UNITED STATES DEPARTMENT OF THE INTERIOR 

William P. Clark, Secretary 

BUREAU OF MINES 

Robert C. Horton, Director 
Library of Congress Cataloging in Publication Data: 

Durkin, John 

Vertical magnetic noise in the voice frequency band within and 

above coal mines. 

(Report of investigations ; 8828) 

Bibliography: p. 21-22. 

Supt. of Docs. no.: I 28.23:8828. 

1. Coal mines and mining-Communication systems. 2. Electromagnetic noise. 3. Voice frequency. I. Title. 11. Series: Report of investigations (United States. Bureau of Mines) ; 8828. 

TN23.U43 [TN344] 622s [622] 83-600 164 
CONTENTS 

Page 

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

Introduction ................................................................. 2 

EM atmospheric noise ........................................................... 2 

Noise source ................................................................. 2 

Earth-ionosphere waveguide ................................................... 5 

Prior atmospheric noise measurements ......................................... 8 

Surface vertical magnetic noise .......................................... 9 

Underground vertical magnetic noise ...................................... 11 

EM vertical magnetic noise field tests ......................................... 12 

Noise measuring instrumentation .............................................. 12 

Noise data ................................................................... 14 

Data analysis ................................................................ 16 

Sumry ........................................................................ 21 

bferences ..................................................................... 21 

Appendix A*-- Abbreviations and symbols used in this report ..................... 23 

Appendix B.--Instrumentation noise ............................................. 24 

Appendix C.--Mine identification ............................................... 27 

ILLUSTRATIONS 

1 . Vertical electric dipole on surface of a perfectly conducting earth ...... 3 

2 . Expected vertical-moment time variation for main cloud-to-ground 

discharge ............................................................... 4 

3 . Expected frequency spectrum of radiation component of electric field. .... 5 

4 . Directionality diagram of average number of atmospherics occurring in 

1 day ................................................................... 5 

Propagation attenuation coefficient of earth-ionosphere waveguide ........ 7 

Relative vertical electric noise field spectrum .......................... 8 

Typical vertical electric field noise measurements ....................... 9 

Coordinate system and earth conductivity model ........................... 10 

Geometry of homogeneous half-space earth model with thin conducting sheet 12 

Field test recording instrumentation .................................... 13 

Playback instrumentation ................................................. 14 

Surface and underground mean vertical magnetic noise values from noise 

data .................................................................... 17 

13 . Regression results for surface and underground vertical magnetic noise 

versus frequency ........................................................ 19 

B-1 . Noise-equivalent model of receiver .................................... 24 

TABLES 

1 . Surface and underground vertical magnetic noise values obtained at different sites ............................................................ 15 

2 . Surface and underground vertical magnetic noise mean and standard deviation values ........................................................... 16 

3 . Regression results for vertical magnetic noise ........................... 18 

4 . Expected vertical magnetic noise values for one-third octaves ............ 20 

C-1 . Mines fromwhich magnetic noise measurements were obtained ............... 27 
A/m 

dB 

dB/Mm 

F/m 

f t 

h 

Hz 

in 

J/K 

K 

kHz 

UNIT OF MEASURE ABBREVIATIONS 

ampere 

ampere meter 

ampere per meter 

decibel 

decibel per megameter 

farad per meter 

foot 

hour 

hertz 

inch 

j oule per kelvin 

kelvin 

kilohertz 

kilometer 

USED IN THIS REPORT 

m meter 

m2 square meter 

PA microampere 

MHz megahertz 

Mm megame ter 

m/s meter per second 

Us microsecond 

PV m microvolt meter 

Pet percent 

n ohm 

rad/s radian per second 

s second 

v/m volt per meter 
VERTICAL MAGNETIC NOISE IN THE VOICE FREQUENCY BAND 

WITHIN AND ABOVE COAL MINES 

By John Durkin 

ABSTRACT 

Information on vertical magnetic noise in the voice frequency band, 

both within and above coal mines, is needed for the evaluation of 

through-the-earth baseband electromagnetic communications at mines 

where horizontal loop antennas are used. This report discusses the 

theory of the source of electromagnetic noise, the propagation of this 

noise to an observation point above a mine, and its interaction with 

the local earth conductivity structure, which gives rise to vertical 

magnetic noise. The relationship of surface noise to underground noise 

is also discussed. 

Bureau of Mines investigators made surface and underground vertical 

magnetic noise measurements at a number of coal mines located throughout the United States. These data were modeled through regression 

analysis to characterize expected noise levels. The results are presented, including results in one-third octaves for use in evaluating 

the expected performance of through-the-earth communication systems by 

articulation-index studies. 

l ~lectrical engineer, ~ittsburgh Research Center, Bureau of Mines, Pittsburgh, PA. 
INTRODUCTION 

The performance of through-the-earth 

(TTE) communication systems is limited by 

noise, which degrades the intelligibility 

of voice reception and causes errors in 

digital data communication. Noise is an 

additive disturbance whose effects can be 

reduced by increasing the signal power, 

by proper signal design, or by signal 

processing. TTE communication systems 

are affected by three basic types of 

noise: instrumentation, atmospheric, and 

manmade. Thermal noise, generated by resistance in the antenna and front-end 

circuits, determines the receiver's ultimate sensitivity. (A discussion of instrumentation noise and its influence on 

electromagnetic (EM) noise measurements 

when using an air-core loop antenna is 

given in appendix Be) Atmospheric noise 

is a natural occurrence caused by lightning strokes which radiate EM impulses 

that propagate great distances. Manmade 

noise is usually caused by power lines 

and can severely limit the performance of 

a TTE communication system. 

Instrumentation, atmospheric, and manmade noise all have different characteristics. The average power of thermal 

noise is fairly constant, whereas atmospheric and manmade noise may vary considerably with time and frequency. The 

probability density distribution of thermal noise is typically Gaussian, whereas 

atmospheric noise contains intermittent 

impulses superimposed on a Gaussian noise 

background. The characteristics of manmade noise vary considerably, but the observed spectrum usually contains several 

discrete frequency components with varying amplitudes. Manmade noise is a 

continuous-wave (CW) interference that 

generally occurs at 60 Hz and at various 

harmonics of 60 Hz extending to several 

kilohertz. 

In order to design a communication system and predict its performance, several 

basic pieces of information about existing noise must be known. The most important aspects are the level of and variation in noise amplitude in the short and 

long term. For example, the amplitude of 

atmospheric noise varies both hourly and 

seasonally. However, before amplitude 

measurements are considered, the type of 

measurement that will extract significant 

and useful information from the noise 

phenomena must be determined. For this 

purpose, the frequency of interest and 

the associated bandwidth of the communication system must be known. Where measurement of broadband noise is required 

for predicting communication system perf ormance , the root-mean-square (RMS) 

noise value is the most useful single 

measurement. This has long been recognized, as shown by the International Radio Consultative Commit tee (CCIR) (8) - . Amplitude variation over the frequency 

band of interest also presents valuable 

information. Depending upon the nature 

of its application, amplitude variation 

information may be in the form of spectral density or it may be broken into a 

number of bands such as one-third octaves. One value of spectral density information is that manmade noise contributions can be easily discerned. Also, 

since TTE communications may be two way, 

both uplink and downlink, information on 

the expected levels and relationships of 

both surface and underground noise must 

be obtained; and spectral density data 

provides this information. 

EM ATMOSPHERIC NOISE 

NOISE SOURCE distant storms from which the EM noise 

propagates in the earth-ionosphere 

The primary source of EM noise in the waveguide. 

extremely low frequency (ELF) through the 

very low frequency (VLF) range can be *underlined numbers in parentheses reattributed to lightning discharges from fer to items in the list of references 

both local thunderstorm activity and preceding the appendixes. 
A lightning stroke consists of three 

main sections--the predischarge, main 

discharge, and slow tail--each of which 

produces energy in a different frequency 

range (15). The predischarge consists of 

a seriz of leaders of very short duration and produces energy in the 30 to 100 

kHz range. This is followed by the main 

discharge, which lasts approximately 100 

PS and produces energy in the 30 to 1,000 

kHz frequency range. The main discharge 

is followed by the slow tail, which lasts 

up to 1/2 s and produces energy below 

1,000 Hz. 

At a distance (d) from a lightning 

stroke, the received noise record (N) is 

controlled both by the source waveform 

(S) and the characteristics of the channel (W) in which the noise propagates. 

In general, the spectral component (f) of 

the noise can be written as 

The signal generated by a lightning 

stroke can be considered to be produced 

by many dipole radiators of different dimensions at the source location. Wait 

(20) has characterized the lightning 

stroke as a single vertical electric dipole source. A vertical electric dipole 

on the surface of a perfectly conducting 

flat earth (fig. 1) produces both electric and magnetic fields. If the current 

along the dipole of effective height (he) 

is assumed to be uniform, the resulting 

RMS electric and magnetic fields are 

Ih 

and Hm -2 27T ($-$), 

where Ez = RMS vertical electric field, 

V/m, 

Hg = RMS tangential magnetic 

field, A/m, 

c0 = permittivity of free space, 

F/m, 

FIGURE 1. - Vertical electric dipole on surface of 

a perfectly conducting earth. (See text and appendix 

A for identification of symbols.) 

d = distance between observation 

point and antenna (and is 

assumed to be large compared to he), 

c = velocity of light, m/s, 

w = frequency, rad/s, 

and i = imaginary number. 

The term in equation 2 associated with 

d3 is the electrostatic field. An electrostatic field is present if the dipole 

consists only of separated stationary 

charges. This can be seen from equation 

2, where the electrostatic term is proportional to the time integral of current, i.e., qahe, where q = charge. The 

induction field is directly proportional 

toI*h,. The radiation term (i.e., 

dI/dtmhe, where t = time), results only 

from a change in current and is directly 

proportional to the current differential. 

During an actual lightning stroke, both 

I and he are functions of time. The current flow in the dipole source creates a 

t ime-variable charge moment of 

I = antenna current, A, 
I where M(t) is the changing vertical electric moment in amperes per meter. 

In most atomspheric noise studies, the 

radiation field is of most interest. The 

electric and magnetic radiation fields 

can be written in terms of the charge 

moment as 

4 1 I I I I I I I 2.0 

0 20 40 60 80 100 120 140 160 180 

TIME, ps 

1 and H+) = - 1 dM(t)/dt. 2n cd (6) 

FIGURE 2. - Expected vertical-moment time 

variation for main c loud-to-ground discharge (23). 

E,/H$ = 377 Q, the free-space wave impedance (1. When equations 5 and 6 are 

used to determine variations in electric 

and magnetic fields, the retarded values 

of M(t) at time (t - d/c) should be used 

in order to account for propagation delay. If the radiation field terms are to 

be measured, the observation point must 

be far enough from the source that the 

electrostatic and induction fields will 

be negligible. At d = X/2r, where X = 

wavelength, the induction and radiation 

terms are equal. Beyond one wavelength, 

both the electric and magnetic fields decay as l/d. Thus, beyond 50 km, the far 

field term dominates for frequencies exceeding 1 kHz. 

are shown in figure 2. The source radiation spectrum can be determined by 

obtaining the Fourier transformation of 

the dM/dt curve from 

- i ut 

S(o) = d.M/dt*exp dt, 

where -r is the duration of the waveform. 

Watt (23) has calculated this Fourier 

transfoGation and the results are shown 

in figure 3. Since dM/dt may vary appreciably, the actual spectrum of any particular cloud-to-ground discharge may 

also vary appreciably. However, the 

spectrum shown in figure 3 can be considered to be the expected noise source 

spectrum for S from equation 1. 

Based on the assumptions presented 

above, the magnitudes of the fields can 

be expected to exhibit an inverse distance dependence. This has been shown 

experimentally by Bradley (7) - for distances from 20 to 200 km. At very short 

distances (d < 20 km), d is comparable to 

the length of the discharge, which then 

does not behave as a dipole source. At 

great distances (d > 200 km), the ionospheric influence becomes appreciable. 

The heights of discharge paths differ 

appreciably, giving rise to large variability in the-electric moment. Watt (23) 

shows typical time behavior curves zr 

the main cloud-to-ground discharge of the 

effective vertical moment and its differI ential and integral forms. These curves 

The direction of arrival of distant 

storms (the source of most EM noise energy) is also discussed by Watt (23). - Figure 4 shows the average number of atmospherics occurring in a 24-h period, based 

on data gathered over 4 days in October 

and plotted as a function of direction of 

arrival. Most noise sources are located 

in one of three azimuth sectors; these 

are Africa, South America, and Indonesia. 

At given observation point, the amplitude 

of the noise and the direction of its arrival are found to coincide with the time 

of day of the buildup of thunderstorm activity in one of these sectors. Local 

storms, which are finite in number, produce an impulsive form at the observation 

point. 
and ionosphere waveguide. How this waveguide influences the transmission of EM 

energy from distant storms has been studied by a number of investigators. A key 

exposition of this propagation mechanism 

was published by Wait (20). Wait pointed 

out that the earth andTonosphere act as 

a waveguide wherein radio energy propagates. Rappert (18) outlined a general 

theory of the propagation of ELF waves in 

H the waveguide. Propagation occurs with a 

vertical electric field accompanied by a 

horizontal magnetic field. This mode of 

propagation is approximated by transverse 

KEY 1800 electromagnetic (TEM) mode propagation 

N Averoge number of atmospherics between parallel conducting plates. Howoccurring in .I day ever, energy losses in both the earth and 

the ionosphere cause bending or "tilt" of FIGURE 4. - Directional ity diagram of average wave rant toward the lossy medium, 

number of atmospherics occurring in 1 day (B). and consequently, a horizontal electric 
field is generated at the surface of the source and observer. The exponential 

earth. The interaction of EM waves with term of equation 11 can be written as 

the earth is the basis of the study of 

magnetolellurics. exp (-i2nSnd/A) = exp (-a, - iB,)d, (12) 

The radiated electric field shown in where a,, the mode decay factor, is equal 

equation 5 can be rewritten in a more 2n f to - Im(S,), common form when the source current is c 

considered in the form of I exp (iot) and 

the propagation delay times appear as in which Im = imaginary part; 

phase shifts of the form 

and where B,, the waveguide wave number, 

- i kd 

rl exp Eo = i - Ih, - 9 

A d 

21T f (8) is equal to-Re(S,), 

C 

where k = wave number. in which Re = real part. 

Following Wait's work, the vertical The units of a, are nepers per unit of 

electric and horizontal magnetic fields distance. If the unit of distance chosen 

from a distant lightning stroke can be is 1,000 km (1 Mm) then the attenuation 

found from can be expressed in decibels per megameter as 

Ez = W Eo (9) 

- 

a, = (20 LOGloe) a, (13) 

and Hg = T Eo/n, (10) 

exp [i(2nd/X - n/4)]. 

In these equations, X = wavelength, km, 

a = Earth's radius, km, 

6, = mode excitation factor (60"112; 

6,"l, where n = 1, 2, 3...), 

h = height of the ionosphere (70 to 

90 km) , 

S, is obtained from the roots of a modal resonance equation. At ELF, and in 

many cases at VLF, the flat earth form of 

the equation 

RgRi exp [-2kh(l -sn2] '/*I - 1 = 0 (15) 

is applicable. % and Ri are the planar 

complex reflection coefficients of the 

ground and ionosphere, respectively. 

- 

Barr (4) has computed the variation of 

a, with Frequency for a realistic daytime 

ionosphere model. The results showed 

that for equal mode excitation factors, 

only the zero-order mode is significant 

in the ELF and lower VLF bands. Results 

for north-to-south propagation are shown 

in figure 5. 

and S, = complex parameter of mode n. Experimental propagation studies have 

shown the earth-ionosphere waveguide to 

The terms W and T above represent the be anisotropic due to the earth's magnetelectric and magnetic transfer functions ic field. The greatest effect of the 

of the waveguide. Also, it is assumed waveguide on propagation is at frequenthat kd >> 1. The distance d should now cies ranging from 1 to 4 kHz. For eastbe considered the arc length between the to-west propagation, the attenuation in 
loo, I I I 11 111 I I 111111 I I 111111 I I I I1111 I I 111111 

- - - - - - - KEY - - - --_- Calculated values - - Range of measured - @ fieid values - 

E 

a0r - 

- \ - - 1 - 

- 

/r - 

- 

z - 

3 

Z 

W 

L ': - - 

a - - 

- - - - - - - 

- - 

- - 

l 1 I I111111 I I 1111111 I 1 111111 

10-I 10' lo2 lo3 lo4 lo5 

FREQUENCY, Hz 

FIGURE 5. - Propagation attenuation coefficient of earth-ionosphere waveguide. 

this frequency range is as much as 20 dB V Ihe -aod 

lower than the north-to-south curve of lEl = h[Xa sin(d/a) ll2 A oexP (16) 

figure 5, while west-to-east propagation 

is as mch as 30 dB greater than this where the factors 6, and So have been 

curve. collected in a mode excitation factor A,. 

Also shown in figure 5 is the range of 

coefficient values for propagation attenuation measured by different inves tigators. Below 10 kHz, the values are based 

on lightning spheric measurements by Jean 

(13), and Chapman (9) and on cavity resonance measurements Xy Balser (3). (Resonance effects are not shown.7 Above 10 

kHz, the values are based on work by 

Considering the noise-source spectrum 

shown in figure 3, the relative expected 

vertical electric noise field spectrum, 

at a given observation point, would appear as shown in figure 6. Plotted in 

figure 6 are the relative spectra of the 

electric field as measured at different 

distances from the source. The null in 

the noise spectras appearing in the 2- to 

Eckersly (10) and Pierce (17). Barr's 3-kHz range is aligned with the peak of 

theoreticalfrequency dependence of the the channel attenuation spectrum of figattenuation of the earth-to-inosophere ure 5 and is consistent with the observawaveguide (5) agrees well with the tions of many studies. 

measurements. 

The observed magnetic noise spectra 

The magnitude of the electric field for would be much like that of the electric 

the zero mode in the far zone can be spectra, but its amplitude would be 

written as smaller (1 to 3 dB) than the magnetic 
100 - 

90 - 

80 - 

Distance from 

FIGURE 6. - Relative vertical electric noise field spectrum. 

field calculated from the free space 

electric and magnetic wave impedance relationship. A smaller amplitude would 

be expected because of an increase in the 

wave impedance below 10 kHz. This increase is caused by waveguide attenuation 

and a phase velocity exceeding the speed 

of light above 1 kHz and below 10 kHz. 

PRIOR ATMOSPHERIC NOISE MEASUREMENTS 

For TTE communications, the range of 

frequencies of interest is approximately 

200 Hz to 6 kHz. Thus both the ELF and 

VLF bands are included. Also, since communication may be uplink and downlink, 

both surface and subsurface noise must be 

considered, While atmospheric noise data 

are readily available for the frequency 

band between 10 kHz and 32 MHz, relatively few reported atmospheric noise measurements have been made below 10 kHz. 

For TTE communication between horizontal 

loops, the subject of this study, the interfering noise component comes from the 

vertical magnetic noise. However, of the 

few noise studies that have been done for 

frequencies below 10 kHz, most have been 

concerned with the vertical electric 

field strength because of their applicability to surface-based, long-range radio 

communications. 

Possibly the best reference on atmospheric radio noise is CCIR Report 322 

(8). This report contains worldwide contour maps of atmospheric noise levels at 

1 MHz for 4-h intervals for 3lnonth periods. With each map, curves of frequency 

dependence are given, but the lower limit 

of each curve is 10 kHz. Thus the results are not directly useful for baseband communications. 

During the 1960's and the 19701s, because of the interest in long-distance 

communications to submarines, some atmospheric noise measurements were made in 

the ELF range. A special issue of the 

Institute of Electrical and Electronics 

Engineers (IEEE) "IEEE Transactions on 

Communications," (21), was devoted to ELF 

communications and-pro j ect Sanguine and 

contains several references to ELF noise. 

Soderberg (19) gives an extensive bibliography on ELF noise and lists presently 

active ground stations with capability 

for measuring ELF noise. 

field strength or the horizontal magnetic 
Vertical electric noise measurements 

were made over the frequency range of 1 

Hz to 100 kHz by Maxwell and Stone (15). 

Some of their results are shown in figure 

7 and are consistent in form with the 

theoretical curves shown in figure 6. 

Maxwell (14) made vertical electric atmospheric Gise field measurements over 

a 2-year period at a number of worldwide 

locations for the frequency range of 20 

Hz to 30 kHz. Average field measurements 

were obtained and amplitude probability 

distributions of the vertical electric 

field were derived. The amplitude probability distributions were also used to 

convert the average measurements to RMS 

values. 

The National Bureau of Standards (NBS) 

made wideband noise measurements both 

within and above numerous coal mines (5- 

- 6). Most of these measurements were maxe 

while the mines were operating, and manmade 60-Hz harmonic noise was generally 

dominant. For rescue TTE communications, 

the mine power would be off, except for 

ventilation, therefore manmade noise 

should not be a factor. The main interf erence would be expected to come from 

atmospheric noise caused by worldwide 

thunderstorm activity. 

Most published data of ELF or VLF atmospheric noise are either of the vertical electric field or the horizontal magnetic field because they are the dominant 

components of both the TEM and the firstorder transverse magnetic (TM) modes in 

the earth-ionosphere waveguide. However, 

for loop-to-loop TTE communications, vertical magnetic noise is the source of 

interference. 

SURFACE VERTICAL MAGNETIC NOISE 

In most applications of EM communications, the vertical electric field 

is used, owing to the propagation characteristic of the earth-ionosphere waveguide. Therefore, noise measurements 

were made of the vertical electric field 

and/or horizontal magnetic field. When 

only one of these two fields was measured, the other was assumed to be related by the free space impedance (377 

521, which would be in slight error as 

previously discussed. 

NBS (1) measured both horizontal and 

vertical magnetic noise in a remote area 

of Utah with no power lines in the vicinity. The vertical component tended 

to be 10 to 15 dB below the horizontal 

FREQUENCY, Hz 

FIGURE 7. - Typical vertical electric field noise measurements (15). 
komponent, which is consistent with ear1 ier dip-angle measurements by Ward (22). I - 

In geophysical prospecting, the magnetotelluric method is often used for locating underground ore bodies (26). This 

method uses the EM freld from a thunderstorm to obtain information on the localized conductivity structure. This source 

field, as previously discussed, has a 

vertical electric field and a horizontal 

magnetic field. Over a homogeneous conducting earth, such an orientation would 

not produce a secondary field with a vertical magnetic field. Where a noise measurement is to be made, it is informative 

to study how the noise field from a distant storm may interact with the local 

earth conductivity structure to produce 

secondary fields that may give rise to a 

vertical magnetic component. 

In the following discussion, it is assumed that at a given observation point 

the horizontal magnetic field is generated by independent distant thunderstorms 

(K) and that a given source (Hi) is located at azimuth angle $ie Using a rectangular coordinate system, the horizontal magnetic field components can be 

resolved into x and y components as 

Hx = - C Hi sin qi i (17) 

The geometry of the situation is shown 

in figure 8. The tangential field components are continuous and, for the frequencies of interest, displacement 

currents can be neglected and the propagation constants (y) in the air and earth 

respectively become 

1 and Y 1 = (iwv0ol )I/z, (20) 

1 where IYOI<<IYI I 

1 Because of the relationship between the 

( propagation constants , the direction of 1 the wave at z = 0 into the earth can be 

( approximated as parallel to the z-axis. 

EM plane waves 

Po* €0 

z =o 

//// //////// 

Pa* 6 

0; ob~*z) 

FIGURE 8. - Coordinate system and earth conductivity model. 

This approximation allows the view that 

the incident field is also parallel to 

the z-axis in the limit as z + 0. The 

primary H-field at the surface (Hp) can 

then be given as 

and 

Hp(z) = Hp exp -Yp 

The total H-field in the region above the 

earth is then a linear combination of the 

primary field and secondary field (H,) 

caused by the conductivity structure of 

the earth and is given as 

where r is some fixed location. 

The secondary field in the earth can be 

related to the surface primary field (24) - 

by 

where 1 

in which m + x, y, z, 
Rmni + surface reflection coefficients from z > o side, 

- and i = i + 7 - E 

Yx i YY i Yzi. 

At the surface, for z = o, 

Therefore, the contribution to the total 

surface horizontal magnetic field is 

based upon R, -1 For the situation 

of a homogeneous earth, the primary 

H-field encounters no variation in the 

propagation medium for z > 0; and thus 

Rmni = -1, and no secondary magnetic 

fields exist . Likewise, for a onedimensional earth with 01 = a1 (z), 

Km,(0) = 0 for all m, n. For a threedimensional earth, al = al(x, y, z); 

there can be reflected secondary waves at 

any angle, and a vertical H-field is created. In this case, K,,,, can be treated 

as a random variable having any value. 

Not only does this information show how 

a vertical magnetic field can be created, 

it also shows that the magnitude relationship between the horizontal and vertical fields is not clearly defined. In 

the literature, it is often stated that 

the vertical magnetic field is smaller 

than the horizontal field, but there is 

no guarantee of this. For example, as 

was shown in the "Noise Source" section, 

there appear to be three primary azimuth 

sectors in which most atmospherics occur 

(fig. 4). It is conceivable that the 

horizontal magnetic noise measurement 

could be aligned so as to minimize the 

response to these noise sources while the 

localized conductivity structure could 

give rise to large vertical fields. 

Hill (12) has - shown how a vertical magnetic noise field can be generated by 

three simple earth models. Hill derived 

equations for the vertical magnetic noise 

field for (1) a conducting earth model in* 

which the earth is homogeneous but the 

air-earth interface is slightly rough, 

(2) an earth model consisting of a thin, 

laterally inhomogeneous conducting sheet 

at an arbitrary depth in an otherwise 

homogeneous half-space, and (3) a homogeneous earth model containing an infinitely long conducting cylinder representative of manmade object such as a wire, 

rail, or pipe or a natural object such as 

a long ore body. Hill's studies of each 

of these models showed how the vertical 

magnetic noise field is created and for 

particular parametric values showed the 

behavior of the field both in space and 

frequency . 

UNDERGROUND VERTICAL MAGNETIC NOISE 

Since downlink communication is impaired by underground EM noise, an understanding of the expected noise levels below the earth's surface must be obtained 

in order to evaluate TTE communications. 

Also, since the assumed method of comrnunications is between horizontal loop antennas lying flat on the ground, vertical 

magnetic noise is the component of 

interest. 

It can be assumed that during a mine 

emergency condition, the primary source 

of underground noise will be from the 

surface noise field. As previously discussed, due to the relative values of the 

propagation constants above and within 

the earth, the noise wave tends to propagate perpendicularly into the earth. 

Therefore, for a homogeneous earth, no 

underground vertical magnetic noise field 

would be expected; and as was the case 

for the surface, a vertical magnetic 

noise would occur underground only in the 

presence of spatial earth conductivity 

variations. 

An interesting study of this problem 

was made by Hill (12). Hill modeled 

the earth as a homo~neous half-space 
containing a laterally periodic thin v_ "0 sheet of high conductivity (fig. 9). The 1 

- cx 

conductivity of the half-space is a,, and 1 t 

the conducting sheet, of thickness-d, is 

located at a depth h. The sheet conduco(x) = o + A cos Bx, 

tivity o(x) is periodic in form, as shown 

below. 

where B = ~T/L and L, 

- 1 1 t A 1 

in which L =the period. Using this L 

earth model, Hill developed equations for 

the vertical magnetic field within the FIGURE 9. - Geometry of homogeneous halfearth and found that it could be approxi- space earth model with thin conducting sheet. 

mated as 

BAdn Hx sin Bx 

H, , 2r1 

iWo, where n =- Y 

n which y = (iwpooo)1/2; 

and 

Hx = horizontal magnetic field 

at surface; 

The values for ad and 1 I'l lh are assumed 

to be small. Also, since the earth's 

permeability is assumed to be that of 

free space, Hz at z = 0 is equal to the 

surface vertical magnetic noise field. 

Equation 27 not only shows how a surface vertical magnetic field can be created due to lateral conductivity changes, 

it also shows both the depth and frequency dependence of the vertical magnetic field within the earth. Equation 

27 also shows that as L becomes very 

large, Hz + 0, which is consistent with 

earlier discussions of the absence of a 

vertical magnetic noise field for a conducting earth with no lateral conductivity changes. Also, if If3/y 1 is small, 

then the exponential term of equation 27 

for the region of z > h reduces to exp 

(-yz), which is the traditional skin effect of a wave in a conducting media. 

Hill's earth conductivity model was 

chosen for use in this study as an aid in 

predicting the behavior of the vertical 

magnetic noise within the earth. However, like any modeling attempt, its value depends upon its ability to explain 

trends in actual field data. 

Due :o the lack of sufficient data on 

vertical magnetic noise above and in coal 

mines, field tests were conducted at a 

number of coal mines throughout the 

United States to obtain recordings of 

this noise. The results are described in 

the following sections. 

EM VERTICAL MAGNETIC NOISE FIELD TESTS 

NOISE MEASURING INSTRUMENTATION noise measurements were made at each 

mine, and when possible, in-mine noise 

Noise recordings were made on-site and measurements were made at the same time. 

later reduced in the laboratory to obtain A diagram of the instrumentation used is 

the desired noise information. Surface shown in figure 10. 
500-turn, PAR model TMII3 

15-in-diam I oop omplif ier 

NAGRA model IV-SJ 

tape recorder 

FIGURE 10. - Field test recording instrumentation. 

The antenna used was a 15-in-diam loop 

of 500 turns of wire. During the tests 

this loop was laid flat on the ground. 

To relate the output voltage of the loop 

to a magnetic field of known frequency in 

which it was immersed, the loop was calibrated by a method described by Greene 

(11). The limit of uncertainity of this 

method is believed to be 53 pct. 

The amplifier used was a Princeton Applied Research3 (PAR) model 113. This 

amplifier has variable gain and variable 

low-pass and high-pass filter settings. 

Its input noise voltage is -165 dB re 1.0 

V-RMS &'I. The input current noise 

does not contribute significantly to the 

overall noise because of a low source 

impedance. 

The tape recorder was a Nagra model IVSJ. This tape recorder has variable attenuation but was maintained for one-toone reproduction throughout the tests. 

The recorder's equivalent input noise 

voltage was found to be -127.8 dB re 1.0 

V-RMS ' . 

The system noise included both the amplifier and tape recorder the input noise 

values and the amplifier gain setting. 

This system noise can be expressed as 

3~eference to specific equipment or 

manufacturers does not imply endorsement 

by the Bureau of Mines. 

where VN = system noise voltage, V-RMS 

4-E-' 

and G = amplifier gain. 

VN was constant over the frequency 

range of interest, and the corresponding 

system magnetic noise was found by referencing the loop calibration factor at the 

frequency of interest. 

Several minutes of noise was recorded 

at each mine site, and attempts were made 

to obtain measurements both above and 

within each mine. All of the recordings 

were made during the afternoon hours over 

a period from March to November. 

For reduction of the noise data, the 

tapes were played through the instrumentation diagramed in figure 11. The tape 

deck and amplifier were the same ones 

used during the field tests. A KrohnHite model 3500 bandpass filter was used 

to eliminate noise outside the band of 

interest. Noise amplitudes were obtained 

at discrete frequencies using a Nicolet 

Scientific model 4448 fast Fourier transform (FFT). 
NAGRA model IV-SJ PAR model TM 113 

tape recorder amplifier 

model FFT 444 

mini- ubiquitous 

FIGURE 11. - Playback instrumentat ion. 

NOISE DATA 

For evaluating a noise communication 

system, the RMS value of the noise is the 

important factor to consider. The noise 

tapes were reduced by performing a highresolution FFT (0.38 Hz noise equivalent 

bandwidth) on the data. Thirty-two independent samples of 4-s duration were 

averaged to obtain the average RMS voltage noise level at a particular frequency. This procedure was repeated to 

obtain the RMS voltage noise levels at a 

number of different frequencies. Using 

the calibration factor of the reproduction instrumentation (fig. 11) , the field 

amplifier gain, and the calibration factor of the loop antenna, magnetic noise 

values were then obtained. 

For each mine where noise was recorded, 

table 1 shows the surface noise field 

values in dB re 1.0 PA m' &' ' -RMS for 

different frequencies. Where possible, 

underground noise measurements were also 

made, using instrumentation similar to 

that used on the surface; these measurements are also shown in table 1, in the 

same units. (The mines listed by number 

in table 1 are identified by name and location in appendix C.) The surface and 

underground measurements were made simultaneously, and at all but four mines 

(mines 24, 25, 26, and 27), the data was 

obtained while the mine was operating. 

Both the surface and underground data exclude manmade 60-Hz harmonic noise, which 

is often much greater than the random 

background noise reported here. 

As stated earlier, the system noise can 

be expected to change with the gain of 

the field amplifier. However, if the 

gain is large, the system noise can be 

attributed to the amplifier noise. This 

was the situation in the majority of the 

cases, and at no time were the data found 

to be system noise limited when the amplifier gain was low. Therefore, table 1 

also includes the equivalent magnetic 

noise level of the field instrumentation. 

Since the noise values were obtained by 

averaging a number (N = 32) of independent noise samples from a given tape, the 

statistical accuracy of the data must be 

considered. For an estimate of a spectral density function S(f) by way of an 

FFT method which calculates both the real 

and imaginary values of S(f), the degrees 

of freedom, df, are twice the number of 

samples obtained as explained by Otnes 

(16). Assuming that the samples were independent Gaussian variables with zero 

mean and unit variance, the summation of 

the square of the samples would be chisquare distributed. Therefore, the confidence interval of S(f) can be written 

as 

Prob (A < S(f) < B) = p. (29) 
TABLE 1 . . Surface and underground vertical magnetic noise values 

obtained at different sites 

(dB re 1.0 PA m'l &-I) 

270 1 630 1 1. 050 

SURFACE MEASUR 

Mine: 

1 ................... 

2 ................... 

3 ................... 

Systemnoise .......... I NAp 1 .36.0 1 .40.5 

ND Not detected . NAp Not applicable . 

System noise .......... 1 .28.6 1 .36.0 1 .40.5 

UNDERGROUND MEAS 

4 ................... 

10 .................. 

16 .................. 18 .................. 24 .................. 25 .................. 26 .................. 27 .................. 28 .................. 

ND 

ND 

ND 

ND 

ND 

ND 

ND 

ND 

ND 

.14.2 

.32.1 

.23.3 

.23.1 

.28.7 

.11.9 

.32.5 

.30.8 

.20.4 

.22.4 

.31.6 

.30.1 

.27.4 

.36.3 

.25.9 

.40.7 

.34.8 

.28.0 
The parameter p is a fixed 

level. A related parameter, 

referred to with 

The confidence limits A and B 

written as 

df $(f) A= 

'df ,a/2 

confidence operating, meaning that the data may have 

a, is of ten been influenced by the mine machinery. 

Analysis of the data should therefore 

result in a conservative estimate of the 

(30) expected natural noise present. Where 

the underground noise was greater than 

can then be the surface noise, the underground data 

were probably mostly influenced by the 

(31) operating mine. This occurred for mines 

4 and 16 (table 1). Therefore, the underground noise data for these two mines 

For the FFT sampling performed on the 

noise data, df = 64. Therefore, a 95-pct 

confidence interval on the noise data is 

were disregarded. 

(32) Expected noise levels were derived by 

statistical inference, using noise models 

or -2.3 to 3.3 dB. These accuracy figures should represent the accuracy of the 

noise measurements since the error of the 

data-gathering and reduction instrumentation is much lower than these figures. 

DATA ANALYSIS 

The purpose of this study was to gain 

an understanding of noise, both on the 

earth's surface and underground, that 

would degrade TTE communications. It is 

expected that underground noise would be 

less than surface noise due to the conducting earth which separates the surface 

from underground locations. Unfortunately, in the majority of the cases, the 

data were obtained while the mine was 

generated from the surface and underground data. A corollary objective of 

the analysis was to understand the interrelationships of the surface and underground noise. 

For the purpose of evaluating a communication system, the most important relationship to determine is that of the 

expected noise level at a given frequency. Table 2 shows the mean and standard deviation noise values for both the 

surface and underground noise measured at 

the mines listed in table 1 and appendix 

C. Also shown in table 2 is the difference, in decibels, between the surface 

and underground mean noise values. (The 

mean decibel difference values are included only to show that expected noise 

values are lower for the underground 

locations. These values do not represent 

expected differences at a given mine 

since the surface data set was for a 

larger number of mines than the underground data set.) 

TABLE 2. - Surafce and underground vertical magnetic noise mean 

and standard deviation values 

Surf ace : 

Mean....................... 

Standard deviation......... 

Underground : 

Mean....................... 

Standard deviation......... 

Mean differential........dB.. 

ND No data collected. 

Frequency, Hz 

270 603 1,050 1,950 2,490 3,030 4,530 5,970 
In agreement with prior atmospheric 

noise studies, the mean noise values in 

table 2 decrease as frequency increases. 

However, no indication of a noise null, 

which has been reported by others, is 

present in the average data. Likewise, 

in almost all of the individual mine surface noise data shown in table 1, no 

noise null is evident. Possibly the explanation for this has to do with the 

frequency-dependent earth reflection coefficients discussed earlier, but additional studies would need to be performed 

to confirm this. Also, since most of the 

tests were performed while the mine was 

operating, the surface measurements may 

have been influenced by underground mine 

impulsive noise. 

The mean noise values are plotted in 

figure 12. It can be seen that the surface vertical magnetic noise values obtained at the mines are in the same range 

as the horizontal magnetic noise values 

found by Maxwell (15) - (fig. 7). 

In evaluating the performance of a communication system, it is valuable to have 

a statistical model of the noise so that 

probability statements can be made about 

the expected value of the noise at a 

given frequency. A common method used 

FIGURE 12. - Surface and underground mean vertical magnetic noise values from noise data. -------- - 
to achieve this is through regression 

analysis. 

Several linear regression models were 

hypothesized and tried. The model found 

to best fit the behavior of the data is 

one in which the mean value of the noise 

level HN is linearly related to the logarithm of the frequency. This is shown by 

where Ta/2,~f is a statistical value 

based on sampling distribution theory, in 

which 

a = 5 pct 

and df = n - 2, 

and where n = number of samples, 

Fj = the particular frequency 

value, 

- 

HN is the vertical magnetic noise level, F = average value of freexpressed in dB re 1 PA m-I &-I. The quency tested , parameters a and Bi are parameters to be 

estimated from the data. The parameter c syx = standard error of the esrepresents a random variable that is nor- timate of the regression 

mally distributed, with expected value relationship, 

zero and a variance which is the same for 

all values of i. and S,, = n - 1 (s,)~, 

The derived regression lines for both 

the surface and underground noise are 

shown in figure 13, and the regression 

results are summarized in table 3. The 

correlation coefficients given in table 3 

(for the regression results of both the 

surface and underground noise) are large 

enough to assume that the linear regression models are reasonably acceptable. 

It was assumed that the errors were 

normally distributed and that the variance was equal across the independent 

variable. These assumptions were considered and it was concluded that meaningful 

statistical inferences from the regression analysis could be made. 

Also shown in figure 13 are bands 

around the regression lines which represent intervals of confidence; within 

these intervals, one can be 95-pct confident that the expected mean relationship 

between noise and frequency actually exists. Such an interval is commonly referred to as a confidence interval (CI). 

The CI is found from 

where S,, is the corrected sum of squares 

for frequency and is the estimate of 

the standard deviation of the frequency 

tested. 

From figure 13 it can be seen that the 

vertical distance between the upper and 

lower band of each of the two confidence 

TABLE 3. - Regression results for vertical magnetic noise (dB re 1.0 PA m-I 

&- vs LOG (frequency)) 

Under 

ground 

noise 

49 

58.72 

-30.03 

-87 

5.46 

-32 

Number of observations... 

Estimated intercept ...... Estimated slope..... ..... Correlation coefficient.. 

Estimated standard error. 

Standard deviation of log 

frequency ............... 

Surf ace 

noise 

216 

67.09 

-30.15 

-80 

9.79 

.43 
FREQUENCY, Hz 

LOG FREQUENCY, Hz 

FIGURE 13. - Regression results for surface and underground vertical magnetic noise versus 

frequency. 

- 

intervals is smallest at Fj = F and that 

this distance - becomes greater the further 

Fj is from F. This means that less 

trustworthy information exists about the 

relationship between noise and frequency 

at the smaller and larger frequencies; 

the regression line is more reliable for 

at those frequencies in the middle range. 

Figure 13 also shows that the expected 

underground noise levels are lower than 

the expected surface noise levels. This 

would be anticipated if the only source 

of the underground noise were the surface noise. However, the expected underground noise levels may be questionable 

since system noise problems were encountered in measuring the noise in mines 24, 

25 and 27. Nonetheless, even though the 

data from these three mines may not represent the true noise levels, the information gathered remains valuable because 

it is known that the true noise levels 

are lower than the system noise. The 
underground noise regression model could 

be used in evaluating downlink communications and would lead to conservative estimates of performance. 

The regression lines in figure 13 provide information on the expected level of 

the vertical magnetic noise at a given 

frequency. In the evaluation of a communication system, estimates of expected 

performance during times of high or low 

noise are also of value. Considering the 

standard error estimates of table 3, a 

reasonable assumption of the range of 

surface noise values would be that of the 

surface regression line, '10 dB. Likewise, for the underground noise values, 

the range of noise variation would be approximately '5 dB around the underground 

regression line. 

A common method used in estimating the 

expected speech intelligibility of a 

communciation system is known as the articulation index (AI) (2). When the A1 

method is used, the noise is generally 

measured in one-third octaves. The expected noise levels derived from this 

study are shown in one-third octaves, 

for both the surface and underground, 

table 4. 

Though the regression models shown 

in figure 13 might be used in making 

probability statements on expected surface and underground noise levels, the 

results should not be interpreted as establishing a relationship between surface 

and underground noise. This is because 

the surface noise measurements were drawn 

from a much larger data base than the underground measurements were. 

To obtain information on the surface 

and underground noise relationship, a 

subgroup of data would need to be taken 

from both the surface and underground 

data base which contained results from 

the same mines. In addition, data for 

such a study should not be thermal noise 

limited. Once the subgroup of data was 

obtained, a 2-parameter linear regression 

model might be found that would relate 

the difference in surface and underground 

noise to mine depth and frequency. Unfortunately, the only subgroup of data of 

this kind from this study contained only 

three mines, mines 10, 18, and 25. Meaningful statistical inferences would be 

difficult to make using such a small set 

of data. 

As discussed earlier in the section, 

"Underground Vertical Magnetic Noise," 

Hill (12) estimated the expected variat ion of the underground vertical magnetic 

field for a homogeneous earth model containing a highly conductive thin sheet. 

TABLE 4. - Expected vertical magnetic noise values 

for one-third octaves 

Band 

l............ 

2............ 

3............ 

4............ 

5............ 

6............ 

7............ 

8............ 

9............ 

lO........... 

11.. ......... 12........... 

13........... 

14........... 

15........... 

Center 

frequency , Hz 

200 

250 

315 

400 

500 

630 

800 

1,000 

1,250 

1,600 

2,000 

2,500 

3,150 

4,000 

5,000 

Bandwidth, 

Hz 

44 

56 

75 

95 

110 

150 

190 

220 

280 

400 

440 

560 

750 

950 

1,100 

Noise, dB re 1.0 MA m'l 

Surface 

14.1 

12.3 

10.5 

8.4 

6.1 

4.5 

2.3 

-1 

-1.8 

-3.5 

-6.0 

-7 -9 

-9.6 

-11.7 

-14.0 

Underground 

6.1 

4.2 

2.4 

.4 

-1.9 

-3.6 

-5.7 

-7.9 

-9.8 

-11.5 

-14.0 

-15.8 

-17.6 

-19.7 

-21.9 
It would be valuable to obtain additional vertical noise to establish the appropridata on both surface and underground ateness of this model. 

I SUMMARY I 

For evaluating the performance of a 

through-the-earth voice communication 

system which uses horizontal antennas, 

information on the expected levels of 

vertical magnetic noise both on the surface and underground is needed. The 

source of this noise and its propagation 

to an observation point was discussed. 

The interaction of this propagating noise 

field with the localized conductivity 

structure was also discussed as it 

lates to the formation of a vertical 

magnetic field and its variation underground. Surface and underground vertical 

magnetic noise measurements were made at 

a number of different mines from which 

statistical models that relate the expected noise level as a function of frequency were derived. The results were 

also presented in one-third octaves, 

which allows evaluation of the expected 

performance of a communication system to 

be accomplished through a method known as 

the articulation index. 

REFERENCES 

1. Adam, J. W., W. D. Bensema, and 

N. C. Tomoeda. Surface Magnetic Field 

Noise Measurements at Geneva Mine. NBS, 

Boulder, CO, Rep. 74-369, June 1974, 

35 PP* 

2. American National Standards Institute. Methods for the Calculation of 

the Articulation Index. ANSI 53.5-1969, 

1969, p. 24. 

3. Balser, M., and C. A. Wagner. Observations of Earth-Ionosphere Cavity 

Resonances. Nature, v. 188, June 1960, 

pp. 638-644. 

4. Barr, R. The Propagation of ELF 

and VLF Radio Waves Beneath an Inhomogeneous Anisotropic Ionosphere. J. Atmos. 

and Terr. Phys., v. 33, 1971, pp. 343- 

353. 

5. Bensema, W. D. Coal Mine ELF Electromagnetic Noise Measurements. NBS, 

Boulder, CO, Rep. 10-739, Apr. 1972, 

90 PP. 

. A Noise Spectum Measurement 

System Using the Fast Fourier Transform. 

IEEE Trans. Electromagn. Compat., v. EMC19, Apr. 1977, pp. 37-43. 

7. Bradley, P. A., and F. Homer. The 

Spectra of Lightning Discharge at Very 

Low Frequencies, J. Atmos. Terr. Phys., 

v. 26, 1964, pp. 1069-1073. 

8. CCIR (International Radio Consultative Committee). World Distribution 

and Characteristics of Atmospheric Radio 

Noise. Rep. 322, Int. Telecommun. Union, 

Geneva, 1965, p. 78. 

9. Chapman, F. W., and R. V. Macario. 

Propagation of Audio Frequency Radio 

Waves to Great Distances. Nature, v. 

177, May 1956, pp. 930-933. 

10. Eckersley, T. L. Studies in Radio 

Transmission. J. IEEE, v. 27, Sept. 

1932, pp. 405-459. 

11. Greene, F. M. NBS Field-Strength 

Standards and Measurements (30 Hz to 1000 

MHz). Proc. IEEE, v. 55, No. 6, June 

1967, pp. 970-981. 

12. Hill, D. A*, and J. R. Wait. Theoretical Noise and Propagation Models for 

Through-the-Earth Communication. BuMines 

contract 50113058, unpublished report, 

1982, 45 pp; available for consultation 

from Harry Dobroski at Pittsburgh Res. 

Center, BuMines, Pittsburgh, PA. 

13. Jean, A. Go, J. R. Wait, and D. F. 

Wasmundt. Observed Attenuation Rate of 
ELF Radio Waves. J. Res. NBS, Sect. D, 

v. 65D, Sept.-Oct. 1961, pp. 475-479. 

14. Maxwell, E. L. Atmospheric Noise 

from 20 Hz to 30 kHz. Radio Sci., v. 1, 

NO. 6, July 1967, pp. 637-6440 

15. Maxwell, Em L., and D. L. Stone. 

Natural Noise Fields From 1 cps to 100 

Kc". IEEE Trans. Antennas and Propag., v. 

Z, 1963, pp. 339-343. 

16. Otnes, R. K., and L. Enochson. 

Applied Time Series Analysis. V. 1, Basic Techniques. Wiley 1978, 449 pp. 

17. Pierce, J. A. Sky-Wave Field Intensity. I. Low and Very Low Radio Frequencies. Cruft Lab., Harvard Univ., 

Cambridge, MA, Tech. Rep. 158, 1952, 

12 PP. 

18. Roppert, R. A., and W. F. Moler. 

Propagation Theory and Calculations at 

Lower Extremely Low Frequencies (ELF). 

IEEE Trans. Comm., v. COM-22, No. 4, Apr. 

1974, pp. 438-451. 

Electromagnetic Wave Propagation Panel, 

Brussels, Belgium, Sept. 21-25, 1981, 

11 PP. 

20. Wait, J. R. Electromagnetic Waves 

in a Stratified Media. Pergamon, 1962, 

372 pp. 

21. . Special Issues on ELF Communication. IEEE Trans. Comm. , v. COM22, No. 4, Apr. 1974, pp. 353-538. 

22. Ward, S. H., J. O'Donnel, R. Rivera, G. W. Wave, and D. C. Fraser. 

AFMAG-Applicat ions and Limi t at ions. 

Geophysics., v. 31, 1966, pp. 576-605. 

23. Watt, A. D. VLF Radio Engineering. Pergamon, 1967, 703 pp. 

24. Word, D.R., H.W. Smith, and 

F. X. Bostic. An Investigation of the 

Magnetotelluric Tensor Impedance Method. 

Electrical Geophysics Res. Lab., Univ. of 

TX, Austin, TX, Tech. Rep. 82, March 

1970, 264 pp. 

19. Soderberg, E. G. ELF Noise Surveys, A Review. NATOIAGARD Meeting of 
APPENDIX A*--ABBREVIATIONS AND SYMBOLS USED IN THIS REPORT 

NOTE.--This list does not include (1) the unit of measure abbreviations listed at 

the front of this report, (2) most abbreviations and symbols that are identified and 

then used only briefly in a single place within the report, and (3) the abbreviations 

and symbols used in (and identified in) appendix B. 

a Earth ' s radius re relative 

A1 articulation index Re real part 

c velocity of light RMS root mean square 

CI confidence interval S(f) noise source spectral density 

CW continuous wave 

d distance 

df degrees of freedom 

function 

t time 

T magnetic field ionosphere waveguide 

transfer function 

Ez vertical electric field TEM transverse electromagnetic 

ELF extremely low frequency TM transverse magnetic 

EM electromagnetic TTE through the earth 

f frequency VN system noise voltage 

FFT fast Fourier transform VLF very low frequency 

G gain W electric field ionosphere waveguide 

transfer function 

he effective height of lightning 

stroke a, mode decay factor 

Hi thunderstorm noise source 6, waveguide wave number 

HN vertical magnetic noise level r vector propagation constant 

H+ tangential magnetic field Y propagation constant 

i imaginary number on mode excitation factor (A is also 

used for this term.) I current 

c permittivity 

IEEE Institute of Electrical and Electronic Engineers rl f ree-space wave impedance 

Im imaginary part 

k planewave number 

K distant thunderstorms 

8 angle (+ is also used for this 

term.) 

A mode excitation factor (0, is also 

used for this term.) 

L period X wavelength 

M lightning stroke charge moment l~ permeability 

N noise measurement CJ conductivity 

NBS National Bureau of Standards T waveform duration 

q charge @ angle (8 is also used for this 

R correlation coefficient term.) 

R,, reflection coefficient Y angle of arrival 
1 APPENDIX B.--INSTRUMENTATION NOISE 

There are universal noise models for generator in parallel with the input. 

any two-port network. The network is Both of these generators may be frequency 

considered as a noise-free black box, and dependent. The antenna signal and noise 

the internal sources of noise are repre- voltages may also be frequency dependent. 

sented by a pair of noise generators lo- The source resistor noise is Johnson 

cated at one port, usually the input. noise and is given as 

The receiving antenna for this study is E~ = 4KTRB, n s 0-1) 

assumed to be a multiturn loop deployed 

in a circle. At lower frequencies, stray where K = Boltzmann's constant (1.38 

capacitance may be ignored, and the loop x lo-23 J/K), 

antenna may be represented by an inductance in series with a resistance. This T = temperature, K, 

receiving loop, coupled with a receiver 

preamplifier, is shown in figure B-1. and B = bandwidth, Hz. 

The amplifier noise voltage (En,) is This noise is independent of frequency. 

represented by a zero-impedance voltage All of these generators may be assumed to 

generator in series with the input port, be independent of each other. Also, it 

The amplifier noise current (I) is is assumed that Rl >> R and R, >> XL 

given as an infinite-impedance current (inductor reactance). 

L Ena 

n a a v v OEou~ 

Ina 0 5 R~~ 

KEY 

Es Antenna signal voltage 

En Antenna noise voltage 

Ens Source resistor noise 

R Antenna resistance 

- 1 - 1 - L Antenna inductance 

Ena Amplifier voltage noise 

I I na Amplifier current noise 

Rin Amplifier input resistance 

FIGURE B-1. - Noise-equivalent model of receiver. 
In choosing an amplifier to couple with amplifier circuit. That is, the highest 

a sensor, a conventional method is to signal-to-noise ratio (SNR) may not be 

choose one that has a low noise figure obtained under the same circuit condi- 

(NF). While NF valves are useful for tions which minimize the NF. 

comparing amplifiers , they are not necessarily appropriate indicators for opti- In determining the NF, En is assumed 

mizing the noise performance of an zero. The NF is defined as 

Input power SNR (amplifier disconnected) NF = 10 LOG Amplifier output power SNR I = 10 LOG K*. 

For the case of figure B-1, K* is found as follows: 

where Z, is the source impedance and the output SNRo is given as 

Theref ore, for a given amplifier, the 

SNR is maximized when R = 0, but this 

sets the NF to infinity. For a given 

source impedance, the least noisy amplifier is the one with the smallest NF. 

In many applications, the source and 

amplifier impedances are given, and the 

task is to match these in some manner to 

provide the maximum SNR. This matching 

can be found by setting 

From this it is found that 

The transformer will perform best 

when working with a given source and 

fier; however, it is an additional component which in itself may be noisy. 

Therefore, before one uses a transformer, 

it must be determined whether the potential improvement will provide an actual 

one. This determination can only be made 

by investigating the nature of the signal 

source. Obviously, if the antenna noise 

voltage (which is caused by EM noise) is 

very high, this will be the limiting factor in performance, and no gain will be 

obtained through matching. In fact, this 

is the situation desired. The performance of the receiver should be determined 

by the external noise and not by the 

instrumentation. 

the value Zop+ being the optimum source To determine the limitations that the 

impedance. To obtain Zap+, transformer receiver amplifier could potentialy place 

of proper turns ratio (a), is used to on the system performance, the nature of 

couple the source to the amplifier such the receiver antenna must be studied. 

that The induced voltage (V) in a multiturn 

a2 = E,,/I,,Z~. (B-7) air-core loop antenna is given by --------- -- 
where f = frequency, Hz, 

N = number of turns in the loop, 

A = loop area, m2, 

p0 = permeability of free space, 

and H = field strength, A/m. 

For the antenna impedance value of 

interest in this study and the typical 

range of In, values the amplifier current 

noise source can be neglected. Therefore, SNRo becomes 

where E: = (7 -89 fNA x H,)~ 

(v2/Hz>, 

H, and H, are the corresponding signal 

and noise field values at frequency f . 

The resistance of the antenna can be 

expressed in terms of A as 

where R, = resistance per unit length of 

wire. 

To prevent thermal noise limiting it is 

necessary that 

or that 

This relationship can be used for determining the sensitivity of an air-core 

loop antenna amplifier arrangement or can 

be used for improving its sensitivity. 

and 
Mine 

APPENDIX Co--MINE IDENTIFICATION 

TABLE C-1. - Mines from which magnetic noise measurements were obtained 

(All mines listed are coal mines .) 

Depth, 

f t 

470 

Ownership 

Youghiogheny & 

Ohio Coal Co. 

Peabody Coal Co. 

Jim Walter 

Resources. 

Cal G~o~~.~~~... 

Eas tover Mining 

Co . U.S. Steel...... 

0.0 dooooo.oooooo 

Gateway Coal Co. 

Allied Chemical 

Corp. 

Alabama ByProducts Corp. 

Monterey Coal 

Co 

Youghiogheny & 

Ohio Coal Co. 

Consolidation 

Coal Co. 

Old Ben Coal Co. 

Owl Creek Corp. 

Peter Cave...... 

Plateau Mining 

Co . Pontika......... 

North American 

Coal Co. 

0.0 doooooooooooo 

Peabody Coal Co. 

Kaiser Steel. ... Ziegler Coal Co. 

Helen Mining Co. 

Bureau of Mines. 

(1) ............. (') ............. Sewell Coal Co.. 

I Mine name 

I Allison......... 

Alston NO. 4.. .. Blue Creek NO. 3 

NO. 21.00000000. 

Highsplint NO. 4 

Gary No. 2 

Gary No. 9 

Gateway......... 

Harewood........ 

Mary Lee No. 1.. 

Monterey No. 1.. 

I Nelms NO. 2..... 

Oak Park No. 7.. 

Old Ben NO. 26.. 

Sue-Jan......... 

NO. 1~~~~~

Star Point NO. 2 

NO. l~~~~~~~~~

Powhatan NO. 1.. 

Powhatan No. 3. . Sinclair No. 2.. 

Sunnyside NO. 2. 

Mine NO. 4...... 

Helen........... 

Lake Lynn.. ..... 5-4 Cave........ 

Woodward Cave.. . Meadow No. 1.. .. 

I Location 

Centertown..... 

Adger.......... 

City 

Beallsville.... 

Silver......... 

Highsplint ..... 

County and State 

Belmont, OH. 

Wilcoe......... 

Filbert........ 

Clarksville.... 

Boomer......... 

Ohio, KY. 

Jefferson, AL. 

K~ox, KY. 

Hrlan, KY. 

McDowell , WV. 

DO 

Green, PA. 

Fayette, WV. 

Goodsprings .... Walker, AL. 

Carlinville.... 

I Cadiz.......... I DO. 

Macoupin, IL. 

Hopedale.... ... 

Sesser......... 

St. Charles. ... Lovely......... 

Wattis......... 

Harrison, OH. 

Lovely.... ..... Powhatan Point. 

0.0 dooooooooooo 

Drakesboro..... 

Sunnyside ...... Johnston City . . Homer City.. ... Fairchance..... 

University Park 

0.0 dooooooooooo 

Loo~ou~~~~..... 

Franklin, IL. 

Hopkins , KY. 

Martin, KY. 

Carbon, UT. 

Martin, KY. 

Delmont, OH. 

DO 

Butler, KY. 

Carbon, UT. 

Williamson, IL. 

Indiana, PA. 

Fayette, PA. I 

Centre, PA. 

1 Do. 

Fayette, WV. 

'On publicly owned property.