Through-the-Earth (TTE) communication systems require minimal infrastructure to operate. Hence, they are assumed to be more survivable and more conventional than other underground mine communications systems. This survivability is a major advantage for TTE systems. In 2006, Congress passed the Mine Improvement and New Emergency Response Act (MINER Act), which requires all underground coal mines to install wireless communications systems. The intent behind this mandate is for trapped miners to be able to communicate with surface personnel after a major accident-hence, the interest in TTE communications. To determine the likelihood of establishing a TTE communication link, it would be ideal to be able to predict the apparent conductivity of the overburden above underground mines. In this paper, all 94 mine TTE measurement data collected by Bureau of Mines in the 1970s and early 1980s, are analyzed for the first time to determine the apparent conductivity of the overburden based on three different models: a homogenous half-space model, a thin sheet model, and an attenuation factor or Q-factor model. A statistical formula is proposed to estimate the apparent earth conductivity for a specific mine based on the TTE modeling results given the mine depth and signal frequency.

In coal mines, frequency and effective electrical conductivity of the overburden are factors that determine the maximum range through which a TTE signal can successfully propagate. The effective electrical conductivity of the overburden cannot be controlled and depends on the mine geological properties and varies between different mine sites. Ideally, we would like to be able to predict the apparent conductivity of the overburden to determine the likelihood of being able to establish a TTE communication link. This includes communications between locations within the mine (horizontal communication) and between the underground and the surface (vertical communication). Obtaining information on the overburden electrical properties is useful for evaluating and improving the performance and reliability of a TTE system at a given mine. The limited information on the electrical characteristics of overburden above U.S. coal mines, however, prevents the development of a detailed theoretical approach.

In the 1970s and early 1980s, the Bureau of Mines measured the propagation of TTE signals for frequencies ranging from 600 Hz to 3000 Hz for 94 representative mines distributed throughout the United States. The TTE transmission data collected at the 27 coal mines were initially analyzed to estimate the apparent earth conductivity based upon a homogeneous half-earth model [

A number of techniques are available for probing the earth electromagnetically with a transmitter and receiver, where conductivity information is contained in the received signal [

each mine had a chance of being selected for this test;

the probability of selection was known beforehand and was based on the relative size of the mine in terms of the number of miners employed;

the selection process was random;

all depth intervals were selected;

test results could be used to make valid inferences about all mines [

The homogenous half-space model can be illustrated by setting either the conducting sheet depth to _{0}, in _{0} and an intrinsic propagation constant of
_{e}_{1} and _{2} both equal to _{1} of the upper layer can be considered to vanish and _{2} =

where

and

In the equations above, _{0}^{3}_{homo}_{0}, _{0}_{0} = (^{2} + _{0}^{2})^{1/2}.

As we will see later, one result from applying the homogeneous model to the data of the 94 mines is that the apparent conductivity appears to decrease as the mine depth increases, which is contradictory to the model itself. However, this dependency might be explained by the presence of a thin highly conducting layer at the surface of the earth. In the thin sheet model, as depicted in

For the earth layer (z<0) and free space (z>0), the magnetic Hertzian potential Π* satisfies the wave equation except at the exciting source:

where

is the intrinsic propagation constant. For free space (z>0), _{1} = 0, hence, _{1} ≈ 0.

In a cylindrical coordinate system, the fields in the half-space (z<0) can be expressed in terms of Hertzian potential

and the fields in the free space (z>0) can be expressed in terms of

Note that the magnetic Hertzian potential

_{0}(_{1}(

The surface vertical H-field in (

in which

For free space, _{1} = (^{2} + _{1}^{2})^{1/2} =

To avoid exponential attenuation when the signal passes through the highly conducting thin sheet, the value of _{0}_{0}_{thin}_{0}, _{thin}_{0},

Since _{0} and/or _{a}_{thin}_{0}, _{0} and _{thin}_{a}

The numerical integration of (

Then the wave number _{i}_{0} =

For the TTE tests at the 94 mines, four transmission frequencies-630, 1050, 1950, and 3030 Hz-were used at each site. The magnetic moment, M=NIA (N is the number of turns of wire), for the in-mine transmitting loop was recorded and calibrated. Corrections have also been made on the overburden depth _{a}

The resulting apparent earth conductivity distribution with overburden depth interval is listed in

It may be possible to explain the behavior of the conductivity on frequency and depth as seen in the previous section by the addition of a thin, highly conducting layer at the surface of the earth [_{0}

While EM measurements of both transmitting and receiving antennas are needed for the models described above, the Q-factor model or attenuation factor model requires only two parameters: the estimated earth conductivity _{0}_{0}

The conductivity of overburdens above mines in U.S. coal fields can be characterized as a function of overburden depth and operating frequency. The overburdens consist of a large number of horizontal layers of different materials and thicknesses. For any given overburden depth, we can expect overburden characteristics such as conductivity to vary from location to location within the coal fields. Hence, we can develop a statistical approach of sampling a representative number of mines within each of the depth intervals of interest in order to characterize the overburden conductivity, and the corresponding variability about the average, as a function of depth and operating frequency.

In the regression model, overburden apparent conductivity is considered to be related to depth and frequency in an unknown pattern. Up to 94 data points were obtained as a result of field tests conducted at each of four frequency levels. With the assumption that the estimated values of apparent conductivity represent a random sample from a normal distribution with a mean dependent upon both frequency and depth and variance independent of both frequency and depth, a regression model can be obtained to describe the dependency of the apparent conductivity on both frequency and depth as shown in (_{a}

In the regression model as described in (

The apparent conductivity of a specific mine with given overburden depth and operating frequency can then be estimated based on this model, with the related coefficients to fit (

The TTE data from all 94 mines recorded by the BOM in the 1970s were analyzed to estimate the overburden apparent conductivity based on three different models: a homogenous half-space model, a thin sheet model, and a Q-factor model. In the past, full analysis of this data was constrained by computing limitations. The apparent conductivities from the 94 mine data were first estimated based on a homogenous half-space model. The results based on this model show that the apparent conductivity decreases with increasing depth and frequency, which is contrary to the expectations of the model. A thin sheet model was then considered, which is able to provide an explanation for the depth dependency of the conductivity. It also predicts the magnitude of decrease in the apparent conductivity with frequency by appropriately setting the properties of the conducting sheet. Alternately, the Q-factor model was also shown to predict the dependency of apparent conductivity on both frequency and depth by appropriately choosing the properties of a highly conducting thin sheet layer. Among those methods, the thin sheet model provides more reasonable estimation since it considers the effect of the relatively high conducting surface on overall apparent conductivity. By combining the features of the other two models, the Q-factor model also gives a good prediction but is mathematically simple. The conductivity behavior was also described based on a linear-logarithm regression model. The results provided in this paper offer more insight into the overburden apparent conductivity and help to predict the path loss. This estimation of earth conductivity can be used by the mine owner/operator or TTE vendor to predict the performance of the TTE system.

A small horizontal loop (vertical magnetic dipole) buried in a dissipative half-space with a thin conducting sheet at the surface.

Estimated apparent conductivities (S/m) change with overburden depth interval (m) for various

Apparent conductivity (_{a}

Estimated apparent conductivities plotted with distribution percentile.

Depth m | Depth ft. | Sampling Size | # Of Active Mines |
---|---|---|---|

<61.0 | <200 | 2 | 73 |

61.3-121.9 | 201-400 | 35 | 369 |

122.2-182.9 | 401-600 | 30 | 309 |

183.2-243.8 | 601-800 | 13 | 199 |

244.1-304.8 | 800-1000 | 4 | 135 |

305.1-365.8 | 1001-1200 | 6 | 58 |

>365.8 | >1200 | 4 | 79 |

MSHA and Bureau of Mines data files as of 1975.

Mine Depth (m) | 630 Hz | 1050 Hz | 1950 Hz | 3030 Hz | |
---|---|---|---|---|---|

50-100 | Mean | 0.6185 | 0.4202 | 0.2564 | 0.1559 |

STD | 0.3062 | 0.3531 | 0.1767 | 0.1240 | |

100-150 | Mean | 0.2760 | 0.1301 | 0.0858 | 0.0511 |

STD | 0.1350 | 0.0732 | 0.0465 | 0.0379 | |

150-200 | Mean | 0.1425 | 0.0942 | 0.0498 | 0.0452 |

STD | 0.0963 | 0.0548 | 0.0347 | 0.0346 | |

200-250 | Mean | 0.1307 | 0.0867 | 0.0378 | 0.0414 |

STD | 0.0826 | 0.0524 | 0.0238 | 0.0233 | |

250-300 | Mean | N/A | 0.0170 | 0.0185 | 0.0140 |

STD | N/A | N/A | 0.0219 | N/A | |

300-350 | Mean | 0.0380 | 0.0250 | 0.0170 | 0.0120 |

STD | 0.0354 | 0.0156 | 0.0141 | 0.0099 | |

350-400 | Mean | 0.0265 | 0.0183 | 0.0130 | 0.0118 |

STD | 0.0261 | 0.0153 | 0.0076 | 0.0049 | |

400-450 | Mean | 0.0220 | 0.0245 | 0.0230 | 0.0090 |

STD | 0.0118 | 0.0035 | N/A | 0.0085 | |

450-500 | Mean | 0.0180 | 0.0170 | 0.0080 | 0.0050 |

STD | N/A | N/A | N/A | N/A |

Observations | 238 |
---|---|

2.1834 | |

-0.2932 | |

-0.5068 | |

Standard Error | 0.1479 |

R Square | 0.4674 |