Vertical Magnetic Noise in the Voice Frequency Band Within and Above Coal Mines

Report of Investigations 8828

By John Durkin

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. Electromag- netic 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 UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT

ampere m meter

ampere meter m2 square meter

A/m ampere per meter PA microampere

dB decibel MHz megahertz dB/Mm decibel per megameter Mm megame ter

F/m farad per meter m/s meter per second

f t foot Us microsecond h hour PV m microvolt meter

Hz hertz Pet percent

in inch n ohm

J/K j oule per kelvin rad/s radian per second

K kelvin s second kHz kilohertz v/m volt per meter

kilometer 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 ~lectricalengineer, ~ittsburghResearch Center, Bureau of Mines, Pittsburgh, PA. INTRODUCTION

The performance of through-the-earth harmonics of 60 Hz extending to several (TTE) communication systems is limited by kilohertz. noise, which degrades the intelligibility of voice reception and causes errors in In order to design a communication sys- digital data communication. Noise is an tem and predict its performance, several additive disturbance whose effects can be basic pieces of information about exist- reduced by increasing the signal power, ing noise must be known. The most impor- by proper signal design, or by signal tant aspects are the level of and varia- processing. TTE communication systems tion in noise amplitude in the short and are affected by three basic types of long term. For example, the amplitude of noise: instrumentation, atmospheric, and atmospheric noise varies both hourly and manmade. Thermal noise, generated by re- seasonally. However, before amplitude sistance in the antenna and front-end measurements are considered, the type of circuits, determines the receiver's ulti- measurement that will extract significant mate sensitivity. (A discussion of in- and useful information from the noise strumentation noise and its influence on phenomena must be determined. For this electromagnetic (EM) noise measurements purpose, the frequency of interest and when using an air-core loop antenna is the associated bandwidth of the communi- given in appendix Be) Atmospheric noise cation system must be known. Where mea- is a natural occurrence caused by light- surement of broadband noise is required ning strokes which radiate EM impulses for predicting communication system per- that propagate great distances. Manmade formance , the root-mean-square (RMS) noise is usually caused by power lines noise value is the most useful single and can severely limit the performance of measurement. This has long been recog- a TTE communication system. nized, as shown by the International Ra- dio Consultative Commit tee (CCIR) (8)- . Instrumentation, atmospheric, and manmade noise all have different character- Amplitude variation over the frequency istics. The average power of thermal band of interest also presents valuable noise is fairly constant, whereas atmos- information. Depending upon the nature pheric and manmade noise may vary consid- of its application, amplitude variation erably with time and frequency. The information may be in the form of spec- probability density distribution of ther- tral density or it may be broken into a mal noise is typically Gaussian, whereas number of bands such as one-third oc- atmospheric noise contains intermittent taves. One value of spectral density in- impulses superimposed on a Gaussian noise formation is that manmade noise contribu- background. The characteristics of man- tions can be easily discerned. Also, made noise vary considerably, but the ob- since TTE communications may be two way, served spectrum usually contains several both uplink and downlink, information on discrete frequency components with vary- the expected levels and relationships of ing amplitudes. Manmade noise is a both surface and underground noise must continuous-wave (CW) interference that be obtained; and spectral density data generally occurs at 60 Hz and at various 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 re- attributed 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 chan- FIGURE 1. - Vertical electric dipole on surface of nel (W) in which the noise propagates. a perfectly conducting earth. (See text and appendix In general, the spectral component (f) of A for identification of symbols.) the noise can be written as d = distance between observation point and antenna (and is assumed to be large com- The signal generated by a lightning pared to he), stroke can be considered to be produced by many dipole radiators of different di- c = velocity of light, m/s, mensions at the source location. Wait (20) has characterized the lightning w = frequency, rad/s, stroke as a single vertical electric dipole source. A vertical electric dipole and i = imaginary number. on the surface of a perfectly conducting flat earth (fig. 1) produces both elec- The term in equation 2 associated with tric and magnetic fields. If the current d3 is the electrostatic field. An elec- along the dipole of effective height (he) trostatic field is present if the dipole is assumed to be uniform, the resulting consists only of separated stationary RMS electric and magnetic fields are 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 Ih toI*h,. The radiation term (i.e., and Hm -227T ($-$), dI/dtmhe, where t = time), results only from a change in current and is directly where Ez = RMS vertical electric field, proportional to the current differential. V/m, During an actual lightning stroke, both Hg = RMS tangential magnetic I and he are functions of time. The cur- field, A/m, rent flow in the dipole source creates a t ime-variable charge moment of c0 = permittivity of free space, F/m,

I = antenna current, A, where M(t) is the changing vertical elec- 4 1 I I I I I I I 2.0 Itric 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

0 20 40 60 80 100 120 140 160 180 TIME, ps FIGURE 2. - Expected vertical-moment time and H+) = -1 dM(t)/dt. variation for main c loud-to-ground discharge (23). 1 2n cd (6)

E,/H$ = 377 Q, the free-space wave impe- are shown in figure 2. The source radia- dance (1. When equations 5 and 6 are tion spectrum can be determined by used to determine variations in electric obtaining the Fourier transformation of and magnetic fields, the retarded values the dM/dt curve from of M(t) at time (t - d/c) should be used - i ut in order to account for propagation de- S(o) = d.M/dt*exp dt, lay. If the radiation field terms are to be measured, the observation point must where -r is the duration of the waveform. be far enough from the source that the Watt (23) has calculated this Fourier electrostatic and induction fields will transfoGation and the results are shown be negligible. At d = X/2r, where X = in figure 3. Since dM/dt may vary appre- wavelength, the induction and radiation ciably, the actual spectrum of any par- terms are equal. Beyond one wavelength, ticular cloud-to-ground discharge may both the electric and magnetic fields de- also vary appreciably. However, the cay as l/d. Thus, beyond 50 km, the far spectrum shown in figure 3 can be consid- field term dominates for frequencies ex- ered to be the expected noise source ceeding 1 kHz. spectrum for S from equation 1.

Based on the assumptions presented The direction of arrival of distant above, the magnitudes of the fields can storms (the source of most EM noise ener- be expected to exhibit an inverse dis- gy) is also discussed by Watt (23).- Fig- tance dependence. This has been shown ure 4 shows the average number of atmos- experimentally by Bradley (7)- for dis- pherics occurring in a 24-h period, based tances from 20 to 200 km. At very short on data gathered over 4 days in October distances (d < 20 km), d is comparable to and plotted as a function of direction of the length of the discharge, which then arrival. Most noise sources are located does not behave as a dipole source. At in one of three azimuth sectors; these great distances (d > 200 km), the iono- are Africa, South America, and Indonesia. spheric influence becomes appreciable. At given observation point, the amplitude of the noise and the direction of its ar- The heights of discharge paths differ rival are found to coincide with the time appreciably, giving rise to large varia- of day of the buildup of thunderstorm ac- bility in the-electric moment. Watt (23) tivity in one of these sectors. Local shows typical time behavior curves zr storms, which are finite in number, pro- the main cloud-to-ground discharge of the duce an impulsive form at the observation effective vertical moment and its differ- point. I ential and integral forms. These curves 70 - -

-. 50- 'C e V)

40 -

30 I I I IlIII I I I I I Ill I I I I 1.1 I I 102 I o3 104 lo5 FREQUENCY, Hz FIGURE 3. - Expected frequency spectrum of radiation component of electric field, normalized to a distance of 1 krn (3). EARTH- IONOSPHERE WAVEGUIDE AFRICA 0" . The noise from distant storms arrives at the observation point via the earth 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 1800 KEY electromagnetic (TEM) mode propagation N Averoge number of atmospherics between parallel conducting plates. How- occurring 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 21T f Eo = i - Ih, - 9 (8) is equal to-Re(S,), A d 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)

S, is obtained from the roots of a mod- al resonance equation. At ELF, and in exp [i(2nd/X - n/4)]. 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 In these equations, X = wavelength, km, complex reflection coefficients of the ground and ionosphere, respectively. -Barr (4) has computed the variation of a = Earth's radius, km, a, with Frequency for a realistic daytime ionosphere model. The results showed 6, = mode excitation factor (60"112; that for equal mode excitation factors, 6,"l, where n = 1, 2, 3...), only the zero-order mode is significant in the ELF and lower VLF bands. Results h = height of the ionosphere (70 to for north-to-south propagation are shown 90 km) , 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 magnet- electric and magnetic transfer functions ic field. The greatest effect of the of the waveguide. Also, it is assumed waveguide on propagation is at frequen- that kd >> 1. The distance d should now cies ranging from 1 to 4 kHz. For east- be considered the arc length between the to-west propagation, the attenuation in loo, I I I 11111 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 -- La ': ------

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 Considering the noise-source spectrum coefficient values for propagation atten- shown in figure 3, the relative expected uation measured by different investiga- vertical electric noise field spectrum, tors. Below 10 kHz, the values are based at a given observation point, would ap- on lightning spheric measurements by Jean pear as shown in figure 6. Plotted in (13), and Chapman (9) and on cavity reso- figure 6 are the relative spectra of the nance measurements Xy Balser (3). (Reso- electric field as measured at different nance effects are not shown.7 Above 10 distances from the source. The null in kHz, the values are based on work by 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 fig- attenuation of the earth-to-inosophere ure 5 and is consistent with the observa- waveguide (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 field strength because of their applica- electric and magnetic wave impedance re- bility to surface-based, long-range radio lationship. A smaller amplitude would communications. be expected because of an increase in the wave impedance below 10 kHz. This in- Possibly the best reference on atmos- crease is caused by waveguide attenuation pheric radio noise is CCIR Report 322 and a phase velocity exceeding the speed (8). This report contains worldwide con- of light above 1 kHz and below 10 kHz. tour maps of atmospheric noise levels at 1 MHz for 4-h intervals for 3lnonth peri- PRIOR ATMOSPHERIC NOISE MEASUREMENTS ods. With each map, curves of frequency dependence are given, but the lower limit For TTE communications, the range of of each curve is 10 kHz. Thus the re- frequencies of interest is approximately sults are not directly useful for base- 200 Hz to 6 kHz. Thus both the ELF and band communications. VLF bands are included. Also, since communication may be uplink and downlink, During the 1960's and the 19701s,be- both surface and subsurface noise must be cause of the interest in long-distance considered, While atmospheric noise data communications to submarines, some atmos- are readily available for the frequency pheric noise measurements were made in band between 10 kHz and 32 MHz, relative- the ELF range. A special issue of the ly few reported atmospheric noise mea- Institute of Electrical and Electronics surements have been made below 10 kHz. Engineers (IEEE) "IEEE Transactions on For TTE communication between horizontal Communications," (21), was devoted to ELF loops, the subject of this study, the in- communications and-pro ject Sanguine and terfering noise component comes from the contains several references to ELF noise. vertical magnetic noise. However, of the Soderberg (19) gives an extensive bibli- few noise studies that have been done for ography on ELF noise and lists presently frequencies below 10 kHz, most have been active ground stations with capability concerned with the vertical electric for measuring ELF noise. field strength or the horizontal magnetic Vertical electric noise measurements Most published data of ELF or VLF at- were made over the frequency range of 1 mospheric noise are either of the verti- Hz to 100 kHz by Maxwell and Stone (15). cal electric field or the horizontal mag- Some of their results are shown in figure netic field because they are the dominant 7 and are consistent in form with the components of both the TEM and the first- theoretical curves shown in figure 6. order transverse magnetic (TM) modes in Maxwell (14) made vertical electric at- the earth-ionosphere waveguide. However, mospheric Gise field measurements over for loop-to-loop TTE communications, ver- a 2-year period at a number of worldwide tical magnetic noise is the source of locations for the frequency range of 20 interference. Hz to 30 kHz. Average field measurements were obtained and amplitude probability SURFACE VERTICAL MAGNETIC NOISE distributions of the vertical electric field were derived. The amplitude proba- In most applications of EM communi- bility distributions were also used to cations, the vertical electric field convert the average measurements to RMS is used, owing to the propagation charac- values. teristic of the earth-ionosphere waveguide. Therefore, noise measurements The National Bureau of Standards (NBS) were made of the vertical electric field made wideband noise measurements both and/or horizontal magnetic field. When within and above numerous coal mines (5- only one of these two fields was mea- -6). Most of these measurements were maxe sured, the other was assumed to be re- while the mines were operating, and man- lated by the free space impedance (377 made 60-Hz harmonic noise was generally 521, which would be in slight error as dominant. For rescue TTE communications, previously discussed. the mine power would be off, except for ventilation, therefore manmade noise NBS (1) measured both horizontal and should not be a factor. The main inter- vertical magnetic noise in a remote area f erence would be expected to come from of Utah with no power lines in the vi- atmospheric noise caused by worldwide cinity. The vertical component tended thunderstorm activity. 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 ear- EM plane waves 1 ier dip-angle measurements by Ward (22).-

Po* €0 In geophysical prospecting, the magnet- z =o Iotelluric method is often used for locat- //// //////// ing underground ore bodies (26). This method uses the EM freld from a thunder- Pa* 6 storm to obtain information on the localized conductivity structure. This source 0; ob~*z) 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 FIGURE 8. - Coordinate system and earth con- earth conductivity structure to produce ductivity model. secondary fields that may give rise to a vertical magnetic component. This approximation allows the view that the incident field is also parallel to In the following discussion, it is as- the z-axis in the limit as z + 0. The sumed that at a given observation point primary H-field at the surface (Hp) can the horizontal magnetic field is gener- then be given as ated by independent distant thunderstorms (K) and that a given source (Hi) is lo- Hp(z) = Hp exp -Yp

cated at azimuth angle $ie Using a rec- tangular coordinate system, the horizon- and tal magnetic field components can be resolved into x and y components as The total H-field in the region above the Hx = - C Hi sin qi (17) earth is then a linear combination of the i primary field and secondary field (H,) caused by the conductivity structure of the earth and is given as The geometry of the situation is shown in figure 8. The tangential field components are continuous and, for the frequencies of interest, displacement where r is some fixed location. currents can be neglected and the propagation constants (y) in the air and earth The secondary field in the earth can be respectively become related to the surface primary field (24)- by

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

1 Because of the relationship between the ( propagation constants , the direction of in which m + x, y, z, 1 the wave at z = 0 into the earth can be ( approximated as parallel to the z-axis. Rmni + surface reflection coeffi- three simple earth models. Hill derived cients from z > o side, 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, and i = i + 7 - E laterally inhomogeneous conducting sheet Yx i YY i Yzi. at an arbitrary depth in an otherwise homogeneous half-space, and (3) a homoge- At the surface, for z = o, neous earth model containing an infinite- ly long conducting cylinder representa- tive 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 Therefore, the contribution to the total magnetic noise field is created and for surface horizontal magnetic field is particular parametric values showed the based upon R, -1 For the situation behavior of the field both in space and of a homogeneous earth, the primary frequency . H-field encounters no variation in the propagation medium for z > 0; and thus UNDERGROUND VERTICAL MAGNETIC NOISE Rmni = -1, and no secondary magnetic fields exist . Likewise, for a one- Since downlink communication is im- dimensional earth with 01 = a1 (z), paired by underground EM noise, an under- Km,(0) = 0 for all m, n. For a three- standing of the expected noise levels be- dimensional earth, al = al(x, y, z); low the earth's surface must be obtained there can be reflected secondary waves at in order to evaluate TTE communications. any angle, and a vertical H-field is cre- Also, since the assumed method of comrnu- ated. In this case, K,,,, can be treated nications is between horizontal loop an- as a random variable having any value. tennas lying flat on the ground, vertical magnetic noise is the component of Not only does this information show how interest. a vertical magnetic field can be created, it also shows that the magnitude rela- It can be assumed that during a mine tionship between the horizontal and ver- emergency condition, the primary source tical fields is not clearly defined. In of underground noise will be from the the literature, it is often stated that surface noise field. As previously dis- the vertical magnetic field is smaller cussed, due to the relative values of the than the horizontal field, but there is propagation constants above and within no guarantee of this. For example, as the earth, the noise wave tends to propa- was shown in the "Noise Source" section, gate perpendicularly into the earth. there appear to be three primary azimuth Therefore, for a homogeneous earth, no sectors in which most atmospherics occur underground vertical magnetic noise field (fig. 4). It is conceivable that the would be expected; and as was the case horizontal magnetic noise measurement for the surface, a vertical magnetic could be aligned so as to minimize the noise would occur underground only in the response to these noise sources while the presence of spatial earth conductivity localized conductivity structure could variations. give rise to large vertical fields. An interesting study of this problem Hill (12)- has shown how a vertical mag- was made by Hill (12). Hill modeled netic noise field can be generated by 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 conduc- - tivity o(x) is periodic in form, as shown 1 1 t below. A 1 o(x) = o + A cos Bx, where B = ~T/Land L,

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 half- earth and found that it could be approxi- space earth model with thin conducting sheet. mated as

BAdn Hx sin Bx H, , 2r1

iWo, earlier discussions of the absence of a where n =- Y vertical magnetic noise field for a conducting earth with no lateral conductiv- n which y = (iwpooo)1/2; ity changes. Also, if If3/y 1 is small, then the exponential term of equation 27 Hx = horizontal magnetic field for the region of z > h reduces to exp at surface; (-yz), which is the traditional skin effect of a wave in a conducting media. and Hill's earth conductivity model was The values for ad and 1 I'l lh are assumed chosen for use in this study as an aid in to be small. Also, since the earth's predicting the behavior of the vertical permeability is assumed to be that of magnetic noise within the earth. How- free space, Hz at z = 0 is equal to the ever, like any modeling attempt, its val- surface vertical magnetic noise field. ue depends upon its ability to explain trends in actual field data. Equation 27 not only shows how a surface vertical magnetic field can be cre- Due :o the lack of sufficient data on ated due to lateral conductivity changes, vertical magnetic noise above and in coal it also shows both the depth and fre- mines, field tests were conducted at a quency dependence of the vertical mag- number of coal mines throughout the netic field within the earth. Equation United States to obtain recordings of 27 also shows that as L becomes very this noise. The results are described in large, Hz + 0, which is consistent with 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 NAGRA model IV-SJ 15-in-diam Ioop omplif ier 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 where VN = system noise voltage, V-RMS which it was immersed, the loop was cali- 4-E-' brated by a method described by Greene (11). The limit of uncertainity of this and G = amplifier gain. method is believed to be 53 pct. VN was constant over the frequency The amplifier used was a Princeton Ap- range of interest, and the corresponding plied Research3 (PAR) model 113. This system magnetic noise was found by refer- amplifier has variable gain and variable encing the loop calibration factor at the low-pass and high-pass filter settings. frequency of interest. Its input noise voltage is -165 dB re 1.0 V-RMS &'I. The input current noise Several minutes of noise was recorded does not contribute significantly to the at each mine site, and attempts were made overall noise because of a low source to obtain measurements both above and impedance. within each mine. All of the recordings were made during the afternoon hours over The tape recorder was a Nagra model IV- a period from March to November. SJ. This tape recorder has variable attenuation but was maintained for one-to- For reduction of the noise data, the one reproduction throughout the tests. tapes were played through the instrumen- The recorder's equivalent input noise tation diagramed in figure 11. The tape voltage was found to be -127.8 dB re 1.0 deck and amplifier were the same ones V-RMS ' . used during the field tests. A Krohn- Hite model 3500 bandpass filter was used The system noise included both the am- to eliminate noise outside the band of plifier and tape recorder the input noise interest. Noise amplitudes were obtained values and the amplifier gain setting. at discrete frequencies using a Nicolet This system noise can be expressed as Scientific model 4448 fast Fourier transform (FFT). 3~eference to specific equipment or manufacturers does not imply endorsement by the Bureau of Mines. NAGRA model IV-SJ PAR model TM 113 model FFT 444 tape recorder amplifier mini- ubiquitous FIGURE 11. - Playback instrumentat ion.

NOISE DATA Both the surface and underground data ex- clude manmade 60-Hz harmonic noise, which For evaluating a noise communication is often much greater than the random system, the RMS value of the noise is the background noise reported here. important factor to consider. The noise tapes were reduced by performing a high- As stated earlier, the system noise can resolution FFT (0.38 Hz noise equivalent be expected to change with the gain of bandwidth) on the data. Thirty-two inde- the field amplifier. However, if the pendent samples of 4-s duration were gain is large, the system noise can be averaged to obtain the average RMS volt- attributed to the amplifier noise. This age noise level at a particular fre- was the situation in the majority of the quency. This procedure was repeated to cases, and at no time were the data found obtain the RMS voltage noise levels at a to be system noise limited when the am- number of different frequencies. Using plifier gain was low. Therefore, table 1 the calibration factor of the reproduc- also includes the equivalent magnetic tion instrumentation (fig. 11) , the field noise level of the field instrumentation. amplifier gain, and the calibration factor of the loop antenna, magnetic noise Since the noise values were obtained by values were then obtained. averaging a number (N = 32) of independent noise samples from a given tape, the For each mine where noise was recorded, statistical accuracy of the data must be table 1 shows the surface noise field considered. For an estimate of a spec- values in dB re 1.0 PA m' &' ' -RMS for tral density function S(f) by way of an different frequencies. Where possible, FFT method which calculates both the real underground noise measurements were also and imaginary values of S(f), the degrees made, using instrumentation similar to of freedom, df, are twice the number of that used on the surface; these measure- samples obtained as explained by Otnes ments are also shown in table 1, in the (16). Assuming that the samples were in- same units. (The mines listed by number dependent Gaussian variables with zero in table 1 are identified by name and lo- mean and unit variance, the summation of cation in appendix C.) The surface and the square of the samples would be chi- underground measurements were made simul- square distributed. Therefore, the con- taneously, and at all but four mines fidence interval of S(f) can be written (mines 24, 25, 26, and 27), the data was as obtained while the mine was operating. 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 ......

System noise ...... 1 .28.6 1 .36.0 1 .40.5 UNDERGROUND MEAS 4 ...... ND .14.2 .22.4 10...... ND .32.1 .31.6 16...... ND .23.3 .30.1 18...... ND .23.1 .27.4 24 ...... ND .28.7 .36.3 25 ...... ND .11.9 .25.9 26 ...... ND .32.5 .40.7 27 ...... ND .30.8 .34.8 28 ...... ND .20.4 .28.0 Systemnoise ...... I NAp 1 .36.0 1 .40.5 ND Not detected . NAp Not applicable . The parameter p is a fixed confidence operating, meaning that the data may have level. A related parameter, a, is of ten been influenced by the mine machinery. referred to with 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 The confidence limits A and B can then be the surface noise, the underground data written as were probably mostly influenced by the df $(f) (31) operating mine. This occurred for mines A= 4 and 16 (table 1). Therefore, the un- 'df ,a/2 derground noise data for these two mines were disregarded. (32) Expected noise levels were derived by statistical inference, using noise models For the FFT sampling performed on the generated from the surface and under- noise data, df = 64. Therefore, a 95-pct ground data. A corollary objective of confidence interval on the noise data is the analysis was to understand the inter- relationships of the surface and underground noise.

For the purpose of evaluating a com- or -2.3 to 3.3 dB. These accuracy fig- munication system, the most important re- ures should represent the accuracy of the lationship to determine is that of the noise measurements since the error of the expected noise level at a given fre- data-gathering and reduction instrumenta- quency. Table 2 shows the mean and stan- tion is much lower than these figures. dard deviation noise values for both the surface and underground noise measured at DATA ANALYSIS the mines listed in table 1 and appendix C. Also shown in table 2 is the differ- The purpose of this study was to gain ence, in decibels, between the surface an understanding of noise, both on the and underground mean noise values. (The earth's surface and underground, that mean decibel difference values are in- would degrade TTE communications. It is cluded only to show that expected noise expected that underground noise would be values are lower for the underground less than surface noise due to the con- locations. These values do not represent ducting earth which separates the surface expected differences at a given mine from underground locations. Unfortunate- since the surface data set was for a ly, in the majority of the cases, the larger number of mines than the under- data were obtained while the mine was ground data set.) TABLE 2. - Surafce and underground vertical magnetic noise mean and standard deviation values

Frequency, Hz 270 603 1,050 1,950 2,490 3,030 4,530 5,970 Surf ace : Mean...... Standard deviation...... Underground : Mean...... Standard deviation...... Mean differential...... dB.. ND No data collected. In agreement with prior atmospheric have been influenced by underground mine noise studies, the mean noise values in impulsive noise. table 2 decrease as frequency increases. However, no indication of a noise null, The mean noise values are plotted in which has been reported by others, is figure 12. It can be seen that the sur- present in the average data. Likewise, face vertical magnetic noise values ob- in almost all of the individual mine sur- tained at the mines are in the same range face noise data shown in table 1, no as the horizontal magnetic noise values noise null is evident. Possibly the ex- found by Maxwell (15)- (fig. 7). planation for this has to do with the frequency-dependent earth reflection co- In evaluating the performance of a com- efficients discussed earlier, but addi- munication system, it is valuable to have tional studies would need to be performed a statistical model of the noise so that to confirm this. Also, since most of the probability statements can be made about tests were performed while the mine was the expected value of the noise at a operating, the surface measurements may 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 where Ta/2,~fis a statistical value analysis. based on sampling distribution theory, in which Several linear regression models were a = 5 pct hypothesized and tried. The model found to best fit the behavior of the data is and df = n - 2, one in which the mean value of the noise level HN is linearly related to the loga- and where n = number of samples, rithm of the frequency. This is shown by Fj = the particular frequency value,

- HN is the vertical magnetic noise level, F = average value of fre- expressed 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 es- represents 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 where S,, is the corrected sum of squares the surface and underground noise are for frequency and is the estimate of shown in figure 13, and the regression the standard deviation of the frequency results are summarized in table 3. The tested. correlation coefficients given in table 3 (for the regression results of both the From figure 13 it can be seen that the surface and underground noise) are large vertical distance between the upper and enough to assume that the linear regres- lower band of each of the two confidence sion models are reasonably acceptable. TABLE 3. - Regression results for verti- It was assumed that the errors were cal magnetic noise (dB re 1.0 PA m-I normally distributed and that the vari- &- vs LOG (frequency)) ance was equal across the independent variable. These assumptions were consid- Surf ace Under ered and it was concluded that meaningful noise ground statistical inferences from the regres- noise sion analysis could be made. Number of observations... 216 49 Estimated intercept ...... 67.09 58.72 Also shown in figure 13 are bands Estimated slope...... -30.15 -30.03 around the regression lines which repre- Correlation coefficient.. -80 -87 sent intervals of confidence; within Estimated standard error. 9.79 5.46 these intervals, one can be 95-pct confi- Standard deviation of log dent that the expected mean relationship frequency ...... 43 -32 between noise and frequency actually exists. Such an interval is commonly referred to as a confidence interval (CI). The CI is found from 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 would be anticipated if the only source this distance- becomes greater the further of the underground noise were the sur- Fj is from F. This means that less face noise. However, the expected under- trustworthy information exists about the ground noise levels may be questionable relationship between noise and frequency since system noise problems were encoun- at the smaller and larger frequencies; tered in measuring the noise in mines 24, the regression line is more reliable for 25 and 27. Nonetheless, even though the at those frequencies in the middle range. data from these three mines may not represent the true noise levels, the infor- Figure 13 also shows that the expected mation gathered remains valuable because underground noise levels are lower than it is known that the true noise levels the expected surface noise levels. This are lower than the system noise. The underground noise regression model could probability statements on expected sur- be used in evaluating downlink communica- face and underground noise levels, the tions and would lead to conservative es- results should not be interpreted as estimates of performance. tablishing a relationship between surface and underground noise. This is because The regression lines in figure 13 pro- the surface noise measurements were drawn vide information on the expected level of from a much larger data base than the un- the vertical magnetic noise at a given derground measurements were. frequency. In the evaluation of a communication system, estimates of expected To obtain information on the surface performance during times of high or low and underground noise relationship, a noise are also of value. Considering the subgroup of data would need to be taken standard error estimates of table 3, a from both the surface and underground reasonable assumption of the range of data base which contained results from surface noise values would be that of the the same mines. In addition, data for surface regression line, '10 dB. Like- such a study should not be thermal noise wise, for the underground noise values, limited. Once the subgroup of data was the range of noise variation would be ap- obtained, a 2-parameter linear regression proximately '5 dB around the underground model might be found that would relate regression line. the difference in surface and underground noise to mine depth and frequency. Un- A common method used in estimating the fortunately, the only subgroup of data of expected speech intelligibility of a this kind from this study contained only communciation system is known as the ar- three mines, mines 10, 18, and 25. Mean- ticulation index (AI) (2). When the A1 ingful statistical inferences would be method is used, the noise is generally difficult to make using such a small set measured in one-third octaves. The ex- of data. pected noise levels derived from this study are shown in one-third octaves, As discussed earlier in the section, for both the surface and underground, "Underground Vertical Magnetic Noise," table 4. Hill (12) estimated the expected varia- t ion ofthe underground vertical magnetic Though the regression models shown field for a homogeneous earth model con- in figure 13 might be used in making taining a highly conductive thin sheet.

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

Band Center Bandwidth, Noise, dB re 1.0 MA m'l frequency , Hz Hz Surface Underground l...... 200 44 14.1 6.1 2...... 250 56 12.3 4.2 3...... 315 75 10.5 2.4 4...... 400 95 8.4 .4 5...... 500 110 6.1 -1.9 6...... 630 150 4.5 -3.6 7...... 800 190 2.3 -5.7 8...... 1,000 220 -1 -7.9 9...... 1,250 280 -1.8 -9.8 lO...... 1,600 400 -3.5 -11.5 11...... 2,000 440 -6.0 -14.0 12...... 2,500 560 -7 -9 -15.8 13...... 3,150 750 -9.6 -17.6 14...... 4,000 950 -11.7 -19.7 15...... 5,000 1,100 -14.0 -21.9 It would be valuable to obtain additional vertical noise to establish the appropri- data on both surface and underground ateness of this model.

I SUMMARY I For evaluating the performance of a magnetic field and its variation under- through-the-earth voice communication ground. Surface and underground vertical system which uses horizontal antennas, magnetic noise measurements were made at information on the expected levels of a number of different mines from which vertical magnetic noise both on the sur- statistical models that relate the ex- face and underground is needed. The pected noise level as a function of fre- source of this noise and its propagation quency were derived. The results were to an observation point was discussed. also presented in one-third octaves, The interaction of this propagating noise which allows evaluation of the expected field with the localized conductivity performance of a communication system to structure was also discussed as it be accomplished through a method known as lates to the formation of a vertical the articulation index.

REFERENCES

1. Adam, J. W., W. D. Bensema, and Low Frequencies, J. Atmos. Terr. Phys., N. C. Tomoeda. Surface Magnetic Field v. 26, 1964, pp. 1069-1073. Noise Measurements at Geneva Mine. NBS, Boulder, CO, Rep. 74-369, June 1974, 8. CCIR (International Radio Consul- 35 PP* tative Committee). World Distribution and Characteristics of Atmospheric Radio 2. American National Standards Insti- Noise. Rep. 322, Int. Telecommun. Union, tute. Methods for the Calculation of Geneva, 1965, p. 78. the Articulation Index. ANSI 53.5-1969, 1969, p. 24. 9. Chapman, F. W., and R. V. Macario. Propagation of Audio Frequency Radio 3. Balser, M., and C. A. Wagner. Ob- Waves to Great Distances. Nature, v. servations of Earth-Ionosphere Cavity 177, May 1956, pp. 930-933. Resonances. Nature, v. 188, June 1960, pp. 638-644. 10. Eckersley, T. L. Studies in Radio Transmission. J. IEEE, v. 27, Sept. 4. Barr, R. The Propagation of ELF 1932, pp. 405-459. and VLF Radio Waves Beneath an Inhomogen- eous Anisotropic Ionosphere. J. Atmos. 11. Greene, F. M. NBS Field-Strength and Terr. Phys., v. 33, 1971, pp. 343- Standards and Measurements (30 Hz to 1000 353. MHz). Proc. IEEE, v. 55, No. 6, June 1967, pp. 970-981. 5. Bensema, W. D. Coal Mine ELF Elec- tromagnetic Noise Measurements. NBS, 12. Hill, D. A*, and J. R. Wait. The- Boulder, CO, Rep. 10-739, Apr. 1972, oretical Noise and Propagation Models for 90 PP. Through-the-Earth Communication. BuMines contract 50113058, unpublished report, . A Noise Spectum Measurement 1982, 45 pp; available for consultation System Using the Fast Fourier Transform. from Harry Dobroski at Pittsburgh Res. IEEE Trans. Electromagn. Compat., v. EMC- Center, BuMines, Pittsburgh, PA. 19, Apr. 1977, pp. 37-43. 13. Jean, A. Go, J. R. Wait, and D. F. 7. Bradley, P. A., and F. Homer. The Wasmundt. Observed Attenuation Rate of Spectra of Lightning Discharge at Very ELF Radio Waves. J. Res. NBS, Sect. D, Electromagnetic Wave Propagation Panel, v. 65D, Sept.-Oct. 1961, pp. 475-479. Brussels, Belgium, Sept. 21-25, 1981, 11 PP. 14. Maxwell, E. L. Atmospheric Noise from 20 Hz to 30 kHz. Radio Sci., v. 1, 20. Wait, J. R. Electromagnetic Waves NO. 6, July 1967, pp. 637-6440 in a Stratified Media. Pergamon, 1962, 372 pp. 15. Maxwell, Em L., and D. L. Stone. Natural Noise Fields From 1 cps to 100 21. . Special Issues on ELF Com- Kc". IEEE Trans. Antennas and Propag., v. munication. IEEE Trans. Comm. , v. COM- Z, 1963, pp. 339-343. 22, No. 4, Apr. 1974, pp. 353-538.

16. Otnes, R. K., and L. Enochson. 22. Ward, S. H., J. O'Donnel, R. Riv- Applied Time Series Analysis. V. 1, Ba- era, G. W. Wave, and D. C. Fraser. sic Techniques. Wiley 1978, 449 pp. AFMAG-Applicat ions and Limi t ations. Geophysics., v. 31, 1966, pp. 576-605. 17. Pierce, J. A. Sky-Wave Field In- tensity. I. Low and Very Low Radio Fre- 23. Watt, A. D. VLF Radio Engineer- quencies. Cruft Lab., Harvard Univ., ing. Pergamon, 1967, 703 pp. Cambridge, MA, Tech. Rep. 158, 1952, 12 PP. 24. Word, D.R., H.W. Smith, and F. X. Bostic. An Investigation of the 18. Roppert, R. A., and W. F. Moler. Magnetotelluric Tensor Impedance Method. Propagation Theory and Calculations at Electrical Geophysics Res. Lab., Univ. of Lower Extremely Low Frequencies (ELF). TX, Austin, TX, Tech. Rep. 82, March IEEE Trans. Comm., v. COM-22, No. 4, Apr. 1970, 264 pp. 1974, pp. 438-451.

19. Soderberg, E. G. ELF Noise Sur- veys, 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 function CW continuous wave t time d distance T magnetic field ionosphere waveguide df degrees of freedom 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 Elec- tronic Engineers rl free-space wave impedance Im imaginary part 8 angle (+ is also used for this term.) k planewave number A mode excitation factor (0, is also K distant thunderstorms 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.) Y angle of arrival R,, reflection coefficient 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 Ina 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 neces- sarily 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 The transformer will perform best SNR is maximized when R = 0, but this when working with a given source and sets the NF to infinity. For a given fier; however, it is an additional com- source impedance, the least noisy ampli- ponent which in itself may be noisy. fier is the one with the smallest NF. Therefore, before one uses a transformer, it must be determined whether the poten- In many applications, the source and tial improvement will provide an actual amplifier impedances are given, and the one. This determination can only be made task is to match these in some manner to by investigating the nature of the signal provide the maximum SNR. This matching source. Obviously, if the antenna noise can be found by setting 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 perform- From this it is found that ance 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 ------H, and H, are the corresponding signal and noise field values at frequency f . where f = frequency, Hz, The resistance of the antenna can be N = number of turns in the loop, expressed in terms of A as

A = loop area, m2,

p0 = permeability of free space, where R, = resistance per unit length of wire. and H = field strength, A/m. To prevent thermal noise limiting it is For the antenna impedance value of necessary that interest in this study and the typical range of In, values the amplifier current noise source can be neglected. There- fore, SNRo becomes or that

where E: = (7 -89 fNA x H,)~ (v2/Hz>, 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 APPENDIX Co--MINE IDENTIFICATION

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

(All mines listed are coal mines .)

Mine Depth, Ownership Mine name I Location f t ICity County and State 470 Youghiogheny & Allison...... Beallsville.... Belmont, OH. Ohio Coal Co. I Peabody Coal Co. Alston NO. 4.. .. Centertown..... Ohio, KY. Jim Walter Blue Creek NO. 3 Adger...... Jefferson, AL. Resources. Cal G~o~~.~~~...NO. 21.00000000. Silver...... K~ox,KY. Eas tover Mining Highsplint NO. 4 Highsplint ..... Hrlan, KY. Co . U.S. Steel...... Gary No. 2 Wilcoe...... McDowell , WV.

0.0 dooooo.oooooo Gary No. 9 Filbert...... DO Gateway Coal Co. Gateway...... Clarksville.... Green, PA. Allied Chemical Harewood...... Boomer...... Fayette, WV. Corp. Alabama By- Mary Lee No. 1.. Goodsprings .... Walker, AL. Products Corp. Monterey Coal Monterey No. 1.. Carlinville.... Macoupin, IL. Co Youghiogheny & I Nelms NO. 2..... Hopedale...... Harrison, OH. Ohio Coal Co. Consolidation Oak Park No. 7.. I Cadiz...... I DO. Coal Co. Old Ben Coal Co. Old Ben NO. 26.. Sesser...... Franklin, IL. Owl Creek Corp. Sue-Jan...... St. Charles. ... Hopkins , KY. Peter Cave...... NO. 1~~~~~~~~~~.Lovely...... Martin, KY. Plateau Mining Star Point NO. 2 Wattis...... Carbon, UT. Co . Pontika...... NO. l~~~~~~~~~..Lovely...... Martin, KY. North American Powhatan NO. 1.. Powhatan Point. Delmont, OH. Coal Co.

0.0 doooooooooooo Powhatan No. 3. . 0.0 dooooooooooo DO Peabody Coal Co. Sinclair No. 2.. Drakesboro..... Butler, KY. Kaiser Steel. ... Sunnyside NO. 2. Sunnyside ...... Carbon, UT. Ziegler Coal Co. Mine NO. 4...... Johnston City .. Williamson, IL. Helen Mining Co. Helen...... Homer City.. ... Indiana, PA. Bureau of Mines. Lake Lynn.. Fairchance..... Fayette, PA...... I (1) ...... 5-4 Cave...... University Park Centre, PA. (')...... Woodward Cave.. . 0.0 dooooooooooo 1 Do. Sewell Coal Co.. Meadow No. 1.. .. Loo~ou~~~~.....Fayette, WV. 'On publicly owned property.