COLLINS 

report 

Collins Radio Company 

Volume 3 Theorert'cal Data ,Base 

Research and Development Contract 

for Coal Mine Communication System 
Bureau of Mlnes, Wash~ngton. D C 

-- - - - 

USBM Contrac~ No H0?32056 

Collir~s Radio Comnpa17y 1 Cedar Rapids, lo wa 
Table of Contents 

Page 

Section 1 Theoretical Approach to VLF Throughthe-Earth Propagat ion .................................... 

Section 2 Signal-to-Noise Analysis for Loop -to-Loop 

Mine Com:munications .................................... 

2.1 Abstract .............................................................. 2.2 Introduction .......................................................... 2.3 Loop-to-Loop Plower Transfer Within a 

Homogeneous Medium ............................................ 2.4 Loop-to-Loop Pa ower Transfer on or Within 

a Lossy Half-Space ................................................ 2.4.1 System Signal ..t o-Noise Analysis ........................... 2.5 Computer Signal.-to-Noise Analysis for 

Loop -to-Loop Mine Communications ......................... 2.5.1 Relation of Loop Design to System 

Performance . ., .................................................... 2.5.2 System Noise Representation ................................ 2.5.3 Signal and Noise Processing ................................. 2.5.4 Results of Siginal-to-Noise Ratio Analysis ............... 2.6 Predictions for Theoretical S/N~ ............................. 

Section 3 The Horizontal Electric Dipole ........................ 

3.1 The Field Equations for a Submerged 

Horizontal Electric Dipole ...................................... 3.2 The Submerged Vertical Magnetic Dipole ................... 3.3 The Submerged HED and VMD ................................. 3.4 The Field Components of a Submerged 

Infinite Line Source ............................................... 3.4.1 Results of the Submerged Infinite 

Line Source Analysis ........................................... 

Section 4 Signal-to-Noise Analysis for Down-Link 

Line Source Mine Communications ................... 

4.1 The Subsurface H-Fields for a Line 

Current Source ...................................................... 4.1.1 Signal-to-Noise Ratios ......................................... 4.2 Computational Results ............................................ 4.3 Theoretical Predictions for S/N~ ............................. 
Table of Contents (Cont) 

Page 

Section 5 LF Communication ......................................... 5-1 

5.1 On Intramine Wireless LF Communications ................ 5-1 

5.1.1 Comparison of Experiment With Theory .................. 5-2 

5.1.2 System Design of Basic Intramine Paths .................. 5-9 

5.1.3 Conclusions andRecommendations ......................... 5-16 

Section 6 The Application of Recent NBS Noise 

Data to Mine Communications .......................... 6-1 

6 . 1 Method of Analysis ..................... .... ........................ 6-1 

6.2 Robena Mine ......................................................... 6-1 

6.3 McElroyMine ....................................................... 6-8 

6 . 4 Itman Mine ........................................................... 6-19 

6.5 Geneva Mine ......................................................... 6-26 

6.6 Summary .............................................................. 6-30 

6.7 Results of Propagation Program Analysis .................. 6-32 

Section 7 Analysis of Mine Communications 

Propagation Programs .................................... 7-1 

7.1 User1 s Guide for the Mine Communication1 s 

Propagation Programs ............................................ 7.2 Program Number One ............................................. 7.3 Program Number Two ............................................ 7.4 Program Number Three .......................................... 7.5 Theoretical Predictions for In-Mine 

Propagation .......................................................... 7.5.1 LF Propagation (Theoretical - Fixed 

Station - NG 14) .................................................. 7.5.2 LF Propagation (Theoretical - Portable . NG 14) ............................................................... 7.5.3 LF Propagation (Theoretical . NG 14) ..................... 7.6 Summary .............................................................. 
List of Illustrations 

Figure Page 

Transmitting VMD ............................................... Transmitting Loop at Surface ................................ Equivalent Background Noise Fields ....................... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (100 m) ........... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (3 00 m) ........... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (500 m) ........... Receive Signal -to-Noise Ratios as a Function of 

Lateral Displacement and Frequency ( 100 m) ........... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (300 m) ........... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (500 m) ........... Submerged Horizontal Electric Dipole ..................... Submerged Infinite Line Source .............................. Submerged Infinite Line Source .............................. Submerged Line Source ........................................ Line Current Source ............................................ Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (3 00 m) ........... Receive Signal -to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (500 m) VMD. ... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (500 m) HMD. ... Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency (300 m) HMD. ... Receive Signal-to-Noise Ratios as a Function 

of Lateral Displacement and Frequency 

(300 m) Loop ...................................................... Receive Signal -to-Noise Ratios as a Function 

of Lateral Displacement and Frequency 

(500 m) Loop ...................................................... Comparison of Theoretical and Measured 

Transmission Losses Between Line 

Sources - ~$14 = "/2.. ........................................ Comparison of Theoretical and Measured 

Transmission Losses Between Line 

Sources - E P/($ = 0 ............................................. Comparison of Theoretical and Measured 

Transmission Losses Between Line 

Sources - H+, += 0 ............................................. 
List of Illustrations (Cont) 

Figure Page 

Comparison of Theoretical and Measured 

Transmission Losses Between Line 

Sources . Hp 4 = 90 ............................................. Comparison of Theoretical and Measured 

Transmission Losses Between Line 

Sources . Hz 4 = 90 ............................................. Portable VMD to Line Source ................................. Portable VMD to VMD .......................................... Line Source to Line Source (Broadside) ................... VMD to VMD ....................................................... Line Source to ~MD/Displacernent . 100 Meters ....... Line Source to ~MD/Displacement . 200 Meters ....... Robena Bensema Noise Spectrum Data/ 

Trolley and Face Area Noise Levels ....................... Robena Bensema Noise Spectrum Data/ 

Noise Components Crosscuts 7 and 9 ....................... Robena Kandu APD-Data Spectrum (RMS) ................. Robena HN(H) Extremes (RMS) Subsurface ............... Robena HN(V) Extremes ........................................ McElroy Spectrum Data/~ertical Noise Fields. 

Face Area. and Location No . 2 ............................... McElroy Spectrum Data/~ertical Noise Fields. 

Headpiece. Crosscut. and Shaft ............................... McElroy Spectrum Data/ApD (RMS) ........................ McElroy Spectrum Data/Additional 

Vertical Field Data .............................................. McElroy Spectrum Data/various 

Locations and Components ..................................... McElroy Spectrum Data/Additional High Vertical 

Noise Fields. Crosscuts and Face Areas .................. McElroy Surface Spectrum Data ............................. McElroy Spectrum Data ........................................ McElroy Spectrum Data/~N Extremes ..................... McElroy Surface Spectrum Data/summary ............... Itman Spectrum Data/Noise Levels - Portal Buses and Cabin Creek ................................ Itman Spectrum Data Farley ~anel/Noise . 

16 Ft From Miner ................................................ Itman Spectrum Data Farley Panel/Noise . 

16 Ft From Miner . Continued ............................... Itman Spectrum Data/30 Ft From Miner .................. Itman Spectrum Data/APD ..................................... Itman Spectrum Data/~xtremes .............................. Geneva Spectrum D~~~/HN(H) East.West .................. 
List of Illustrations (Cont) 

Figure Page 

Geneva Spectrum D~~~/HN(H) North.South ................ Geneva spectrum D~~~/HN(v) ................................. Geneva Spectrurn/~at aExtremes ............................ All ~ined~xtremes ............................................. Vector Relationships of Electric and Magnetic 

Field Components for Printouts on Pages 6-34 

Through 6-83 ...................................................... Loop-to-Loop :Lateral Transmission for 

Varying Displacements ......................................... Line Source to Loop Lateral Transmission 

for Varying Di:;placements .................................... Loop-to-Loop S/N Ratio for Various 

Displacements - Noise Grade 14 ............................. Loop-to-Loop S/N Ratio for Various 

Displacements . Noise Grade 2 .............................. Loop-to-Loop :Lateral Transmission for 

Varying Displacements ......................................... Line Source-to-Loop S/N Ratio for Various 

Displacements Down-Link ..................................... Line Source-to-Loop S/N Ratio for Various 

Displacements Down-Link ..................................... Line Source-to-Loop S/NO Ratio for Various 

Displacements Down-Link ..................................... Down-Link Loop-to-Loop S/N Ratio for 

Various Displacements ......................................... Down-Link Loop-to-Loop S/N Ratio for 

Various Displacements . Continued ......................... Down-Link Loop-to-Loop S/N Ratio for 

Various Displacements . Continued ......................... Down-Link Loop-to-Loop S/N Ratio for 

Various Displacements . Continued ......................... Up-Link Loop-to-Loop S/N Ratio for 

Various Displacements ......................................... Up-Link Loop-to-Loop S/N Ratio for 

Various Displacements . Continued ......................... Up-Link Loop-to-Loop S/N Ratio for 

Various Displacements . Continued ......................... Up-Link Loop-to-Loop S/N Ratio for 

Various Displacements . Continued ......................... LF propagation (Theoretical . Fixed Station . 

NG 14) ................................................................ LF Propagation (Theoretical . Portable . 

NG 14) ................................................................ 7-19 LF Propagatioin (Theoretical - NG 14) ..................... 
Section 1 

Theoretical Approach to VT,F 

Through-the-Earth Propagation 

A knowledge of the mechanics of wave propagation through the earth is essential if reliable 

communication systems are to be designed for coal mine environments. To obtain a reliable 

basis from which accurate propagation predictions could be drawn, a series of theoretical 

studies have been prepared for the US Bureau of Mines by Mr. Ramsay ~ecker ofSpectra 

Associates, Inc. through a subcontract with Collins Radio Group. These reports formulate 

the analytical techniques from which we may de:r ive frequencies and antenna configurations 

that yield the optimum signal-to-noise ratios over the greatest distances in mine environments. 

The reports of sections 2 and 4 deal with analytical techniques for determining the signal-tonoise ratio within a mine environment for loop-to-loop and line source-to-loop antenna configurations. The analytical results of these reports were then implemented into computer 

programs to obtain predictions concerning through-the-earth signal propagation. These preliminary predictions are based on noise data co:mpiled by Bensema, Maxwell and Stone, and 

WVU prior to the extensive research conducted by the National Bureau of Standards (NBS). 

These initial measurements indicated a 20- to 30-dB lower noise level than that measured 

recently by NBS. The recent NBS data is that u,sed by Collins in the final predictions. 

The following outline indicates the order and sulbject matter treated in the subsequent sections: 

Section 2 - Signal-to-Noise Analysis for Loop-to-Loop Mine Communications 

Section 3 - The Horizontal Electric Dipole 

Section 4 - Signal-to-Noise Analysis for Down-Link Line Source Mine Communications 

Section 5 - LF Communication 

Section 6 - The Application of Recent NBS Noise Data to Mine Communications 

Section 7 - Analysis of Mine Communication Propagation Programs 
Section 2 

Signal-to-Noise Analysis for 

Loop -to-Loop Mine Communications 

2.1 ABSTRACT 

A method is developed for determining the signal-to-noise power density ratio for a horizontal surface loop (vertical magnetic dipole) to an underground horizontal loop antenna system 

for use in mine communications. The analysis accounts for the loop weight and diameter, 

depth, lateral displacement, and external noise fields. The analytic results provide for a 

computer method of numerical computation which can incorporate available noise data and 

data which may be derived from noise measureinent programs in progress. 

2.2 INTRODUCTION 

Within the last few years there has been a concentration of theoretical and experimental investigations related to the delineation of teleconnmunications systems performance in mines. 

This has been emphasized because of the Mine Safety Act of 1969 and the several recent occurrences of mine disasters. The net result has been to stress the need for the requirements of 

an optimally integrated mine communications system, one in which both the operational and 

disaster modes could be accommodated. 

As a first step in understanding those modes which may be useful in such systems, we consider through-the-earth propagation paths. Lour frequency waves are transmitted through 

overburdens ranging in thickness from 150 to 1,500 feet. Two common methods of coupling 

into the mediums are employed; the loop or magnetic dipole and the line source, sometimes 

referred to as an earth probe (surface) or roof lbolt (subsurface) antenna. This report considers loop-to-loop paths, and in particular onlj~ horizontal loops, (vertical magnetic dipole). 

Such loops (parallel vertical magnetic dipoles) exhibit maximum coupling when coplanar, 

while horizontal magnetic dipoles exhibit nulls and maxima as the antenna rotates, making it 

an unattractive coupling device for mine communications. Horizontal magnetic dipoles (HMD)* 

however, may be used as a subsurface source element for location determination since they 

produce a null in the vertical magnetic field connponent, and thus a VMD* used for detection 

would yield a higher S/N ratio since the surface atmospheric noise usually has a strong horizontal component; an additional argument in favor of the VMD. 

*Horizontal magnetic dipole, HMD; vertical magnetic dipole, VMD. 
2.3 LOOP-TO-LOOP POWER TRANSFER WITHIN A HOMOGENEOUS MEDIUM 

Layman* has recently published his doctoral dissertation in which he is concerned exclusively 

with communications through the earth between VMD's. The expressions are written for the 

magnetic field of a transmitting VMD (figure 2-I), located within a homogeneous medium of 

infinite extent (spherical coordinate system): 

in which I = current in loop - amperes 

A = loop area - square meters 

6 = the skin depth - meters 

where 6 = - meters 

o = conductivity -mhos/meter 

p = permeability4 n x 10-7 henrys/meter 

f = frequency in Hz 

Figure 2-1. Transmitting VMD. 

* Layman, G. E., "Optimization of an EM through the Earth Communication Systemf1 WU PhD 

Thesis, Morgantown, West Virginia. 
The vertical magnetic field at loop 2 is 

Hz, = Hr cos 0 - Hg sin 0 

and the open circuit voltages at the loop 2 terminals: 

V02 = 4 noN2A2H,zz x 10-7 volts (2-4) 

When the receive loop is matched to the real part of its self-impedance, the available received 

power is 

L; 

v02 

pr =-- watts 

while the input power to the transmit loop is 

PT = I~~R~ watts (2-6) 

so that 

R1 and R2 consist of the ohmic loss resistance plus the radiation resistance of the transmit 

and receive loops, respectively. The radiation resistance of an electrically small loop in 

free space is 

where k=2n - 

X 

a = loop radius in meters 

n = number of turns 

X = wavelength in meters 

If the loop were to be completely immersed and surrounded by the lossy medium, a considerable increase in the radiation resistance would olccur. This situation is, however, neither 

operationally desirable nor advantageous from a propagation standpoint. It is far more realistic to consider the loop within an air filled cavity, in which case the effect of the lossy 

medium may be calculated: 

where b is the cavity radius < < A. 

This equation shows simply that at typical cavity radii that loop wire losses greatly exceed 

the radiation resistance for frequencies below, say, 100 kHz. 
Thus, considering only loop wire losses with coplanar loops, Q = "/2 radians 

H2z = -HQ 

then VO2 = -4 noN2A2H~ x 10-7 

so that 

Similarly for Q = n , coaxial magnetic dipoles 

The low frequency loss resistance of the loop can be estimated from R1 = 2nNaRw where Rw 

is the wire dc resistance ~/m. The ratio of received to transmit power now becomes: 

-- 

The terms which have a frequency dependence are collected viz f2 [ ] e ', a differentiation 

with respect to f is performed, and an fopt determined for the two cases: 

6 

f - 2*03 lo , where r is in meters. 

or 

2 

These fOpt1s in turn yield a skin depth at the optimum frequency. The maximum power transfer condltlons are found when these are substituted in equations (2-12) and (2-13). 
and 

showing that under the assumed conditions fopt is a function only of conductivity and loop 

separation and that at fopt the power loss is prolportional to separation to the tenth power. 

2.4 LOOP-TO-LOOP POWER TRANSFER ON OR WITHIN A LOSSY HALF-SPACE 

mile the above analysis has shown some interesting results, the presence of the air-earth 

interface poses the problem which is considerably more realistic, that is, loop-to-loop communication on or within a lossy half space. Layman proceeds to formulate the classic boundary.value problem (flat earth) with the magnetic Hertz vector, and a solution given in terms 

of a primary field and a secondary field resulting from the effect of the boundary. The 

secondary field was presented in terms of some rather cumbersome integral and numerical 

integrations which were performed. Calculations were made for various depths, loop separations, conductivities, for loops on the surface to1 subsurface loops and between subsurface 

loops. The upshot of these calculations showed the dominance of the primary field at the 

lower frequencies (corresponding to the infinite homogeneous medium) with respect to the 

secondary field. As a result, Layman was able to show that the maximum power transfer 

condition derived on the basis of an infinite homogeneous medium was also essentially valid 

for the lossy half space. The secondary field generally increased the power transfer at higher 

frequencies and thus is in essential agreement with Wait's* results, although a direct comparison is difficult since Layman failed to show losses between VMD loop on surface to subsurface VMD loop directly beneath. 

The important observations from this analysis are as follows: 

a. The transmission path between two loops w:ithin a mine separated by a distance much 

greater than the depth is primarily through the upper half space at high frequencies. 

b. Placing the transmitting loop at the surface rather than within the mine results in only a 

small loss in received power if the range (13) is at least four times the depth (h). (See 

figure 2-2,) 

Figure 2-2. Transmitting 1,cdp at Surface. 

*Wait, J. R., "Location of a Buried Source by the EM Induction ~echni~ue:, IEEE Transactions 

of Geoscience Electronics, April 197 1. 
While the analysis has produced some meaningful results, and particularly in view of the 

second observation above, we are led to conclude that Wait's*,** recent analyses relative to 

VMD loops on or within a lossy half space are most applicable to the solution of mine S/N 

calculations. In an elegant fashion Wait proceeds to show that when the boundary value problem is properly formulated and the solution reduced to integrals that can be handled easily 

numerically that a lower loss is encountered through the medium than would be calculated by 

equation (2-1) or (2-2). 

Now we consider a buried VMD with a receive loop on the surface. The vertical component of 

the magnetic field at the surface is 

where h = depth of transmit loop, km 

I = current in transmit loop in amperes 

N = number of turns in transmit loop 

and 

D = normalized lateral displacement of receive loop, ~/h 

om = earth conductivity in millimho/meter 

P r Proceeding as before we find for -, 

Pt 

NOW, of all the ways in which one can describe the practical limitations on loop size, weight 

and diameter have the most significance. Therefore, equation (2-19) will be rewritten in 

these terms. First, we substitute for the ohmic wire losses (dc) 

R1 = 2nN a R approximately (2-20) 1lw 

now 

*Wait, J. R ., "Location of a Buried Source by the EM Induction Technique1', IEEE Transactions of Geoscience Electronics, April 197 1. 

**Wait, J. R., vSubsurface EM Fields of a Circular-Loop of Current Located Above Ground", 

IEEE Transactions on Antennas and Propagation, July 1972. 
and 

ow = wire conductivity, mhos/meter 

Aw = wire area square meters 

Aw =- square meters 2 naNP 

w = weight in kg 

P = wire density kg/,3 

combining the above relations we have 

now 

with al, a2 in meters W in kg, h in km, equation (2-22) becomes 

R1 and R2 have been taken simply as the dc resistance of loop. Because of skin effect the 

effective ac resistance will be somewhat higher. From Terman* for typical multilayer air 

core loops, 

- -- 1 2 d02x 4 

Rdc - +7(5.2m) (r) - 64 for x7 2.5 

where x = ,1078 d fi 

d = wire diameter in cm 

m = number of layers 

dg = effective wire spacing factor 

C 

diameter of wire (cm) where effective wire spacing factor = center-center spacing between turns on same layer 

P r P r Equation (2-23) will reduce -for both loops, hence - should be divided by - Pt Pt 

C E::)2 for 

identical loops. 

*Terman, F. E., Radio Engineers Handbook, MclGraw Hill, 1943, p 81. 
2.4.1 System Signal-to-Noise Analysis 

The equivalent noise figure of a receiving system is 

where Fx = the external noise figure 

Fr = the receive-noise figure 

')A = the efficiency of the receive antenna 

multiplying equation (2-24) by kTo 

where K = Boltzmann's constant 

TO = temperature in degree Kelvin 

The first term on the right is the available received noise power, hence we write 

where Rr is the radiation resistance of a lossless antenna and RL is the loss resistance. Now 

for systems analysis, it is reasonable to require the external noise contribution to be say 10 

times that due to receiver noise and antenna inefficiency, hence we write 

2 -7 substituting voc = 8 n fN2A210 HN 

where HN is the external noise field in amperes/m/dE 

since RL = 2 nN2a2RW 

and 
Solving for a2, the minimal radius of the receive loop is 

1.26 x 

a2 > fH~ /+ meters 

The Q1 of the transmitter or receive loop can be estimated from the approximate inductance 

2 L 2.92aN log10(96.5a) x Henrys 

Using the above relations for weight and wire losses we find 

Now on the assumption that equation (2-27) holds, the system noise power/~z bandwidth is 

Combining this with equation (2-22) we have finailly for the received S/N power density ratio 

The equivalent background noise fields are shown in figure 2-3 for various noise conditions. 

These have been derived from Bensema*, WVU*:*, and Maxwell and Stone***. In the next paragraph, we shall describe a computer method for the S/N analysis which will incorporate the 

noise data of figure 2-3. 

2.5 COMPUTER SIGNAL-TO-NOISE ANALYSIS FOR LOOP-TO-LOOP MINE 

COMMUNICATIONS 

Based on the methods described in the preceding; paragraphs, a computer method was written 

and calculations performed over the parametric ranges of interest. 

*Bensema, W. D., l7Coal Mine ELF EM Noise Measurements," NBS Report 10739. 

**Mine Communication and Monitoring Second Quarterly and Intermediate Annual Technical 

Progress Report (5 September 1971 to 4 December 1971) Department of Electrical Engineering, 

WVU, Morgantown, West Virginia. 

***Maxwell and Stone, PGTAP, May 1963, page 339. 
Figure 2-3. Equivalent Background Noise Fields. 
2.5.1 Relation of Loop Design to System Performance 

From equations (2-28) and (2-29), we note that the gain-bandwidth product of a loop-to-loop 

communications system is proportional to 

at frequencies generally in the audio range. From this, we see that the diameter of the transmit loop is far more important for information transfer than loop weight. When transmit loop 

diameter is maintained at a practical maximum and weight held at a minimum, then not only 

is the gain-bandwidth product improved, but it blecomes more feasible to match the receive 

loop Q to the transmit loop Q so as to approach the minimum required radius of the receive 

loop. In other words, the minimum radius of the receive loop is not practically realizable for 

matched loop Q's unless the radius to weight ratio of the transmit loop is quite high, which 

increases the system gain-bandwidth product in the process. This requires a solution to the 

following equation: 

The number of turns in a loop is 

where W = loop copper weight in kg 

a = loop radius - meters 

Ac = loop wire area in circular-mils 

Thus, an optimal transmit loop is one of large diameter with a minimal number of turns. 

The minimum number of turns for a fixed receive loop radius is 

1'1 min f2~N2~c x 4a2 3 
2.5.2 System Noise Representation 

As shown in figure 2-3, equivalent background noise fields were derived from the data of 

Bensema, WVU and Maxwell and Stone. For the down-link path three noise grades were 

established as follows: 

Noise Grade 1: Bensema figure 30, severe trolley noise. For frequencies above 3 kHz, 

this was merged into WVU's maximal noise data. 

Noise Grade 2: Bensema figure 27, no trolley noise. For frequencies above 3 kHz, this 

was given a frequency decrement derived from typical WVU data. 

Noise Grade 3: Bensema figure 37, 100 feet from borehole. For frequencies above 3 

kHz, this was merged into WVU minimal noise. 

For the up-link path, two noise grades were established as follows: 

Noise Grade 1: Maxwell and Stone "quasiw maximum surface noise. For frequencies 

below 1 kHz this was merged into Bensema's figure 25. 

Noise Grade 2: Maxwell and Stone median surface noise. For frequencies below 1 kHz 

this was merged into Bensema's figure 39. 

2.5.3 Signal and Noise Processing 

Low data rate transmission, which can be accommodated in the system bandwidth, offers no 

difficulty insofar as signal attenuation calculations at a specific carrier frequency is concerned. For broadband, for example, direct up or down-link voice transmission, however, 

the rms signal power must be calculated over the bandwidth of interest, that is, 

The rms noise power is handled in exactly the same way. 

If the noise is primarily broadband impulsive, then the integral in equation (2-34) becomes 

simply a summation of the harmonic noise components. Because the effect of the overburden 

is to integrate the transmitted signal, it is self-suggestive that for broadband application the 

signal be differentiated before transmission and signal and/or noise differentiated upon reception. A. D. Little in their working memorandum no. 5 has considered this and has come to 

the conclusion that there is little to be gained by differentiation except for mine depths of 

approximately 400 feet or less. For the shallower depths, a 6-dB improvement in received 

S/N ratid can be realized for the same transmitter output power. 

*These noise grades were based on the noise data available at the time the analysis was done. 

They were ultimately replaced by new data. (See section 6 for more recent data.) 
Reference should also be made to A. D. Little working memorandum no. 8 in which a hybrid 

harmonic commutator type filter is described. The author indicates a practical method of 

rejecting the impulsive harmonic content of the external noise fields. 

2.5.4 Results of Signal-to-Noise Ratio Analysis 

The techniques of the preceding sections have been incorporated in a computer method for the 

calculation of expected received signal-to-noise ratios. For the examples selected 0 = .O1 

mho/m, a value which according to G. Keller is a good value to assume for coal mines less 

than 1,000 feet in depth. For the up-link we have assumed the following: 

a1 = 0.6 m (transmit loop radius) 

Pt = 10 watts 

Noise grade 2 

For the down-link we have the following parameters: 

al = 10 m 

Pt = 10,000 watts 

Noise grade 3 

The received signal-to-noise ratios were calculated for depths of 100, 300, and 500 meters 

and lateral displacements of 0, 100, 200, 300, 400, and 500 meters. The results are shown in 

figures 2-4 through 2-9 of this section. We note at the shallower depths the optimal frequency 

is extremely broad, for example, where the depth equals the displacement. In fact a secondary 

maxima occurs at about 20 kHz. This is in essential agreement with Layman. With increasing 

depths the peak is nore pronounced and occurs essentially at 2 kHz. It appears that for an 

up-link with a portable transmit loop and a reasonable transmitter power, a 20 dB S/N~ is 

practical on the surface for the 90 percentile mine depth of 300 meters. At the 500-meter 

depth with a maximum S/N~ of 0 dB, obviously only extremely low data rates could be employed. The down-link curves indicate that at least a 40-dB increase in system gain can be 

achieved with respect to the up-link case. See page 2-14 for the correction factor for other 

transmit loop weights and diameters. 

2.6 PREDICTIONS FOR THEORETICA 1, s/NO 

From the foregoing development of theoretical signal-to-noise analysis for the loop-to-loop 

configuration, we may state the following: 

a. VMD (verticle magnetic dipole) arrangement yields a higher S/N~ ratio than does HMD 

(horizontal magnetic dipole). 

b. The transmission path between two loops within a mine separated by a distance much 

greater than the depth is primarily through the upper half space at high frequencies. 

c. Placing the transmitting loop at the surface: rather than within the mine results in only a 

small loss in received power if the separation is at least four times the depth. 
d. Diameter of the transmit loop is far more important for information transfer than loop 

weight. By maintaining transmit loop diameter at a practical maximum and weight at a 

minimum, improved gain bandwidth can be obtained and it becomes more feasible to 

match the receive loop Q to transmit loop Q. 

e. Optimal frequency range is extremely broad at shallower depths, but becomes more 

pronounced with increased depth. 

f. Correction factor for loop-to-loop transmission is as follows: 

10 log (-$) + 20 log( + 10 log (6) 

where W = weight of transmitting loop 

WO = weight of reference loop 

a = radius of transmitting loop 

a. = radius of reference loop 

P = power into transmitting loop 

Po = power into reference loop 


ffi 

3 

cd 

E! 

M 

.r( 

C/2 

e, 

> 

.d 

e, 

0 

0 

ffi 
Figure 2-7. Receive Signal-to-Noise Ratios as a Function of Lateral Displacement and Frequ


Section 3 

The Horizontal Electric Dipole 

We shall now develop the signal-to-noise power density ratio for a horizontal electric dipole 

as we did for the loop source in section 2. A method described by Sommerfeld in 1909 forms 

the basis for determining the field components due to an elementary vertical or horizontal 

dipole located near the interface of a conducting half space. The hertz vector in this problem 

is comprised of the primary potential of the source plus the secondary potential due to the 

interface. 

3.1 THE FIELD EQUATIONS FOR A SUBMERGED HORIZONTAL ELECTRIC DIPOLE 

Assume a plane interface between air and earth, with the horizontal hertz dipole source 

located on the z-axis in the conducting half space at a depth of +h and aligned with the x-axis 

(figure 3-1). A cylindrical coordinate system is employed, with the z-axis vertical with p 

measured radially along the surface, and with th~e angle 9 measured from the x-axis. A time 

factor eiwt is assumed. 

Figure 3 -1. Submerged Horizontal Electric Dipole. 

The hertz potential underground for this case has two components that follou~ directly from 

Sommerfeld: 
where 2 

Y1 = j~~a(o~ + j cla) 

2 

Yo = jp0o(j coo) 

Equations (3-1) and (3-2) represent a solution of the wave equation that satisfies the boundary 

conditions requiring the tangential components of E and H to be continuous across the boundary, between media. 

The electric and magnetic fields may be obtained from 

and 

1CI 2 E = grad div I1 - Y1 I1 

H=- curl I1 

jop 

CCI - 

from equations (3-3) and (3-4), we obtain the tangential and vertical components of E and H: 
Thus we see that for E p 

where 

(primary field) 

where 

-ul(z+h) 

I1x(s) = - hdh 

U 1 

(secondary potential due to interface) 

The primary field E~(P) follows easily from equation (3-12). 

(p) = -1d1 cos +e-" 2 

E~ 3 (~7 r 11 + yr + y2r2 -(E) r [3 + 3Yr+ Yzr2]] (3-14) 

4n(o+ iro)p 

where p = r (point P at same depth as HED) 

EP (p) = +1d1 cos q)e -Yp [~p+ 11 

2n(or+ ic~)~ 3 

Utilizing the recurrence relations for the derivatives of the Bessel functions: 

and 

The secondary field (including that due to IIZ) is therefore: 
Similarly for E+: 

E$,(s) = 477( o+ ico) - hdh 

We are interested primarily in 

, and E+ , and H+ , and 

Hz , and Hq, 

E~P (P) = -1.l 477 sin + e-" p2 ($) [ Yr + 1 ] [ -- r 
(s) = -Id1 sin Ad X 

-1d1 sin %rn -- '~(XP) U1-U~ -U +z+h) 2 

2 2 e X dX 

2 n Yo N u+u 101 

(p) - Id1 sin$ 

Hz - 477P 2 (+y e-yr [Y r + 11 

(s) = Id1 sin$ U1-Uo hZdX 

e - 

4n u 1 

Thus we see that broadside to the dipole ($ = n/2), we have Hp and Hz field components, 

whereas at 4 = 0, H+ is the only magnetic field component. The primary field contributions 

to Hp and H+ vanish however at p = r (receiving point at same depth as the dipole). 

3.2 THE SUBMERGED VERTICAL MAGNETIC :DIPOLE 

For completeness in intramine communications we shall indicate the expressions for the 

submerged VMD. The VMD on the surface has been treated exhaustively by Wait 1, 2; however, computational procedures are needed for the submerged VMD which will adequately 

account for the interfaces. The hertz potential is 

and 

by some simple algebra we find 

1. Characteristics of Antennas Over Lossy Earth, J. R. Wait. Chapter 23 of "Antenna 

Theory," Edited by Collin and Zucker. 

2. On Radio Propagation Through the Earth, J. R. Wait. IEEE Transactions on Antennas and 

Propagation, volume AP-19, no. 6, November 1971, pp 796-798. 
and 

3.3 THE SUBMERGED HED AND VMD* 

From the foregoing development we may write the expressions for the primary fields at a 

point P (p,+,z) for a submerged HED. 

For the VMD our prime concern is Hz 

HZ 

(P) = .-yr er [ p3 

-1 - Yr(l + Yr) + [I -41 r I] (3-34) 

r 

where A = I (dl) B=- I(dl) c - IAN 

4n(a+ ico) 4rr 4 rr 

*(a) The Field Equations for a Submerged Horizontal Electric Dipole, 4 January 1973, R. P. 

Decker, Spectra Associates, Inc. 

(b) The Submerged HED and VMD-11, 8 January 1973, R. P. Decker, Spectra Associates, Inc. 
For the computation of the secondary fields we define the following integrals: 

The field equations therefore become 

E = ~p(~) + A cos$(I1-12) + 2A cos 6 

v2 (I3 -I4) 

2 Eq, = E+(') - y1 A sin$15 + A sin$12 + 2A 
Now we introduce the transformations used by Wait 

R (x) = uo - 

U1 + KUO 

The transformed integrals become 

00 

3 I = J0(x)R (x) exp( -UD) Ux dx 3 p5 0 
As pointed out by Wait, these integrals must be integrated cautiously because of the various 

branch points and poles. Following the same approach we define the limits of each subinterval used for integration. 

The results of this analysis will be described in paragraph 3.4. For the line source, we shall 

use a contact resistance of 100 ohms. For the VMD, the current moment will be computed 

from 

where W = weight of loop in kg 

Pt = transmitted power in watts 

a = loop radius in meters 

3.4 THE FIELD COMPONENTS OF A SUBMERGED INFINITE LINE SOlrRCE 

In this note we assume a wire of infinite length located in the xz-plane at a depth, h, and 

carrying a current of uniform amplitude and phase, reiot. Such an antenna radiates a cylindrical wave, in contrast to the spherical wave radiated from a hertz dipole (figure 3-2). We 

are concerned first with an expression for the primary hertz potential, that is, that under 

ground. 

Figure 3 -2. Submerged Infinite Line Source. 
The hertz potential due to the elementary current moment I(dx) is 

where R = dm and r =dm 

and R is the distance between the current element and point P (in y-z plane), and r =dy2 + (y-h) 2 

is the radial distance of P from the wire. 

This potential has only an x-component. The total potential at P is 

dR =- R dR since R 

we have 

I e I1 = 2n(o+ ito) dR rn 

Let R = rp, where p is a new variable of integration and r is a fixed radial distance. Then 

since 

equation (3 -63) becomes 

Here, H~(~) is the second kind of Hankel function of zero order. Its asymptotic form at large 

distances is 

This is clearly an outgoing cylindrical wave. 
By the use of the Sommerfeld integral representation for the Hankel function 

The Weyl transformation 

and the boundary conditions 

We finally arrive at the hertz potential below ginound 

where ul and uo are defined on page 3-2. 

Note that the upper sign applies when z > h and the lower sign when 0 I z <_ h. 

Now since 

We have finally 
3.4.1 Results of the Submerged Infinite Line Source Analysis 

From paragraph 3.4, the field components can be restated as: 

These can be suitably transformed by 

so that uO = [X2 - (%I2] l/j/ 

When z F h these integrals offer no particular difficulty in integration. With z = h, there are: 

-jUowl [~~os(Ay)dX + Ex = U e 2 n 1 

The first integrals in Ex and Hz cannot be evaluated as they stand. However, they are related 

to the modified Bessel functions: 

Considerable effort has been made to evaluate KO and K1, without resorting to special numerical techniques. Further work must be done, however, for adequate accuracy. The field 

components that are valid have been computed, viz those on the surface and Hy at z = h. 
The results have been prepared in terms of S/N~ as a function of frequency for a transmitter 

depth of 300 meters, 0 = 0.01 mhos/m and Pt = 100 W*. Figure 3 -3 depicts S/NO at the surface, whereas figure 3-4 shows S/NO at 300 meters and a displacement of 200 meters taken 

from elementary dipole computations. 

These generally show an optimum up-link frequency of about 10 kHz, and an optimum intramine frequency for a displacement of 200 meters of 25 to 50 kHz. 

Figure 3 -3. Submerged Infinite Line Source. 

*With preliminary noise grades. 
h 

r H = 300 M 

a= -01 

PT = 100 W 

MAXIMUM NOISE 

RECEIVE POINT 

DEPTH - 300 M 

DISPLACEMENT 200 M 

/ 

C 

1 K 1 OK 1 OOK 

Figure 3-4. Submerged Line Source. 
Section 4 

Signal-to-Noise Analysis for Down-Link 

Line Source Mine Communications 

This section is part of a continuing series of notes regarding analytical techniques for calculating signal-to-noise ratios in a mining environment. These propagation modes consist of 

low-frequency waves transmitted through the earth or within the mine itself. 

Some of the antenna configurations that may be used for coupling energy into the medium and 

detection are loop-to-loop, line source-to-loop, line source-to-line source, etc. Except for 

intramine loop communication, the loop-to-loop case was handled previously. This note considers a line current source on the surface for down-link communications. 

4.1 THE SUBSURFACE H-FIELDS FOR A LINE CURRENT SOURCE 

Consider a line current source (figure 4-1) in which there are no variations in the z direction. 

I v 

Figure 4-1. Line Current Source. 

Then from Wait* the H-field components below the surface at (x,y) are 

*J. R. Wait and K. P. Spies, "Subsurface EM Fields of a Line Source On A Conducting Half 

Space," Radio Science 6, 8-9, 1971 page 781. 
where 

and 

The electric field is 

where 

4.1.1 Signal-to-Noise Ratios 

Now in the case of surface line sources, the current produced by a given input power is dependent to a large extent on the contact resistance that can be obtained near the earth probes. 

According to Dr. Geyer llporous pots1' may be used to reduce this resistance to as low as 10 

ohms. Typical values for the input resistance to a line source will then range from 109 to 

2009. 

As before, the ratio of received to transmit power is 

for a loop receive antenna 

so that 

2 2 22 

Pr 40 N2 A2 B (H, X) x 10-l4 -- - 

Pt R 1~2h2 

the noise power received per Hz bandwidth is 
therefore 2 P,B (H, X) 

S/No = l2 - (h in meters) 

Hn R~ 

Line source on surface to VMD subsurface 

and 

line source on surface to HMD subsurface. 

Likewise for the E field at a submerged line source 

where L2 is the length of the receive line source. 

Since 

22 2 -14 16n f F (H, X)P, x 10 

where En is the electric noise field in v/~/Hz. 

The above relations for S/NO all assume the loolp or line source is adequately dimensionetl 

so that the external noise pickup exceeds receiver noise. 

4.2 COMPUTATIONAL RESULTS 

Equations (4-8) and (4-9) were employed in a colmputer method for the calculation of S/NO for 

depths of 300 m and 500 m as a function of frequency for various displacements (figure 4-2). 

Since Wait's A, B, and F functions are similar to his P and Q functions, the modification to 

the computer program was straightforward. All of these various S/NO calculations can now 

be made with the basic computer program by selection of the desired option. 

The results are shown in figures 4-3 through 4-7 (with preliminary noise grades). A contact 

resistance of 100Q has been assumed for the line source. The VMD, of course, will produce 

a null directly below the line source, thus there would be a preference for the HhII>. At the 

500-meter displacement, however, there is little difference between the two. 

For comparison purposes, figures 4-6 and 4-7 show a 100-meter radius loop, 200-kg weight 

driven by the same power as the line source. The subsurface S/NO is comparable to the line 

source case considering the size of the transmit loop. 
The E-field signal-to-noise ratios were not presented because of the inadequacy of E-field 

subsurface noise data. A few sample calculations made with Dr. Geyer's* line source surface 

noise data indicate that with the same subsurface noise fields, the signal-to-noise at 2 kHz 

would be comparable to the H-field cases. 

Future plans call for the injection of new noise data in the computer program as it becomes 

available and the consideration of intramine paths. 

4.3 THEORETICAL PREDICTIONS FOR S/N~ 

As a result of the theoretical analysis of this section, several predictions can be made. For 

a line source, typical values of input resis'.ance will range from 10 to 200 ohms. For a loop 

receiving antenna, the HMD orientation is preferable to the VMD orientation at shallower 

depths due to the null created by the VMD in the horizontal plane. However, at depths around 

500 meters, the two arrangements are relatively equal. For the line source transmitter configuration, the frequencies in the 1- to 2-kHz range appear to yield the optimum signal-tonoise ratios. 

*R. Geyer, G. Keller, M. Major. "Research on the Transmission of Acoustic and EM Signals 

Between Mine Workings and the Surface." Quarterly technical report. Colorado School of 

Mines, December 30, 1971. 

FREQUENCY 

Figure 4-3. Receive Signal-to-Noise Ratios as a Function of 

Lateral Displacement and Frequency. 
Fr. 
w 

0 

C 

0 

-4 

C, 

0 

!=! 

3 

Erc 

a 5 
1 KHz 

FREQUENCY 

Figure 4-6. Receive Signal-to-Noise Ratios as a Function of Lateral 

Displacement and Freq,uency. 
1 KHz 

FREQUENCY 

Figure 4-7. Receive Signal-to-Noise Ratios as a Function of Lateral 

Displacement and Frequency. 
1 KHz 

FREQLI ENCY 

Figure 4-6. Receive Signal-to-Noise Ratios as a Function of Lateral 

Displacement and Frequency. 
1 KHz 

FREQUENCY 

Figure 4-7. Receive Signal-to-Noise Ratios as a Function of Lateral 

Displacement and Frequency. 
Section 5 

LF Communication 

Paragraph 5.1 provides an overview of the mechanics of wave propagation within a coal mine 

and a preliminary look at optimum intramine frequencies. The report employs the techniques 

developed in the prior reports to analyze overall propagation for loop-to-loop and line sourceto-loop transmission for both HED and VMD ori.entations. There are 10 basic input parameters for computer programs. These are as follows: 

a. Transmitted output power 

b. Weight of VMD in kg 

c. Radius of VMD in meters 

d. Frequency in Hz 

e. Relative dielectric constant of overburden 

f. Conductivity of overburden in mhos/m 

g. Earth probe contact resistance of HED 

h. Depth of HED or VMD in meters 

i, *Noise grade 

j. Length of HED in meters 

Seven field components, five for submerged HED and two for VMD, are calculated for each 

receiving point. Comparison of theoretical and Collins measured values of transmission 

losses between line sources and the magnetic field components produced by these line 

sources are also included. While the agreement is fairly good, there are certain discrepancies. These can be explained at least partially by the following: 

a. Elementary dipoles employed in theory instead of extended sources 

b. The array of roof bolts between transmitter and receiver can and undoubtedly do distort 

the E and H fields 

5.1 ON INTRAMINE WIRELESS LF COMMUNICATIONS 

Collins has recently completed a series of brief but significant mine communications experiments.** In this section we wish to comment on their relevance to intramine communications 

and compare their results with theory in the frequency range 1 kHz to 100 kHz. 

The theory presented in the previous sections ham been incorporated into a basic computer 

program which evaluates five field components for the submerged HED: 

a ntl 

'~14 = 0, and 4 = n/2, Hplm.rI ?, 

For the VIVID we compute EIz and E 

"Preliminary noise grades. 

**Coal Mine Communications Field Test Report, Collins Radio Company, December 29, 1972. 
The basic input parameters for the computer program a r e a s follows: 

Transmitted output power 

Weight of VMD in kg 

Radius of VMD in meters 

Length of HED in meters 

Frequency in Hz 

Relative dielectric constant of overburden 

Conductivity of overburden in mhos/m 

Earth probe contact resistance of HED 

Depth of HED or VMD in meters 

Noise grade 

For each set of the above parameters, the seven field components are computed for receiving 

point depths of 0 to 350 meters in 50-meter steps and for receiving point displacements of 

100 to 1000 meters in 100-meter steps. The seven field components required the integration 

of 10 Sommerfeld type integrals, which were effectively performed simultaneously. As indicated previously, due caution was employed in the determination of the various subinterval 

limits and experimentation performed near the branch points and poles until confidence was 

obtained for adequate engineering accuracy.* 

5.1.1 Comparison of Experiment With Theory 

In figures 5-1 through 5-5 of this section, we have shown a comparison of Collins measured 

values of transmission losses between line sources and the magnetic field components produced by these line sources with their corresponding theoretical values. Collins measured 

field components, which, for an elementary dipole do not exist viz E + at C#J = 0, Ep at + = rr, 

H4 at4 = n, Hp at 4 = 0, and Hz at 4 = 0. For an extended line source, particularly for 

the first three components, these fields actually do exist, of course, since the fields should be 

integrated over the length of the conductor. 

Referring now to figure 5-1, we have shown E4at4 = n (line sources broadside). For 

this and those through figure 5-5 we have selected Er = 10, and o = 0.005 mhos/m. This 

value appeared to offer the best fit in the loss decrement characteristic with frequency and 

distance and therefore is probably reasonably close to the average overburden value. We 

note insofar as this field component is concerned, theory actually indicates a lower loss than 

experiment below 50 kHz, but a higher value above 50 kHz. In figure 5-2, Ep at 4 = 0 (line 

sources end fire) we find the same effect, however, somewhat more emphasized. Figure 5-3 

shows H+ at 4 = 0 now plotted in magnetic field strength dB > lP~/m. We find now that 

theory predicts a lower loss (about 10 dB) than experiment indicates. For Hp at $ = 90" 

(figure 5-4) and Hz at 4 = 90" (figure 5-5) a good agreement with an rms error of 2 to 3 dB 

is observed. 

While the agreement is fairly good, the discrepancies can be explained partially at least by 

the following: 

a. Elementary dipoles employed in theory instead of extended sources. 

b. The array of roof bolts between transmitter and receiver can and do undoubtedly distort 

the E and H fields. 

*R. P. Decker, "Signal-to-Noise Analysis for Loop-to-Loop Mine Communications," Subject 

Data C-684420, 25 September 1972. 
1 KHz 10 KHZ 

Figure 5-1. Comparison of Theoretical and Measured Transmission 

Losses Between Line Sources - 

E$5 = n,2. 
1 KHz 10 KHZ 100 KHz 

Figure 5-2. Comparison of Theoretical and Measured Transmission 

Losses Between Line Sources - Ep 1 + = 
- - 

1 KHz 10 KHZ 100 KHz 

1 'I - , THEORY 

I 

EXPERIMENT 

"+I+= 

0 PC \/ 

3001 

h31 

.. 

'01 

1 --- (1. (3- -- \ 

C)- \- 

h -- - 

Figure 5-3. Comparison of Theoretical and Measured Transmission 

Losses Between Line Sources - H+ '+= 0. 

lb 

O'\ \ 

\ 

\ 

\\ 6561 

\ I 
Figure 5 -4. Comparison of Theoretical and Measured Transmission 

Losses Between Line Sources - += 90' 
- - I - THEORY 

I EXPERIMENT 

I 

Hz I+= 90 DEGREES 

1 

J\ 

\ 

\ 

\\ 

656 1 

Figure 5-5. Comparison of Theoretical and Measured Transmission 

Losses Between Line Sources - 

Hz I $ = 90' 
The extended line sources can be handled fairly easily as far as their primary fields are 

concerned; however, the "bed of nails" in the overburden may be an intractable theoretical 

problem. 

As time permits we will calculate the effect of an extended source on the received field 

strength and open circuit voltage of a receiving line source and the vertical magnetic field 

component, with the receiver at the same depth as the transmitter. 

For Ep, $ = 0 

The open circuit voltage on an identical receive line source is: 

For E+"), +O = n/2 

For Hz('), $ = "/2 

A significant aspect of this data is that above 50 kHz, say 50 to 100 kHz, theory is consistently pessimistic for both the E and H field components. Also, field components exist where 

none would under the half-space model and elementary dipole conditions. From the Collins 

measurements apparently these components are seldom less than 15 dB below the main 

component. 
5.1.2 System Design of Basic Intramine Paths 

With the basic computational tools in hand, we now proceed to examine some basic intramine 

path configurations. Consider first a personal portable transmitting loop with a receiving 

line source within a mine working section. For this we have taken 0 = 0.01 mhos/m, depth 

222 meters, a displacement of 100 meters (half the length of a working section) a power of 1 

watt into a 6-inch-diameter loop with a weight of 0.25 kg. We need, of course, E-field noise 

data which is essentially nonexistent. However, by establishing the quiet mine E-field noise 

at 20 kHz deduced from Collins measurements and the use of R. Geyer's limited surface 

noise data, we have been able to assemble a first or zero order approximation to the max and 

min values of this noise from 1 to 100 kHz. 

The results are plotted in figure 5-6 in terms of S/NO. They show a possibility for quite 

acceptable voice quality in the frequency range of 70 to 100 kHz. This would also include a 

"loop orientation variabilityrr margin of at least 15 dB. 

In figure 5-7 we have taken the same transmit loop, but now reception is on another VMD. 

Adequate noise data is available for this case and the S/NO is shown versus frequency for the 

extreme cases.* Here we find essentially the same optimum frequency range; however, the 

maximum S/NO is approximately 28 dB lower than in the case of the line source receiver. 

The next type of intramine path which is self-suggestive is a line source to line source link 

between working sections (figure 5-8). We have taken a power of 100 watts and a line source 

length of 16 meters and a displacement of 200 mieters. Using the maximum noise characteristic, the optimum frequency range of 25 to 50 kHz produces an output S/NO of about 55 dB. 

This should also be an acceptable value for a voice link. (Note that larger paths exhibit a 

lower optimum frequency range.) 

The next logical case is VMD to VMD between working sections (figure 5-9). Here we have 

used a 4-meter diameter 10-kg transmit loop wi.th a power of 100 watts. We find the same 

optimum frequency range as the previous one, but the (max) S/NO is 10 dB lower. This could 

be made up by a 12-meter diameter transmitting loop, but would be considerably more expensive and less convenient than line source to line source. 

Figure 5-10 depicts the expected S/NO for a line source transmitter to a VMD receiver within 

a working section, Pt = 100 watts and a line source length of 16 meters. Figure 5-11 is 

identical except for a displacement of 200 meters. 

This clearly demonstrates that a line source with a reasonable power input at maximum 

noise conditions has a maximum voice range of (about 140 meters (460 feet).* 

*With preliminary noise grades. 
1 KHZ 10 KHz 

Figure 5-6. Portable VMD to Line Source. 

100 KHZ 
Figure 5-7. Portable VMD to VIVID. 
Figure 5-8. Line Source to Line Source (Broadside). 
10 KtiZ 

Figure 5-9. VMD to VMD. 
0 

(1 

MIN NOISE 

f\ 1/10 

K ti Z 

MAX NOISE 

0 

t++ PT = 100 W 

LS = 16 METERS 

U = -01 MHOS/M 

DISPLACEMENT 100 METERS 

DEPTH 222 METERS 

I 

10 KHz 100 KHz 

Figure 5-10. Line Source to ~~!I~/~is~lacement - 100 Meters. 
1 KHZ 10 KHZ 100 KHZ 

Figure 5-11. Line Source to ispl is placement - 200 Meters. 
5.1.3 Conclusions and Recommendations 

From the above analysis we can formulate some basic conclusions for intramine communications: 

a. For personal portable If wireless communications within a working section a loop-line 

source 2-way link is indicated as optimum in the frequency range of 70 to 100 kHz. The 

portable loop input power should be approximately 0.5 to 1.0 watt. 

b. For relayed transmission between working sections a line source to line source (broadside) 2-way link is indicated as optimum in the frequency range of 25 to 50 kHz. Line 

source lengths should be 16 meters (or more) with an input power of about 100 watts. 

While these conclusions are quite significant, the VMD to line source link needs experimental 

verification and a series of measurements should be outlined to confirm the efficacy of the 

link under maximum noise conditions encountered in a working section. Also, we must again 

stress the urgent need for subsurface E-field noise data. 
Section 6 

The Application of Recent NBS Noise 

Data to Mine Communications 

Recently, NBS has generated a considerable amount of surface and subsurface mine noise 

data, principally that of the horizontal and vertiical magnetic field components at a representative sampling of locations, all under power-on conditions. The spectrum date of W. Bensema 

generally covers the range of 1 to 100 kHz, while Kandu's APD data was taken at 6 or 8 frequencies beginning at 10 kHz and extending into the hf range. While the location sampling was 

representative, there appeared to be considerablle attention given to finding the maximum 

noise possible (for example, trolley noise with car pull). Also, the spectrum data was again, 

in several instances, system noise limited, which is an inherent problem with wide bandwidth 

analysis in setting the system gain unless a low-pass filter is employed below, say, 10 kHz. 

An additional comment is that frequencies of interest were generally considered to be below 

20 kHz, whereas, frequencies for certain intramine paths exhibited optimal S/N performance 

at frequencies in the range of 30 to 90 kHz, based on previously available noise data. All 

things considered, the data is of excellent quality, covers several types of mines, and lends 

itself well to mine communication system analy,sis. 

The following discussions consider data from the following mines: 

MINE TYPE: 

Robena 600 V dc, rail haulage 

McElroy ~c/dc, underground rectification, 

belt a~nd rail haulage 

Itman Same as McElroy 

Geneva ~c/dc, rail haulage 

6.1 METHOD OF ANALYSIS 

Each curve of W. Bensema's spectrum data was subjected to a regression analysis to determine the equivalent running average of the minimum noise between spectral peaks. About 

100 sampling points were used for each curve. This was done principally to improve the 

accuracy of noise representation and facilitate the injection of this data into the general intramine path propagation program. The functional dependence was determined entirely in terms 

of dB > /p~/meter/ m. 

6.2 ROBENA MINE 

The Robena mine is a 600 V dc mine, (dc conversion on surface) with rail haulage. The summary of the equivalent background (between peaks) noise fields are shown in figures 6 -1 

through 6-5. Both horizontal and vertical magnetic field noise components were measured 

and a few roof-bolt measurements were included. Figure 6-1 shows trolley and face area 

noise levels. The trolley noise indicated in the irpper curve represents some of the highest 

noise fields ever measured in a mine. The face area levels are many dB less, hut the vertical component at the face area is roughly 25 dB higher than either horizontal component. 
Figure 6-2 represents noise components in crosscuts 7 and 9 in which the spectrum display 

was system noise limited. The only conclusion that can be obtained from these curves is 

that the true noise levels are no greater than those shown in this figure. The APD data in 

figure 6-3, shows generally the same levels of noise that were determined from spectrum 

data aside from trolley noise. We note here a high degree of variance of horizontal component with frequency. Figure 6 -4 illustrates the extremes and means of the subsurface horizontal component and figure 6-5 the same for the vertical component. 

The mean of the vertical component is about the same as the mean of the horizontal component. The vertical component of the surface noise field is also shown in figure 6-5. The 

roof-bolt noise data was examined, but the conversion factor to absolute values was lacking. 

As soon as this conversion is available, W. Bensema will inform the writer. 

The conclusions that were reached from the Robena data are as follows: 

a. There is no preference between the horizontal and vertical magnetic noise fields from 

the standpoint of their mean values as a function of frequency. 

b. Less system gain protection factor is needed for the vertical component to allow for 

noise level variations with location. 

c. Noise pickup on roof bolts does not increase with separation. 

d. The surface noise fields were less than the minimum power-on subsurface fields, for 

the data presented. 

e. The extreme noise fields represented, for example, by trolley noise may preclude the 

application of LF quasi-static propagation paths intramine with receive antennas near 

this noise source. 
a 

cll 

. & 

cd 

E 

a 

cll 




6.3 McELROY MINE 

The McElroy mine is a dc mine with underground rectification and belt and rail haulage. 

Summaries of the equivalent background noise fields are shown in figures 6-6 through 6-15. 

Vertical noise fields in the face area and in location no. 2, which have a relatively small 

variation in the means, are shown in figure 6-6. The composite of this data is shown in 

figure 6-12 and can be considered to be a quasi-maximum average of face area noise. Kanduls 

APD equivalent of Bensemals figure 97-83 is also shown, but there is little correlation except 

at 10 kHz. Vertical noise fields for the head piece, middle of crosscut, and elevator shaft 

are shown in figure 6-7. There appears to be quite a bit of variance in these noise fields; 

however, considerably quieter fields are noted at the elevator shaft. 

Figure 6-8 summarizes Kanduls APD measurements, showing about the same mean levels as 

in figure 6-7 at 10 kHz and for corresponding conditions in the Robena data, but with less 

variance. Figure 6-9 shows additional vertical field data at the head piece and arc welder. 

The 10-kHz peak for the head piece is an extremely high level for this frequency. An assortment of various locations and components is shown in figure 6-10. 

The power entry is a maximal noise condition, while the site farthest from the power entry 

exhibits the quietest noise fields. Figure 6-11 shows additional high vertical noise fields in 

crosscuts and face areas. We note here the extension of high noise fields out to 50 kHz. 

Surface noise fields are shown in figure 6-12. These fields are relatively quiet and show a 

small degree of variance. The extremes and the means of the noise fields for the McElroy 

mine are shown in figure 6-14. The extremes for Robena are higher than those of McElroy, 

principally because of trolley noise, but the means are rather close except that McElroy 

exhibits higher levels between 12 and 50 kHz. McElroy also shows lower power-on minimums 

than Robena. Figure 6-15 shows the surface noise summary for McElroy and the correlation 

of McElroy data with Robena, Maxwell and Stone, and Geneva. The agreement is reasonably 

good with a relatively small degree of variance. Roof-bolt noise was not examined because 

of lack of calibrating data. 

The conclusions that may be drawn with respect to the McElroy mine data are as follows: 

a. Mean noise fields are about the same as Robena noise fields. 

b. The surface noise fields lie between the mean and minimum subsurface noise fields, 

power -on. 

c. There appears to be a high degree of correlation between the surface noise data for the 

McElroy and Robena mines. 

Figure 6 -7. McElroy Spectrum ~ata/~ertical Noise Fields, 

Headpiece, Crosscut, and Shaft. 

1 OOK 
1 OK 1 OOK 

F - HZ 

Figure 6-8. RIcElroy Spectrum D~~~/APD (RMS). 


Figure 6-11. hlcElroy Spectrum ~ata/~dditional High Vertical Noise Fields, 

Crosscuts and Face Areas. 

(- 

1 

I I 

AREA, 

MINER 

I I 90-83 H~(v) 

1-1 

I Ill 

Ill 89-83 CROSSCUT HN(v) 

1 OOK 

Figure 6-13. McElroy Spectrum Data. 


6.4 ITMAN MINE 

The Itman mine is also a dc mine with underground rectification and belt and rail haulage. 

Summaries of the equivalent background noise fields are shown in figures 6 -16 through 6-21. 

All magnetic field noise data correspond to the vertical component. Figure 6-16 shows noise 

levels for portal buses and in the Cabin Creek area. Figures 6-17 and 6-18 were recorded at 

the Farley Panel and Bensema's figure 39-85 (figure 6-17) is considered to be an especially 

good representative sample of noise 16 ft from the miner in the 10-kHz to 100-kHz region. 

Figure 6-19, 30 ft from miner, also exhibits very similar characteristics to the previous 

three figures with little variance. Figure 6-20, Kandu's APD data is also consistent with the 

previous data except for data from the 2nd day .which exhibits anomalously high fields in the 

50- to 100-kHz region. The extremes and the nneans of the Itman data are shown in figure 

6-21. Note the small variance between the mean and the maximum. The sudden drop in the 

minimum level at 10 kHz is due to the inclusion of APD data. 

The general conclusions which may be drawn with respect to Itman data are as follows: 

a. The noise data is quite consistent with little variation in the medians. 

b. The means are lower than either Robena or McElroy, particularly above 5 kHz. 

Again, the roof-bolt noise was not examined, beleause of the lack of a calibration factor. 
Figure 6-16. Itman Spectrum ~ata/~oise Levels - Portal Buses and Cabin Creek. 
~igure 6-17. Itman Spectrum Data Farley ~anel/~oise - 16 Ft From Miner. 

1 OOK 

1 OOK 

F - HZ 

Figure 6-19. Itman Spectrum ~ata/30 Ft From Miner. 
MEDIANS 

2ND DAY 

1ST DAY 

Figure 6-20. Itman Spectrum D~~~/APD. 

6.5 GENEVA MINE 

The Geneva mine is also a dc mine with underground rectification and belt and rail haulage. 

All measurements on hand for the Geneva mine are surface noise fields. Summaries of the 

equivalent background noise fields are shown in figures 6-22 through 6-25. These results 

show generally that there is a small variance in the means of the horizontal component, but 

very little variance in the mean of the vertical component. The surface fields measured at 

Geneva are the quietest of the four mines. 

EAST-WEST 

Figure 6-22. Geneva Spectrum ~ata/~~(~) ~ast-west. 


Figure 6-25. Geneva ~~ectrum/~ata Extremes. 
6.6 SUMMARY 

The data from the above mentioned four mines by the NBS/ITS team is valuable data and is 

characteristic generally of noise conditions encountered under power -on conditions. Suffi - cient data has been reduced to represent various mine locations for 3 mine types, plus surface 

noise. Fourteen noise grades have been defined as follows: 

NOISE GRADE 

1. 

600 Y dc mine [ 2. 

Ac/dc mine 

Quieter ac/dc 

mine 11. 

Dc mine, maximum trolley 

DC mine, face area, mean 

Dc mine, face area, minimum 

Ac/dc mine, head piece, maximum 

Ac/dc mine, face area, quasi-maximum 

Ac/dc mine, mean noise 

Ac/dc elevator shaft 

Ac/dc power-on, quasi-minimum 

Ac/dc maximum (Itman) 

Ac/dc mean 

Ac/dc quasi-minimum 

Surface noise - mean 

Surface noise - power-on, minimum 

Mean noise - all mines subsurface 

The extremes and means of the four mines are shown in figure 6-26. The maximum level is 

that due to Robena trolley noise, while minimum levels are principally due to Itman. The 

mean has been determined by averaging all data and is given by the following: 

The above relation and the application of the 14 noise grades should shed new light on optimal 

intramine frequencies. In the next section we shall give results of the S/N analysis for various paths and noise conditions. 

6.7 RESULTS OF PROPAGATION PROGRAM ANALYSIS 

Figure 6-27 shows the relationships of the electric and magnetic field components from 

transmit line and loop sources respectively in the spherical coordinate system for the computer printouts on the following pages. 

The printouts incorporate the updated noise data with the communication propagation analysis 

program; for example, if we required the magnetic field component from a transmit line 

source at some perpendicular distance Y, from the source, we could read this component 

from the Hz (PHI=90) column at a specific transmitter depth and displacement. Such would 

be the case if the perpendicular magnetic field component were required for a receiving loop 

in the X-Y plane at some displacement from the transmit line source. For a horizontal surface loop to an underground horizontal loop antenna, the Hz (perpendicular field component) 

is taken from the Hz (VMD) column of the printout at the desired loop displacement and 

separation. 

Although the depth of transmitter is a variable, as far as the printout is concerned, reciprocity still applies and transmit position and field sample points may be interchanged. All data 

is referenced to dB greater than 1 ampere/meter or 1 volt/meter. 

To apply the data to a typical situation, one must first calculate a correction factor for that 

situation. See figure 6-27 for correction factor formulas. This factor is then added to the 

printout data to correct relative field intensity data to the actual power level, loop diameter, 

line source length or loop weight used. Subtracting the appropriate noise grade from the 

corrected field intensity data yields the S/N~ ratio at the sample point in question. If it is 

necessary to know the open-circuit volts from a loop immersed in a known field, one can 

apply the equations from section 2 to the corrected field data from the computer printout. 
Z TX LINE SClURCE 

Z TX LOOP SC>URCE 

P L 

C.F. = 10 LOG - +20 LOG LO 0 

P - Y 

P R C.F. = 10 LOG - + 20 LOG - P R 0 0 

W + 10 LOG - 

X W 0 

Figure 6-27. Vector Relationships of Electric and Magnetic 

Field Components for Printouts on Pages 6-34 

Through 6 -83. 

FlifOo 1000.00 HZ CI1NO.= .C1 HtlCl\/w EPS- 13.00 POhFR= 10.00 nGTT5 XMIT LOOP WEIG

LINE SOURCE CONTACT RESISTANCE = 100.00 OHMS 

?iGISE = 

hOISE = NOI'iE = 

I*OISE = NOIC,E = erOISF = 

ruOI',€ = 

NOISE = 

hlOIC,t = IJOI SE = 

tuOISE: = NnISt = NOISF = N014F. = NOISE = 

-66.00 OH *GT. lA/M NQISE GRAOE ? 

-49.03 OH .GT. lA/M NOISE GRADk = 2 

-110.OC DR .GT. 1A/M NOISE GRPDE 3 

-77.00 Oh .CT. 1A/M NOISE GRADE 4 

-Q0.00 OH .GTe lA/M NOISC GRntE = 5 

-97.0~ no .~r. IA/W msz GRLDE = 6 

-119.09 DL? .GTe 1A/# "JOISE GRADE = 7 

-119.00 Ob .GT. 1A/M NOISE GRhOE n -86.00 OB eGTe 1A/H NOISE GRADE = 9 

-97.09 OH .GT. /AIM NOISF GnACF r 1O 

-114.02 0s .GT* 1A/M NOtSF GRAOE II 

-125e00 Dl' eGTe LA/# NOISE CRAnE = 12 

-144.06 Dt? eGTe 1A/M NfJISE GRAOE a 13 

-96.00 D9 .GT. lA/M NOISt GRAOE 14 

-91.00 DL .GTe 1V/M NOISE GRpOE = 15 
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SE a -107.00 OR oGT. 1A/F NOISE GRADE m 4 

SE a -129.00 00 .GT. lAIH NOlSE GRAOE a 7 

SE m -139-00 06 oGTo lA/M NOISE GRAOE 8 

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LINE SOURCE CONTACT HESIST4NCE = 100,00 OHMS 

NUlSE o -71.00 Dh .GTo 1A/H NOISE GHAbE 1 I 

NOiSE P -103.00 Dl3 .GTo 1A/P NOISE GHAOE 2 

NOISE -128000 05 OGT. LAIH NOISE GRBffE 3 3 

NOISE p -87.00 DH AT. ~AIH GRAOE 4 

NOISE = -99.00 OR oGTo 14/H NOISE GRADE 5 

NOISE o -107.00 DD OGTo 1A/H NOISF GRkOE 4 

NOISE -L29000 DH .GTo 1A/M HOISF GSAOE 7 

NOISE m -139.00 DH .GT. lAIM NOISE CHAOE - 8 

NOISE a -100.00 08 OGT. 1A/H NOISE GRADE * 9 

YOISE -113.00 OR -GT- LAIH NOISt GRADE 1 10 

NOISE a -123.00 Oh .GTo 1A/H NOISE GRADE 11 

NOISE t -130oOG 0B .GTo 1A/M NOISE G8AOE 12 

NOISE = -147.00 08 .GT. lA/H HOISt GRAOE 13 

NOISE = -107.00 DB .GT. lA/N NOISE GRADE = 14 

NOISE x -95.00 OB .GTo 1V/M NO1 Sf GRADE 15 
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ClNF SCJURCE CONTACT RESISTANCE - 10Q.00 CIHHS 

NOISE .I -82.50 DB OGTo 1A/N NOISE GRADE 1 

NOISE a -113.00 08 .GTo lAIH NOISE GRADE 2 

NOISE a -141.00 CR .GTo l4IM NOISE GRAOE 3 

NOI5E m -106.00 Db .GTo lA/# NOISE GRADE 4 

FJOlSE a -113.00 OR .GT. tA/H NOISE CRADE m 5 

NOISE o -120.03 Ob OGT. 1AIM NOISE GRADE = 6 

NOISE t -136.00 OH mCT. 1AIH NOISE GRADE t 7 

hOlSE = -160.00 DB OGTm 1A/Y NOISE GRAOE 8 

NOISE a -118.00 00 oGT. 1A/M NOISE GRADE 0 '9 

NOISE 1 -128.00 DH OGf 1A/H NOISE GRAUE * 10 

I~OISE a -137.00 Dn .GTo lA/M NOISF CRAOE 1I 

KOISE = -144.00 08 .GI. 1A/H NOISE GRADE 12 

NOISE r -153.00 DU .GTe 14/M NOISE GRAOE * 13 

NOISE z -119.00 OR .GT. lA/H NOISE GRADE 14 

NOISE = -107.50 DH .GT. Iv/n NOISE GRADE 6 15 

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FREQ= 7000.00 tiL CUN0.o ,01 MItOS/E EPS* 10.00 PC)WERo 10.00 WATTS XMlT LOOP WEIG

XMIT LOOP RADIUS= 20.00 M LINE SOURCE LENGTH- ~OO,QO H DEPTH QF TRANSMITTER- 300~

LINE SOURCE CONTACT RESfSTANCE t 100,OG Ohus 

NOISE 

NOISE = NOIZE J 

NOISt = 

NOISE = YOiSE = ronlsE m 

NOI5E = 

NOISE = NOISE = 

NOISE = NOISE = NOISE = 

NOISF = 

NOISE = 

00 mGTm IA/H NOISE 

08 mGTo 1A/M NOISE 

09 eGTe 1A/H NOIS: 

08 mGTm lA/H NOISE 

Od .Gl. 1A/M NOISE 

CP ,GT. lA/M NOISE 

OH mGTm 1A/Y NOISE 

OB mGTm iA/M NOISE 

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OR .GT. lA/M NOISE 

06 mGTm lA/M NOISE 

on .GT. 1A/n NOISE 

OU .GT. lA/H NOISE 

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GRADE 

GRAOE 

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1 LINE: SflURCE CONTACT RESISTANCE = 100.03 OIiHS 

NOISE = 

NClI SE = NOISE 

r\lOICJE = NOISE a 

NOISE = 

NOIEE = 

NO1 SE = NOISE = NO1 S€ = NOISE = 

NOISE = 

NOISE = NOISE = NOISE = 

0GTo 1AIW NOISE GRADE f 

.GTo iA/M NOISE CR40E i 

.GT. iA/H NOISE GRAOE = 3 

OGTO lA/M NOISE GRAOE t 4 

.GTo lA/H NOISF GA40E 5 

oGTo lA/M NOISE GRAOE C 

0GT- lh/N NOISE GRAOt a 7 

.CTo tA/M NOISE GRAOE a $ 

0GTo lA/H NOISE GRAOE = '3 

oGT0 IA/W NOISF CR&@E 1 10 

.GTO 1A/M NOISF GRADE = li 

OGTO lA/M NOISE GRADE a 12 

.CT. iA/H NOISE GRADE = 13 

0GT. 1A/M NOISE GRADE 14 

oGT0 IV/U NOISE GRADE 15 
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NOISE = -:SI.OS oe .G 

NOISE rn -101.00 OB oG 

NOISE 0 -123-00 0t5 aG 

NOISE = -125.00 00 oG 

NOISE 9 -137m00 DC oG 

NOISE P -165.00 08 .G 

NOISE rn -131.00 OE .G 

NnISF e -142.00 08 aG 

YOISE r -161.00 OP oG 

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GRAOErt 2 

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GRAOE 4 

GHAUE= 5 

GRAOE = 6 

GRAOE = 7 

GRdOE 8 

GRADE 9 

GRADE = 10 

GRdUE a 11 

GRAOE = 12 

GRAUE = 13 

GRADE = 14 

GRAOE = 15 
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XMIT LOOP RADIUS= 20.00 H LINE SOURCE LENGTH= 100.00 H DEPTH OF TRANSNITTER- 50

LINE SOURCE CONTACT RESISTANCE r 100.00 OHMS 

NOISE m -122e03 DH eGTe 1A/H NOISE GRADE a 1 

NOISE a -137e00 CB eGT. IA/M NOISE GRAOE + 2 

NOISE 1 -143.00 OB eGTe 1A/H NOISE GRADE 1 3 

NOISE s -136.03 08 .GTe 1A/R NOISE GRADE - 4 

NOISE -126e60 08 eGTe lA/H NOISE GRADE - 5 

NOISE m -137e00 08 .GTm 1A/M NOlSF GRAUE b 

N~I:F = -154.00 00 .GT. LAIN NOISE GRADE 7 

NOISE 8 -f67e00 00 -GT. 1A/M NOISE GRAOE * 8 

NOISE a -L51.00 08 eGT. 1A/M NOISE GRADE 9 

NOISE = -158e00 08 .GTe lA/M NOISE GRaOE a 10 

WOISE = -181.00 08 eGT. LA/H NOISE GRAOE = 11 

NOISE = -172e00 00 eGTe 1A/M NOISE GRADE s 12 

NOISE m -179-00 D8 .CTe L&/M NOISE GRAOE 13 

NOISE I -148e00 08 eGTe lA/H NOISE GRACE = 14 

NOISE = -1le.aa oe .GT. iv/n NOISE GRADE = is 
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XHIr LOOP RAOfUS= 20.00 N LINE SOURCE LENGTH- 100.00 M DEPTH OF TWAYSR~TTERI 200~

LIhE SOURCE CONTACT RESISTANCE = 100.00 OHMS 

NOISE -122.03 OH OGT. IA/M NOISE GRADE = 1 

NOISE o -177000 08 .GT. 1A/H NOISE GRdDE 2 

NOISE s -163.00 08 .GTo 1A/# NOISE GRAOE 3 

NOISE v -138.00 00 .GT. lA/M NOISE GRADE 4 

NOISF = -126000 OH .GT. lA/N NOISE GR4OE = 5 

N015E = -137.00 OH .CT. 1A/U NOISE GRADE = 6 

NOISE m -154.00 OR .GT. 14/H NOlSF GRADE 7 

NOISE = -167.00 08 .GT. lA/H NOISE GRAOE = 6 

NOIqE a -131-00 UH .GT. 1A/M NOISE GRAOE a 9 

NOISE r -158.00 DB OGT. AA/M QOISE GRADE 1C 

NOISE a -181.03 OH OGTo 1A/H NOISE GRADE m 11 

NOISE = -172.00 Of3 .GT. LA/H NOISE GRAOE m 12 

NOISE m -179o00 09 OGTm 1A/M NOISE GRAOE 13 

NOISE a -148.00 08 mGT. l&/H NOISE GRADE a 14 

NOISE 0 -118.50 00 DGT. lv/M NOISE GRADE 15 
FREQr 50000e00 HZ CONDo= 001 MHOS/H EPS- 10.00 POWER= 10000 WATTS XMIT LOOP WEIG

XWfT LOOP RADIUS- 20.00 H LINE SOURCE LENGTH= 100.00 H OEPTH OF TRANSWITTERm 30000

LINE SOURCE CONTACT RESISTANCE - 100000 OHMS 

NOISE rn -122000 08 oGTe IA/W NOISE GRADE 5 1 

NOISE - -137.00 00 oGTo lA/M NOISE GRADE 2 

NOISE m -163.00 OR oGT, 1A/H NOISE GRADE 3 

NOISE * -138.00 00 eGTe lA/M NOISE GRAOE 4 

NOISE p -126.00 08 oGTe 1A/M NOISE GRADE = S 

NOISE I -13'7-00 00 eGT. lA/M NOISE GRADE t 6 

NOISE m -154.00 08 oGTe 1A/M NOISE GRADE 7 

NOISE -167.00 08 eGTo 1A/M NOISE GRADE = 8 

NOISE * -151.00 00 .GTe 1A/n NOISE GRADE = 9 

NOISE - -158.00 OR oGTe 14/H NOISE GRAOf = 10 

NOISE m -181e00 OB oGTo lA/M NOISE GRAOE 8 11 

NOISE w -172.00 08 oGTo lA/M NOISE GRADE = 12 

NOISE I -179.00 DB .GTe 1A/W NOISE GRAOE 13 

NOISE * -146.00 OB oGTo LA/H NOISE GRADE = 14 

NOISE = -110050 Of3 oGTo 1V/M NOISE GRADE 15 
FHL~= 7n000.00 VL CUNU.- -01 MHOS/M E?S= 10.00 POHER- 10.00 kATTS XMiT LOOP W

XMIT LOUP HAUIUS= 20.00 M LIN~ SOURCE LENGTHS 100.00 M UEPTH OF TRANSMITTER= 

LIhE SOUSCE CONTACT RESISTANCE = 190.00 OHMS 

:VOISE = ~uUISE = lvOISE a 

NOISE = NOISE = NOlSt: = NOlSt; - 

lvU1SE a 

hOISE = NUISE = hQlSE = NOISE = l\O I St = NOISL 

NOISE 

NOISEGRADE= 1 

NOISE GRADE * 2 

NOISE GRADE = 3 

NOlSt GRADE - 4 

NOISE GRADE * 5 

NOlSt GRADE * 6' 

p4OISE GKADE = 7 

NOISE GRADE - 8 

14OISE GRADE = 9 

JOISE GRADE * 10 

NOlSt CHADE 8 11 

NOISE GRAUE * 12 

NOISt GRADE 1 13 

NOISE GKADE = 14 

NOISE G8ADE * 15 

WWWWWWWWWWWWWWW 

mwmmmmmmm#mmm#m 

8 

.- Lu 

, C' W \ 0 C' 

m3z 

CCI 

ICE+ 

I: V) 

h - 

-'zm 

0-W 

. -J (* 

Oc~OOOGOGCOOO 

CCOCCCOCCCOC 

............ C C C C C C 

C C C C C C 

COOOOCOGCOOC 

000000000000 

-*-*-a a-*-*-*-*.*-a *-a 

Y~UYCCCCCCCC 

C\rfiYY-CCCCCC : - fiPP 
FREn= 7h000.00 ~7 CnND9m -01 MH~SIH FPSr 10.00 ~OWER- tO.00 WATTS XMIT LOOP W

XMJT Lnop RADIIIOI 20.00 w LIP!€ SnUqCF LENGTH- 106.00 M nEPTH nF TRANSMITTER- 20

LINE SOURCE CONTACT RESISTANCE = 100.00 OHMS 

,126,00 Dl3 .GT, 14/M NOISE GRADE r 1 

-141.00 DR ,GI. 14/~ NOtSE GRADE - 2 

-163.00 DR .GT, I&/M NOISE GRADE r 3 

-141.00 DR .CT, 14/M NbI9E GRADE r 4 

wj31.6n DB ,GI, lr/M NOISE GRADE = 5 

,153,06 DR ,Gt, 14/M NWSE GRADE = 6 

-158.00 DR ,GT, 14/M NOISE GRADE 7 

-171.06 DR ,GI, 14/M NOISE GRAOE r 8 

-iAb,flb DB ,GT, 141~ NOISE GQADE - 9 

-153.@n D8 .CT, 14/M NOISE GRADE r 10 

-!8i906 DB ,GT, 14/~ NOISE GRADE r 11 

-175.00 DR ,GI, 14/M NOISE GRAOE r 12 

"186.00 DP ,GI; 14/M NOISE GRADE 13 

-f55,06 DB .GI, 14/M NOISE GRADE 14 

-123.56 D9 .GT, lV/M NOISE GRAOE 1 15 
0 r 0 I WWWWWWWWWWWWWWW 4 0 PPP~~PP~EclPRca~a 

4444444444<<444 

o a~mam~aacraw~aa~ 0 UJuoUoUJooUUUJUaUa a . z 0 WWWWWWWWWWWWWWW e c cncnncnmmnmwwanc~ww C! - CCCnLCuuCLLuLCC 

Z COaGCCGC~COC~O@O 

W zzzZzzzzZzzzzzz 
PPXNCk 

COOCCOu-uhj 

00000000UIVVV 

............ 

OOGOOOCOCCCO 

OOOCGOCOCOOC 

...m...m .-. . 000000000000 

CCCCCCCCCCOC 

h C 

X) 

0 

0 m r n3 002 

c C. 

ZC. 

+OH 

D 

3 0 

-4 

a o, -1 Cr7 -4 

DCC 
WWWWWWWWWWWWW WW POPC~QO~~DP~D~C 

<4<444<4<44<<<< 

tYKLrPtY tYb(tI*tlrtYKbK 

aaamammaaamac5aa 

WWWWWWWWWWWWWWW mQtoU3v,cnv,cnu,u,Y,u,rr,mv, 

CCCCCCCGc~COCCCC 

CCCGCCCOGCCCCCF 

............... 

w~09hO-CC1m0C-4m 

tv9h-ur,c~~maaa~~n 

----*.-&----he-+ 

11&188&It~I&tIt 
OWER- 40.00 WATTS XMIT LOOP WEIGHT= 6.00 KG 

S 

l 1 

2 

= 3 

4 

- S = 6 

m 7 l 8 = 9 

10 

11 

l 12 

= 13 

. 14 = 15 
wt2e,on DR ,GT, 14/M NDlSE GRADE a 1 

-144.00 DR ,GT, 14/M NOISE GRAnE = 2 

rI9O.on DR ,GT, 14/M NOISE GRADE = 3 

,r44,an DR .GT, 14/14 NOISE GRADE 4 

,(37,nn DR ,GT, 14/M NnlSE GRADE 5 

-163.00 DR ,GT, !AIM NOISE GRADE = 6 

.lnl.na DR .GT, 14/14 NO~SE GRADE = 7 

.!no.nn DR .Gt, 14/M N~SE GRADE A 

-15n.oo DR .GT, lt/M NOISE GRADE 0 9 

-164,ao DB .GT, 64/14 NOISE GRADE = 10 

-1Rl.oO DA .GT, I~/M N@lSE GRAIYE = 11 

rlA6,OO DR .GT, 14/M NOISE GRADE 12 

-19n.00 DR .GT, 14/M ~b19E GRADE 0 13 

-161.00 DR .GT, ~A/M NOISE GRADE 14 

-j35.56 DR .Gym i\/l14 NOISE GRADE 15 
CCCCCC 

UPUW-39CDY01Ul4~w~ 

m 0 h) 0 

noz 

0- u ZO. 

-401 * 

,3 1 + 

;Or. mu0 

CnLu Pt V, x -4-1 

D33 

ZCCb 

a.D\ rnOf 

'T 

1 

r 19 m Q 

Z V, - u7 1 

0 4 

0 x 

I0 0 

0 0 0-0 

CCD-CCC 

UPU~~OO0YObUIUN- 
LINE SnURCE CONTACT RESISTANCE B 100.04 OHMS 

'SF . :SF + 

:SF B 

:SF 

SF r 

'SF . SF I 

'SF r 

SF 

SF . SF r 

SF 

SF + 

SF r 

SF r 

-130.00 DR .GT, 14/H NOTSE GRADE = 1 

-14A.nO DB ,GT, 14/M NnTSE GRADE = 2 

-190,no DR .GT, 14/M NOISE GRADE = 3 

.t50,00 DR .GT, 14/M NnfSE GRAOE = 4 

-145.40 D9 ,GT, 14/M NnISE GRADE = 5 

-177,On D9 ,GT, 14/M NOISE GRADE = 6 

-1E7,On DR .GT, 14/M NOISE GRADE 1 7 

-1R6,oO DR .GT, lr/M NoTSE GRADE r b 

-!hb,oO DR .GI, 14/M NOISE GRADE = 9 

-t74,00 DR ,GT, 14/M NOISE GRADE 10 

-!R3.00 DR .6T, lr/H NOTSE GRADE = 11 

,tQR,on DR .GT, 14/~ NOISE GRADE = 12 

-1QR.00 DB .GT, lq/M NOISE GRADE 1 13 

-176.0n DR .~t, 141~ Nnw GRADE 14 

-149.50 DR .GT, 1)I/M N01SE GRADE 15 
CCCCCC 

UPUWrO90YOUPU~- 
WWWW~~W~WWWWWWW 

wl u! u> u. UJ c, V.' UJ an ui u; m u. v, CCtCCCCLtCChCLC 

CCCCCCCCCCCCCCC 

ZzzZZZZZzZzzzZZ 

CCCCCCCCCCCCCCC 

CCCCCCCCCCCCCCu 

............... 

CCCOmhhOOamCGCO 

cwom*haff ShCQQhW 
Section 7 

Analysis of Mine Communications 

Propagation Programs 

In paragraph 7.1 "User's Guide for the Mine Communication's Propagation Programs,'' computer programs are presented for the complete analysis of specific through-the-earth electromagnetic links. These links include the following: 

a. Communications between a VMD on the surface and a submerged VMD. 

b. Communications between an infinite line source on the surface and a submerged line 

source or VMD. 

c. Intramine communications between submerged horizontal electric dipoles (HED), between 

HED and VMD, or VMD to VIVID. 

d. Intramine communications from an infinite line source. 

7.1 USER'S GUIDE FOR THE MINE COMMUNICATION'S PROPAGATION PROGRAMS 

In the course of the analytical work which was accomplished under subcontract Purchase 

Order No. C-684420 to Collins Radio Group for their Bureau of Mines project, several basic 

computer programs were written. These programs were generated for the following specific 

tasks: 

a. Communications between a vertical magnetic dipole (VMD) on the surface and a submerged VMD.* 

b. Communications between an infinite line source on the surface and a submerged line 

source or VMD.* 

c. Intramine communications between submerged horizontal electric dipoles (HED), between 

HED and VMD, or VXlD to VMD.** 

d. Intramine communications from a submerged infinite line source. 

The first program is employed for most up-link or down-link paths. It computes the H-fields 

on the surface from a submerged VMD at various displacements, or the subsurface H-fields 

from a VMD on the surface. It will also compute the subsurface E- and H-fields of interest 

from an infinite line source on the surface. 

The results are displayed for various receiving point depths and displacements in terms of 

signal-to-noise spectral density. 

*With preliminary noise grades. 

**Includes updated noise grades defined in section 6. 
The input requirements are as follows: 

FORTRAN NOTATION MEANING 

PT Transmitter power in watts 

W1 Weight of transmit loop, kg 

AC Circular mils area of loop wire 

A1 Radius of transmit loop, meters 

A2 Radius of receive loop, meters 

SIG 

RNF 

NOISE 

LINK 

IT 

ITYPE 

Overburden conductivity mhos/meter 

Receiver noise figure, dB 

Noise grade; 1, 2, or 3* 

= 1 up-link, = 2 down-link 

If IT = 1, a large diameter surface XMIT is used 

= 1, vertical H-fields from VMD 

= 2, vertical H-fields from infinite line source 

= 3, horizontal H-fields from infinite line source 

= 4, E-fields from infinite line source 

LL Number of frequencies to be skipped. 

7.2 PROGRAM NUMBER ONE 

The printed output first consists of a 2-dimensional array of Wait's functions used to compute the fields. After a listing of the basic input parameters, the noise power density, the 

minimum receive loop turns and the Q of the transmit and receive loops are presented. A 

2-dimensional (depth and displacement) array of S/N~ is then printed out. 

1 *Preliminary noise grades. 
H 430- . . 4 + *OW mOhU 

.\(YO C mC\' .MA 

CZ 8- em-CV I I 

03 4\G .zm a * 

tom- .fir= e CC hC *COW- m 

4f (P+9 l maen r.O-m1C\ reb 

C *@-+4 .C(Ua# 

Ch m8CC .mc a 

OZ)CLL **r9 t .O 

I ..C .h a< . n-woto mol *I -* r DC W - Od I a-Ce. • t A C\ .fi8CM I C r a 

OZC- • an actn LL: M ? .-znn.oo\ • 1 r-93W .C rn.O > rABwCd 4993) t 

OX * 4 smo *d I c. 

C aC\C l *C 4 m rn 

C\ .C *CF? -dC B- N *C e= 0-34 8 Y 

rO CH-~ l 

*COV 8lC r l md Y 

00 . t *\OO- t Z OOrg 4C- r- 4 w 

CC 4M *a*+ a0 1 4-0 ,SHr'?&r: . . . . .I- c * L .-If I .d$. ?. - =C 2 7 fi 

00-t *DO -c t L 

cc . *.r+ .-- l C 

hCCO • mO.4 .C Z 

.C . *&-N a\ . oh-Cl?- CCCC LL c rm& t m DU L 

c B m--'am#-, t x KCU rC- 0-h • a .C .C .2 tf t C c2 F- 

.CcC *CC-C a • C C 

CC=~CI-.- 8 ~CC =rc C1\9 I . 43 OW LLn r re I~WU-O I 6 

we *. C . .5 l *2c GdO .r)0 LC, -_LC CC. rU4 L . -0 --- 

C,C'-l- C rC. .I-lC b cc't C (CC ld t tl.C *. DC a L-C: 

*r+t l r 0-v t CW-x a a .CCt-'CrL a -4 rcZc 0-c ..~.Lc tr mnc---- CC- *hC(.Ch a ZS- .Cd -C *r;-lr .TCC 3fi3CC-k 

\Cdr I f L\ 0- Od DY(3 

CC- I rfi-lr t UkLt .Z 

UhZ .CC .rL'LC; .\l.-,Zht-Lt 

b mZLT .CM I CCav *-;jR L a- DCT r mi-(\ t-ey) 

c a BK--CYCP cbnk 

(Can rICR *C\~LL~CIC~~ 

bCt IC *.*< t lC-lt*l?-L-< 

qcc DCC .r .I ax-LL'CLL~LLW 

C-EUC .- tCCLLCLCXLL-X-2 

e -C\rt-WchCi 

--N 

+ 

d 

4 - e rl 

n<u 

- 

\ 

* u. * . G - 4 

- CX 

T r * - 

- 

-. I: 

l 

a 

flc 

ir 

. 

(C LL 

- OZ 

. tu-LL 

C C - h C--- \ F-a- -- CQ 

* 4 C', t 

ncca<lL a 

"\-LAIL-a r 

22 .LLI 

--arz 

ICtk*LL 

-a Oh. 

r l ~md l .a .P 

ac > - a 

- 

C-k-Uk 

11- 11-;c 

z2 

LLL-f-2' 

- 

u;--MU 

-L 2 k 

m 

4 

A 

C 

(3 

t 

0 

t 

LL 

fr 

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* 

u 

CL 

L 

w 

fi 

c' 

c: + 4 x 

C3 4 

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.(3 

- C h' 

(U - 3- C 

* 3: 

- Q 

a 

hh 

6' a 

-3 

-ua .* 

LO 

+a- * 2 

. * -C* - 

*-a -- T bar d CIJ hC l I - . I--, w - u 3 

-a- - a \ 

-ac b (L - \kd 4 .& --E 

--ire CCLL I I 

CLLC -C- XLL 

*r-C\.lAC#-"- . - >-a 

*uU+*+%dF+c 

murc ear IC 

tu' .eCs*3t~-~ . +- #C R D+ r w ~II. 0----+ucxlL -.-c u~w u~a a-11- 

-uchCIChueC 

#I C 5 - .C'-. -.- l A 

~-L~II--uz~ WILT 

LCQ~ZU>C~~FU 
6 fl~rA~C(SIlY) 

7Fcn.t ~.n. )r!=l,F-iO 

IFIITVPE~GT.~ 1 Gn Tn 73 

~~~~-~~,+~~,*ALO~~QI~~.~~~~~I I-Ic),*A~~~GIQ(~~,*PI*~~)+?~~*A~-~cIo(A~*Q 

1 )cnIIM163,*~f ~G~o~H)+IO.*AI 1751:)(PT) 

r:n rn 

73 SNP=?~~*AI~~C~~~O ;M)-PIIM+ I n,~~~n~in~p~/~oo, 1+60, 

r raljTtOit FOR TTyPF 1 ~~J~SIIRFEPF 1,T:IE SOIIWCE NOISF F 1t;LllS AD€ OY1.Y ~PPRU 

r YT,-IATF 

1F ITYPE,ED,~ 1 S~QPS~IQ+?~,*~I~QG~~(Y*FRE )-lflc?os 

78 CsfK, J)mf' 

7 r?%(K, !)=SnlR 

PRT~IT 1O 

13 F~DWBT( l~l,//~~n~,~w~!T~ n c(ltiCTInv~,//) 

PRtvT 19,0!? 

rfl Ffl~~b~clx~11F11.~/) 

!F~TTYP~,GT,~) Cn Tn 34 

PRINT R#FYF~PT~~;~:I?~A 1 a A?mS7CaYINKa~3ISEm~?hlF 

8 FOP~AT(IMI,~AX~~FRE~~,-~SFF.~,~ HZ TRANSMITTER BOWEP r,Fpe0,bw4TTS 

1 ~M77 LnOP ~FTr7~7 b,Ffi,?,p KC HCVE LOOP YFIGHl @aFh,?Ob KG #,//a 

?cOy,ey~lT I nOP Rn111s @,Fh,?,b M RCVE LnOP H~l~lclS n.Fh,?,@ M 

7~nhln, 0aF6,?0' ~Y(lS/td em A4, 'LINK NOISE='. I2rt RCVR NF=@mFAeO.' 

Gn9b l 

PPtNT (3,Phf771aNfi~~1.f31? 

(7 FOD"A~~//,~~Y,~C~TSF Pnw~F4 r+FbrSITY b8F7eIma Qf?h. Rrvr LnnP TUkNS 

I '*!AmB YYTT I-OI?P Q brFR,7m'DnC\IF !f)fIp fl '#F4.?) 

r,n rn 77 

34 PR T~IT 75,FPF,PT ,c 7G.MTNK ,~IPI qF, QhlF 

95 F~D~AT(~~~,~OX~'~R~TS.~~,FH~~)~~ 47 THAbJS F'flWEY @mFR,Omr NATTS CnN 

1. F.? M ',,A4,'LIMY V~TFEJ@,I?~) RCVH k~Fa)~Fd,q#' nn' 

7 1 

PWthiT 76 

76 F(~QYAT( //.nr\~ .#I-; q SO~IYPF r ntfNCrw* 1 

77 PH!h1f o 

3 F~PV~T(///,?~M, pnF~FlvEn SlGhllL Tn hUISE SPFCIRAI- DFNFITY~,//,~QY# 

1~1JtSPI ACFYFhJTmYM,O/s' PF07n(~q) ,O() q5 10 -15 .?> n 

fl .75 .31. 35 *AD .d5 .so 'a/] 

tit! 1 n 1 =Im I? 

MZ:A~+,T)~;*FI AT r ,--I 1 

10 PpTfiJT 11,u, I~Y(Mml-),M=l,l 1) 

11 F3~~47(1Ymfh,?m?ymllF7.1/1 

12 rnh~f t rl(tF 

r:n TP 9 

F P 

L ccc z CCC 

s CCC 

LL. I ccc 
7.3 PROGRAM NUMBER TWO 

The second program is used for most intramine paths. It computes the five field components 

of interest emanating from a submerged HED and the two field components due to a submerged VMD. These components are calculated on the surface and at the transmitter depth 

for various displacements. The input requirements are as follows: 

FORTRAN NOTATION MEANING 

PT Transmitter power in watts 

W1 Weight of the transmitting VMD, kg 

A1 Radius of transmitting VMD, meters 

Length of transmitting HED meters 

FRX Frequency in Hz 

EPS Re1 at ive dielectric constant of overburden 

SIG Conductivity of overburden mhos/meter 

RS Contact resistance of submerged HED 

DS Depth of transmitter, meters 

NOISE Noise grade (subsurface) 1, 2, or 3 

The number of displacements in 100-meter increments from the transmitter. 

The format for this data is (9F8.2, 212). An arbitrary number of these cards may be inputted 

for whatever combination of parameters are desired. The last card in the data deck is blank. 

The frequencies selected must be one of the following: 1 KHz, 2 KHz, 3 KHz, 5 KHz, 10 KHz, 

20 KHz, 50 KHz, 70 KHz, 100 KHz. 

The field components computed are 

For the transmitting VMD, the field components are Hz and E+. 

The output format first displays the basic input data and the noise fields for the three noise 

grades. The above seven field components are then printed out for the indicated displacement 

for receiving points located at the surface and at. the transmitter depth. 
DATA ~W~~.~~~.D~O,~A~O~D~OO.~~OO./ 

f'183.141592654 

-a - - -. -- - - -- r)=~1./(36.*~I))+1.~ 

Cm2.3 3796E+d 

J3=6,4?i*L.E-7 - - - - - - -- - 

- T TEA0 T-~,~T~~~~A~.LI~FRRDE~SDSTC~KSDCS~NUISE~LT- - 

2 FiJ?lAr(YFd.2~212) 

- - 

IF(~T.LT..OOC~) CALL EXIT --- - - - - - 3J 15 I*l.IP 

THE TZST FUN ErJ9AL 1 TY BcT *EEh bOpl- ICIIEGEPS MAY PLJT BE MEAPJIN~FUL. 

- 

IF(FffY,hE,FflE3(1)) GO TO 16 

FXE*F?k - -- 

ha20rPI*FUE 

~12rUO*~t(oo~l.)*~Si~+~ooDlo~*EPs*~G*~) --- -T:xrS3FTrPT-/r:S1 - - - - -. -- - - - - - . - 

GJ.-( 4/C) **2 

GI=SS~R~(G~Z) 

------DJRVW~Kl-WGRfTwl3PT* b .52E+Jj -- -- 

- - - -- - - - - - 

K~(SIG+(O.al~)*EPS*EO*w)/((O~al~)*EO*W) 

A~~CU?*LI)/(~.*PI*(S~G+~O~D~.)*EPS*EO*~)~ *' - tf b-,TPfl - -- - 

CK*CU~PI/(~.+PI) 

m f.-(O..l0)*bO*k*CU4M/(4,*PI) rr7r - -- - -- - -- 

DP(21m~s 

DO 12 Jm1.2 

- -- - - 
Gc, 19 71 

997 f0 I *-l.19 - - 

G=P( :* ) 

F_rP(''tl i 

CALL C~MLJ ( I0brE0r007O0K.GA~sfi -. -. - - . - - - . - DO 15 11.10TC 

15 H(~I)~H(~I)+O(II) 

7 COVTIP:ut - --- - - pp 71 FJKTf'4~E 

C C3* pL;r~ PdIhARY FItLIjS 

- .- EP~-~*~~~?I-C~*R)*(~.+G~*P+G~~*U~*?-(RC~J/~I**~~(J.+J.*G~*H+G~~- - - - - T) ) IF * 13- 

EPH=A~~E~PI-G~*R)*~G~~~P~~~+G~~R+~.)/R.*J 

EPPV=~*CEXP(-GI*R)*~~HO*(G~*R+L~)/RI*~ 

~PFFJ~aE!~CEXF(mG~*P~*ZGf*k+~.) *t;C)RT7i.-TRTiT)iR)*r2)/Fi**z---- --- - 

IF(CPo~~HPh~mLT,1.E~Y~HPH~~1~E-9.1mE.~9~ 

-- 

~E=B~CF~P(-G~*F)~P~U~(G~*~+I.~~-~~~*~ 

HZZVTK*7XXPT-GI*;) * (-1 .-€l*R-Gl%*R**2+ 11 .;(I?H-~,~F~~) **2C(J.Y-(-1-,S~1+ 

1)+612*R**2))/R1*3 

- - 

FEP(J,L)~~~.*AL~GIO(CABS(EP+A*~~(I~-H(~))~RHO**~+~.*A*(H(~)-H(~~

mnm-o* * 5 TT - - - - - -- - 

FE~~(J,L)~~G~*ALOG~O(CAF~S~EP~-A*G~~*~(~)/~~~~~+A*H(~~/

14)/Rt40**5) ) 

-TRPHLLLl 82D-,-*3cb3X 0 1 CA B-STWp)c+'FB*Ff f 6 mD3 *T2+2-.*B* ( H ( 8 ) 0 H ( 7 T 1 / ( 6 0 

iRHO*r4))) 

FHP(J~L~~~O~*AL~G~~(~ABS~HPH+BIH(~)/RHO**~+~~*~*H~~~- 

H L ( J L I iZ7tX2S~T7XJTS ( F?74?WTP3T7RL!6*-*-ZTT 

IF(Z.LEelooANDeDSeLEolo) GO TO 12 

FHZV(J,L)~20,*ALCGlO(CABS~~ZV-Cti*~~(1O)/RHO**3)) 

~~-~*~~XBS~H-~RmlT - 

12 CONTINUE 

0- 

PRINT 30 P 

PRINT ~~.FRE.SIC.EPS~PT~~~~.A~.L~~DS~,RS 

L7 FORMAT(//.lOXa'FREQ. '.F9e2aP HZ CON0.r 'aF6.2.p MHOS/M EP$. 

~.Fo.z. e Pmm-vmw-mns xm LOCIY W~TI b.F602e@ KW~II. 

2lOXa~KMIT LOOP RADIUSm 'rF8.2.e M LINE SOURCE CLNCTHw e,F#.S4@ H 

3 ORPIC) OF TRANSMITTER^ '.Q(Se2,//.20X.@LINE.SOURCL CONTACT RE$BSTR)I. - - - - - - - -- - - - lCE ~'.FBeT70h~~.j/i-- 

IF(l,S~ol7) GO 'TO 221 

DO 79 ~~IS€~1.15 
22 FCQIIT(ZOX.eNCISE - -- - - - a D.F1022.' - Cb - eG1.- 1A/J- Y'JISE GRADE r'aI41 

2 ~-PR-!XT - i8 
SJQqOJTINf FIJA( X.Q,LU,<SG~~.S) 

-COTTQ-ETn- <aSISi2ai,J.!AOaRsTaE. 

DI.IEVSION S( 13) 

'J=CSQ?T( Y**Z+G12) 

Y=Yss?-Z]**2 

IF(f.LTada) 'J~~CYPL~(O~~SSHT(A~S(~))) 

IF(Va;~.3e) !.~~~CYDLX(S~HT(V),~,) 

SITVUScl I /IU+Y *U9 ) 

To( JD*J)/(UO+U) 

IF(I.LT.~~E+S) GO TO 1 

4nTe 

5a3. 

SI F3 2 

TAISSSL ma I 1 

BmBSSL ( Xa 3 1 

2 E=CEXP(-U*Dl 

3-7-rE3lT*E3 v* X 

5(2lo3*T*E*X**2/~ 

3(3 )=Is~sE*V~X**~ 

5-2 3.aS(5)=4*T*E*X/U 

S( elrA*T*E*X A Srr)ry.n*t*x*rz 

S(3)=A*R*E*X,r3 

S(91=8*T*€*A**2/~ 

S(iw]rA*r*E*~.*j 

HEf URN 

END 
7.4 PROGRAM NUMBER THREE 

The third program in the series pertains principally to the submerged infinite line source. 

It computes the E-field parallel to the line source, the vertical H-field and the horizontal 

H-field normal to the line source. The input requirements are as follows: 

FORTRAN NOTATION MEANING 

PT Transmitter power, watts 

FRX Frequency, HZ 

EPS Relative dielectric constant 

SIG Overburden conductivity, mhos/meter 

RS Line source contact resistance, ohms 

DS Line source depth 

NOISE Noise grade: 1, 2, and 3 

The number of displacement increments to be 

computed 

The basic input parameters are first printed out after which is displayed the noise fields for 

the three noise grades. The three field components of interest are then printed out at the 

surface and at the transmitter depth. These are repeated for each displacement. The last 

data card is left blank. 
)

+ ~[~)=?~I-Y>EI rl 

4 r(~Ir7fl+~El n 

I c (r )t'~+T'~k?l (-pFPf (r;!?I ) 

b Df<)c7**:>(4 1 

F(r)o-t,cDfnl 

P171~4,*P[4) 

* :>(~lr',*v(Aj 

P(OlrtR.*P(~~ 

"(1 9P (611q~J 5 

+ QA ~)~3.*t=r1.~-1) 

e I'li 13 ,121 ,7 

J=hR. *Fl ')At J-1 ) 

* 7F(JeF*>.7) l*'S 

* 77r7/1 S 

7 '.O 17 (-1 rl T 

• r\wn=tnr).rf[iib 1 (~-1 ) 

q=(, .dr! tp? 

* r~~s on I 5 I , J 

O; .,(I I lt(n..n.) 

(.? 7 ,*+I, 17 

+ tanrt~) 

(~E'fP41) 

. ~LI I -in(-lr,l-F f j ,~:.E.~~,II~,~,'P~~~~:~) 

I r1 jc. lIaI,;4 

1.-, ~~(71)~~4(1l14* (11) 

7 r llr,T 1 -*(IF 

t vf tw{ )='~n~*Ai-~~~lr,~llf~*~*Cdk*~,9~~S~~~~ 11 )/(?.*PI I ) 

+ &kc.(( Iwb I 02n*rnL~rLi1[rIrlJw*CAa5[ 74t7) )/f2.*P1 *'I$) )

: 0 1 1s I, $4 

"* 3 r=l,S? 

r=Yr'* t*Y( I) 

f:Al I FIJ~f<s~s*flBl,[a,j~,~) 

'ilj 4 ,'el l 3 

r, -'(~~b$~~('~) +.+:( 1 )*soA) 

2 f (1) t 1 IF. 

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-4: 7 I a1 ,%3 

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Et 

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rrj1~Pf 6 11 r;17.CB~10U~~*F.0FrT 

-yb$r PIC 1:)r, q ( I 

:l=rSrb?T ( ~**3&r,1 Y 

Y=~c*3-/~\rr7 

Tc(Y.l f .~.IIJ~ =CAP\ )((fi..S.YC?r(~:l$IY) ) J 

1Ft *o*~~,d~~e )~~fl=r'!pl $('jlJh'T(Y) #c-) y= (lI"~lf1) / (lJ4llfl) 

TF tr*r;r* 1.1 b=1 

rF(7.1 ?.I .)A=-I. 

' "A. 

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7Ft3,' F, t ,)C=rd 

F-rKvt~ ( -114 r,h$ I I!-1 . ) ) 

F=*F~~l(-l/+(ll+t,) ) 

?( 1) trrS( X*F# c (F-+T*F ) ri-; 

?(?larf7'4( dr[J1*(F*c+r*F) 

Sfl)taCT:J( f*M)*(r*A+.T*c)*t/\,! 

I.'F ~1jD. 

f iJ? 
7.5 THEORETICAL PREDICTIONS FOR IN-MINE PROPAGATION 

From the analysis programs described in paragraph 7.1, a computer printout was obtained 

and its results listed in paragraph 6.7. These results incorporated the latest NBS noise data 

listed in paragraph 6.6. 

The received signal strengths for various antenna configurations are combined with the 

specified noise grades and an equivalent s/NO is calculated. These resulting signal-to-noise 

ratios are plotted for various antenna configurations and displacements in figures 7-1 through 

7-16 for a transmitted power of 10 watts into the specified transmitting antenna. It should be 

noted that a 37-dB s/NO ratio is the minimum requirement for communication of normal 

speech assuming 75-percent word intelligibility and a l-Hz normalized bandwidth. From 

these experimental results, predictions are drawn concerning optimum usable frequency 

versus maximum transmission displacement for various antenna configurations. Figures 

7-1 through 7-16 are the basis for these predictions. 

The predictions that follow assume a noise grade 14 (mean noise-all mines subsurface) and 

an input power of 10 watts. 

a. Loop (VMD) to loop (VMD) provides highest s/NO ratio. 

b. For 20-meter radius transmit loop, a maximum of approximately 225 meters/740 ft 

separation can be achieved. (This assumes a minimum of 37 dB S/N~ ratio for adequate 

information transfer with an optimum frequency of 10 kHz to 20 kHz.) At lesser separations, the 100-kHz to 200-kHz range provides the higher signal-to-noise ratios. 

c. For 8-inch/0.3032-meter diameter transmit loop, a maximum of approximately 80 meters/ 

263 ft separation can be achieved at an optimum frequency of 70 to 100 kHz (37 dB S/NO 

ratio was minimum). 

d. For 100-meter/328-ft line source transmitter, a maximum of 200 meters/656 ft can be 

achieved at a frequency of 10 kHz. At separations below 500 ft, however, the 100-kHz 

frequency range provides the higher s/NO ratio. 

e. For up-link and down-link propagation, maximum transmit depth for 13.58 meted44.68 

foot radius loop was 175 meters/574 ft at a frequency of 10 kHz, and for the line source 

transmit, maximum depth was 225 m/730 ft at a frequency of 10 kHz (37 dB s/NO ratio 

was minimum). 

Predictions for transmission from a loop to line source could not be made because reliable 

E-field noise data was not available for this mode of propagation. In the experimental measurements presented in volume 4 (Experimental Measurements), line source to loop trans - mission is included. 

Figures 7-17 through 7-19 show typical mine entries and crosscuts with If and vlf theoretical 

predictions illustrated. Darkened areas indicate loss of transmission. 

D=100 M 

4 - Z 

25 - '300 M 

I0 

* , lo W 

NOTE: LlNE SOURCE SHOW

INTO PAGE 

-1 TRANSMISSI

LENGTH = 10

WEIGHT = 1

NOISE GRAD

MEAN ALL M

1 OOK 

FREQUENCY (HZ) 

Figure 7 -2. Line Source-to-Loop Lateral Transmission for Varying Displacement

I UK 1 OOK 

FREQUENCY (HZ) 

Figure 7-4. Loop-to-Loop S/N Ratio for Various Displacements - Noise Grade 2. 

b 

-TRANSMISSION 

4% D=lOO 

DIAMETER 8 IN

WIRE SIZE NO

NOISE GRADE 

HIGH MEAN 

WEIGHT 2 LB/

(>- (3 D=200 M 

25 300 M a

1 K 1 OK 1 OOK FREQUENCY (HZ) 

Figure 7-6. Line Source-to-Loop S/N Ratio for Various Displacements Down-Link

F 

1

SHOWN INTO 

PAGE 

O+ 

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

.. 

--A- - 

TRANSMISSIO

LENGTH = 200 

WEIGHT "62.86 

NOISE GRADE 

MEAN SUBSUR
1 OK 1 OOK FREQUENCY (HZ) 

Figure 7-7. Line S~urce-to-Loop S/N Ratio for Various Displacements Down-Link
FREQUENCY (HZ) 

I 1 NOTE:' LINE SOU

INTO PAG

TRANSMISS

LENGTH = 

WEIGHT = 

NOISE GRA

MEAN SUR

1 OOK 

Figure 7-8. Line Source-to-Loop S/N~ Ratio for Various Displacements Down-L

1 OK 

FREQUENCY (HZ) 

1 OOK 

Figure 7-10. Down-Link Loop-to-Loop S/N Ratio for Various Displacements - Cont

D=O M (1 

, 50M FD

-5

* OS

TRANSMITTER 

- WEIGHT - 4.0 

) \)RADIUS - 13.58 

WIRE SIZE - 

CIRC LOOP L = 

RDC - '28 OH

~=400 M LOOP ClRC - 8

--- 

-)NOISE LEVEL 

--- MEAN S U B S U R 

A 

Figure 7 -12. Down-Link Loop-to-Loop S/N Ratio for Various Displacements - Contin

FREQUENCY (HZ) 

Figure 7-14. Up-Link Loop-to-Loop S/N Ratio for Various Displacements - Contin

1 OK 

FREQUENCY (HZ) 

1 OOK . 

Figure 7-16. Up-Link Loop-to-Loop S/N Ratio for Various Displacements - Cont
Figure 7-17. I,F Propagation (Theoretical - 

Fixed Station - NG 14). 

7.5.1 LF Propagation (Theoretical-Fixed Station - NG 14) 

20-meter radius loop (fixed station) to loop transxnission 

VAlID to VMD 

Frequency - 10 to 20 kHz 

37-dB minimum S/N~ 

10-watt input 

Darkened areas indicate loss of transn~ission 
Figure 7 -18. LF Propagation (Theoretical - 

Portable - NG 14). 

7.5.2 LF Propagation (Theoretical - Portable - NG 14) 

8-inch-diameter loop (portable) to loop transmission 

VMD to VMD 

Frequency - 70 to 100 kHz 

37-dB minimum S/N~ 

10-watt input 

Darkened areas indicate loss of transmission 
I Figure 7-19. LF Propagation (Theoretical - NG 14). I 

7.5.3 LF Propagation (Theoretical - NG 14) 

100 -meter line source to loop transmission 

VMD to VMD 

Frequency - 10 kHz 

37-dB minimum S/N~ 

10-watt input 

Darkened areas indicate loss of transmission