robinson 

Run and Federal No. 1 mine data. These discrepancies could be attributed to some limitations in the simple theoretical model used, and/or 

to some unaccounted for differences or variations in equipment calibration, experimental procedures, or equipment malfunction. As a result 

of telephone discussions with T. Cory of Spectra Associates regarding 

the latter, and further thought about the former, we conclude that both 

factors appear to be contributing to the differences observed between 

some of the predicted and measured absolute levels of field strength. 

Arthur D Little, lnc 
We also reviewed the second installment of Spectra Associates' 

three-layer model and five-layer model computer analyses and comparisons 

with data, and subsequently compared the theoretical results of R. Decker 

of Spectra Associates and those of the ADL model using Decker's derived 

values of conductivity. The ADL results were found to be generally 

higher than the Spectra results, but in closer agreement with the slopes 

of the data curves than the Spectra results. 

Finally, the ADL theoretical model was used to generate plots of 

signal strength versus frequency for two ranges of interest, 400 m 

(1312 ft.) and 200 m (656 ft.) for the following ranges of coal and rock 

conductivity (3 x 10-5 a, 5 10-3 mho/m, 3 x 10-2 5 or 5 1 mholm). 

These plots were compared with a representative curve of rms mine noise 

versus frequency to illustrate the procedure of identifying the most 

favorable operating frequency as a function of range, mine conductivities, 

and noise conditions. These results will be presented in the interim 

summary report. 

During March, the effort was concentrated mainly on the analysis 

of the data taken at the Peabody No. 1 mine in the Herrin No. 6 seam 

in Illinois, and the consolidation of signal attenuation rate results 

from all six mines in time for use in an Information Circular being 

prepared for a mine communications technology transfer seminar. 

The data from the last of the six mines, the Peabody No. 10 mine, 

were analyzed and found to be better behaved than the data from both 

the VP No. 1 mine (Pocahontas No. 3 seam) and the Inland No. 1 mine 

(Herrin No. 6 seam). The results confirmed the high signal attenuation 

rate behavior experienced in the Inland No. 1 mine in the same seam. 

Furthermore, the analysis revealed Peabody No. 10 to be a mine with an 

even higher signal attenuation rate and a coal conductivity 2.5 to 4 

times that of the Inland No. 1 mine. Generally favorable agreement 

was also found between theoretical and experimental field strength 

behavior with distance and frequency. Aspects of the measurements, 

data, and mine environments to date were discussed with T. Cory of 

Spectra Associates via telephone. 

The signal attenuation rates, a, taken from all six mines 

expressed in dB/100 ft. and plotted versus frequency in,a single 

graphic presentation as shown in Figure 1. (This data consolidation was 

completed in time for use in a more simplified form in the Mine Communications Technology Transfer IC on SectionIPlace Communications.) 

As suspected, the limited sample of data to date reveals that different 

seams appear to exhibit distinctly different signal attenuation rates, 

and with the present exception of the extremely high-loss Herrin No. 6 

seam, the variation between mines within a seam is less than the variation between mines in different seams. If this property is further 

supported by tests in the remaining four mines to be measured, the 

easily obtainable attenuation rate may become the most convenient and 

useful predictor of expected MF mine wireless radio performance for 

mines in the major coal seams. Figure 1 also indicates that the 

Arthur D Little,lnc. 
important Pittsburgh seam is the most favorable seam investigated to 

date, and that the attenuation rate is so severe in the Herrin No. 6 

seam that radio performance is likely to be acceptable only when in the 

vicinity of metallic mine conductors. 

Table I presents the corresponding values of coal and rock conductivity derived for each of the mines measured. These values are used 

to generate the theoretical magnetic field strength versus range curves 

from the three-layer model field expressions. Figure 2 illustrates a 

set of theoretical curves generated for the VP No. 1 mine in the 

Pocahontas No. 3 seam while Figure 3 shows the similarity of the corresponding experimental data measured by Spectra Associates. Similar 

curves for all the mines have been included in the interim summary 

report. 

Finally, initial consideration was given to obtaining a semiempirical estimate of the mode coupling factor or the correction 

factor required as a function of frequency to provide a closer match 

to the absolute value of the data. Such a semi-empirical relationship 

might also suggest a simple physical explanation or relationship for 

the observed differences, and might also reveal a variation between 

coal seams similar to that exhibited by the attenuation rate. 

During April, May and June, the effort was reduced to a low level 

consisting primarily of minor administrative matters and the preliminary 

formulation of ideas on other methods of mode coupling and data analysis, 

while awaiting a contract modification for additional technical support 

to PMSRC on this task order. 

During July, August, and September effort resumed at a moderate 

pace, and was related primarily to simple semi-empirical methods for 

analyzing differences between theoretical and experimental results; 

revisions and additions to the interim summary report; interaction 

with other Bureau-sponsored investigators, and initial planning of an 

EM Guided Wave Workshop to be sponsored by the Bureau. 

Several semi-empirical methods were examined for comparing theoretical and experimental absolute field values to identify systematic 

differences or trends in the effective coupling factor, effective 

source magnetic moment, or effective seam height and medium conductivities. The most promising approach appears to be one in which the 

differences between theoretical and experimental values of field 

strength expressed in dB are determined as a function of frequency at 

a fixed reference distance from the source. 100 meters was chosen as 

a representative distance that allowed most of the data from both low 

loss and high loss mines to be included, while avoiding most near 

field effects. The computed quantity [HTH(dB) - HEX(dB)I can be considered a measure of the departure of the theoretical magnetic moment 

or coupling factor from that observed experimentally. Plots of these 

differences reveal that the simple three-layer model appears to apply 

best between about 200 and 1000 MHz, where it produces a relatively 

3 

Arthur D L.~ttle Inc 
well-behaved overestimate of the field strength which is essentially 

independent of coal seam and less than about 7 dB. To get a more 

definitive and systematic measure of this observed behavior, we plan 

to analyze these differences statistically during the next reporting 

period. 

Additions and revisions were also made to the interim summary 

report, incorporating the above results and new insights, together with 

adding to and completing the considerable amount of graphical artwork. 

We anticipate that this report will be completed and submitted to 

PMSRC during the November reporting period. 

Finally, at the request of the technical project officer, 

R. Spencer and A. Emslie of ADL participated with J. Wait and D. Hill 

of NOAA and ITS and H. Dobroski, K. Sacks, R. Bartholomae, and J. Nagy 

of the Bureau of Mines and MESA in a meeting at PMSRC, Bruceton, PA., 

in July. The meeting was convened by PMSRC for the internal dissemination and transfer of information on related projects being sponsored 

by the Bureau, and for the initial planning a£ an EM Guided Wave Workshop to be held in Boulder, Colorado. Subsequent planning and coordination activities by R. Lagace and R. Spencer have been minor, 

consisting primarily of telephone discussions with K. Sacks of PMSRC 

and J. Wait of NOAA. Any significant effort required of ADL staff 

related to this Bureau-sponsored workshop will require additional 

funding, perhaps by means of a separate task order having its own 

statement of work and funding. 

During the next reporting period, we plan to perform the statistical analysis described above and continue work on the interim summary 

report. 

Arthur DLittle,lnc 
-3 3 a:, ~. .~ ~..~ ~ . :~ . ,, .=. ~~~~ ~,~ < :c~ ".=" ~~"~.~ ~.,*.; . .,c.,, 

,.. . ,. .* .- 478.39 

Pisure 1 

Composite Ploc at Signal ir:enuation 

Races in d3/100 fc. !or six ~ines in 

Three Different Coal Seams 

. - - a Eaelu5QN Ruri 

~~~~ . 

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. ~ 

~ -~ 

~ ~ 

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PITTSRUKGH SEAM 

(Trelancl, Kobinson Kun $ 

Federal -1 m;ne5j 

! 1 li;:! 500 I000 1000 5030 

FREQUENCY, KHz 
TABLE I 

CONDUCTIVITIES DERIVED FROM THE a VERSUS f PLOTS 

Mine h u 

C u 

Kc r Seam (n) (Mholm) (Mho Im) 

Robinson Run 1.5 6 0.3 x 10'~ 0.085 Pittsburgh 

Federal No. 1 2 - 6 0.26 x 0.084 Pittsburgh 

Ireland I1 2 6 1. 0 0.054 Pittsburgh 

Ireland I 2 6 2.0 1.09 Pittsburgh 

1.4 x 0.3 Pittsburgh 

Inland No. 1 3 6 1.0 0.22 Herrin No. 6 

Peabody No. 10 

1 Main South 

1st West 2nd 2 6 4 0.3 Herrin No. 6 

North 

1 South 

5-1/2 East/ 2 6 2.5 x loe3 0.3 Herrin No. 6 

1 South Jct. 

Pocahontas No. 1 

3 South Area 1.37 6 3 0.01 Pocahontas No. 3 

Entry A 

3 South Area 1.37 6 3 lo-5 0.0077 Pocahontas No. 3 

Entry B 

2 North No. 1 1.19 6 6 

(Plow Area) 

0.017 Pocahontas No. 3 

Arthi~r n I ittlp lnc 


EIGHTEENTH MONTHLY TECHNICAL LETTER REPORT 

COVERING PERIOD FROM 

1 OCTOBER TO 30 OCTOBER 1977 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

Technical Support on the In-Mine Electromagnetic Wave Propagation 

Measurement Program 

During this reporting period, effort was devoted primarily to the 

statistical analysis of the differences observed between the measured 

and theoretically predicted values of field strength, and secondarily 

to the interim summary report, and to telephone conferences with J. Wait 

of NOAA and K. Sacks of PMSRC related to: the upcoming Bureau-sponsored 

Guided Wave EM Workshop, reports of ADL and others on the propagation 

of radio waves in mines and near conductors, and planned Bureau radio 

propagation measurements and associated data analyses. 

To statistically assess the goodness of fit of the simple threelayer theoretical model results to the measured data, the difference 

A = H(Theoretica1) - H(Experimenta1) in dB was studied. The statistical 

analysis was restricted to data for the frequencies between 100 kHz and 

1000 lcHz at a reference distance of 100 meters. For frequencies outside 

the 100-1000 kHz range, the data indicated that the simple three-layer 

model was breaking down; i.e., H(Theoretica1) was diverging from 

H(Experimenta1). One hundred meters was chosen as the reference distance 

because it allowed most of the data from both low and high loss mines 

to be included, while avoiding near field effects in most cases. The 

differences between theory and data were analyzed by: 

Computing the Sample Mean for all mines and 95% Confidence 

Intervals for both the population and sample mean at frequenc!.es 

from 100-1000 kHz. 

Computing the Sample Mean for each seam (there were too few 

samples within each seam to compute a standard deviation on a 

seam basis). 

Plotting each of the characteristics found and analyzing the 

graphs. 

Testing the hypothesls that the theoretical model fit the data 

at the 95% level for the frequencies between 100 kHz and 1000 

kHz. 

From this analysis, the following observations and conclusions 

were made. The differences between the model and the experimentally 

Arthur D Littleinc 
recorded data were similar for all coal seams. The shapes of the curves 

for each seam average followed the same pattern and did not differ from 

one another by more than 1 or 2 dB, with the exception of the Herrin /I6 

seam at frequencies below 400 kHz. At these frequencies, data for only 

one mine in the Herrin /I6 seam was available. However, at 400 kHz to 

1000 kHz, the Herrin 116 seam average curve paralleled those of the other 

seams. This homogeneity implied that pooling all the data to compute 

a Grand Mean for all mines was a valid technique, and that the results 

from any analysis could be applied back to all the mines uniformly. 

Furthermore, it was shown that: 

Between the frequencies of 200 kHz to 900 kHz there is no significant difference between the model and the actual data readings. 

- 

In this band of frequencies the average difference, A, ranged 

from 1.1 dB to 3.9 dB. 

The range from 200 kHz to 600 kHz appeared to be the best range 

for the model with both the variance and average difference 

between the model and actual data being smallest, and positive, 

within this frequency range. 

In summary, based on the statistical analysis applied to the data 

available to date, it can be concluded that: 

The Grand Mean difference for all mines may be used in all 

analyses. Furthermore, it may be used to represent the individual seam averages; 

The simple three-layer model fits the experimental data in the 

200 kHz to 900 kHz frequency range at the 100 meter reference 

distance. It does not fit the experimental data outside the 

range of those frequencies. 

The details of this analysis and the tabulated and plotted results were 

also summarized in a memorandum entitled "Attenuation Rate for Radio 

Signals in Coal Mines: Model Goodness of Fit." 

During the November reporting period we plan to complete the interim 

sunnnary report, include the statistical analysis results in this report 

or in a separate working memorandum, continue earlier work on the 

analysis of coupling to conductors in mines, and collaborate via telephone with PMSRC staff, T. Cory of Spectra Associates, and 3. Wait of 

NOAA related to the Bureau's in-mine measurement programs, as required. 

Arthur D Little Inc. 
TWENTY FIRST THROUGH TWENTY FIFPH COMPOSITE 

MONTHLY TECHNICAL LETTER REPORT 

COVERING PERIOD FROM 1 JANUARY THROUGH 28 MAY 1978 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

Technical Support on the In-Mine Electromagnetic Wave Propagation 

Measurement Program 

During this reporting period substantial effort was. expended and 

progress made in the analysis and understanding of experimental MF radio 

propagation data taken in conductor-free areas of U. S. coal mines, and 

in the development of a simple theoretical model for describing the 

coupling of loop antennas to a single cable installed in a tunnel in a 

coal seam. Data have now been analyzed from ten mines in six different 

seams, and have been summarized in a way that identifies the principal 

factors affecting MF radio wave propagation performance in different 

coal seams. In addition, two major reports were completed, and submitted to PMSRC, which summarize all of the theoretical modelling and data 

analysis completed to date. These reports are entitled "Modelling and 

Data Analysis of In-Mine Electromagnetic Wave Propagation" (Interim 

Report, May 1978) consisting of 105 pages and "Analysis of MF Propagation Data from Margaret No. 11, Nanty Glo, Ehrenfeld, and Adrian 

Coal Mines" (Working Memorandum, May 1978) consisting of 52 pages. 

During June we plan to complete all work on this Task Order and to submit the draft final report to PMSRC. We have reached the 75% expenditure point, and do not anticipate a significant overrun or underrun 

provided no unanticipated difficulties are experienced in the analysis 

of the data from the last mine. We have also discussed with the Technical Project Officer recommendations for a timely and moderate increase 

in scope of work related to analyzing the mine data in a new and 

improved way that has recently been developed that would make the 

results of this study more valuable and readily applicable to Bureau 

of Mines MF radio programs. 

During January the effort was primarily related to the analysis of 

data taken by T. Cory in conductor-free areas and in the vicinity of 

cables in the Margaret No. 11 mine, and to the initial developments of 

a theoretical approach for the coupling of loop antennas to a cable 

installed in a tunnel in a coal seam waveguide. The conductivities 

of the coal and surrounding rock were computed by means of a more precise least square method involving a practical minimum search procedure. 

This Margaret No. 11 mine in low coal was found to have a conductor-free 

area attenuation versus frequency characteristic which lies between 

that of the Pocahontas No. 3 seam and that of the Herrin No. 6 seam. 

The magnetic field strength behavior along cables in mine tunnels 

in the Margaret No. 11 mine was analyzed with respect to the longitudinal attenuation rate of the magnetic field signal along the cables. 

Three attenuation rate patterns are apparent. The first is noticed 

within an approximately 90' angular sector which is bisected by the 

perpendicular drawn from the loop to the cable. In this sector the 

field attenuation rate along the cable is on the order of 700 dB per 

1 

Arthur D Little,lnc 
kilometer, and represents the direct contribution of the coal seam mode 

field generated by the loop transmitter. Once beyond this. region, the 

longitudinal attenuation rate reduces by one to two orders of magnitude, 

and is caused by a cable-guided mode excited by the transmit loop. In 

a tunnel containing only a single power cable, this cable guided mode 

was found to exhibit an attenuation rate of less than 10 dB per kilometer. However, in a tunnel containing a belt, pager phone line, and 

belt control lines a significantly greater longitudinal attenuation rate 

of 30 to 40 dB per kilometer occurs. We believe this higher attenuation 

rate in the beltway is due to shunt loading caused by the beltway supporting structure which is terminated into roof bolt anchors, and to the 

close coupling of the pager phone and control cable lines to this heavily shunt loaded beltway. This behavior resembles that of a shunt 

loaded trolley wirelrail Line. The development of a theoretical model 

describing the degree of coupling between a transmit loop and a single 

cable installed in a coal seam waveguide centered on an integral 

approach for computing the current induced in the cable as a result of 

the sumation of the infinitesimal emf's induced along the cable by 

the coal seam mode magnetic field generated by the transmit loop. 

Communications were also maintained with T. Cory and H. Dobroski 

via telephone regarding the data taken at the Margaret No. 11 mine, T. 

Cory's transmission line approach for measuring the in situ conductivity 

of the coal, and' the selection of coal mines to be visited. 

During February the major effort was devoted to developing theoretical expressions for the coupling to a cable in a coal seam waveguide. 

Convergence problems were encountered in the integral approach used to 

derive an expression for the current induced in the cable by a transmit 

loop located at distance r away from the cable. The objective was to 

compute the value of cable current produced at a large distance down 

the cable from the location of the transmit loop. This approach was 

finally abandoned in favor of a different approach suggested by the 

principle of reciprocity. Namely, it was decided to derive the coupling expression by computing the open circuit voltage induced in the 

receive loop by the current-carrying cable. This approach was used 

with the method of images, to account for the effects of the roof and 

floor above and below the coal seam. 

Expressions were first derived by having all the return current 

carried by only the first two images. Subsequently, the contributions 

from all images were included. Convergence problemswereexperienced 

with the infinite set of images method for both cases examined, namely 

by including and ignoring the presence of the coal. Even after solving 

the convergence problems, the computed theoretical values for the horizontal magnetic field in the coal seam were found to be significantly 

below those values measured experimentally. It was finally realized 

that the midpoint in the coal seam where the field was being computed 

was the location of a minimum or null in the horizontal magnetic field 

component perpendicular to the cable. In other words, the current 

carrying cable was not exciting the expected coal seam waveguide TEM 

mode. Ambiguities and other seeemingly unusual behavior of the plotted 

data were cleared up via telephone discussions with T. Cory, and suggestions were made for obtaining better experimental estimates of the 

low longitudinal rates experienced along the cable. 

Arthur D Little. lnc. 
R. Lagace of Arthur D. Little, Inc., visited PMSRC twice during 

the month. The first visit was to make a progress report, and the 

second was to meet with representatives of Franklin Institute, PMSRC, 

and Motorola on problems associated with the coupling of electromagnetic 

radiation and waves to electrical blasting circuits in mines. The meeting on blasting circuits resulted in the identification of shortcomings 

in the theory and information that now exist, a preliminary agreement 

on the most important radio frequencies and applications for which definitive rulings may be possible in the near future, and the suggestion 

that this subject be treated at the March electromagnetic guided wave . -- . - Workshop in Boulder, Colorado. 

During the March reporting period the major effort was devoted to 

developing theoretical expressions for the coupling of loops to cables 

in coal seam waveguides and to refining the three-layer model for propagation in conductor-free areas. A major advance in understanding and 

simplicity was obtained by switching to a Fourier series representation 

for the cable current and its associated images in the rock, and by 

representing the wave generated by these currents as a bound guided 

wave propagating in the longitudinal cable direction and evanescent in 

the transverse direction to the cable. This allowed the contribution 

of each Fourier series harmonic to the resultant field at a radial distance r away from the cable to be simply computed. It also became 

readily apparent that only the first few harmonics made important contributions to the resultant field. The first and strongest harmonic 

produces only a vertical component of magnetic field at the seam midpoint; the horizontal component due to this harmonic passes through 

zero at that point. Thus, agreement with experimental horizontal H 

data taken at this point, would have to rely on an accidental rotational 

misalignment of the loop or a displacement of the loop from the midpoint. 

Unanticipated chance agreement could also occur if the roof and floor 

material had asymetrical electrical properties. The contribution to 

the horizontal component at the midpoint due to the second harmonic 

contribution of the current, although present, was found to be insignificant. Consequently, the Margaret No. 11 mine data in the vicinity 

of cables are not adequate to prove or disprove the theoretical predictions, and a new set of measurements that examine the response to all 

polarizations has been defined for the last mine to be visited by T. 

Cory. 

As a result of these analyses, the Fourier series approach was 

pursued and documented -.- in the'form of a paper presented at the electro; 

magnetic guided wave Workshop in Boulder, Colorado, at the end of March. 

Curves were generated for loop-to-loop coupling via the cable, for the 

case in which both loops are separated from each other by a large longitudinal distance, and from the cable by radial distances of x and x 1 2' and for the case where one of the loops is placed immediately underneath 

and adjacent to the cable. 

The success of this Fourier series approach also led to its use in 

refining the derivation of the coal seam mode magnetic field produced 

Arthur D l.ittle inr 
by a vertical loop in the coal seam waveguide. Namely, the transmit 

loop and its images in the rock can also be represented by a Fourier 

series having in this case a DC term which couples to the quasi-TEM 

coal seam propagating mode. 

The Fourier series approa'ch to the coupling to cables in coal seam 

waveguides was also applied to the case of two or more cables located 

in a vertical plane within the coal seam waveguide. It was found that 

when a loop is located at large distances compared to the thickness of 

the coal seam, for example one pillar away in an adjacent tunnel, the 

loop couples more strongly to a common mode (monofilar) excitation of 

the cables in which the currents in all the cables travel in the same 

direction and the return current flows in the rock. However, when the 

loop is located close to the cable, at distances on the order of or 

less than the spacing of the cables, then better coupling will be made 

to a differential (bifilar) mode of excitation of the cables. 

Assistance was also received from 3. Wait, who was most cooperative in supplying us with values for the longitudinal phase constant 

for a wave propagating along a single cable located in a tunnel, values 

which were recently calculated for presentation at the electromagnetic 

guided wave Workshop in Boulder at the end of March. 

During the electromagnetic guided wave Norkshop, as a result of 

interactions with T. Cory, we conceived of a simple crossed loops 

method for making localized in situ measurements of the conductivity 

of coal and rock in mines, and derived theoretical expressions for the 

output signal as a function of conductivity of the medium to be 

measured. 

During the April reporting period major effort was devoted to 

analyzing the data from the remaining three mines visited by T. Cory, 

to developing simpler methods of deriving the coal and rock conductivities by using the least square method, and to thinking of better 

ways to compare theoretical and experimental magnetic field strength 

behavior as a function of frequency and range. 

At the beginning of April, technology transfer meetings were conducted at Arthur D. Little, Inc., between B. Austin of South Africa 

and R. Lagace and R. Spencer of Arthur D. Little, Inc. During two 

days of meetings, a considerable transfer of information and ideas on 

MF communications in mines was achieved. The subjects covered included 

sys tem efficiency and intrinsic safety considerations in the design of 

antennas for personal MF radios; size and location of fixed station 

loops for wireless and cable coupled communications in mines; the 

coupling to mine AC power cables for the transmission of monitoring 

data to receiving stations; circuit design and fabrication considerations in the construction of mine worthy radios by South Africa; the 

effects of geological parameters on the polarization of MF waves in 

coal mines versus gold mines; hoist shaft communications to closed 
cages; coupling to and comunications up a drill string and means to 

locate cutting heads sheared off from the drill string; and historical 

development and evolution of personal radio hardware for emergency 

communications in South African mines. 

Several telephone discussions were also conducted with T. Cory, 

and H. Dobroski and K. Sacks of PMSRC. Discussions with Cory centered 

on detailed descriptions of the mine environments in which the measurements were taken at the most recent three mines, and with the types of 

measurements to be made in the last mine for verifying or disproving 

the ADL developed theory for coupling to cables in coal seams. Discussions with H. Dobroski centered on the types of measurements to be made 

in the final mine to be measured by T. Cory, and on upcoming mine tests 

planned for the new South African radios received by PMSRC. Discussions 

with K. Sacks centered on design problems and capabilities related to 

the fabrication of ferrite loaded loop antennas for use by miners as a 

substitute for air-core bandolier type loops. 

Attenuation versus frequency plots for all four mines were determined and the associated conductivities were derived for rock and coal 

by using an improved version of the least square method for computing 

the conductivities. It is a method easily adapted to a pocket calculator, and it has been described in the working memorandum referred to 

at the beginning of this report. Plots of theoretical and experimental 

values of magnetic field strength at a reference distance of 100 m 

versus frequency were also compared for several of the latest mines 

measured. 

During May the major effort was devoted to completing all data 

analyses of the quasi-conductor-free area data taken at the four low 

coal mines visited by T. Cory, and to documenting all the results to 

date in two major reports which were completed and submitted to the 

Bureau. 

The experimentally derived a versus f results for all four low coal 

mines measured by T. Cory were converted to dB1100 ft. units and plotted 

upon the composite plot for all mines visited to date. It was found 

that these mines lie between those of the Herrin No. 6 and Pocahontas 

No. 3 seams, thereby making the favorable Pittsburgh seam behavior the 

exception rather than the rule so far. Two methods were also reviewed 

for the presentation and comparison of theoretical and experimental 

values of the magnetic field versus distance from the transmit antenna 

in conductor-free areas. One method involved the drawing of both theoretical and experimental H versus frequency curves at a standard range 

of 100 meters instead of the ratio of %heor/HExpt previously used. 

The second method involved using the coupling factor, C, defined by the 

intercept of the HA versus r curve with the HA vertical axis. Experimentally determined values for this coupling factor were compared with 

theoretically derived ones from the coal seam mode three-layer model 

magnetic field expression. 

Arthur D Littlelnc 
Since the coupling factor intercept with the vertical axis is a 

more fundamental quantity than the magnetic field at a reference distance of 100 m, it was decided that subsequent comparisons of the 

theoretical and experimental absolute values of the magnetic field should 

be based on this coupling factor C. This coupling factor was shown to 

be relatively insensitive to the coal and rock conductivities. This 

theoretical coupling factor expression also generally overestimates the 

field strength value below about 1 MHz while underestimating it at 

frequencies above 1 MHz. 

The dependence of coupling factor and attenuation rate on coal 

seam thickness, h, was also examined. The coupling factor C was found 

to be moderately dependent on the coal seam thickness, h, and the attenuation rate a more strongly dependent on it. Consequently, curves 

were drawn showing how the coupling factor versus frequency and attenuation rate versus frequency behavior was influenced by the coal seam 

height. Increasing seam thickness was found to shift the coupling fac- - - 

tor curve downward by a relatively constant amoun_t_at all MF frequencies, 

and to shift the attenuation rate curve downward by an increasing amount 

with increasing frequency. This behavior indicates that longer comunication ranges will be obtained in high coal seams than in low coal 

seams having the same rock and coal electrical properties. 

All the results for the analysis of the conductor-free area data 

for the first six mines were documented in an interim report entitled 

"Modelling and Data Analysis of In-Mine Electromagnetic Wave Propagation" 

consisting of 105 pages. This report includes a section on the selecting of operating frequencies for MF systems designed for installation 

in different types of coal seams. The results and the analytical techniques developed and refined for the last four mines were also documented in a Working Memorandum entitled "Analysis of MT Propagation 

Data from Margaret No. 11, Nanty Glo, Ehrenfeld, and Adrian Coal Mines" 

consisting of 52 pages. This latter report includes a detailed description of the simplified procedure for deriving the coal and rock conductivities from the a versus f plots by the least square method. 

R. Lagace visited PMSRC at the beginning of May to provide a progress report on the work completed to date. At the end of the May 

reporting period, another progress report was given to H. Dobroski of 

PMSRC at Arthur D. Little, Inc. Several discussions were also conducted 

by telephone and in person with PMSRC technical staff regarding MF radio 

installations for the Lucerne mine, the applicability of the Geonics 

conductivity measuring equipment in mines, and a crossed loop method 

for measuring coal and rock conductivity. Telephone collaboration was 

also maintained with T. Cory regarding measurements made at the last 

low coal mine. Arrangements have been made for the delivery of the 

data to ADL by the end of the first week in June. 

During the next reporting period we plan to complete the analyses 

of the data from the last mine measured by T. Cory, and to compile and 

complete the draft final report for this Task Order for submission to 

PMSRC. 
TWENTY SIXTH THROUGH TWENTY EIGHTd COMPOSITE 

MONTHLY TECHNICAL LETTER REPORT 

COVERING PERIOD FROM 29 MAY THROUGH 27 AUGUST 1978 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

Technical Support on the In-Mine Electromagnetic Wave Propagation 

Measurement Program 

During this reporting period the conductor-free area data from the 

last low coal mine, the Stinson i!3 mine, was analyzed and a highly 

satisfactory agreement obtained with the ADL three-layer model. Furthermore, the attenuation characteristic of this mine places it between that 

of the Pocahontas 113 seam and the Herrin 116 seam. After careful analysis 

the conductor proximity data were found to be unusable for comparison 

with the ADL cable-in-a-coal-seam model, and the data were found to exhibit some presently inexplicable behavior. 

The attenuation versus frequency data from the first six mines were 

analyzed by the least square error method for deriving the rock and coal 

conductivities used for the last four mines. Coupling factor curves 

were generated for all mines measured to date, and analyzed statistically 

to determine goodness of fit of the coupling factor to the data. The 

model was found to be in extremely good agreement with the data in the 

200 to 1000 kHz band of interest for mine wireless radio contmunications. 

A Working Memorandum was completed and submitted to PMSRC documenting the crossed loop method for in situ measurement of coal or rock 

conductivity. Two reports received from T. Cory were also reviewed. 

During this reporting period the Stinson 1/3 mine report was received 

from T. Cory, and the conductor-free area data were analyzed to obtain 

curves of attenuation rate a versus frequency, coupling factor C versus 

frequency, and the rock and coal conductivities. Very good agreement 

with the theoretical model was obtained for this mine, both with regard 

to a versus f, and C versus f behavior. The conductivi ies found for 

this mine are a, = i. 1 x Nhos/m and ac = 3.0 r lo-' Mhosim. We 

also found that the Stinson data place this mine between the Pocahontas 

113 seam and the Herrin 116 seam regarding attenuation versus frequency 

characteristics. Below 500 Wz the attenuation rate versus frequency 

curve falls within the range found for the Pocahontas #3 seam. Above 

500 kHz the attenuation versus frequency characteristic rapidly moves 

up through the band occupied by the Lower Freeport, the Upper Freeport, 

and the Lower Kit+anning seams reaching attenuation rate values near the 

lower limit of those found for the Herrin 116 seam at 3710 kHz. 
Considerable time was spent examining the conductor proximity data 

taken at the Stinson 113 mine before concluding that they were not suitable for comparing with the single cable in a coal seam model previously 

formulated. The principal reason for this conclusion was that the tunnel contained four or five parallel conductors distributed over the 

tunnel cross-section instead of one, and the transmit loop was located 

at a position halfway betwen two of them instead of immediately adjacent 

to, and in the plane of, the conductor closest to the perpendicular path 

traversed by the receive antenna. This fact makes it very difficult to 

calculate a coupling factor, to compare with the signals measured, without introducing considerable ambiguity. A second measurement problem 

with respect to the data is the presence of a component of magnetic 

field parallel to the cables that also increases with increasing frequency, We cannot presently explain this behavior for a parallel set 

of conductors. However, such behavior could occur if a "spur" conductor was present running perpendicular to the main set of cables going 

perhaps to a pump or pager phone or other electrical device either 

within the main tunnel or down cross cuts adjacent to the cross cut in 

which the receive antenna was located. T. Cory is not certain whether 

such perpendicular spur conductors were present at the time of the 

measurements. 

In an attempt to find some data that could be used to verify or 

contradict the single cable in a coal seam model derived by ADL, we 

revkwed and examined in detail the conductor proximity measurements 

made in the first mine ever visited by the Collins Radio/T. Cory 

measurement team, namely the Consolidation Coal Rose Valley Mine in 

West Virginia. It appears that these data will also be inappropriate 

for comparing with the ADL coupling to cable model. Examination of 

these data did uncover a situation in which a magnetic field component 

parallel to the main run of cables was also measured. However, the 

component was measured at a cross cut intersection just beyond the end 

of a pager phone line spur running into the cross cut perpendicular to 

the main run of cables. In this case the presence of this pager phone 

line perpendicular to the main run of cables offers a plausible explanation for the presence of the parallel magnetic field components. 

We initiated and completed analyzing the attenuation versus frequency data from the first six mines using the improved least square 

error method of determining the coal and rock conductivities. The 

coupling factor, C, defined by the intercept of the straight line far 

field approximation of H& with the vertical axis (r = O), was also 

computed and plotted for these mines. All the experimental and theoretical attenuation versus f, coupling factor versus f, and conductivity 

results form all mines were assembled, plotted up, and examined in considerable detail for reasonableness, consistency, and overall integrity 

prior to subjecting the coupling factor data to statistical analysis. 
In some cases, mainly for some of the data taken at the Inland 

No. 1, Peabody No. 10, Pocahontas No. 3, Nanty Glo and Robinson Run 

mines, substantial time and effort were spent checking, recalculating 

and rethinking the data reduction methods, experimental procedures and 

data, analytical techniques, and overall veracity andapplicability of 

the data. Telephone collaboration with T. Cory assisted this effort. 

As a result, errors were found and purged in some of our previous data 

reduction/analysis and in some of the data themselves. A small amount 

of the data, or the conditions under which they were taken, were also 

judged to be highly inconsistent or suspicious based on several criteria. 

These were justifiably excluded from the statistical analysis of goodness of fit of the simple coupling factor theory to the experimental 

data. These few deviant data have not been totally ostracized however; 

they will be included in the final report where they can receive further 

observation and possible diagnosis of the cause of their aberrant 

behavior by other practitioners. 

The quantity AC = CTmOR - C R (in dB) was analyzed statistically 

in seven frequency bands coveringE%E range from 83 kHz to 4750 kHz, to 

determine the mean difference AC, the 95% confidence limits on the mean 

difference, and the 95% confidence limits on the differences for the 

sample population. The ADL simple three-layer model was found to fit 

the data extremely well over the frequency range from 200 to 1000 kHz 

which is of greatest interest for coal mine applications. In particular 

we found a mean difference of less than +l dB, a 95% confidence interval 

of about t2 dB for the mean, and a 95% confidence interval of about 

t(7 - 10) dB for the population. The theory was found to overestimate 

the coupling factor above 1000 MHz and below 200 kHz, giving a mean 

difference of about +5 dB around 100 and 2000 kHz. 

We also found a good way to visually present the derived conductivities; namely by characterizing each test location in each mine as 

a point on a graph where the coal conductivity is plotted along the 

ordinate and the rock conductivity along the abscissa. The results to 

date appear to reveal trends and clusterings that define the average, 

high, and low signal attenuation rate conditions. 

A Working Memorandum was completed and submitted to PMSRC documenting the simple crossed loops method for making localized in-situ 

conductivity measurements. The Working Memorandum is entitled "A 

Method for Nonintrusive In Situ Measurement of Coal and Rock Conductivities in a Coal Mine Tunnel." 

The Draft Final Report submitted to the Bureau by T. Cory was 

reviewed, as well as the special technical report issued by T. Cory 

entitled "In Situ Measurement of Coal Seam Conductivity Using a Parallel 

Wire Transmission Line Method." We note in this latter report that the 

values of coal conductivity derived by T. Cory from these measurements 

are within the same order of magnitude as derived by the ADL three-layer 

model, but that the values of T. Cory are approximately twice as high 
as the values obtained from the three-layer model. A relative dielectric constant of about 2 is also obtained by T. Cory as opposed to the 

value of 6 assumed in the ADL three-layer model. An unexpected benefit 

to the ADL low impedance line demonstration experiment also occurred. 

T. Cory's technique for determining B of the line was modified slightly 

and used to measure the wavelength along normal and low-Z lines at the 

McElroy mine. 

During the next reporting period we plan to request from the mine 

companies the petrographic analyses of the coal in the vicinity of the 

measurement sites at all mines visited by T. Cory, in order to statistically analyze these data relative to their impact on the values 

obtained for the coal conductivity in each mine. From this analysis 

we hope to determine whether any correlation exists between the values 

of coal conductivity and any of the quantities routinely analyzed by 

mines to assess the marketability of its coal. We also plan to start 

writing sections of the draft final report,and to continue telephone 

collaboration between H. Dobroski of PMSRC; the measurement contractor, 

T. Cory; and J. Wait and D. Hill of ITSINOAA as required. Preparation 

and submission of the draft final report for this task order was 

deferred to accommodate the additional analyses requested in Modification 4 to this Task Order. 
TWENTY NINTH THROUGH FORTIETH COMPOSITE 

MONTMY TECHNICAL LETTER REPORT 

COVERING PERIOD FROM 28 AUGUST 1978 TO 25 AUGUST 1979 

CONTRACT NO. H0346045 

TASK ORDER NO. 4 

C-78453 

Technical Support on the In-Mine Electromagnetic Wave Propagation 

Yeasurement Program 

During this reporting period effort was spent primarily on examining 

the implications of the data analyses and associated theoretical models 

on the expected performance of MF radio systems in coal mines, and on 

preparing the draft final report. 

,, Average" values for coal and rock conductivities based on the 

processed propagation data to represent high, moderate and low loss coal 

seams were selected, and curves of coal seam coupling factor versus seam 

height and frequency were plotted. These representative values of conductivity were then applied to the theoretical coal seam propagation 

model, together with mine electromagnetic noise data, to generate curves 

of predicted maximum radio commtinication range versus frequency in high 

and low coal seams under "mine noise" and "receiver set noise" operating 

conditions. 

Maximum radio comnications range versus frequency in conductorfree areas was found to exhibit a broad peak centered between 300 and 

700 kHz, a band well within the 200 to 1000 kHz frequency band over 

which the model is in extremely good agreement with the propagation 

data. Within the optimum frequency band of 300 to 700 kHz, maximum 

ranges were found to be highly dependent on attenuation rate, and thus 

on the electrical conductivities of the coal seam and its surrounding 

rock. Consequently, maximum communication ranges for portable, intrinsically safe radios can be expected to vary from low values of about 

75 to 100 meters in a high-loss seam such as the Herrin No. 6, to high 

values of about 300 to 400 meters in a low-loss seam such as the 

Pittsburgh. 

A significant part of the writing, editing, tables, and artwork 

were also completed on the draft final report. During the writing of 

the draft report, many final checks and searches were made regarding 

assumptions, methods of analysis and presentation, regions of model 

applicability, and plausible reasons for unexpected and/or unexplained 

data in both conductor-free areas and in the vicinity of mine cables. 

We are attempting to present the results of a large amount of data analysis and related propagation modelling in a comprehensive, but concise 

and easy to follow and use, format for the final report. The supplementary volume for limited distribution will include the working 
memoranda documenting many of the details, and preliminary steps, 

results, models, and analysis techniques for future reference by others. 

During the next reporting period, we plan to receive coal petrographic/proximate analysis data from the test mines, analyze them to 

determine if any significant relationships exist between the proximate 

analysis data and the derived electrical conductivities, and incorporate 

the results in the draft final report. We also plan to complete the 

draft final report and submit it to PMSRC for approval. 
11. BACKGROUND THEORY FOR MEASUREMENT PROGRAM ON MEDIUM AND HIGH 

FREQUENCY RADIO TRANSMISSION IN COAL SEAMS - Working Memorandum 

August 1976. 

/,rrhur D Little ini 
WORKING MEMORANDUM 78453 August 3, 1976 

BACKGROUND THEORY FOR MEASUREMENT PROGRAM ON MEDIUM 

AND HIGH FREQUENCY RADIO TRANSMISSION IN COAL SEAMS 

This memorandum gives the background theory needed to guide 

the forthcoming measurements on MF and HE radio wave propagation in 

coal seams and to reduce the data obtained in the measurement program. 

In the frequency range of interest, namely, 50-1,000 kHz, 

the free-space wavelength is in the range of 6,000-300 m and is therefore very large compared with the thickness of a coal seam and with 

the transverse dimensions of a coal mine tunnel. Under these conditions, the only useful mode of propagation is an approximately TEM 

mode in the coal seam with the magnetic field horizontal and the 

electric field approximately vertical. This kind of mode can be 

launched and received by loop antennas placed in a tunnel with the two 

loops in the same vertical plane. Since the wavelength is so large 

compared with the tunnel dimensions, the transmission from one loop to 

the other is practically the same as if the loops were immersed in a 

virgin coal seam. 

The magnetic field H at a distance r from the transmitting 

loop in the direction of the receiving loop is given by the formula (1,2) 

where 

M = NIA is the magnetic dipole moment of the transmitting 

loop 

b - b + 36 is the effective half-height of the coal seam 

e r 

Arthur D Little,inc 
b = actual half height of the coal seam 

6 = skin depth in the rock bounding the coal seam 

r 

k = B - ia is the complex propagation constant 

H~(~) (z) = derivative of the first order Hankel function for an 

outgoing wave 

The constant B is related to the actual wavelength X in the 

medium by the relation B = 271/X. The wavelength depends on the electrical properties of both the coal and the rock strata above and below 

the seam, and on the frequency. It is generally much smaller than the 

free-space wavelength , partly due to the dielectric constant of the 

0 

coal seam, but mstly due to the conductivities of the coal and the 

bounding media. 

The constant a determines the propagation loss (dB/m) and 

depends on the same quantities as B, but in different ways. 

To provide a complete understanding of the factors on which 

the wave propagation depends, the experimental program should therefore 

be arranged to measure both a and B at a number of frequencies. Determination of the phase constant B in addition to the attenuation constant 

a exactly doubles the amount of information available for constructing 

a good theoretical model of the electrical properties of the coal seam 

and the surrounding strata. The experimental equipment should therefore 

measure both the amplitude IH/ and the phase angle $ of the magnetic 

field H as functions of the distance r from transmitter to receiver. 

From these measurements one can obtain both a and B from 

Eq (11, at each frequency separately. The procedure is as follows. 

Arthur D Lttle.Inc 
On substituting the asymptotic expansion for the Hankel 

function, we can express the magnetic field in the form 

where 3Tr' 2 

A = 

i+ 

and R and S are series(3) in inverse powers of kr. From these series 

we obtain for the real and imaginary parts of iR + S, up to inverse 

eighth powers, 

Re (iR + S) = 0.87500 cos 8 + 0.44531 sin 28 + 0.19043 cos 38 

lkrl /kr12 lkrjj 

- 0.21469 sin 48 - 0.37130 cos 58 + 0.85008 sin 68 

Ikrl' /krI5 lkrlb 

2.40432 cos 78 8.06757 sin 88 + - 

Ikrl/ /krl" (4) 

Im(iR + S) = 1 + 0.8700 sin 0 - 0.44531 cos 28 + 0.19043 sin 38 

Ikr/ IkrlL /kr15 

+ 0.21469 cos 48 0.37130 sin 58 0.85008 cos 68 - - 

Ikrlq /kr15 lkrlb 

+ 2.40432 sin 78 + 8.06757 cos 88 

lkrl' IkrI" 

where 

-1 a 8 = tan (T) 

1 

/k/ = (a2 + 62)2 

Arthur D Little,lnc 
From (2) we obtain the relations, 

These equations can be rewritten in the form 

where the terms containing iR + S are small for large r, as can be seen 

from (4) and (5). This suggests that we determine 0 and a by a two-step 

iteration. 

In the first step we omit the iR + S terms and determine 

preliminary values of B and a from the first terms in (10) and (111, 

evaluated from the slopes of the experimental $ r and ln(l~Im E r 

curves at as large a value of r as possible, with due regard to the 

signal-to-noise ratio. In the second step we use the preliminary values 

of 0 and a to evaluate the iR + S correction terms in (10) and (ll), at 

the same value of r as used in the first step, and add the corrections 

to the preliminary values of 0 and a. Simulated tests of this procedure 

show that the final errors in 0 and a are within 1% at 20 kHz and within 

0.3% at 1000 kHz. 

The next problem, after 0 and a have been determined at a 

number of frequencies, is to use this information to obtain the electrical properties of the coal seam and the bounding layers of rock. TO 

do this we use the transmission line formula 

Arthur D Little,Inc 
where 

Z = sum of surface impedances of rock at upper and lower 

S 

interfaces with coal seam (ohm/ ) 

L=ph 0 

h = 2b = height of coal seam 

o = conductivity of coal 

C 

E = permittivity of coal 

C 

A simple model, which we have used to interpret attenuation data for 

the Ireland Mine,") is (1) that only the rock adjacent to the coal 

seam is important and that its conductivity a is large compared with 

r 

ws and (2) that the permittivity cc of the coal is known. Under 

r ' - 

these conditions there are only two unknown quantities, namely, a and 

r 

a on the right hand side of (12). Therefore, on separating real and c' 

imaginary parts of this equation, we can determine both a and a at 

r c 

each frequency. 

For this model, surface impedance Z is given by the relation 

s 

Arthur D Littleinc 
On equating real and imaginary parts of (12) and solving for ar and ac 

we obtain the formulas 

where 

Reference to other 

report or paper? 

If the model is valid the values of ar determined by (14) and (15) 

should be independent of frequency. This was found to be approximately 

true for the case of the Ireland mine except at the lower end of the 

frequency band at 57.5 kHz, for which the wave penetrated far enough 

into the rock above and below the coal seam to reach strata of lower 

conductivity. 

Since virgin coal is readily accessible on the side walls of 

the mine tunnel, it would be very useful to measure ac and cc directly 

in each mine visited. Then one could determine the surface impedance 

of the rock as a function of frequency by means of (12) written in the 

form 

Arthur DLittleInc 
From Z vs w one would be able to develop a more detailed model of the 

S - 

rock strata if the simple model discussed above were to show noticeable 

variation of ar with w. 

References 

1. Arthur D. Little, Inc., Task F - Final Report - Propagation of Radio 

Waves in Coal Mines, Chapter IV - "Propagation of Low and Medium 

Frequency Radio Waves in a Coal Seam," U. S. Bureau of Mines Contract 

H0346045, Task Order No. 1, October 1975. 

2. Emslie, A. G., and R. L. Lagace, "Propagation of Low and Medium 

Frequency Radio Waves in a Coal Seam," Radio Science, %:4, 253 

(April 1976). 

3. Abramowitz, M., and I. A. Stegun (Eds), Handbook of Mathematical 

Functions, 3rd printing, with corrections, pp. 364-365, Nat. Bur. 

Stand. (U.S.) Applied Math Series, 55, Sup. of Doc., U. S. Government Printing Office, Washington, D. C. 20402. 

*Follow-up note: It was subsequently decided not to include a B measurement in this underground measurement program because of its complexity 

and impracticality for the anticipated experiments and its nonessential 

nature. 

Arthur D Little,lnc. 
111. tIODELLING AND DATA ANALYSIS OF IN-MINE ELECTROMAGNETIC WAVE 

PROPAGATION - Interim Report, May 1978 

Arthur- 13 L:.tt!e lilc 
MODELLING AND DATA ANALYSIS OF 

IN-MINE ELECTROMAGNETIC WAVE PROPAGATION 

Robert L. Lagace -- Task Leader 

Alfred G. Emslie, Michael A. Grossman 

INTERIM REPORT 

On 

Task Order No. 4 

Contract No. H0346045 

May 1978 

C-78453 

Arthur D. Little, Inc. 

Cambridge, Massachusetts 

Arthur D Little.Inc 
I. 

11. 

111. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

X. 

TABLE OF CONTENTS 

INTRODUCTION 

THE MODE OF PROPAGATION 

DERIVATION OF a VERSUS f CURVES FROM THE DATA 

DEDUCTION OF CONDUCTIVITIES FROM a VERSUS f CURVES 

MAGNETIC FIELD CALCULATED FROM THE CONDUCTIVITIES 

DETERMINATION OF THE CONDUCTIVITIES AT EACH FREQUENCY 

SEPARATELY 

STATISTICAL ANALYSIS OF THEORETICAL AND EXPERIMENTAL 

DATA VERSUS FREQUENCY 

SELECTION OF OPERATING FREQUENCIES 

CONCLUSIONS 

REFERENCES 

FIGURES 

APPENDIX 

Arthur D Littlelnc 
I. INTRODUCTION 

Initial propagation measurements by T. S. Cory in the Consolidation Coal Co. Ireland Mine in the Pittsburgh coal seam, and their 

subsequent analysis by ADL, revealed unexpectedly long comunication 

ranges which could be attributed to exceptionally favorable geological 

conditions from an electromagnetic wave propagation standpoint. Namely, 

the waves in conductor-free areas of the mine were found to propagate 

in a parallel plane coal seam waveguide filled with coal having a conductivity near the low end of the range of coal conductivity values, 

and bounded top and bottom by rock having a conductivity near the high 

end of the range of rock conductivity values. Therefore, to determine 

whether these favorable propagation conditions were typical or exceptional for U. S. coal mines, additional measurements were performed in 

six coal mines having coal and rock geological characteristics both 

similar to and different from those found in the Ireland mine. The 

analysis and modelling of these additional data are the subject of 

this report. 

The results show that significant variations in signal attenuation 

rates do occur between mines located in different coal seams. Of the 

three seams examined, the Pittsburgh seam measured in northern West 

Virginia has the most favorable attenuation rate, the Herrin No. 6 in 

Illinois is the worst with an order of magnitude higher attenuation 

rate than the Pittsburgh seam, while the Pocahontas No. 3 seam in western Virginia falls between them with a moderate attenuation rate. The 

simple three-layer model is seen to be a convenient and practical one 

which fits the experimental data best in the frequency band from 200 

kHz to 900 kHz, the band which also promises to provide the most favorable performance for portable radio communications in coal mines. 

Simple and convenient methods are developed for calculating and characterizing a mine in terms of attenuation rate versus frequency, coal 

and rock conductivities, and a coupling factor. The methods are based 

on the three-layer model and a transmission line formulation for the 

Arthur D Little,lnc 
propagation constant. The influences which the desired range of conrmunication and the rock and coal conductivities exert on the choice of 

operating frequency are also examined. 

The analysis of conductor-free area propagation data from an 

additional five mines, primarily in low-coal seams, is currently being 

performed, together with the analysis of data taken in the vicinity of 

electrical conductors found in mines. The results of these analyses 

will be included in the final report for this task order. 

Arthur D Little.1~. 
11. THE MODE OF PROPAGATION 

At low and medium frequencies the only mode that propagates for 

useful distances in the stratified medium comprising the coal seam and 

the surrounding rock above and below the seam is the lowest mode, which 

is basically similar to the TEM mode for two infinite, parallel, horizontal metal plates. In both cases the mode can be either a plane wave 

or a cylindrical wave, with the H-field horizontal and the E-field 

approximately vertical. The cylindrical wave is of interest for the 

type of mobile communications desired within U. S. coal mines. 

For simplicity, we consider only a three-layer model in which 

the coal seam, of height h, has a conductivity o and a dielectric 

C 

constant K which we assume to have a fixed value of 6. The rock 

C 

above and below the coal seam has a conductivity or which is assumed 

to be much higher than UE and also much higher than oc. r' 

When a vertical transmitting loop of magnetic moment M is placed 

at the center of a tunnel in the coal seam, the effect of the rock 

above and below the loop can be represented(3) by an infinite set of 

images of the loop, each with magnetic moment M, distributed along a 

vertical line with equal spacing given by the complex number 

where h is the coal seam height and br is the skin-depth in the rock, 

given by 

The set of images, including the transmitting loop itself, can be 

regarded as a periodic distribution m of magnetic dipole moment per 

unit spread along the vertical axis. The periodic function m can be 

represented by a Fourier series which has a constant term (zero-order 

hanmnic) 

Arthur D Little.Inc 
This zero-order harmnic generates the TEN cylindrical wave of interest 

for communication purposes. The higher harmonics generate higher-order 

modes that are beyond cut-off for low and medium frequencies, and 

therefore die out very rapidly with range. 

The uniform magnetic moment m distributed along the axis produces 

a cylindrical wave with magnetic field components 

imk H = -ing -L.~(2) (kr) r4 r 1 

imk H = -os@H(~)' (kr) @ 4 1 

where H(~) is the first order Hankel function for an outgoing wave, and 1 

H:~)' is the derivative of the Hankel function. The complex propagation 

constant k is given by 

k = 6 - la, (7) 

where a and B are the attenuation and phase constants which depend 

on theelectricalproperties of the strata and the frequency. The 

attenuation and phase constants are given by the mode condition 

derived from the boundary conditions of continuity of the tangential 

components of E and H at the interfaces between the coal and rock 

strata. More general analyses of the propagation waves within stratified media are given by Wait (4'5) and Gabillard. 1n this report, 

however, we obtain both cx and B from the simple transmission line formula 

which, for the three-layer model, takes the form 

Arthur D Little inc 
where Z = (1 + i)/ Prsr) is the surface impedance of the rock. We 

s 

calculate a and 0 from the real and imaginary parts of the right hand 

side of (9). 

At range r greater than about l/a from the transmitting loop in a 

direction in the plane of the loop, the magnetic field equation for 

IH I is obtained by using the asymptotic form of the Hankel function + 

in Eq. (5), setting + = 0, and substituting for m in Eq. (3), to give 

the formula 

Since this simple three-layer model describes the observed behavior 

in terms of a uniform, homogenous, surrounding rock medium having a 

conductivity or, asymmetry in the electrical properties of the overand underlying rock cannot be detected by analyzing the experimental 

data using this model. This shortcoming is not a serious one in the 

present application. 

Arthur D Little,lnc 
111. DERIVATION OF a VERSUS f CURVES FROM THE DATA 

It is very desirable to find a simple way to characterize radio 

propagation in each coal mine. Curves of attenuation consgant a versus 

frequency provide such a characterization and are readily obtained 

directly from the experimental data. (8) 

Eq (10) shows that for ranges greater than about l/a, 

From (11) we obtain the relation 

1 a = -- 1 

- (20 LogH C 10 Log -F-- ) , 8.686 dr r 

0 

where r is any convenient range such as 100 m. Eq (12) indicates that 0 

if one adds 10 log (r/rO) to the experimental values of E, expressed in 

dB, and replots the result as a function of r, the resulting graph should 

be a straight line, except at small values of r. The slope of the straight 

line (dB/m), divided by 8.686, gives a in ml. 

Figure 1 shows an example of the technique applied to data from the 

Robinson Run mine at 228 Eiz. It is seen that a good straight line is 

obtained, except for the expected departures at r = 30 m and 62 m. The 

slope is 54.4 dB1500 m which, when divided by 8.686 dB/Neper, gives 

a = 0.0125 m-l. 

The same method has been applied to the data at all the frequencies 

used at Robinson Run. The results for a versus f are shown in Figure 2. 

Similar plots for other mines are given in Figures 3 to 8. In all the graphs 

but one, the values of a are based on straight line plots as unambiguous 

as the example in Figure 1. 

Arthur D Little.lnc 
The exception is the case of the Ireland "11" mine (Figure 5) where 

cables were present in entries adjacent to the entry in which the measurements were made. It appears that the TEM mode with which we are 

concerned couples to a guided type of mode involving a cable and the 

surrounding coal and rock. Since the guided mode has a smaller attenuation constant than the TEM mode, the effect is that the coupling back 

and forth between the two modes causes the signal to die off less rapidly 

beyond a certain ranae. The effect is shown in Figure 9, where the signal enhancement at 100 kHz sets in beyond about 180 m. In drawing the 

straight line to deterkine a, we disregard data points beyond this distance, and also the first data point for the reason previously mentioned. 

The line is therefore based on only the second and third data points. 

A similar selection of the data points is required at the other frequencies. The plot in Figure 5 is therefore less r'eliable than the other 

a versus f plots. It is seen, however, that the graph shows the same 

monotonic increase of a with f. 

Figure 10 shows how the a versus f curves vary from mine to mine. 

Here a is given, for convenience, in dB1100 ft.,and a log scale is used 

for f in order to give a better spread of the low frequency points. It 

is seen that the mines fall into three groups. 

The mines in the Pittsburgh seam, comprising Ireland, Robinson Run, 

and Federal No. 1, have the lowest attenuation rates and, not surprisingly, are somewhat comparable with each other in attenuation. The 

Pocahontas No. 3 mine has an attenuation that overlaps that of the Pittsburgh seam mines at low frequencies but rises more rapidly with increasing frequency. The mines of the Herrin No. 6 seam, namely Peabody No. 

10 and Inland No. 1, have considerably larger attenuation rates. 

It is to be noted that all the attenuation curves when plotted as 

dB/100 ft. versus log f have similar concave-upward, monotonicallyincreasing shapes except for the Inland No. 1 curve, which is S-shaped. 

It is thought that the point at 2000 kHz is greatly in error and that 

the dotted line more nearly represents the correct trend for the Inland 

No. 1 mine. 

Arthur D Ljttlelnc 
JV. DEDUCTION OF CONDUCTIVITIES FROM a VERSUS f CURVES 

The conductivities oc and or can be derived from any a versus f 

curve by means of equation (9). On eliminating 6 from this 

equation, by separating the real and imaginary parts, we obtain the 

equation: 

nfu a 2 

r 

where 

For a given point on the aversus f plot we calculate or's from (13) for 

a sequence of values of o ,and plot or versus qc. The curve obtained C 

is a constant-a curve corresponding to the chosen point on the a versus f 

plot. The same procedure is applied to all points on the a versus f plot. 

Figure 11shows the set of constant-a curves corresponding to Figure 

2 for Robinson Run. Ideally the constant-a curves would all intersect 

at a single point, corresponding to an unambiguous pair of values of 

u c' However, owing to experimental error, non-uniformity of the r ' 

coal seam, errors in computing the a's from the slope of the H 

vs r curves, etc., the constant a curves fail to have a single intersection, but do neck down and then fan out again. The star on the graph 

represents a kind of center of gravity of the curves at the neck, and 

Arthur D Little Inc 
yields the values o = 0.3 x Mho/m, or = 0.085 Mholm. Figure 12 

C 

shows the set of ideal constant-a curves which all intersect at the point 

o - 0.3 x er =.0.085. C 

Figure 13 shows the constant-a curves corresponding to the a vs f 

plot for Federal No. 1 mine (Figure 3). The best choice of the o's in 

this case is o - 0.26 x or - 0.084. In Figure 14 we compare the 

C 

experimental a vs f plots for the two mines with theoretical a vs f 

graphs calculated by Eq (9) for the selected 0'6. It is seen that quite 

good fits are obtained. 

Unfortunately, the method does not work so well for the other mines. 

as seen, for example, in Figure 15 for Ireland I and'Figure 16 for Inland 

No. 1. In both cases it is difficult to select the best pair of 0'6. 

The values shown on the graphs are therefore very tentative. Under such 

conditions it is better to try to match the experimental a versus f plot 

directly by a theoretical curve based on Eq (9). 

Figure 17 shows a set of theoretical curves made to pass through 

the 955 KHz point on the Inland No. 1 a vs f plot. It is seen that the 

theoretical curve C, with oc = 10 x Mho/m, or = 0.22 Mho/m gives a 

fair match to the data points. 

Figure 18 shows similar plots for Ireland I, with all theoretical 

curves made to pass through the experimental point at 335 kHz. Curve D, 

with oc = 2.0 x lom4 Mho/m, or = 1.092 Mho/m appears to give the best 

fit to the experimental values. These values of the u's are close to 

the values oc = 1.4 x Mho/m, or = 1.0 Mho/m determined previously (1) 

by matching H versus r curves. It is worth noting, however, that the 

value of or is very sensitive to which theoretical curve is judged to 

be optimum. Curve C, for example, gives almost as good a fit as Curve D, 

but the value of or is reduced to about 0.3 Mho/m, which is a more acceptable value for rock conductivity. 

Figure 19 shows the case of Ireland 11, with two theoretical curves 

arranged to pass through the experimental point at 950 Wlz. Curve A seems 

to give the better overall fit, with or = 1.0 x Mho/m, or = 0.54 Mbo/m. 

9 

Arthur D Little Inc 
TABLE I 

CONDUCTIVITIES DERIVED FROM THE UVERSUS f PLOTS 

Coal Mine h Kc omal Orock Coal Seam 

(rn) (Mholm) (Mholm) 

Robinson Run 

Federal No. 1 

Ireland "11" 

Ireland "I" 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Pocahontas No. 1 

3 South Area 

Entry A 

3 South Area 

Entry B 

Pocahontas No. 3 

Pocahontas No. 3 

2 North No. 1 

(Piow Area) Pocahontas No. 3 

Inland No. 1 Herrin No. 6 

Peabody No. 10 

1 Main South 

1st West 2nd 

North 

1 South 

51 /2 East1 

1 South Jct. 

Herrin No. 6 

Herrin No. 6 

Arthur D Littlelnc 
y. MAGNETIC FIELD WCULATED FROM THE CONDUCTIVITIES 

From the conductivities given in Table I one can calculate a and 0 

from Eq (g), 6r from Eq (2), and H versus r from Eq (10). The results 

are shown in Figures 25-46 in comparison with the experimental H versus 

r plots. It is seen that the theoretical curves correspond qualitatively 

with the experimental data. The agreement is best for Robinson Run 

(Figures 25 and 26) and Federal No. 1 (Figures 27 and 28). This is not 

surprising since for these mines the derivation of oc and or from the a 

versus f plots is quite unambiguous. It may be concluded that the threelayer model is valid for these two mines and also that the theoretical 

formulas (10) and (9) are correct. However, in spite of the generally 

favorable overall agreement with regard to form and relative variations 

with frequency, there remain some annoying differences in absolute level 

between the theory and data to be resolved. Namely, the theoretical 

curves for the Robinson Run mine are about 4 dB too high for the frequencies 

up to 500 WIz and about 14 dB too high above 500 kHz; while the Federal 

No. 1 theoretical curves are all about 10 dB too high. The nature of these 

differences strongly suggests a systematic irregularity in either the theory 

or measurements. 

The comparison for Inland No. 1 (Figures 29 and 30) shows good 

agreement for the frequencies up to 955 kHz but wide divergence for 

2000 and 4750 Uz, as was to be expected from the peculiar behavior of 

the a versus f plot (Figure 6). The agreement at the lower frequencies, 

where scattering and resonance effects would be unlikely, indicates that 

the three layer model is valid at least for these frequencies. 

In the case of Ireland "11" (Figures 31 and 32) the agreement is surprisingly good, considering the uncertainties due to the presence of 

electrical cables in adjacent entries. Again the three-layer model seems 

to be justified. 

Figures 33, 34, and 35 show theoretical H vs r curves corresponding, 

respectively, to the a's for curves B, C, and D for Ireland "I" in Figure 

18. Comparison with the experimental data (Figure 37) shows that the 

Arthur D Little,lnc 
theoretical curves do not reproduce the wide spread in level of the 

experimental curves. Figure 33. with oc = 1.0 x 10'~ Mho/m and or 

0.1172 Mho/m seems togive the best fit. The slopes of the theoretical 

curves are about right but the spread in level is too small and the 

average level is too low. 

Figure 36 shows earlier calculations made by a cut-and-try procedure 

aimed at getting the best fit at 920, 350, and 230 KEz. It is seen that 

when this is done the 115 and 57.5 Mlz curves turn out to be much too 

high compared with the experimental curves. It is to be noted that oc 

is about the same for Figures 33 and 36, while or is 0.1172 Mho/m for 

Figure 33 and 1.0 Mho/m for Figure 36. It seems therefore that the 

slopes can be matched approximately to the experimental values for u C 

= 1 x Mho/m but that matching the level requires a value of ar of 

about 1 Mho/m for the highest frequency and about 0.1 Mho/m for the lowest frequency. 

As pointed out in our earlier report, this means that a three-layer 

model with frequency independent constitutive properties (ar, dC, Kr, Kci 

is not quite adequate for the Ireland "I" mine for frequencies below about 

200 KBz. Since the skin depth increases with decreasing frequency, rock 

material farther removed from the coal seam will be sampled by the wave 

at lower frequencies. If this material is of significantly lower conductivity than the rock material adjacent to the coal seam, it will present 

to the lower frequency a lower effective rock conductivity than that observed at higher frequencies. Thus an even larger skin depth results, 

which in turn increases the loss and reduces the coupling to the mode 

as shown by the + (1 - i)6r]-1 factor in Eq (3). Such considerations 

suggest that a five-layer model like the one examined by R. Decker of 

Spectra Associates might be useful to represent the behavior of the - Ireland "I" mine location. 

Figures 38 and 39 for the 3 South area, Entry A of Pocahontas No. 1 

mine show that the theory is in fair agreement with the experimental 

results except at the highest frequencies of 3200 and 3800 kHz, for 

which the experimental results show a decrease in attenuation rate at 

13 

Arthur D Little, Inc 
ranges beyond about 70 meters. This trend is very probably due to the 

presence of conductors in the form of an air line in the adjacent entry 

and a track and trolley wire two entries away. 

Figure 41 for Entry B in the same area of the Pocahontas mine, but 

one entry farther away from the conductors, still seems to show some 

effect from the conductors at 920 and 2720 kHz but agrees qualitatively 

with the theoretical curves in Figure 40. The experimental curve for 

51 kHz in Figure 41 gives only relative values. 

Figures 42 and 43 refer to the 2 North No. 1 Plow area of the 

Pocahontas No. 1 mine. The measurements were made along an entry adjacent to an entry containing a track and trolley wire, with the transmitter 

located in the adjacent entry two entries away from the track and trolley 

wire. Again the effect of the conductors is clearly seen in the difference between the theoretical and experimental curves for 3100 kHz. 

Figures 44 to47 show comparisonsoftheoretical and experimental 

results for two areas in the Peabody No. 10 mine. There is good qualitative agreement between theory and experiment at all frequencies, with 

no evident effect of conductors. 

Arthur D Littlelnc 
VI. DETERMINATION OF THE CONDUCTIVITIES 

AT EACH FREQUENCY SEPARATELY 

In principle one should be able to determine oc and qr from the 

H 6 versus r plot at a single frequency by taking into account the vertical position of the Hfi versus r straight line as well as its slope, 

i.e., by noting the value of H on the line at some selected point ro. 

For example, the 255 KHz data for the Inland No. 1 mine, shown in Figure 

48, give a slope a = 0.0468 ml, and a field level H (80 m) = 12 dB re 

1 uA/m. Knowing a and taking a trial value of o we calculate or and B c' 

from Eq (9), 6r from Eq (2), and H (80 m) from Eq (10). This procedure is repeated for a succession of values of oc until the target 

value H (80 m) = 12 dB re 1 @/m is reached, as shown in Table 11. 

TABLE I1 

H (80 m) VERSUS a- 

(for a = 0.0468 ml) 

Oc o 

r B 6r H (80 m) 

(Mho/m) (Mho/m) (m-l) (m) (dB re 1 wA/m) 

6 0.0675 0.0320 3.844 9.7 

It is seen that the target value of H is reached for o between C 

8 x lo-' and 9 x lo-' Mho/m. On interpolating linearly we find that 

o = 0.85 x mo/m, or = 0.20 ao/m, B = 0.0341 m1 and 6 = 2.335 m. 

c r 

The final step is to calculate H (r) by Eq (10) and compare the result 

with the original experimental data, as in Figure 49, where it is seen 

that the fit is quite good. 

Arthur D Little Inc 
The same procedure applied to the data for 335, 495, and 955 KHz 

gives approximately the same value of or. We therefore assume that or 

= 0.2 Mho/m for all frequencie~and then determine the value of oc that 

gives the best theoretical fit to the experimental H versus r plot at 

each frequency. The values of oc so obtained and the degree of fit are 

shown in Figures 49-54. The values of uc at 2000 and 4750 KHz are to 

be regarded as effective values that allow for whatever mechanism causes 

the abnormal values of a at these frequencies, as seen in Figure 6. 

It turns out that the method illustrated in Table 11, although 

successful for the Inland No. 1 mine, does not work in most other cases. 

The reason is that the range of the calculated values of H(ro), which 

may differ by less than only 1 dB for a large variation of o usually c' 

does not overlap the experimental value H(ro). . 

Arthur D Little, lnc 
VII. STATISTICAL ANALYSIS OF THEORETICAL AND 

EXPERIMENTAL DATA VERSUS FREQUENCY 

Figures 55-63 show plots of HTHEOR/%nT, expressed in dB, versus 

frequency, at a standard range of 100 m which was chosen to be beyond 

the longitudinal skin depth l/a but within the range of most of the 

data. HEXpT at a given frequency is the value determined from the H& 

versus r plot at 100 m, while hEOR is the theoretical value determined 

fromthecoal and rock conductivities derived from the a versus f curve. 

For the mines of the Pittsburgh and Pocahontas seams, Figures 55-60, 

HTHEOR/spT is greater than 0 dB on the average and does not seem to 

have any systematic trend with increasing frequency. On the other hand, 

the mines of the Illinois seam (Figures 61-63) appear to show that 

%HEOR/HEXPT is about 0 dB on the average but tends to increase with 

frequency. 

These differences in behavior can be attributed, as pointed out 

previously, to departures of the geological structure of the mines from 

the three-layer model assumed in the theory and to some extent random 

uncertainties in the measurements. If the overburden and underburden 

are not uniform in conductivity, as supposed, the surface impedances 

of the over- and underburdens no longer have a phase angle of 45' as in 

the case of a medium of uniform high conductivity. This alters the 

form of the transmission line equation, (9), and the effective magnetic 

mment equation (3). Therefore, it changes the way in which the attenuation constant a varies with frequency and the coupling to the coal 

seam TEM mode. 

To determine the goodness of fit between the simple three-layer 

model predicted results and the measured data,the theoretical and 

experimental values have also been compared on a statistical basis. 

The ratio A = HTHEOR/l$WT expressed in dB was analyzed statistically 

as a result of trends shown by the Figures 55-63 plots of A versus 

frequency, at the standard range of 100 meters, for data taken from 

each of the mines. The A plots showed a small and relatively uniform 

Arthur D Little,lnc. 
disagreement, mainly on the high side, between about 100 and 1000 kHz, 

and progressively increasing disagreement, again on the high side, below 

100 kHz and above 1000 kHz. The data at the higher frequencies also 

demonstrated considerable scatter relative to the predicted results. 

The statistical analysis of A was restricted to data for the frequencies between 100 kHz and 1000 kHz at the reference distance of 100 

meters. For frequencies outside the 100 to 1000 kHz range, the A plots 

indicated that the applicability of the simple three-layer model was 

breaking down. One hundred meters was chosen as the reference distance 

because it allowed most of the data from six mines in both low and high 

loss coal seams to be included, while avoiding near field effects in 

most cases. The ratio A in dB between theory and data in the 100 to 

1000 kHz band was analyzed by: 

ZA Computing the Sample Mean = - for each seam and the variance 

n 

of A for the total sample population as a function of frequency 

(there were too few samples within each seam to compute a 

standard deviation on a seam basis). 

Computing the Sample Grand Mean for all mines in all three 

seams, and 95% Confidence Intervals for both the population and 

Sample Grand Mean as a function of frequency. These results 

are plotted in Figure 64. 

Testing the hypothesis that the theoretical mdel fits the data 

at the 95% Confidence Level for the frequencies between 100 kHz 

and 1000 kHz. 

A detailed description of the statistical analysis is presented in the 

Appendix. From this analysis, the following observations and conclusions 

were made. The differences between the model and the experimental data 

were similar for all coal seams. The shapes of the curves for each 

seam average followed the same pattern and did not differ from one 

another by more than 1 or 2 dB, with the exception of the Herrin #6 seam 

at frequencies below 400 kHz. (At these frequencies, data for only one 

mine in the Herrin 86 seam was available.) This homogeneity implies 

Arthur D Little. lnc. 
that pooling all the data to compute a Grand Sample Mean for all mines 

is a valid technique, and that the results from any analysis can be 

applied back to all the mines uniformly. 

The plot of the sample and its 95% Confidence Intervals in Figure 

64 is a visual hypothesis test (t-test) that the model fits the experimental data, against the alternative hypothesis that the model does not 

fit the data. The analysis showed that between the frequencies of 200 

kHz to 900 kHz, there is no significant difference between the model 

and the actual data, i.e., the Confidence Interval includes zero. In 

this band of frequencies the average ratio, A, ranges from 1.1 dB to 

3.9 dB. The range from 200 lcHz to 600 ldIz appears to be the best range 

for the model; both the variance and the average A between the model 

and actual data being smallest, and positive, within this frequency 

range. 

Arthur D Little,lnc 
VIII. SELECTION OF OPERATING FREQUENCIES 

The data analysis and theoretical modelling of coal seam waveguide 

radio wave propagation presented above provide a firmer foundation, than 

previously available, on which to base the selection of operating frequencies for wireless mine communication in the MF band. Large variations in signal attenuation rate have been found between the three 

coal seams investigated, seams widely separated geographically. The 

Pittsburgh seam, measured in northern West Virginia was found to be the 

most favorable, while the Herrin No. 6 seam measured in southern 

Illinois was found to exhibit extremely high loss. 

In this section we briefly examine the behavior of the signal 

field strength in conductor-free areas versus frequency at two ranges 

of interest, 400 m (1312 ft.) and 200 m (656 ft.), as a function of 

the spread of coal and rock conductivity values, u and or, found in 

C 

the mines and seams listed in Table I. The magnetic field strengths 

H in dB re 1 uA/m were calculated based on the three-layer model 

equations (10) and (9), without applying the statistically determined 

correction of Figure 64. The results are plotted in Figures 65 to 

68 for the range of 200 m, and in Figures 69 to 72 for the range of 

400 m. For each range, a series of four figures is used to illustrate 

the change in signal behavior as the coal conductivity is increased 

through the values 3 x loe5, 3 x and Mho/m, while 

the rock conductivity is allowed to take on values from 3 x to 

1.0 Mho/m in each case. To reduce the number of variables for this 

comparative analysis, we have assumed a K = 6, a seam thickness of 

C 2 h = 2 m, and a transmit magnetic moment of 2.5 A-rn . 

Also plotted on these figures for comparison are magnetic field 

noise levels versus frequency. These noise levels represent the upper 

bound envelope of average rms values found in active areas of coal 

mines, and a lower bound noise level representing the intrinsic 

receiver noise for a narrowband FM radio receiver having an IF bandwidth B = 12 kHz, noise figure F = 6 dB, and loop antenna effective 

Arthur D Little,lnc 
2 

turns area NA = 1 m . The active mine noise levels were taken from 

Figures 73 and 74, which in turn were derived from the sample of magnetic field, time-averaged, rms noise levels measured at spot frequenices 

in three coal mines by Bensema, Kanda, and Adams (9'10y11) of the National 

Bureau of Standards. 

Examination of Figures 65 to 72 reveals that performance is best 

for the combination of lowest coal conductivity and highest rock conductivity. Increasing coal conductivity increases the shunt loss in 

the coal seam waveguide, while decreasing the rock conductivity increases 

the series loss, both of which increase the signal attenuation rate. 

Furthermore, as this attenuation rate increases, the frequency behavior 

changes from a broad bandpass filter type of characteristic centered 

around 1 MHz for low attenuation rates like those found in the Pittsburgh seam, to an increasingly attenuated low pass filter characteristic 

having a steadily decreasing cutoff frequency as the attenuation rate 

increases to values like those found in the Herrin No. 6 seam. This 

trend toward the attenuated low pass filter behavior is of course more 

accentuated for the longer communication ranges, i.e., 400 m vs. 200 m. 

The most favorable frequencies for communicating to these ranges 

can be estimated by comparing the signal level curves with the noise 

level curves plotted on each Figure. The most favorable operating 

bands are seen to be those where the slopes of the signal and noise 

curves are equal or nearly equal. Since the signal curves also represent levels for the largest, intrinsically-safe transmit moment, an 

absolute measure of performance can also be estimated by noting the 

number of dB that the signal level curve lies above the noise level 

curve at the frequency of interest. For example, a radio service 

performance level of Circuit Merit Figure No. 3 (occasional message 

repetitions required) requires that the average rms carrier-to-noise 

ratio at an FM receiver be at least 10 dB or better for the mine noise 

condition prevailing during the message transmission. 

The equivalent receiver noise curve is probably the most representative for conrmunication in conductor-free areas that are located 

at least one or two entries .em separated by one or two pillar 

Arthur D Little, Inc 
widths) away from mine electrical conductors carrying high noise currents. On the other hand, the active mine upper bound noise curves 

most likely give an overly pessimistic view. In this latter instance, 

these levels occur in the immediate vicinity of high power machinery 

and electrical conductors, locations where the signal will also be 

enhanced by the presence of the conductors. Thus an active area noise 

curve approximately half way between the two noise extremes is probably 

more indicative of worst case "conductor-free area" noise levels. 

These levels are likely to occur in transition regions between 

conductor-free and conductor-present locations. 

ExaminationofFigures 69 to 72 reveals that conductor-free area 

portable-to-portable radio ranges on the order of 400 m will be attainable only in highly favorable, low attenuation seams like the Pittsburgh 

seam. Furthermore, the performance will occur only at operating frequencies between about 900 kHz to 2 MHz, and under noise conditions 

approaching the receiver noise limited case. Furthermore, Figures 64 

to 68 illustrate that conductor-free ranges of 200 m will not be attainable in high lcss seams such as the Herrin No. 6 seam, even at frequencies below 100 kHz and under receiver noise limited conditions. The 

outlook is somewhat improved, but not much, for moderate-to-high loss 

seams like the Pocahontas No. 3 seam, where 200 m ranges should be 

possible over a broad band of operating frequencies between about 150 

kHz to 1.5 MHz under receiver noise limited conditions. 

On a more positive note, the in-mine measurements of Cory and 

others have also shown that greatly improved radio comunication ranges 

are obtainable in coal mines when the portable units are located in a 

tunnel having electrical conductors such as a power cable, pager phone 

line or trolley wirefrail line. Significant range improvements have 

even been experienced with one and sometimes both of the units located 

in a tunnel separated by a coal-pillar width from the tunnel with the 

conductors. In some cases. improvements have also occurred with one 

of the units located in a tunnel separated by two coal pillars from the 

tunnel having the electrical conductors. Since these conductors are 

Arthur D Little. lnc 
generally located in haulageways and working sections where miners 

requiring communications are also located, this propagation condition 

is an important one. .Moreover, it is one that may allow the desired 

radio communication ranges to be achieved and exceeded even in coal 

seams having high signal propagation attenuation rates. Therefore, 

additional dataarepresently being taken in the vicinity of mine electrical conductors by Cory, and being analyzed by ADL to quantitatively 

model and assess the impact of such conductors on the attainable radio 

communication range. 

Arthur D Little,lnc 
IX. CONCLUSIONS 

Based on the physical and statistical analyses applied to the data 

available to date, it can be concluded that: 

a MF band radio wave attenuation rates experienced in coal mine 

conductor-free areas are highly dependent on the coal seam in 

which a mine is located; and that this attenuation rate versus 

frequency can be determined in a simple way from measurements of 

H vs r. 

a The simple three-layer model fits the experimental data in the 

200 kHz to 900 Hz frequency band at the 100 meter reference 

distance, with the best agreement occurring between 200 and 

600 kHz. This is the band that also promises to provide the 

most favorable performance for portable radio communications 

in coal mines. 2, The attenuation rates become unacceptably 

high above 1 MHz. 

- 

a The Sample Grand Mean, A, of the ratio H,,,REOR/~EXPT expressed in 

dB may be used to represent the Means for individual coal seams. 

Unlike the attenuation rate, the mode coupling factor appears 

to be independent of the coal seam in which a mine is located. 

a Practical MF system performance estimates may be made in the 

200 to 900 kHz band by applying the simple three-layer model 

to seams in which the attenuation rates have been measured, and 

using the appropriate to correct the predicted field values. 

Data to date have come primarily from high-coal seams. Data from 

four additional mines in low-coal seams will be analyzed in the near 

future to assess the applicability of the model in thinner coal seams, 

and as a more rigorous test of the theory. 

Arthur D Little Inc 
X. REFERENCES 

(I)A. G. Emslie and R. L. Lagace, "Propagation of Low and Medium Frequency 

Radio Waves in a Coal Seam, " Radio Science, vol. 11, no. 4, pp 253-261, 

April 1976. 

(2)Arthur D. Little, Inc., "Propagation of Radio Waves in Coal Mines" 

Chapter IV, Final Report on Task F, Task Order No. l., Contract No. 

H0346045, October 1975. 

(3)~. R. Bannister, "Approximate Results for the Mutual Electromagnetic 

Coupling of Loops over a Homogeneous Ground," Naval Underwater System 

Center Report #NL-3029, New London Laboratory, 23 November 1970, NTIS 

No. AD717351. 

(4)~. R. Wait, "Note on the Theory of Transmission of Electromagnetic 

Waves in a Coal Seam," Radio Science, vol. 11, no. 4, pp 263-265, 

April 1976. 

("5. R. Wait, "Electromagnetic Waves in Stratified Media," Pergamon 

Press, 2nd Ed., 1970. 

(6)~. Gabillard and F. Louage, "Telecommunications a Travers le Sol Dans 

un Terrain Stratifie, Theorie Generale," Annales des Telecommunications, 

Tome 25, Nos. 1 - 2, Janvier-fevrier 1970. 

(7)~. Gabillard and F. Louage, "Telecommunications a Travers le Sol Dans 

un Terrain Stratifie, Application au Guide D'Ondes Geologique," 

Annales des Telecomnications, Tome 25, Nos. 3 - 4, Mars-Avril 1970. 

(8)~. S. Cory, "Propagation of EM Signals in Underground Mines," Collins 

Radio Group, Rockwell International Corporation, Final Report, Bureau 

of Mines Contract H0366028, April 18, 1977. 

(''w. D. Bensema, M. Kanda, and J. W. Adams, " Electromagnetic Noise in 

Robena No. 4 Coal Mine," Nat. Bur. Stand. (U.S.), Tech. Note 654, 

194 pp., Bureau of Mines Contract H0133005, April 1974. 

(lO)w. D. Bensema, M. Kanda, and J. W, Adams, "Electromagnetic Noise in 

Itmann Mine,"Nat. Bur. Stand. (U.S.), NBSIR 74-390, 112 pp., 

Bureau of Mines Contract H0133005, June 1974. 

('I'M. Kanda, J. W. Adams, and W. D. Bensema, "Electromagnetic Noise in 

McElroy Mine,"Nat. Bur. Stand. (U.S.), NBSIR 74-389, 170 pp., Bureau 

of Mines Contract H0133005, June 1974. 

25 

Arthur DLittle,lnc 









70 - 

c Robinson Run 

65 - a Federal # 1 

d Ireland "11" 

60 - c Ireland "I" 

VP ,^ 1 SO. 

55 - 6 VP * 1 NO. 

i- Inland # 1 

50 - Peabody -Y 10 

Radio Signal 

Attenuation 

Rate 

(dB1100 FT.) 

Frequency, kHz 

FIGURE 10 COMPOSITE PLOT OF SIGNAL ATTENUATION RATES 

IN dB1100 FT. FOR SIX MINES IN THREE DIFFERENT COAL SEAMS 

Arthur D Little.Inc 












Best Fit Theoretical a versus f Curve 

to a versus f Data 

1000 2000 3000 

FREQUENCY IN kHt 

48 
FREQUENCY \N kHz 

49 















RANGE, k, IN METERS 

RANGE, r, \N METERS 

RANGE, IN METERS 











$ 

= +- 

Ia- 

;: 

XI- 







\ 

\ 1-- 

- \ 

\ 

\ 

\ 

\ \- / .' /'- 

- 

/ 

\ / 

\ ___------ '.--A- c---*- 

- /---\ I' 

- 

Sample Mean 

95% Confidence Intervals For: - , - Population A - - - - - - Sample Mean A 

I 

100 200 300 400 500 600 700 800 9001000 

Frequency, kHz 

FIGURE 64 STATISTICAL SUMMARY OF HTHEOR/HEXPT RATIOS IN dB 

Arthur D ~ittlelnc 


i 

I-' 

2 

a3 

-a - 





Ploned Noise Levels Normalized to 12kHz Bandwidth - Measured with 1 kHz 

Instrumentation Bandwidth 

- - - Vertical Field Component 

- . - Vertical Component - "Quiet Time" 

Horizontal Field Component 

McElroy Mine - Continuous Miner Section and Nearby Rail Haulagemy 

o Near end of rail haulage line 

o Near intersection of rail hablageway and conveyor belt 

+ Near operating continuous mining machine 

o Near section power distribution center 

Frequency in kHz 

Source: National Bureau of Standards (Report NBSIR 74-389. June 1974) 

FIGURE 73 REPRESENTATIVE RMS MAGNETIC FIELD NOISE LEVELS 

MEASURED IN THE McELROY COAL MINE 

Arthur D Little. Inc 
Plotted Noise Levels Normalized to 12kHz Bandwidth - Measured with 1 kHz 

Instrumentation Bandwidth 

- - Vertical Field Component 

- .-Vertical Component - "Quiet Time" 

Horizontal Field Component 

ltmann Mine - Longwaii Panels 

4 At longwall face head end - Farley panel 

-& 230 ft from longwall face - Farley panel 

A At longwall face head end near main conveyor belt - Cabin Creek panel 

Robena Mine - Rail Haulageway serving continuous miner section. All curves for 

same location approximately 300 meters from face area 

o Horizontal (E-Wl - 1st day 

-a Horizontal (N-Sl - 1st day + Vertical - 1st day 

h Vertical - 2nd day 

therefore should not be considered 

representative. 

Frequency in kHz 

Source: National Bureau of Standards (Reports NBS Technical Note 654, April 1974 Robena; 

and NBSlR 74-390, June 1974, Itmann) 

FIGURE 74 REPRESENTATIVE RMS MAGNETIC FIELD NOISE LEVELS 

MEASURED IN THE ROBENA AND ITMANN COAL MINES 

Arthur D Little.Inc 
APPENDIX 

Detailed Description of the Statistical Analysis 

Since all the analyseswereperformed at the 100 meter range, all 

the datawere checked to insure the signal had actually traveled that 

far. Any mine in which the attenuation rate was so great that the 

signal did not reach 100 meters was eliminated from the analysis. The 

only exception was in the Peabody /I10 mine where at one of the frequencies the signal was only measured to 94 meters. A straight line 

extrapolation was made for this data point. 

Table A-I shows each mine, its seam, and the difference, A = 

H~~~o~'H~~~~ at 100 meters for the frequencies of 100 kHz to 1000 kHz. 

The differences A were obtained by taking straight line interpolations 

between the actual frequencies tested to derive values every 100 kHz. 

Below the raw data of Table A-I is the work sheet of computations used 

- 

to obtain the average difference, A, the variance of x, and the 

variance of A. 

Table A-I1 shows the same average, as well as the average for all 

mines, for the differences A = HTHEOR - HEWT in dB at 100 meters between 

100 kHz and 1000 kHz. For the Herrin /I6 seam at 100 kHz and 200 kHz 

the average is composed of one data point from one mine. The Pittsburgh 

seam average is composed of measurements at 4 locations from 3 mines; 

the Pocahontas seam has 3 locations from 1 mine; and the Herrin 116 has 

- 

2 locations, one each from 2 mines. The seam average values, A, from 

Table A-I1 are plotted in Figure A-1. This figure shows the differences 

to be homogeneous over all the mines. With the exception of 100 and 

200 kHz, where the Herrin //6 seam had readings from only the Peabody 

U10 mine, there is only at the most a 2 dB difference between any of 

the graphs. Therefore, no information is lost by pooling all the data 

and studying the composite data rather than continuing the analysis on 

a seam basis. Conversely, the results of the analyses can then be 

applied back to all mine seams uniformly. 

Arthur D Little,lnc. 
2 Figure A-2 is a graph of the variance of the differences, S (A), 

every 100 kHz. The population variance was neither very large, nor did 

it fluctuate widely, although it was of the same order of magnitude as 

the average difference between the model predictions and the experimentally recorded data. 

Figure 64 in the body of the report is a graph of the Grand ban, 

- 

A, and 95% Confidence Intervals for the A and z. As noted before, the 

95% Confidence Interval for is equivalent to a visual hypothesis test 

(t-test) that: 

Ho' 'THEOR = %XPT 

versus 

%HEOR # H~~~ 

at each frequency from 100 kHz to 1000 kHz. To visually interpret the 

test, one must only check to see if zero is included in the interval. 

Whenever the Confidence Interval contains zero, no significant difference 

between the theoretical model and the actual readings exists. This 

can be visually checked by looking at Figure 64. As an example, the 

actual hypothesis test (t-test) at 100 kHz and 200 kHz will be performed. 

The hypothesis test is given below (a 1-sample t-test): 

The test statistic is: 

- 

X - Eo 

sl J;;- 

and it is compared to a t-statistic on n-1 degrees of freedom at the 

1-a12 level; t(n-1, 1-~12). For 100 kHz, n = 8 and a = 5%; and for 

200 kHz, n = 9 and u = 5%. If the computed statistic is greater in 

absolute value than the t-statistic, then the null hypothesis is 

rejcted; i. e., the model does not fit the data. If the computed test 

statistic is less than the t-statistic, then the null hypothesis cannot 

Arthur D Little.lnc 
be rejected. From this last case, based on the data given in Table A-I, 

we draw the conclusion that the model did, indeed, fit the data for the 

frequencies between 200 kHz and 900 kHz. For 100 kHz: 

E -. 0 since the null hypothesis Ho is A 

0 

- 

X-E 

s/K 

The null hypothesis is rejected at the 5% level (95% chance of happening) and the model does not fit the data at 100 kHz. 

0s 

For 200 kHz: 

The null hypothesis, Ho, cannot be rejected at the 5% level and we draw 

the conclusion that at 200 kHz the model fits the data. 

Thus, the Grand Mean may be used in all analyses, and it may be 

used to represent the individual seam averages. Furthermore, the model 

fits the experimental data in the 200 kHz to 900 kHz frequency range at 

100 meters. It did not fit the experimental data outside the range of 

those frequencies. 

REFERENCES 

Brownlee, K.A., Statistical Theory and Methodology in Science and 

Engineering, J. Wiley, N.Y., 1967. 

Neter, J., and Wasserman, W., Applied Linear Statistical Models, Irwin, 

Honewood. Illinois, 1977. 

Arthur DLittle.lnc 
TABLE A-I 

FREQUEtlCY 

NINE SCAM 100 200 300 400 500 600 700 8

Ireland (I) Pi tt 12.50 2.50 -2.00 -3.00 -4.50 -5.50 -6.00 -6

Ireland (11) Pi tt 2.00 4.50 5.50 4.00 2.00 1.50 1 .OO 0

Federal 11 Pi tt 8.00 4.00 4.00 5.50 6.50 6.00 6.00 6

Robinson Run Pitt 6.00 1.00 1.00 2.00 2.00 6.00 8.50 10

Pocahrmtas 11 

3 SO. Entry A POC 

Pocahontas 11 

3 SO. Entry B POC 

Pocahontas C1 

2 No. Irl Plow POC 10. 50 5.50 2.50 0.50 - 0.50 

Inland 11 Herrin 16 --- --- 4.00 3.00 1 .OO 

Peabody $10 

1 SO. 5.5 East Herrfn 16 - 6.00 - 6.50 - 5.50 - 3.00 - 0.50 0 

w 

L X 42.50 12.00 10.00 11.50 10.50 

(rx)'/n 225.78 --- --- -.- --- (:lot Listed on Table) 

sum of squares 228.97 --- --- --- --- 

95% Population Confidence (-8.22, (-7.46, (-6.79, (-5.23, (-5.64. 

Interval 18.84) 10.46) 8.99) 7.79) 7.98) 

95: Sample Mean Confidence (0.53, (-1.67, (-1.53, (-0.89, (-1 .lo. 

Interval 10.09) 4.67) 3.73) 3.45) 3.44) 

s - Sqlc Standard Deviation 
TABLE A-I1 

AVERAGE RATIO 

A1 1 Pittsburgh Pocahontas Herrin #6 

Frequency Mines Seam Seam Seam 

100 5.31 7.13 7.33 - 6.00* 

200 1.50 3.00 2.17 - 6.50* 

300 1.10 2.13 1 .OO - 0.75 

400 1.28 2.13 1 .OO -0- 

500 1.17 1.50 1.33 0.25 

600 1.94 2.00 2.00 1.75 

700 2.72 2.38 3.00 3.00 

800 3.28 . 2.88 3.67 4.00 

900 3.83 3.38 4.33 5.25 

1000 5.63 6.85** 3.67 6.50 

*Data from 1 mine, 1 location only 

**Data from 3 mines, 3 locations, Pittsburph Seam 
NOTE: 

- 

1 

BURGH SEAM 

- 

> HERKIN *& SEAM 

,. (SES NOTE) -. 

POC4HONTAS *3 SEAM .* 

I I I I -..met I I I I 

LOO 200 300 400 500 600 700 800 400 iO00 

FREQUENCY \N kHz 

FREQ 100 1 ZOO = -6 , 300 =-0,lS 

Figure A-1 Seam Average Values (dB) 

2 Figure A-2 Variance of the Differences S (A) 

(All Mines) 

10 5 

7r I I I I I I I. I I 

6 - - 

5 - 

4 - 

5' (A> 

(dB) 

3 - - 

Arthur D Littlelnc 

2 

1 

- - 

- - 

O6 

I I I I I I I I I 

100 200 300 400 500 600 700 800 900 LOO0 

FREQUENCY IN kHz 
IV. .4NALYSIS OF MF PROPAGATION DATA FROM MARGARET NO. 11, NANTY GLO, 

EHRENFELD, AND ADRIAN COAL MINES - Interim Report, May 1978 

Arthur D I.ittle Inc 
ANALYSIS OF MF PROPAGATION DATA FROM 

MARGARET NO. 11, NANTY mo, EHRENFELD, 

AND ADRIAN COAL MINES 

Robert L. Lagace -- Task Leader 

Alfred G. Emslie 

WORKING MEMORrnUM 

On 

Task Order No. 4 

Contract No. H0346045 

May 1978 

C-78453 

Arthur D. Little, Inc. 

Cambridge, Massachusetts 

Arthur D Littlelnc 
TABLE OF CONTENTS 

I. INTRODUCTION 

11. REDUCTION OF TfiE DATA 

III. DETERKLNATION OF u VERSUS f P~OTS AND m~ CONDUCTIVITIES 9 

IV. THE COWLING FACTOR 23 

V. EFFECT OF SEAM HEIGHT ON a AND C 

VI . REFERENCES 

APPENDIX 

Arthur D LittleInc 
I. INTRODUCTION 

Several improvements have been made in the analytical procedures 

applied to the data takenby T. S. ~ory'l) at the four primarily lowcoal mines examined in this memorandum. The mines are located in the 

Upper Freeport, Lower Freeport, and Lower Kittaning coal seams, thus 

bringing the number of seams samp1ed.u~ to six. 

The H& versus r method of plotting the data, to get a straight 

line graph from which the attenuation constant a can be obtained by 

inspection at each frequency f, is used in the same way as before. (2) 

The derivation of the coal and rock conductivities from the a versus f 

data is now, however, carried out by a convenient graphical scheme 

which determines those values of the two conductivities that produce a 

theoretical a versus f curve that gives a least square fit to the experimental a versus f data. Furthermore, the theoretical magnetic field 

signal levels derived from the conductivities are now compared with 

the corresponding experimental values by means of the respective 

coupling factors Ctheor and Cexpt. The experimental coupling factor, 

at each frequency, is defined as the intercept of the H& versus r 

straight line with the HA axis. The theoretical value is calculated 

as a function of frequency from the conductivities by means of the 

coal-seam mode magnetic field equation (1). This type of comparison 

is more fundamental than the previous method of comparing theoretical 

and experimental values of magnetic field at some standard range. 

In addition to these improvements in analytical technique, we have 

worked out a theory of the coupling of the coal-seam mode to a cable. 

This theory, which was presented at the recent EM Guided Wave Workshop 

in Boulder, Colorado, makes use of image theory, Fourier analysis, and 

the principle of reciprocity. The theory was compared in a preliminary 

way with experimental results from the Margaret No. 11 mine. A more 

complete test requires experimental measurements, now in progress, of 

the effect of loop orientation on the degree of coupling to the cable. 

Arthur D Littlelnc 
A copy of the paper(3) describing the theory for coupling of the 

coal seam mode to a cable in a mine tunnel and its application to data 

taken at the Margaret No. 11 mine is included in the Appendix of this 

working memorandum. Also included is a copy of a paperc4) describing 

the three-layer theoretical model and its use in the analysis of the 

quasi-conductor-free area propagation data taken by T. S. Cory in the 

first six mines. 

Arthur D Little, lnc 
11. REDUCTION OF THE DATA 

The coal-seam mode of propagation at medium frequencies is essentially a TEM transmission-line mode between parallel conducting plates, 

with the E field vertical and the H field horizontal. The conducting 

rock above and below the coal seam forms the "plates" while the much 

less conducting coal acts as the "lossy dielectric" layer between the 

plates. This mode can be excited by a vertical loop antenna, and the 

magnetic field H falls off with horizontal distance r from the antenna, 

in the plane containing the loop, according to the formula (1) 

where C is a coupling factor, and a is the attenuation constant. This 

formula is valid when r is greater than l/a. 

Eq (1) can be mitten in the form 

which shows that a plot of H& (in dB) versus r (in meters) will be a 

straight line withslope8.686~ and intercept C (in dB). Plotting the 

experimental values of H versus r in this way therefore provides a very 

simple way to obtain both a and C directly from the data. Since the 

experimental results give H in dB re 1 vA/m versus r in meters, the 

following simple conversion of the data must first be carried out: 

Figure 1 shows the original data at 890 kHz for the fresh air 

entry in the 5-Cross Area of the Nanty Clo mine. Figure 2 shows the 

same data transformed by means of Eq (3). It is seen that the effect 

of this transformation is to straighten the curve, as expected, in 

support of Eq (1). 

The slope of the straight line drawn through the data points in 

-1 Figure 2 gives a = 0.0600 m . The intercept gives, for the coupling 

Arthur D Littlelnc 
10 0 150 

RANGE, r, in meters 

factor, C = 70.0 dB re lp~/m~'~. The first data point lies within the 

distance l/a = 16.7 m, and was therefore disregarded in drawing the 

straight line. The last data point was also disregarded, since it is 

close to the noise level. The remaining six points lie on a reasonably 

straight line. Since the straight line in Figure 2 is completely 

specified by a and C, these two parameters represent all the data 

taken at 890 kHz. 

On carrying out the same procedure for all the other frequencies, 

we can make plots of a and C versus frequency, as shown in Figures 3 

and 4. These two plots sunrmarize the MF characteristics of the particular propagation path under consideration, as determined directly from 

the experimental measurements. 

Arthur D Little,lnc 


111. DETERMINATION OF a VERSUS f PLOTS AND TEIE CONDUCTIVITIES 

An experimental plot of the a versus f data, such as in Figure 3, 

contains enough information for the determination of the conductivities 

o and a of the coal and rock, respectively. The connection between 

c r 

a and the conductivities is given by the transmission-line formula (1.2) 

where Zs, the surface impedance of the rock, is given by 

where 6 , the skin depth in the rock, is given by r 

and h is the height of the coal seam, w is 2~f, Kis the dielectric 

C 

constant of the coal which we assume has the value 6, and po and co 

have their usual free space values. 

The problem is to find values of oc and o which produce a theorr 

etical a versus f curve that gives a least square fit to the experimental a versus f plot in Figure 3. For given values of o o f, and c' r' 

h, one can calculate a theoretical value a by taking the real part of 

Eq (3). This can be done for each of the experimental frequencies fi, 

and the set of theoretical and experimental a's can be used to calculate a sum-of-squares error given by 

- a ) Eocor theor ' 

i=1 

where N is the number of frequencies atwhich experimental data were 

taken. We have found it convenient to use a programmable hand calculator such as the HP67 for this calculation. This calculator is capable of carrying out the calculation of E(oc. or) for 5 frequencies in 

40 seconds, including both Eq (3) and Eq (6). 

Arthur D Little,lnc 
We search for the minimum E on a o o diagram by the straight- c' r 

forward strategy shown in Figure 5, for the experimental data in Figure 

3, with h = 1.04 m and N - 5. We start by making a traverse, labeled 

A, starting at the point o = 12 x or = 10 x and proceeding C 6 from right to left at constant, o . The calculated values of 10 E are 

r 

entered on the diagram at evenly spaced intervals in o . It is seen 

C -5 that a subsidiary minimum of E = 303 x occurs at o = 9 x 10 , C 

u = 10 x Mho/m. It has been found, for the 100 to 1 scale ratio r 

between or and oc, that the E-topography usually has a deep valley 

from the upper right to the lower left. We therefore expect to find 

-5 minima at (10 x 10 , 11 x and (8 x 9 x but we do 

not know which is the lower. To find out, we next try traverse B which 

has a higher mini- than for traverse A. We therefore do traverse C, 

followed by D and E and find continually decreasing minima, which are 

indicated by circles. For traverse F, however, the minimum rises 

again. We have therefore narrowed the search for the absolute minimum 

of E to a small area around the point (6 x 7 x 

To obtain higher precision, we expanded the scale and continued 

the procedure as sham in Figure 6. The absolute minimum is found, to 

-5 two-figure accuracy, to be at oc = 6.2 x 10 Mholm, o = 7.2 x 

r 

Mholm with E - 168.1 x m-2. The root mean square value of the 

error in a is 

From the least-squares conductivity values, we can return to Eq (3) 

and calculate a theoretical a versus f curve. This curve is shown, in 

comparison with the experimental a versus f data plot, in Figure 3. 

The goodness of fit indicates that the simple transmission line 

equation (3), which is based on a three layer model, is valid over a 

wide range of frequencies. It further suggests that the experimental 

method used is an excellent way to determine the coal and rock 

conductivities. 

Arthur D httlelnc 
Figure 5 

Search Procedure for Calculating U c and Or 

for Least Square Fit, Ed,,, to a versus f Data-Coarse Grind 

10~~7~ Nanty Glo Mine - 5 Cross Area 

M holm) 

15 

14 

13 

12 

11 

lo 

9 

7 

6 

5 

4 

3 

2 

1 

OO 1 2 345 6 7 8 4 LO 11 12 13 14 15 

lo5 DL (~hojrn) 

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

1 

Figure 7 shows a versus f results for an entry in the Main-N area 

of the Nanty Glo mine located 16 miles from the 5-Cross area. Considerable heaving of the floor is present in this entry, which causes 

partial blockage of the tunnel cross-section. Comparison of the 

experimental plots of Figures 3 and 7 shows that the low frequency 

results are comparable in the two areas, whereas the values of a at the 

two highest frequencies are much lower in Figure 7 than in Figure 3. 

This may be due in some way to the floor heaving in the Main-N area. 

However, it may instead be due to the fact that the batteries began to 

run down during the Main-N measurements. We have therefore calculated 

least-square conductivities and theoretical a versus f curves for the 

Main-N case for the four lowest frequencies, as well as for all six 

frequencies. The Main-N results for four frequencies agree approximately with those for the 5-Cross Area, while the results by using 

all six frequencies are much larger than those for the 5-Cross Area. 

Figures 8 to 11 show a versus f plots, obtained in the same way, 

for the Ehrenfeld, Adrian, and Margaret No. 11 mines. As before, the 

theoretical curves derived from Eq (3) can be made to agree well with 

the shapes of the experimental data plots for properly chosen values 

of the conductivities. In the case of the Adrian mine (Figure 9) the 

fit is exact since only two experimental points are available. In 

Figure 12, the a versus f curves for these four mines have been added 

to the composite plot of a versus f curves for the first six mines 

measured, taken from reference (1). Examination of Figure 12 reveals 

that the attenuation rates for the mines in all three new seams fall 

between those for the high loss Herrin No. 6 seam and the moderate loss 

Pocahontas No. 3 seam. The Upper Freeport seam in Pennsylvania exhibits 

the highest attenuation rate behavior among the three seams, falling 

close to values found for the Herrin No. 6 seam, but it has significantly 

different values than the Upper Freeport seam in West Virginia. On 

the other hand, the Lower Freeport and Lower Kittaning seams in Pennsylvania exhibit nearly similar behavior which lies close to that 

found in the Pocahontas No. 3 seam in Virginia below about 500 kHz, and 

Arthur D Littlelnc 





Composite Plot of Signal Attennation 

Rate. in dB/100 fr. for Ten nines in 

. 

~ - ... 

FREQUENCY, KHz 
which approaches that found in the Herrin No. 6 seam in Illinois above 

1 MHz. As mentioned previously, the high frequency results for the 

Nanty Glo Main-N area (dashed part of curve) are unreliable. 

Table I gives a comparison of the conductivities obtained for the 

four mines in their respective coal seams. It is seen that the coal 

and rock conductivities differ by a factor of about 100. It is this 

large contrast between rock and coal conductivities that makes the MF 

coal-seam mode of propagation possible. However, it is seen that the 

coal and rock conductivities do not differ significantly from each 

other from mine to mine and seam to seam,with the possible exception 

of the Adrian mine results which were derived from measurements at only 

two frequencies. These coal and rock conductivities can be compared 

with those (1) derived from the mines in the first three seams measured, 

shown in Table 11. We find that the Table I values are most similar 

in value to those obtained for the Pocahontas No. 3 seam in Virginia. 

In summary, the signal attenuation rates for most of the seams 

examined to date fall in the moderate to high loss category, and it 

appears that the low losses found in the Pittsburgh seam may be the 

exception rather than the rule, unfortunately. The reasons for this 

are not yet apparent. However, enough propagation data may now be available to determine whether any correlation exists between the electrical 

properties of the coal and its chemical composition. Since chemical 

analyses of the coal are generally available for each mine, statistical 

regression analyses of these chemical and electrical data appear to be 

both practical and desirable. 

Arthur DLittle,lnc 
TABLE I 

DERIVED COAZ, AND ROCK CONDUCTIVITIES 

FOR FOUR MINES 

(For K n = 6) 

Seam Height a Coal u Rock 

Coal Mine h (m) (Mho/m) (Mho /m) 

Nanty Glo 

5-Cross Area 1.04 6.2 x 7.2 x l0i3 -5 

Main-N Area (lowest 4 1.04 (to .61) 6.6 x 10 11 x 10- 

Ehrenf eld 1.12 6.3 x lov5 5.4 

Margaret No. 11, 1 Butt Sec. 

N 1.30 -5 

w Tx, Rx in same entry 16 x 13 x 10; 3 

Tx, Rx one entry apart 1.30 12 x 10 6 x 10- 

Adrian (Only 2 frequencies) 1.83 3.4x10-5 1.9x1~-3 

Cdal Sedm 

Lower Kittani

Lower Kittani

Lower Freepor

Upper Freepor

Upper Freepo

Upper Freepor
TABLE ll 

CONDUCTIVITIES DERIVED FROM THE (nVERSUS f PLOTS 

Coal Mine Coal Seam 

~ittsb"rgh 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Robinson Run 

Federal No. 1 

Ireland "11" 

Ireland "I" 

Pocahontas No. 1 

3 South Area 

Entry A Pocahontas No. 3 

3 South Area 

Entry B Pocahontas No. 3 

2 North No. 1 

(Plow Area) Pocahontas No. 3 

Inland No. 1 Herrin No. 6 

Peabody No. 10 

1 Main South 

1st West 2nd 

North Herrin No. 6 

1 South 

5112 East1 

1 Sourn JC~. Herrin No. 6 

Arthur D Little. Inc 
IV. THE COWLING FACTOR 

The factor C in Eq (1) is given theoretically by the expression (1) 

where M is the transmitter mangetic moment. From the conductivities, 

we can calculate a, 6, and 6r as functions of frequency by means of 

Eqs (3), (4), and (5). Therefore a theoretical curve of C versus f can 

be derived from Eq (7). Such a curve is shown for the Nanty Glo mine 

in Figure 13, in comparison with the experimental intercept values of 

Figure 3 obtained from the H& versus r plots for this mine. The 

agreement is seen to be fairly good. Similar coupling factor comparisons 

for the other mines are shown in Figures 14 to 18. It is seen that the 

theory generally underestimates the experimental values below about 

1 MHz and overestimates them above 1 MHz. 

Figure 14 for the Main-N area of the Nanty Glo mine shows that the 

experimental values of C for the two highest frequencies are considerably out of line, due probably to the effect of considerable floor 

heaving in this tunnel. We have therefore included in Table I only the 

conductivity values derived from the experimental data taken at the 

four lowest frequencies for this case. 

The comparison of theoretical and experimental values of the coupling factor, defined by the H& axis intercept at r = 0, is more fundamental than the comparison of theoretical and experimental values of 

magnetic field at some standard range. Therefore, we recommend that the 

/C ratio 'theor expt expressed in dB be analyzed statistically, instead 

Htheor/Hexpt (@ 100 m), to assess the goodness of fit between the 

three-layer model and the data as a function of frequency. 

Arthur D Little,lnc 






V. EFFECT OF SEAM HEIGHT ON a AND C 

It is of interest to know how the attenuation constant a and the 

coupling factor C depend on the seam height h if all other parameters 

are kept constant. Figures 19 and 20 show what would happen if the 

seam height of the Nanty Glo mine were 2.08 m instead of 1.04 m. It 

is seen from Figure 19 that a is markedly reduced, especially at the 

higher frequencies. This would result in a considerable increase in 

range of communication. On the other hand, Figure 20 shows that the 

coupling factor is decreased by about 5 dB at all frequencies. This 

loss of coupling in the high coal case would by no means nullify the 

larger gain in signal strength caused by the decrease in u. Thus, MF 

radio communication will be more favorable in high coal than low coal 

seam waveguides having the same electrical properties. 

Arthur D Littlelnc 


VI. REFERENCES 

(l)~. S. Cory, Summary Data Reports for Margaret No. 11, Nanty Glo, 

Ehrenfeld, and Adrian Mines on Bureau of Mines Contract H0377053, 

Subcontract C-651672, Winter-Spring 1978. 

(2)~. L. Lagace and A. G. Emslie, "Modelling and Data Analysis of InMine Electromagnetic Wave Propagation," Interim Report on Bureau of 

Mines Contract 80346045, Task Order No. 4, May 1978. 

(3)~. L. Lagace and A. G. Emslie, "Coupling of the Coal-Seam Mode to a 

Cable in a Tunnel at Medium Radio Frequencies," presented at the 

1978 Guided Wave EM Workshop, 28-30 March 1978, Boulder, Colorado. 

(4)~. G. Emslie and R. L. Lagace, "Medium Frequency Radio Propagation 

and Coupling in Coal Mines," presented at the 1978 Guided Wave EM 

Workshop, 28-30 March 1978, Boulder, Colorado. 

Arthur DLittlelnc 
APPENDIX 

Arthur D Little,lnc 
COUPLING OF THE COALSEAM MODE TO A CABLE 

IN A TUNNEL AT MEDIUM RADIO FREQUENCIES 

R.L. Lagace and A.G. Emslie 

Arthur D. Little, Inc. 

Cambridge, Massachusetts 

INTRODUCTION 

The lowest order coal-seam mode is a parallel-plate TEM transmission-line type of propagation' of medium frequency radio waves in a conducting coal seam which is bounded above 

and below by more conductive rock, with the electric field vertical and the magnetic field horizontal. This mode can be excited by a vertical loop antenna placed in a tunnel in the coal seam. 

In a conductor-free region of the coal mine the magnetic field falls off with distance with a 

cylindrical spreading factor multiplied by an exponential loss factor. However, when a conduc-- 

tor, such as a power cable, is present in a parallel tunnel, the field is found experimentally' to 

level off to a much lower rate of decay after a certain fairly well defined distance. 

The effect can be attributed to coupling of the coal-seam mode to a low attenuation 

mode guided by the cable. Experiment showsZ that a slowly decaying current is indeed present 

in the cable. The purpose of this paper is to investigate the nature of the coupling. The method 

is to start with a current in the cable, calculate the magnetic field produced by this current at 

the location of the loop antenna, determine the voltage induced in the loop by this field, and 

finally use the reciprocity principle to determine the current induced in the cable when the 

loop acts as a transmitter. 

MAGNETIC FIELD DUE TO CURRENT IN CABLE 

Figure 1 shows the cable at a distance y = d from the center of the coal seam. The cable 

carries a current I which produces an infinite set of images3 with current 

located at the (complex) positions: 

where 6, = ((rfi0 fn)* is the skin depth in the rock. The images, including the cable itself, form 

a periodic distribution of current of period: 

To calculate the magnetic field due to the set of images it is convenient to represent the 

discrete currents by a Fourier series: 

" / ~UPY I(y) = Z Apcos - + Bp sin - \ . L L 

This work was supported by the U.S. Department of the Interior, Bureau of Mines, Pittsburgh Mining and 

Safety Research Center, under USBM Contract H0346045. 
CABLE WlTH CURRENT I+ I) IN 

COAL MINE TUNNEL WlTH IMAGES (- I) IN ROCK 

I 1 

:db+~ ~+(l-i16,I"" '"'" 

X/ Coal 

I,,///; /, 

--------- -- __ - 

Reflecting Plw 

L 

which contains no constant term since the total current in cable and rock is zero. For the 

currents defined by (I) and (2) the Fourier series takes the form: 

2rr~ 4zd . 4rry I(Y) = - cos - +sin - . L L L sm- L 

6nd + cos - 6rr~ 8nd . 8rry 

L cos - +sin - 

L L 

mL 

The magnetic fields corresponding to the first harmonic of the yz current sheet, for a wave 

propagating along the cable, are readily found to be: 
where I, is the current in the cable at z = 0. 

For the second harmonic, the field is: 

The magnetic field lines for the two harmonics are shown in Figure 2. 

FIGURE 2 

MAGNETIC FIELD LINES FOR TWO HARMONICS 

- - - - - - - Reflecting Phne 

1st 

-- 

Harmonic 

w 

Reflecting Phne 

--- "7- - - - - Reflecting PI~M 

2nd H8rmonic - 

The k's are related by the formula: 

kx2 + ky2 + kZ2 = kO2 

where k, is the freespace propagation constant and k, is the z-directed propagation constant 

for the cable-guided wave. For medium frequencies, kZ is not very different from ko4 95 

(".75k0) and both are small in mapitude compared with ky. Therefore, Equation (14) can 

be written to a good approximation as: 
If we make the further approximation that lkyd I:.< 1, and let y = 0, we obtain the simple 

results: 

1 n(h+6,) x (?Il = ,Ie- (h + S,)' + 6,' 

where the subscripts 1 and 2 refer to first and second harmonics, respectively. 

EXCITATION OF THE CABLE BY A TRANSMITTING LOOP ANTENNA 

By the principle of reciprocity, we can use the above results to find the current I, induced 

in the cable by a loop antenna situated at a distance x from the cable. The result is: \ 

where M is the magnetic moment of the loop, 2, is the characteristic impedance of the cable 

transmission line, and (H/I,) is the appropriate ratio from Equations (16 - 19). 

Measurements by T.S. Co~y' in the Helvetia Coal Co. Margaret No. 1 1 mine with a vertical transmit loop parallel to, and placed at a distance of 14 meters from, a power cable are 

shown in Figure 3. The fint part of the magnetic field plot represents the decay of the incident field of the coal-seam mode. Beyond about 80 m along the cable, the measured field is 

due to the current induced in the cable. This current is estimated from the data, and from the 

size of the receiving loop located adjacent to and in the plane of the cable, to be about 

6 x A. From other measurements taken in a conductor-free area of the same mine, we 

can infer that the conductivity of the rock, a,, is in the range 0.01 to 0.02 Mho/m. For a, = 

0.01 Mho/m, the skin depth in the rock is 6, = 5.3 m. 

If the transmitting loop is oriented vertically, so as to generate the TEM coal-seam mode 

with the magnetic field horizontal, it is seen from (16) and (18) that coupling to the cable 

occurs only via the second and higher-order even harmonics. Using the above value of skin 

depth, 6,, and the experimental values d = 0.45 m, h = 1.3 m, and x = 14 m, theoretical estimates of the current induced in the cable are obtained from Equation (1 8) for the second 

harmonic. Equation (18) gives IHx/I, 12 = 1.2 x m-' . Equation (20), with M = 2.5 A - 

mZ and 2, = 300 52, then gives I, = 1.4 x lo-' A. Thus, the predicted current value for a 

vertically oriented transmit loop is about 50 times less than the experimentally determined 

value. 
MAGNETIC FIELD VS. DISTANCE 

ALONGPOWERCABLE 

MARGARET NO. 11 MINE, FREEPORT SEAM 

Vdcdl TRnvnit Loop Load F'aralkl To 

and 14 Marr Awy horn Cab* 

Fnqwncy - 000 kHz 

Transmit ~ommt M - 2.5 A*' 

Rwiw Loop Adjacent to and in Plane of Cable 

0 20 40 80 80 1W 120 140 180 180 200 220 2p0 

Dimnca Along Powr Wh in M.tat 

This disagreement implies that the excitation of the cable-guided mode is not brought 

about by the TEM coal-seam mode. Rather, it is brought about by a higher-order mode, below 

cutoff in the coal seam at MF frequencies, which has circular lines of E about a vertical axis 

and an H field with both radial and vertical components. This type of mode is generated by 

a horizontally oriented transmitting loop which couples to the cable via the fmt harmonic 

which produces a nonzero y-component of magnetic field. Equation (1 71, which applies for 

this case, gives IH,,/I, 1, = 2.06 x lo-=. Equation (20) then gives I, = 6.1 x 10- A, which is 

10 times larger than the experimental value obtained for a vertical antenna. An accidental 

tilt of the antenna of about 6 degrees away from the vertical would therefore make theory and 

experiment agree. 

An alternative explanation of the coupling of a vertical loop to the cable is that the rock 

conductivity above the coal seam is appreciably different from that below the seam. Under 

these conditions the two reflecting planes are not symmetrically located with respect to the 

coal seam. In that case, as shown in Figure 4, a vertical loop now couples to the fmt harmonic 

of the cable field. A vertical displacement of the loop with respect to the center of the tunnel, 

with symmetrically placed reflecting planes, also gives coupling to the first harmonic. 

FIGURE 4 

VERTICAL LOOP COUPLING TO IST HARMONIC WHEN COAL 

SEAM NOT CENTERED BETWEEN REFLECTING PLANES 

- - - - - - - Refkctins Pbm 

1st Hnmonic fl . Coal Sum 

H Wblo \L=P 

------- RwflKting Phw 
COMMUNICATION BETWEEN HORIZONTAL LOOP ANTENNAS IN THE . PRESENCE OF CONDUCTORS 

The foregoing analysis suggests that horizontally oriented loop antennas may provide an 

efficient communication system in areas where conductors such as power lines, trolley lines, 

and rails are present. The vertical component of magnetic field at a distance x, from a cable 

due to a horizontal transmitting loop at a distance x, from the same cable is from Equation 

(1 7) (used twice) and Equation (20), 

Figures 5 and 6 show graphs of H versus x, + x, for various frequencies, for rock conductivities of 0.01 and 0.1 Mho/m. The horizontal bar on each line indicates the intrinsic 

receiver noise level at that frequency for a 12 kHz bandwidth. It is seen that the maximum 

value of x, + x, depends strongly on the conductivity and is 38 m for or = 0.01 Mho/m, but 

only 18 m for a, = 0.1 Mholm. The optimum frequencies are 300 kHz and 100 kHz, respectively. No allowance has been made for loss along the cable itself. The results are not valid 

for very small values of either x, or x2. 

FIGURE 5 

VERTICAL MAGNETIC FIELD AT DISTANCE X2 FROM CABLE 

DUE TO HORIZONTAL TRANSMIT LOOP AT DISTANCE X1 

(Rock Conductivity or = 0.01 Mho/mI 

Srrn Thikmp h - 2 rn 

20 Tr~anit Mom M - 2.5 ~-m' 

- lmrinric Reaim Noin for 12 kHz BW 

10 

0 

-10 

-20 

30 

-40 - 

-60 - 

-60 

0 10 20 30 40 50 

Total of Lateral Distan~a xl + x2 in mmrg 
FIGURE 6 

VERTICAL MAGNETIC FIELD AT DISTANCE X2 

FROM CABLE DUE TO HORIZONTAL TRANSMIT 

LOOP AT DISTANCE XI 

(Rock Conductivity or = 0.1 Mholm) 

FiBures 7 and 8 show similar plots, derived from (1 7) and (20), for the field at the cable 

itself, (as measured by a square coil of edge 0.67 m held with one edge alongside the cable) due 

to a horizontal transmitter loop at a distance x from the cable. The maximum distances for the 

two values of rock conductivities are 57 m and 22.5 m, and they occur at 100 kHz and 50 kHz, 

respectively. 

CONCLUSION 

A theoretical model for predicting the coupling behavior between loop antennas and conducting cables in coal mine tunnels is currently under development, and the results are wmparing favorably with the limited amount of experimental in-mine data taken to date. Further re 

finements of this theoretical model, together with comparisons with more comprehensive data 

from two additional coal mines, will be performed in the near future. 
. . - - . . - . 

MAGNETIC FIELD AT THE CABLE DUE TO 

HORIZONTAL TRANSMIT LOOP AT DISTANCE X FROM THE CABLE 

(Rock Conductivity a, - 0.01 Mholm) 

%am Thicknas h - 2m 

Tnnmit Moment M - 2.6 ~-rn~ 

- lnninuic Receiver Noiw for12 kHz B 

Receivs Lwp Adjaemt to and in 

- 

FIGURE 8 

MAGNETIC FIELD AT THE CABLE DUE TO 

HORIZONTAL TRANSMIT LOOP AT DISTANCE X FROM THE CABLE 

lRok Conductivity or = 0.1 Mholml 

Smrn Thickmu h - Zm 

Tmit Mnnmt M - 2.6 ~-rn~ 

- lntrinrie Ruaim Noim For 

12 kHz BW 

- 

- 
REFERENCES 

1. A.G. Emslie and R.L. Lagace, "Propagation of Low and Medium ~re~uenc~ Radio Waves 

in a Coal Seam," Radio Science, vol. 11, no. 4, pp. 253-261, April 1976. 

2. T.S. Cory, "~lectromagnetic Noise and Propagation in LowCoal Mines, Helvetia Coal Co. 

Margaret No. 11 Mine," Summary Data Report 1 to Collins Group, Rockwell International Corporation, under Bureau of Mines Contract H0377053. 

3. P:R. Bannister, "Approximate Results for the Mutual Electromagnetic Coupling of Loops 

over a Homogeneous Ground," Naval Underwater System Center Report #NL-3029, New 

London Laboratory, 23 November 1970;NTIS No. AD71735 1. 

4. J.R Wait and D.A. Hill, "Guided Electromagnetic Waves Along an Axial Conductor in a 

Circular Tunnel," IEEE Trans. Antemas and Propagation, AP-22(4), pp627-630, July 1974. 

5. D.A. Hill and J.R. Wait, "Pulse Transmission Along Cables in Circular Tunnels," Proceedings of U.S. Bureau of Mines Guided Wave EM Workshop, Transmission Session I, 

 arch 1978. 
MEDIUM FREQUENCY RADIO PROPAGATION 

AND COUPLING IN COAL MINES 

A.G. Emsliefl R.L. Lagace and M.A.Garcamon 

Arthur D. Little, Inc. 

Cambridge, Massachusetts 02140 

EXCITATION OF THE COAL-SEAM MODE IN A CONDUCTOR-FREE REGION 

Medium frequency waves can propagate in a conducting coal seam, bounded above and 

below by more conductive rock, in an approximate TEM transmission line mode with the electric field vertical and the magnetic field horizontal.' The magnetic field components produced 

by a transmitting loop antenna located at the center of the coal seam in a vertical plane are, in 

terms of cylindrical coordinates with the origin at the center of the loop, the z-axis vertical, 

and the loop in the r-z plane: 

H, (') is the fmt order Hankel function for outgoing waves, k is the propagation constant of the 

coalseam mode, and m is the effective magnetic moment per unit length, distributed along the 

z-axis, that is equivalent to the magnetic moment M of the loop antenna located in the coal 

seam waveguide. 

The effects of the currents induced in the rock by the transmitting loop can be represented 

by an infinite set of uniformly spaced loop images, each. of magnetic moment M distributed 

along the z-axis with complex spacing' 

where h is the thickness of the coal seam and 6, is the skin depth in the rock. The magnetic 

moment density m, which couples to the TEM coal seam mode, is the zero-order component 

of the Fourier series that represents the set of magnetic moment images and is given by: 

The higher order Fourier series components couple to higher order coalseam modes which are 

highly damped, and can therefore be ignored. 

This work was supported by the U.S. Department of the Interior, Bureau of Mines, Pittsburgh Mining and 

Safety Research Center, under USBM Contract H0346045. 

44 
The propagation constant k is given by 

where (Y and fi can be calculated by means of the usual parallel plate transmission line formula: 

which in this case takes the form: 

& is the surface impedance of the rock, given by 

where 

and or, o, are the rock and coal conductivities, ec is the coal permittivity, and w is the angular 

frequewy. The permittivity of the rock e, is ignored since UE, * o, for the frequencies of 

interest here. 

On taking the asymptotic form of the Hankel function, we fmd for the direction 4 = 0, in 

the plane of the loop, that the magnitude of the azimuthal component of magnetic field is: 

IHI- M (a2 + 6')s e*' . - (10) 

(8nth [(h + SJ2 + 6r2 I 

This expression is approximately valid at ranges for which ar > 1. 

ATTENUATION RATE VERSUS FREQUENCY 

Medium frequency transmission measurements have been made by T.S. Cory3 in six coal 

mines. From a communications point of view, one can make a very meaningful comparison of 

the various mines directly from the experimental data, by plotting the attenuation constant a 

versus the frequency f. For this purpose, Equation (10) shows that if, for a given frequency, 

the experimental values of HK expressed in decibles, are plotted against r, a straight line of 

slope proportional to u should be obtained. 
Figure 1 shows such a plot of H fi versus r for Consolidation Coal Company's Robinson 

Run Mine (No. 95) at a frequency of 477 kHz. It is seen that the experimental points plotted 

in this way do indeed conform to Equation (1 0). The slope of the best straight line drawn 

through the plotted points gives an attenuation constant ct = .01253 m*' . It is to be noted that 

the range r has, for convenience, been divided by an arbitrary standard range of 100 m in the 

derivation of H \TT from the data. The value H = 24.0 dB re 1 pA/m on the straight line at 

this standard range, along with the slope ct = 0.01 253 m* I, completely specify the experimental 

data at this frequency. 

On repeating this procedure for the data at each frequency used in the experiments, we 

obtain the ct versus f plot shown in Figure 2. It is seen that a increases monotonically with f. 

This type of curve is found for all the mines. 

Figure 3 shows ct versus f plots for a large number of mines. It is seen that the mines fall 

into three categories, representative of the seams in which they lie, namely: the Pittsburgh seam, 

the Pocahontas No. 3 seam, and the Herrin No. 6 seam, which are in order of increasing attenuation rate a. 

DETERMINATION OF THE CONDUCTIVITIES 

By separating the real and imaginary parts of Equation (7) we obtain the following expressions for a and 0: 

where: 

For an assumed value K, 5 6 for the dieiectric constant of coal, we can determine the values of 

a, and a, that give the least square fit between the theoretical and experimental a versus f curves. 

The solid line in Figure 2 corresponds to oc = 3.0 x lW5 Mholm and or = 8.5 x 1W2 hlholm. 

The RMS error in u is 0.001 8, which is about 5% of the mean a over the frequency range 

covered. Table I shows values of the o's determined in this way for the various mines. 
FIGURE 1 

PLOT OF H 6 VERSUS r AT f - 477 kHz 

ROBINSON RUN COAL MlNE 

FIGURE 2 

PLOT OF u VERSUS f BEHAVIOR 

ROBINSON RUN COAL MINE 

-60 

-70 

-80 

-90 

a, = 3.0 x 10.' Mholm 

or = 8.5 x 10.' Mholm 

For Llan Sqrum Fit 

- 

- 

- 

Sum Thickness h - 1.5 m 

Cml Dielmnric Concmnt Kc = 6 

0 100 200 300 400 5 

Range jn Maws 
FIGURE 3 

COMPOSITE PLOT OF SIGNAL ATTENUATION 

RATES IN dB1100 FT. FOR SIX MINES IN 

THREE DIFFERENT COAL SEAMS 

o Robinson Run 

d Inland "I I" 

v VP#lsO. 

-=- Inlmnd # 1 

+Pub~dy#lO 

Radio Siprvl 

Attenrution 

Rate 

ldB1100 FT.) 

COMPARISON OF CALCULATED AND EXPERIMENTAL 

VALUES OF THE MAGNETIC FIELD 

From the values of o, and a,, we can determine a and 5 from (1 1) and (12) and then calculate I H I versus r from (10) for each frequency. The results are shown in Figure 4 for the 

Robinson Run mine. The experimental curves are given in Figure 5. It is seen that the pattern 

of the intersecting experimental curves is well accounted for by the theory, although the 

theoretical values are in general somewhat too high. 

The theoretical and experimental values have also been compared on a statistical basis to 

determine the goodness of fit between the simple three-layer theoretical model predicted results 

and the measured data. The ratio A = H (Theoretical)/H(Experimental) expressed in dB was 

analyzed statistically as a result of trends shown by plots of A versus frequency, at the standard 

range of 100 meters, for data taken from each of the mines. The A plots showed a small and 

relatively uniform disagreement, mainly on the high side, between about 100 and 1000 kHz, 

and progressively increasing disagreement, again on the high side, below 100 kHz and above 

1000 kHz. The data at the higher frequencies also demonstrated considerable scatter relative 

to the predicted results. 
TABLE I 

CONDUCTIVITIES DERIVED FROM THE aVERSUS f PLOTS 

Coal Mine h Kc Dcoal oro& Coal Seam 

(ml (Mholm) (Mholm) 

Robinson Run 1.5 6 

Federal No. 1 2 6 

Ireland "I I" 2 6 

Ireland "I" 2 6 

Pocahontas No. 1 

3 South Area 

Entry A 1.37 6 

3 South Area 

Entry B 1.37 6 

2 North No. 1 

(Plow Area) 1.19 6 

Inland No. 1 3 6 

Peabody No. 10 

1 Main South 

1st Wen 2nd 

North 2 6 

1 South 

5112 East/ 

1 South Ja. 2 6 

~ittsburgh 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Pittsburgh 

Pocahontas No. 3 

Pocahontas No. 3 

Pocahontas No. 3 

Herrin No. 6 

Herrin No. 6 

Herrin No. 6 

The statistical analysis of A was restricted to data for the frequencies between 100 kHz and 

1000 kHz at the reference distance of 100 meters. For frequencies outside the 100 to 1000 kHz 

range, the A plots indicated that the applicability of the simple three-layer model was breaking 

down. One hundred metem was chosen as the reference distance because it allowed most of the 

data from six mines in both low and high loss coal seams to be included, while avoiding near 

field effects in most cases. The ratio A in dB between theory and data in the 100 to 1000 kHz 

band was analyzed by: 

- ZA 

Computing the Sample Mean A = for each seam and the variance of A 

for the total sample population as a function of frequency (there were too 

few samples within each seam to compute a standard deviation on a seam 

basis). 

Computing the Sample Grand Mean for all mines in all three seams, and 95% 

Confidence Intervals for both the population and Sample Grand Mean as a 

function of frequency. These results are plotted in Figure 6. 

Testing the hypothesis that the theoretical model fits the data at the 95% 

confidence level for the frequencies between 100 kHz and 1000 kHz. 
FIGURE 4 

THEORETICAL CURVES OF He VERSUS r WITH FREQUENCY AS A PARAMETER 

BASED ON oc AND or DERIVED FROM DATA 

ROBINSON RUN MINE 

- Frequencies in kHz 

-..-.. 98.5 

--- 485 

----- pa ...a.m... 1047 

- 2030 

-.-.- 4760 

h-1.5m 

Kc-6 

~=2.5~-m~ 

All Frequencies in kHz 

FIGURE 6 

EXPERIMENTAL H VERSUS r DATA 

ROBINSON RUN MINE 

M#mtic FiM Stmngth Va. 

bnge in Owi.Conductor.Frm Arw 

Frequency 

0 08.5 kHz 

0 228 kHz 

m 485 kHz 

1047kHz 

2030 kHz 

A 4750 kHz 

Tmmit Moment 

M - NIA = 2.5 ~-rn~ 
FIGURE 8 

STATISTICAL SUMMARY OF 

H (THE0RY)IHiEXPERl RATIOS IN dB 

Sample Mean, A 

95% Confidenra Intervals For: 

,,,, Sample Mean A 

1rn~300UK)WOBMmosooswlKm 

Fnqinny. kHz 

From this analysis, the following observations and conclusions were made. The differences 

between the model and the experimental data were similar for all coal seams. The shapes of 

the curves for each seam average followed the same pattern and did not differ from one 

another by more than 1 or 2 dB, with the exception of the Hemng #6 seam at frequencies 

below 400 kHz. (At these frequencies, data for only one mine in the Herring #6 seam was 

available.) This homogeneity implies that pooling all the data to compute a Grand Sample 

Mean for all mines is a valid technique, and that the results from any analysis can be applied 

back to all the mines uniformly. 

The plot of the sample and its 95% Confidence Intervals in Figure 6 is a visual hypothesis test (t-test) that the model fits the experimental data, against the alternative 

hypothesis that the model does not fit the data. The analysis showed that between the 

frequencies of 200 kHz to 900 kHz, there is no significant difference between the model 

and the actual data. In this band of frequencies the average ratio, A, ranges from 1.1 dB to 

3.9 dB. The range from 200 kHz to 600 kHz appears to be the best range for the model; both 

the variance and average A between the model and actual data being smallest, and positive, 

within this frequency range. 

CONCLUSIONS 

Based on the physical and statistical analyses applied to the data available to date, it can 

be concluded that: 
MF band radio wave attenuation rates experienced in coal mine conductorfree areas are highly dependent on the coal seam in which a mine is located; 

and that this attenuation rate versus frequency can be determined in a simple 

way from measurements of H vs r. 

The simple three-layer model fits the experimental data in the 200 kHz to 

900 kHz frequency band at the 100 meter reference distance, with the best 

agreement occuning between 200 and 600 kHz. This is the band that also 

promises to provide the most favorable performance for portable radio 

communications in coal mines.(' ) 

The Sample Grand Mean, 2, of the ratio H(T)/H(E) expressed in dB may be 

used to represent the Means for individual coal seams. 

Practical MF system performance estimates may be made in the 200 to 900 

kHz band by applying the simple three-layer model to seams in which the 

attenuation rates have been measured, and using the appropriate to correct 

the predicted field values. 

A more comprehensive theoretical development, analysis of data, and presentation of results can be found in reference 5. Data to date have come primarily from high-coal seams. 

Data from four additional mines in low-coal seams will be analyzed in the near future to 

assess the applicability of the model in thinner coal seams, and as a more rigorous test of the 

theory. 

REFERENCES 

1. A.G. Emslie and R.L. Lagace, "Propagation of Low and Medium Frequency Radio Waves 

in a Coal Seam," Radio Science, vol. 11, no. 4, pp 253-261, April 1976. 

2. P.R. Bannister, "Approximate Results for the Mutual Electromagnetic Coupling of Loops 

over a Homogeneous Ground," Naval Underwater System Center Report #NL-3029, New 

London ~aboratory, 23 November 1970, NTIS NO. AD^ 1735 1. 

3. T.S. Cory, "Propagation of EM Signals in Underground Mines," Collins Radio Group, 

Rockwell International Corporation, Final Report, Bureau of Mines Contract H0366028, 

April 18, 1977. 

4. Lagace, R.L. and Emslie, A.G., "Antenna Technology for Medium Frequency Portable 

Radio Communication sin Coal Mines," Proceedings of U.S. Bureau of Mines Guided 

Wave EM Workshop, Session 111, March 1978. 

5. Lagace, R.L., and Emslie, A.G., "Modelling and Data Analysis of In-Mine Electromagnetic 

Wave Propagation," Arthur D. Little, Inc., Interim Report, Task Order No. 4, Bureau of 

Mines Contract No. H0346045, to be published, Spring 1978. 
V. A METHOD FOR NONINTRUSIVE, IN-SITU MEASUREMENT OF COAL AND ROCK 

CONDUCTIVITIES IN A COAL MINE TUNNEL - Working Memorandum, 

June 1978. 
.-. 

WORKING MEM0RANI)UM -- June 23, 1978 

A METHOD FOR NONINTRUSIVE, IN-SITU MEASUREMENT 

OF COAL AND ROCK CONDUCTIVITIES IN A COAL MINE TUNNEL 

While at the EM Guided Wave Workshop in Boulder, Colorado, a 

method for in-situ measurement of coal and rock conductivities was 

conceived. A brief description of it is presented here to encourage 

comment and discussion. 

The method is based on the idea that a crossed pair of noninteracting transmitting and receiving loop antennas will become coupled to 

each other when placed near a wall of a coal mine tunnel. The arrangement is shown in Figure 1 where the transmitting loop TX, with its 

center located a distance h from the tunnel wall, produces an image 

TX' at a (complex) distance h + (1-i)6 beyond the tunnel wall (according to the image theory of Peter Bannister). The image TX' couples to 

the FiX loop and gives a signal that depends on the skin depth 6, which 

is related to the conductivity u of the wall material (coal or rock) 

by the formula 

where f is the frequency, IJ is the magnetic permeability of the rock 

-7 (usually equal to the permeability IJ, = 4n x 10 H/m of free space) 

and o is the rock or coal conductivity. Eq. (1) is valid when f is 

chosen so that a/2rrf is much less than the permittivity E of the rock 

or coal. 

If the loop dimensions are small compared with 6, the magnetic 

field component, H perpendicular to the plane of the receiving loop I' 

FiX caused by the magnetic moment M of the image TX' (which is equal to 

the magnetic moment of TX) is given by 
112 (14) 8 COAL, ROCK 

/ I ',AIL/ 0 // 0 /// 

I 

TUNNEL WALL 

h I -0P AIR 

I NOTE: The Image TX of the TX loop couples to the RX LOOP, 

and produces a signal which depends on the skin-depth 

6 of the rock or coal. 

Figure 1 

Crossed TX and RX Loops Near a Tunnel Wall 

Arthur DLittlelnc 
This expression is the vector sum of the free space static field 

components produced by the image loop which replaces the coal or 

rock medium in this method of analysis. 

The magnitude of this field is given by 

2 As an example, let M = 0.1 Am , h = 0.2 m, 6 - 2 m. Then IH I= 

-4 L 1.3 x 10 A/m. Since a field of 0.1 uA/m is easily detected by small 

receiving loops (supported by MF in-mine measurements of T. Cory) the 

signal-to-noise ratio should present no problem. 

It is possible, if the phase of the RX signal, relative to the TX 

current is measured as well as the amplitude, that the dielectric constant of the rock or coal can be determined in addition to the conductivity. This probably requires some amplification of the simple image 

theory used above. 

For sampling the tunnel side wall conductivity, this method is 

still plagued by the conflicting goals of wanting to sample deep 

within the coal pillar from outside it, while not sampling the nearby 

roof and floor material. Low interference from the roof and floor 

is achieved when the skin depth, 6, in the coal is small compared to 

the seam thickness. But then the method unfortunately samples only . 

the near-in coal material which may be non-representative if it has 

dried out somewhat and lost moisture after the mining has advanced 

significantly beyond this location. Sampling in the immediate face 

area may help to avoid this dried-out wall problem. When the skin 

depth is large, leading to deep penetration, the effects or' the roof 

and floor are introduced, and this "local" in-situ measurement starts 

to resemble more and more the propagation measurement technique 

that uses widely separated, independent transmit and receive loops. 

Arthur DLittle,lnc 
For sampling the roof and floor conductivity, the mine tunnel 

geometry may permit the method to be less influenced by the presence 

of coal than the sidewall measurements are influenced by the presence 

of the roof and floor materials. The dried out condition will still 

be present however, and in addition, the closeness of the roof to the 

floor may require both floor and roof images to be accounted for. 

Even though the above method and other available techniques may 

be of some merit for measuring the local in-situ values of coal and 

rock conductivity, the uncertainties and difficulties associated with - ----.-z-- .. them lead us to still conclude that a propagation measurement - that -- - - - 

spans a representative transmission path probably provides the most 

practical and useful "average" measures of coal and rock conductivity 

for MF portable radio applications in coal mines. However, we do 

agree that if meaningful, local, 

-- 

direct in-situ conductivity -. - - - .. -. - - - -- - - 

measurements can be easily and economically - - - -. Gde . with an available, P - small ______ 

hand-held instrument, this too would be a useful but not necessary 

way for checking the findings to date. We do not believe that a - -- 

special development effort to create such an instrument - - is warranted 

at this time. 

Arthur D Littlelnc 
VI. MODELLING AND DATA ANALYSIS OF IN-MINE ELECTROMAGNETIC WAVE 

PROPAGATION FROM 50 to 5000 kHz - Interim Report, December 1979. 

Arthur D Littleinc 
MODELING AND DATA ANALYSIS OF 

IN-MINE ELECTROMAGNETIC WAVE PROPAGATION 

FROM 50 - 5000 Mi-- 

Robert L. Lagace -- Task Leader 

Alfred G. Emslie, Michael A. Grossman 

INTERIM REPORT 

On 

Task Order No. 4 

Contact No. H0346045 

December 1979 

Arthur D. Little, Inc. 

Cambridge, Massachusetts 

Arthur D Little. lnc 
I. SUMMARY 

A. OBJECTIVE 

The objective of this work was to formulate simple theoretical 

models characterizing medium frequency (MF) radio wave propagation in 

underground room and pillar coal mines for the purpose of predicting 

maximum communication ranges between portable radios carried by key 

miners. This objective has been achieved and confirmed experimentally 

for conductor-free areas of coal mines. In areas where a conductor 

such as a power cable is present, applicable data must yet be taken 

before the propagation model for this case can be confirmed. 

This interim memorandum compares some theoretical results with 

experimental measurements made by T. Cory in a large number of mines 

located in various coal seams, and summarizes the findings and their 

implications for portable radio comunications between roving miners. 

B. PROPAGATION hT CONDUCTOR-FREE AREAS 

A three-layer propagation model with a transmission line formulation for the propagation constant was developed that is both practical 

and sufficiently accurate for the application and frequency band of 

interest. General analyses of radio wave propagation within multilayer stratified media can be found in the work of Wait and Gabillard. 

For the low, medium, and high frequencies of present interest (50 to 

5000 kHz), the mode of propagation takes the form of a parallel plane 

(0,O) TEM transmission-line type mode Gith the electric field vertical 

and the magnetic field horizontal within a planar coal seam bounded 

above and below by higher conductivity rock as shown in Figure 1. 

Higher modes at these frequencies are well beyond cutoff since the 

wavelength is much larger than the thickness of the coal seam. Coupling 

to this TEM mode is accomplished with loops, the antennas most favorable 

for this frequency band and application. 

Arthur D Littlelnc 
I Loop Images Q 

Rock - or 

FIGURE 1 THEORETICAL MODEL FOR A LOOP ANTENNA 

TRANSMITTING IN A COAL SEAM WAVEGUIDE 

Reflecting Plane --- ----------- 

T, LOOP& h I-D - r coal - o, e, 

Loop Images 

---.--- ---- ------ 

Reflecting Plane 

- -- 4 i Rock - or 

C9 

. P 
Comparison of theory and experiment for conductor-free areas allows 

one to determine the electrical conductivity both of the coal seam and 

of the bounding rock. The comparison also establishes the validity of 

the theoretical formulas for the coupling of the transmit loop to the 

propagating mode and for the mode attenuation rate as a function of 

frequency. These simple formulas allow predictions to be made of radio 

comunication range under various conditions of operating frequency, 

transmit magnetic moment, mine radio noise, seam thickness, and coal and 

rock conductivities. 

The results show that significant variations in attenuation rate 

occur between mines located in different coal seams. Of the seams 

examined, the Pittsburgh seam measured in northern West Virginia has 

the most favorable attenuation rate, the Herrin No. 6 seam in Illinois 

is the worst with an attenuation rate en order of magnitude higher 

than that of the Pittsburgh, while the other five seams measured in 

the Appalachian coal fields have moderate to high rates that fall 

between those of the Pittsburgh and the Herrin No. 6. 

Maximum radio communication range behavior versus frequency is 

shown to exhibit a broad peak centered between 300 and 700 kHz, a 

band well within the 200 to 1000 kHz frequency band over which the 

model is in extremely good agreement with the data. Within the optimum 

frequency band of 300 to 700 kHz, maximum ranges are found to be highly 

dependent on attenuation rate and thus on the electrical conductivities 

of the coal seam and its surrounding rock. Consequently, maximum 

communication ranges for portable, intrinisically safe radios can be 

expected to vary from low values of about 75 to 100 meters in a 

high-loss seam such as the Herrin No. 6, to high values of about 

300 to 400 meters in a low-loss seam such as the Pittsburgh. 

C. PROPAGATION IN THE PRESENCE OF A CONDUCTING CABLE 

The above remarks apply to conductor-free areas in coal mines. 

When a conductor, such as a power cable, is present in a coal mine 

tunnel, a different type of propagation mode exists which is essentially 

Arthur D Littlelnc 
a coaxial TEM transmission line mode with the cable acting as the center 

conductor and the coal and rock as the outer conductor. The electric 

and magnetic fields are approximately transverse to the cable and fall 

off exponentially with distance in the transverse plane. A properly 

oriented transmitting loop antenna, located not too far from the cable, 

can couple to this cable mode. The wave so generated travels along 

the cable with low attenuation, and can be picked up by a similarly 

oriented receiving loop which is also located not too far from the 

cable, thereby greatly extending portable radio co~mnunication range 

along the cable. A simple theory for this type of transmission is 

given, and is compared with some measurements made by T. Cory in coal 

mine areas containing conductors. There are discrepancies between 

theory and experiment, especially with regard to antenna orientation. 

More experimental data taken under carefully controlled conditions are 

needed to help resolve these discrepancies. 

Arthur D LittleInc 
11. PROPAGATION IN CONDUCTOR-FREE AREAS 

REDUCTION OF THE EXPERIMENTAL DATA 

The asymptotic form of the theoretical equation for the magnitude 

of the azimuthal component of the magnetic field H in the plane of the 0 

transmitting loop is given by 

where C is the coupling factor, and a is the attenuation constant. This 

simple asymptotic form of the field propagation equation gives a good 

approximation to the magnetic field for ranges greater than l/a. . 

The theoretical equation (1) predicts that if measurements of the 

magnetic field at various ranges from the transmitting loop are plotted in 

the form HG (in dB re luA/&) versus r, a straight line should be 

obtained. The data at 485 kHz for a quasi-conductor-free area in the 

Stinson No. 3 coal mine, shown in Figure 2, conform fairly well to the 

prediction. The straight line drawn through the experimental points 

gives the values a = 0.0381 m-' and C = 57.0 dB re lpA/& , ~XP ~XP 

derived from the slope and vertical intercept of the line respectively. 

It is to be noted that the first and last experimental points are 

above the straight line. This effect occurs repeatedly in the data 

from different mines at various frequencies. The explanation is that 

the first point is usually at a range where the asympototic form of the 

Hankel function is not a good approximation, and the last point is at 

a range where the noise level adds significantly to the received signal. 

For example, in the case of Figure 2, the first data point is taken 

at 20 m, which is within the distance defined by l/a - 26m. 

fXP 

In some mines, several points were found to lie above the straight 

line at ranges greater than about 100 meters. In these cases we concluded 

that the transmit antenna was also coupling to a low attenuation rate 

cable-guided mode supported by a cable located in an adjacent parallel 

tunnel. 

Arthur D Littlelnc 
100 

.80 

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

- 

- 

- 

Intercept = C = 57.0 dB re 1 p~lm% 

40 - 

- Slope = a = 0.0381 m- 

H r 

(dB re 1 PA/ 20 - 

mx) 

- 

0- 

- For: M = 2.5 A - m 2 

-20 

-40 

h = 1.37 m 

- - Derived from T. Cory Data 

- 

I I I I I I I I 

0 50 100 150 

Range in Meters 

FIGURE 2 DETERMINATION OF ATTENUATION RATE a AND COUPLING FACT

FROM STRAIGHT LINE FIT TO H-DATA PLOTTED VERSUS r 

FOR STINSON NO. 3 MINE AT 485 kHz 
The two derived experimental parameters a and Cexp, namely, the 

exp 

attenuation constant and the coupling factor, completely specify the field 

strength data taken along a traverse of a coal mine tunnel at a given 

frequency. The set of values of a and C for all the frequencies 

exp =P 

investigated represents a complete description of all the data taken in 

a particular tunnel. The conductor-free area data taken in all mines 

were reduced in this manner. 

B. ATTENUATION RATE VERSUS FREQUENCY 

Experimentally derived attenuation rates a plotted as a function 

exp 

of frequency are shown in Figure 3 for eleven coal mines located in seven 

seams in the Appalachian and Illinois coal fields. Examination of Figure 3 

reveals that the attenuation rates increase with increasing frequency as 

expected from theory, and that the mines sampled fall roughly into three 

classes with respect to attenuation rate--low, very high, and moderateto-high. The mines sampled in the Pittsburgh seam in northern West 

Virginia exhibit the lowest attenuation rates recorded. On the other 

hand, mines sampled in the Herrin No. 6 seam in southern Illinois exhibit 

prohibitively high attenuation rates from a radio communication standpoint. The attenuation rates of the mines sampled in the remaining 

five seams in Pennsylvania, West Virginia, Virginia, and Kentucky fall 

into a rather broad moderate-to-high category characterized by values 

which approach those of the Pittsburgh seam at low frequencies and those 

of the Herrin No. 6 seam at high frequencies. Unfortunately, it appears 

that the low Pittsburgh seam rates, which result in the longest communication ranges, may be the exception rather than the rule. The reason 

for this is not yet clear. 

C. DETERMINATION OF THE CONDUCTIVITIES 

Each a versus f curve contains enough information for the 

exp 

determination of the conductivities 0 and 0 by means of the transc r 

mission line formula. This is best accomplished by means of a least 

square fit of the real part, a theor' of the right-hand side of the 

transmission line formula to the experimental values a for the set of 

exp 

frequencies used, with 0 and 0 treated as adjustable parameters. In 

c r 

this procedure a constant average value E /E0 = 6 is assumed for the 

C 
FIGURE 3 EXPERIMENTAL AlTENUATlON RATES sXp VERSUS FREQUENCY 

FOR ELEVEN COAL MINES IN SEVEN COAL SEAMS 

8 Arthur D Little lnc , 
dielectric constant of the coal, since a is found to be very theor 

insensitive to E /E . The thickness h is taken to be the actual measured 

C 0 

value of coal-seam thickness. 

Figure 4 shows a comparison of the least square fit curve a with theor 

the experimental values a for the Stinson No. 3 mine. The optimum 

=pq5 fit occurs for o = 3.0 x 10 Mho/m. The root mean square difference 

C 

between atheor and a is = 0.0013 m-I which is about 2% of the 

exp 

value of a at 890 kHz. This close fit gives further justification theor 

for the use of the simple transmission-line equation and for the threelayer model on which the equation is based. The good fit also means 

that experimental determination of u at a number of frequencies can 

be viewed as an excellent nonintrusive method for obtaining the 

conductivities of both the coal and the rock. Figure 5 shows a plot of 

o versus o where each test location in each mine is characterized by c r 

its pair of u a values for all mines sampled. Figure 5 shows that c' r 

there is a rough correlation between oc and or and that or/ uc is 

about 100 on the average. The tendency of the two conductivities to 

vary together may be caused by a correlation in the water contents of 

the coal and adjacent rock layers. Decreases in mode attenuation rates 

occur as the coal and rock conductivity values move downward and to the 

right respectively in Figure 5. Based on the trends and clusterings shown 

in Figure 5, the following (u,, ) conductivity pairs were chosen to r 

represent low, moderate-to-high, and very high attenuation rate propagation 

conditions respectively; (2.5 x 8 x lo"?), (5 x 8 x 

and.2 x 1) in Mho/m 

D. COMPARISON OF THE THEORETICAL AND EXPERIMENTAL COUPLING FACTORS 

A comparison of the theoretical coupling factor, C theor with 

experimental coupling factor C exp provides an absolute test of the theory 

of the coal-seam mode. Figure 6 shows such a comparison for the Stinson 

No. 3 mine. It is seen that the agreement is quite good over the whole 

frequency range of 98 kI-z to 3710 Biz. 

The agreement between the experimental and theoretical values for 

the coupling factor was tested for all mines in seven frequency bands 

ranging from 83 kHz to 4570 kHz. The range of frequencies and number of 

runs in each of the seven bands is shown in Table I. The coupling factors 

for all mines were studied simultaneously, the only stratification being 
.14 I I I I I I I I I I I I I I I I I 

- 

0 Experiment-Derived from T. Cory ~ata(~) 

.12 - 

- 5 Theory for oc = 3.0 x 10' , or = 4.1 x loJ mholm 

Frequency in kHz 

FIGURE 4 LEAST SQUARE FIT a VERSUS f 

THEORETICAL CURVE TO a DATA 

FOR STINSON NO. 3 MINE 

0 Experiment-Derived from T. Cory ~ata(~) 

5 -Theory for a, = 3.0 x 10- , or = 4.1 x 10- 3 

h = 1.37111 

M = 2.5 A-m 2 0 

70 

Frequency in kHz 

FIGURE 6 COUPLING FACTOR, C, THEORETICAL CURVE AND EXPERIMENTAL 

DATA VERSUS f FOR STINSON NO. 3 MINE 
the seven frequency bands. Therefore, the results of the analysis within 

each band are applicable to all mines examined. 

TABLE I 

FREQUENCY RANGES USED FOR 

EXPERIMENTAL MEASUREMENTS 

Band No. 

Frequency 

Range (kHz) 

83 - 115 

218 - 252 

335 - 350 

420 - 495 

880 - 1047 

1750 - 2030 

2720 - 4570 

No. of 

Runs 

12 

17 

4 

14 

15 

13 

12 

The difference, AC = Ctheor - C between theoretical and 

exp' 

experimental values for the coupling factor expressed in dB was calculated 

for all available measurements. These differences were then tested 

statistically using a one-sample t-test for each of the seven frequency 

bands to assess the goodness of fit of the model to the data. In bands 

2 through 5 there is a mean difference of less than +1 dB between the 

three-layer model and the experimental data, and the variance of the 

mean is less than 1.3 dB within these bands. 

The one-sample t-test used to statistically test the hypothesis that 

the model fits the data within each frequency band showed that this 

hypothesis cannot be rejected at the .05 level for bands 2 through 5. 

(This is equivalent to a 95% confidence interval for the mean i? containing 

the origin, i.e., the mean difference can be zero.) Based on this series 

of tests, the less than +1 dB mean difference between theoretical and 

experimental coupling factors and the very small variance of the mean 

difference, we conclude that the three-layer model fits the data extremely 

well between the frequency ranges of 218 kHz and 1047 kHz. Outside this 
range, the model either does not fit the data, or the large variability 

in the data may be hiding a significant mean difference; i.e., the large 

positive and negative errors may be fortuitously canceling each other 

out in band 7. 

E. EFFECT OF SEAM THICKNESS ON THE ATTENUATION RATE AND THE COUPLING 

FACTOR 

The attenuation coefficient a and the coupling factor C depend on 

the seam height h as well as on the conductivities of the coal and rock. 

Figures 7 and 8 show a versus f and C versus f curves, respectively, . . . . - . . - - - -. . . . . -. . - . - . - - . - -- - - .. . . - 

calculated from theoretical equations.for chree values of h, for constant -. .- . .. . - -- . . - - .- - - . . . -A- - . . - - . . - - . . . - - . . - 

values o = 5 x lo-' Mho/m and or = 8 x Mho/m of the conductivities. C 

These conductivities are representative of several moderately high loss 

mines, as seen by the clustering of points around this pair of values in 

Figure 5. 

It is seen in Figure 7 that a, at any given frequency, depends 

strongly on h. At 2000 kHz, for example, a is about twice as large for 

a low-coal mine with h = 1 m as for a high-coal mine with h = 3 m. This, 

by itself, means that the range of communication would be much greater 

for the high-coal seam. 

Figure 8 shows, on the other hand, that C, although greater for a 

low-coal than for a high-coal mine, changes quite slowly with h. The 

gain in coupling factor for the low-coal mine, however, by no means offsets 

the larger loss in signal strength caused by the increase in a . Thus 

MF radio communication will be more favorable in high-coal 

than in low-coal seam waveguides having the same electrical properties. 

F. MAXIMUM COMMUNICATION RANGE AND OPTIMUM FREQUENCY 

The parameter of greatest predictive interest is the maximum 

theoretical communication range r at a given frequency, determined by m ' 

the signal propagation loss and the noise level at the receiver. We consider 

the following two cases: 

C 

(dB re 1 p~/m%) 

5 For o, = 5 x 10- mholm 

3 or = 8 x 10- mho/m 

E~=~E~ 

100- I I I I I I I I I I I I I I 1 I I I I I I 

- 

90 - h = 1 Meter 

- 

80 - 

- 

70 - 

FIGURE 8 THEORETICAL COUPLING FACTOR, C, VERSUS FREQUENCY CUR

WITH SEAM THICKNESS, h, AS A PARAMETER 

20 

10 

- 

- 

- b 

I I I I I I I I I I I I I I I I I I I I I I 

0 1000 2000 3000 4000 

Frequency in kHz 
for the equivalent magnetic field rms noise level N in dB re 1 uA/m, 

for a receiver having a noise figure of 6 dB, bandwidth of 12 kHz, and 

- 

Z loop antenna turns area of 1 m . f is the frequency in kHz. 

(2) limitation by average mine noise, given by the formula 

f < N = 34 - 20Log(=), for 10 kHz = f 1000 kHz 

(17) 

f N = -6 - 15Log(rn), for 1000 kHz f 6 10,000 kHz 

with N representing the "average" rms mine noise level in dB re 

1 uA/m. This representation of mine noise level is based on data taken 

in mines by the National Bureau of Standards and consolidated by 

Arthur D. Little, Inc. 

In each case we define a maximum range as that range where the 

signal-to-noise ratio decreases to 10 dB. Thus 

H(rmax ) = 10 + N in dB re 1 dm (19) 

For an FM system, a 10 dB average rms carrier-to-noise ratio gives a 

Circuit Merit Figure 3 radio service performance level (occasional 

message repetition required). 

Figures 9 and 10 show values of r versus f for seam heights of 

max 

2 m (high coal) and 1 m (low coal), respectively, when performance is 

limited by receiver noise. The values were calculated for three 

representative pairs of coal and rock conductivities. These pairs 

represent the Pittsburgh Seam (o = 2.5 x 

or 

-2 = 8 x 10 Mho/m), 

-3 and the Herrin No. 6 Seam (o = 2 x 10 , or = 1.0 Mho/m), which are 

low- and high-loss extremes, respectively, and a seam of intermediate 

-5 loss characteristics (o = 5 x 10 , or = 8 x Mho/m) like the - 

Pocahontas No. 3 and lower Kittaning seams. 

Arthur D Littlelnc 

rmax 

(Meters) 

FIGURE 10 THEORETICAL MAXIMUM RANGE ESTIMATES (r,) VERSUS FREQUENC

UNDER RECEIVER NOISE CONDITIONS IN COAL FOR THREE 

REPRESENTATIVE SEAMS 
It is seen that in all six cases r rises fairly rapidly with frequency max 

to a maximum and then declines more slowly. The figure indicates that 

a frequency range of 400 to 500 kHz is optimum for the three types of 

seam taken together. Figures 11 and 12 show values of r when 

max 

performance is limited by mine noise in high and low coal respectively. 

The maximum range is reduced and the optimum frequency range is 

increased slightly to 600 to 700 kHz. 

The values of predicted maximum communications range shown in 

Figures 9 to 12 are also in good agreement with those derived by T. Cory 

for specific mines, based on measured values of signal magnetic field 

strength and independent estimates of receiver noise and mine noise 

conditions. Figures 9 through 12 taken together, suggest that the optimum 

frequency for all types of seams, for both kinds of noise, and for 

both seam heights, is about 500 kHz. It is indeed fortuitous that 

this frequency lies near the center of the frequency band of 200 - 

1000 kHz for which the theory is in best agreement with experiment. 

Arthur D Little Inc 
rmax 300 

(Meters) 

100 1000 

Frequency in kHz 

I I 1 1 11 111 I I I I1 101 I I I I 

- 5 2 

A - oc = 2 x 10- , or = 8 x 10- mholm - "Pittsburgh Seam" 

5 3 B - oc = 5 x 10- , or = 8 x 10- mholm - "Pocahontas No. 3 and Lower Kittaning Seams" - 3 

C - oc = 2 x 10- , or = 1 mholm "Herrin No. 6 Seam" 

- For h = 2 Meters 

M = 2.5 A-m 2 

- 

- 

- 

- 

- 

- 

- 

- 

- 

- 

I I 

FIGURE 11 THEORETICAL MAXIMUM RANGE ESTIMATES (rmax) VERSUS 

FREQUENCY UNDER "AVERAGE" MINE NOISE CONDITIONS IN 

HIGH COAL FOR THREE REPRESENTATIVE SEAMS - 
rmax 

(Meters) 

FIGURE 12 THEORETICAL MAXIMUM RANGE ESTIMATES (rma,) VERSUS FREQUE

UNDER "AVERAGE" MINE NOISE CONDITIONS IN LOW COAL FOR THR

- 

REPRESENTATIVE SEAMS 

300 

200 

100 

0 

10 

I I I 111111 I I I I IIII I I I I 

- 5 A - o, = 2 x 10- , a, = 8 x mholm - "Pittsburgh Seam" 

- 3 B - oc = 5 x 1w5, or = 8 x 10' mho/rn - "Pocahontas No. 3 and Lower Kittaning Seams" 

3 

C - o, = 2 x 10- , or = 1.0 mholm - "Herrin No. 6 Seam" 

- For h = 1 Meter 

M = 2.5 A-m 2 - 

- 

- 

- 

- 

- '\ 

- 

- 

.

- 

, 

0' 

- #' 

0'. 

C 

I I I Ill I I I 11 1111 I I I I 

100 1000 

Frequency in kHz 
CAMBRIDGE, 

MASSACHUSETTS 

SAN FRANCISCO 

WASHINGTON 

ATHENS 

BRUSSELS 

LONDON 

PARIS 

RIO DE JANFRO 

TORONTO 

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