An efficient procedure for modeling medium frequency (MF) communications in coal mines is introduced. In particular, a hybrid approach is formulated and demonstrated utilizing ideal transmission line equations to model MF propagation in combination with full-wave sections used for accurate simulation of local antenna-line coupling and other near-field effects. This work confirms that the hybrid method accurately models signal propagation from a source to a load for various system geometries and material compositions, while significantly reducing computation time. With such dramatic improvement to solution times, it becomes feasible to perform large-scale optimizations with the primary motivation of improving communications in coal mines both for daily operations and emergency response. Furthermore, it is demonstrated that the hybrid approach is suitable for modeling and optimizing large communication networks in coal mines that may otherwise be intractable to simulate using traditional full-wave techniques such as moment methods or finite-element analysis.

Throughout history, mining tragedies have emphasized the need for communication systems in the mining industry with improved survivability. In response to such types of disasters, the United States Congress passed the Mine Improvement and New Emergency Response Act (MINER Act) in 2006, considered to be the most significant mine safety legislation since the Federal Mine Safety and Health Act of 1977. Over the years, researchers have performed extensive research on the design optimization and implementation of communication systems for use in coal mining operations [

MFs are identified for their ability to parasitically couple into conductor infrastructure within a mine tunnel and propagate large distances through various room-and-pillar architectures with relatively low attenuation [

The current modes that can be excited along multiple-conductor configurations within a coal mine tunnel are characterized as differential mode (DM) and common mode (CM) propagations. DM refers to propagation 180 degrees out of phase along conductors; CM refers to in-phase propagation along conductor networks whereby currents return through surrounding mine-earth boundaries. Many times, one mode is dominant in a communication system; however, the most general propagation is a superposition of both CM and DM. Furthermore, CM and DM propagation modes can experience discernible differences in attenuation and coupling efficiency from antenna to transmission line (TL) [

In order to determine what factors most influence the behavior of MF propagation in coal mines, extensive numerical and analytical modeling is required. Many previous models of MF propagation in earth-bounded systems [

Ultimately, a primary objective of this work is to facilitate system-level optimization of coal mine communication networks. For example, optimizations may include maximizing power transfer from a transmitting antenna to a receiving antenna and minimizing standing-wave ratio (SWR). Another goal may be to design an MF communication system that is more survivable during disaster events. In order to efficiently optimize such large problems, specialized global search algorithms were used in conjunction with the proposed hybrid model to analyze fitness of candidate network designs. Such an optimization technique, which may require hundreds or even thousands of function evaluations, would not be feasible without the significant improvement of solution times afforded by the hybrid approach. For demonstration, the final example in this work minimized SWR near the transmitting and receiving antennas of an MF communication network. Subsequently, a line break was introduced to the previously optimized design, simulating the event of a mine collapse. Once again, the hybrid approach was applied by modeling the broken TL with a full-wave region, and it was shown to accurately reproduce the corresponding propagation effects and power losses. These effects would be difficult to reproduce applying only TL equations; however, on the other hand, the entire communication network is too large to model and optimize using MoM or finite-element method techniques alone. The solution is to use both full-wave and TL models in a hybrid approach, which is formulated in the follow sections with examples to demonstrate the efficiency, accuracy, and modeling versatility it can offer.

When constructing the hybrid models, it is important to both maintain accuracy and minimize solution times. That is, when properly implemented, a hybrid model should yield results consistent with its full-wave counterpart (i.e., no TL equations) and reduce the corresponding calculation time. MF propagation in a coal mine, whether along multiple conductors in a DM state or those involving lossy earth return paths, can commonly be approximated as transverse electromagnetic (TEM) modes [

There are two major steps to perform when constructing a hybrid model for a given MF communication system: 1) determine adequate sizes for all full-wave sections, capable of capturing sufficient detail of the near-field interactions within the system, and 2) determine the TL equations that best represent the uniform MF propagation occurring in the coal mine communication network. In other words, “what is the correct ratio of full-wave sections to TL equation sections?” This is important since the smaller and less frequent the full-wave sections are, the smaller the resulting computational cost will be.

Starting with the determination of the full-wave sections, consider two examples of particular interest for analyzing and optimizing the survivability of a communication network. First, consider a TL excited by a transmitting antenna. The length of the full-wave section in the vicinity of the transmitter must be adequately long in order to capture the correct antenna-to-line coupling. A hybrid model with this type of full-wave section could be used to determine how best to excite an MF communication network in an underground mine. That is, because the antenna coupling section is modeled using full-wave techniques, it would be straightforward to move the antenna, change its orientation, or change its position and then use the TL equations within the hybrid approach to calculate the impressed currents on the remainder of the communication network. For the second important example, consider a broken TL due to a collapsed tunnel. Again, it is extremely important to use a full-wave region sufficiently large enough to accurately model the power losses associated with the broken TL.

Based on the experience gained from this work, there is no generalizable procedure that can answer how much of a given MF communication network should be modeled using full-wave sections and how much can be modeled using TL equations. In fact, this highlights the motivation behind the hybrid approach. That is to say, if the designer could trivially model and predict how various antennas would couple to a given communication network and how that network would respond to extreme environmental changes induced by a mine collapse, then analytical expressions, such as TL equations, would suffice alone. Unfortunately, this modeling task is not so straightforward. Hence, choosing the appropriate full-wave sections must be done on a case-by-case basis.

To show how this was typically done in this work, an example was constructed, which is outlined in _{0} = 911Ω). The TL, which was terminated at both ends with loads Z, was positioned near two small loop antennas (20-cm diameter) separated by a distance L that were displaced from the plane of the TL by a distance Δx. The objective in this example was to determine what length of the TL near the two antennas must be modeled using MoM in order to accurately calculate the power transferred from T_{x}, operating at 500 kHz, to R_{x}. First, for a given L and Δx, the power transfer was calculated using strictly moment method (i.e., no TL equations) to establish a baseline. Then, a hybrid model was created starting with full-wave sections 2 m long, symmetrically positioned about the antennas’ respective positions. Next, the power transfer for shorted, matched, and open terminations was calculated. If the power transfers were within 10% accuracy of their full-wave-only counterparts, then the goal was met. If the power transfer error for any termination type was greater than 10%, the full-wave section of the hybrid model was increased by 2 m, and the power transfers were calculated again. This process was subsequently continued until the accuracy goal was met and was performed for three different L values (0.7, 1, and 2 km), each with 11 different Δx values (linearly spaced from 0 to 50 m). The result from this experiment is shown in _{0} ≈ 600 m). It is also apparent that this relationship was independent of L due to the identical TL characteristics in each case.

Note that although this example suggested rather short full-wave sections were required to model accurate antenna coupling, all of the examples explored in the remainder of this paper made use of longer (~

In order to apply TL equations to the hybrid models, the propagation constant and characteristic impedance associated with the system must be calculated beforehand. With these data, TL equations may be formulated to calculate the equivalent loading and excitation on the full-wave sections associated with the sources and loads (e.g., transmitters and receivers), respectively. The TL propagation constant and characteristic impedance can be calculated using either numerical or analytical techniques. Typically, closed-form solutions are preferred due to the ease with which calculations can be made; however, they are not always available for the diverse range of geometries and materials commonly encountered in coal mines. Many times, only approximate solutions or more complex modal equations can be formulated. In this respect, it can be most straightforward to use available commercial codes to model prescribed geometries and calculate the associated propagation characteristics. For example, when considering low-loss TL, it can be shown that the propagation phase and attenuation constants are approximated by [

Here, _{sc} and _{oc} are the input impedances for shorted and open terminations, respectively. Finally, the characteristic impedance can be calculated by [

This way, the parameters required for the TL equations of the hybrid approach can be solved by calculating only the input impedances corresponding to open and shorted terminations. This technique, when applied to modeling performed with commercial codes, provides an efficient alternative when straightforward analytic methods are not available. Once propagation characteristics have been calculated, TL equations can be implemented in the hybrid approach and subsequently applied to optimization procedures. The remainder of this paper will concentrate on examples were the hybrid approach was applied.

Ultimately, it is desired to model and optimize full-scale mines with the hybrid approach. Before this is done, it is instructive to demonstrate the efficiency and accuracy of the hybrid approach for a less complex geometry. The initial example considered demonstrates the accurate modeling of a TL T-intersection in free space, where _{0} ≈ 600 m) was used to feed the network. The twin-lead TLs were assigned a separation distance of 2 m and a wire radius of 1 mm. Each branch of the T-intersection was chosen to be 500 m long and was terminated with a load Z, which, for TL analysis, was chosen to be open, shorted, and matched. As shown in

In the previous example, the computational time required by the hybrid model depended only on the size of full-wave sections used for the source and load regions. Subsequently, the hybrid approach allows networks to increase in size without discernible change in computational times, whereas an equivalent full-wave model using MoM would require more computational time and resources as the physical size of the model increases. This not only makes the hybrid approach attractive for large problems but also facilitates modeling of full-scale mines, whereas using MoM would not be feasible, even with notable computer resources.

In the next example, this fact was exploited and tested. Specifically, a TL 27 _{0} long at 500 kHz (i.e., 16.2 km) was placed between two parallel plates of lossy earth in order to test the hybrid model subject to environmental loading, which is an important consideration when modeling MF communication networks in coal mines. The TL possessed the same separation and wire radius as in the previous example. A 10-cm radius loop antenna with a wire radius of 1 mm was used for both the transmitting (T_{x}) and receiving (R_{x}) antennas. T_{x} was fed by a 1-W power source operating at 500 kHz. This geometry is illustrated in _{x} were calculated for shorted and open terminations and are compared for the hybrid and full-wave models in

In order to account for the various possible MF propagation modes in coal mines, it is also important to consider those that use the surrounding earth material as a current path. This may occur when either a multiple wire system is experiencing CM propagation or a single wire conductor is placed within the coal mine tunnel. In the following sections, the modeling of a single wire conductor placed close (i.e., much less than one wavelength) to a lossy earth material is considered. This geometry, as shown in

Propagation with earth return has been a topic of interest for almost a century. First reported in 1926, Carson [

The difficulty with Wait’s approach is that

Next, a hybrid model was constructed using the D’Amore approximation outlined in the

The current calculations in

As was previously suggested, the D’Amore approximation can be effectively utilized due to the TEM nature of MF waves in coal mines, where most of the EM energy is confined between the wire conductor(s) and the nearest tunnel boundaries. The next example considered employing the hybrid technique to support this argument. In this example, we made use of the fact that if a wire conductor is positioned closer to one tunnel boundary than the others, such as is shown in

In the next example, a 1-km-long wire conductor was positioned 50 cm above a mine tunnel floor. The tunnel cross section was assigned typical coal mine dimensions with a height of 2 m and a width of 6 m; however, due to the approximation used here, these dimensions were not expected to greatly affect the propagation characteristics. That is, only the mine floor material parameters and distance the wire was positioned from that surface would dictate the EM properties of the TL. An ideal voltage source operating at 500 kHz was positioned opposite to either a short or open termination. This geometry is illustrated in _{g} = 10): _{g} = 1e−2 S/m and 1e−3 S/m. The corresponding currents that were calculated are compared in

As previously mentioned, the main motivation behind the hybrid approach was to facilitate large-scale optimizations of coal mine communication networks that would otherwise be very challenging due to the limited analytic solutions or the large computational cost of full-wave (MoM) computer models. With the previous examples establishing the basic tools for constructing communication networks with the hybrid approach, two final optimization examples were formulated and are presented next.

The first example optimized power transfer from a single transmitter to three receivers through a large TL network placed in free space, as shown in _{x} to be −156.3, −148.9, and −157.4 dB to R_{x1}, R_{x2}, and R_{x3}, respectively. Using the same terminations in an equivalent full-wave model, the calculated power transfer was determined to be −156.3, −148.6, and −157.4 dB to R_{x1}, R_{x2}, and R_{x3}, respectively. Hence, even for a large communication network, the hybrid model produces extremely accurate results.

The second and final example optimized a communication network similar to what could be used within a room-and-pillar mine architecture such as that shown in

_{j}_{x} was fed by a 1-W ideal power source operating at 500 kHz. Only the 200-m full-wave sections nearest to the antennas were left in the hybrid model. _{x} in order to indicate overall power transfer from T_{x} to R_{x1} and R_{x2}. The agreement between currents was extremely good considering the beneficial improvement in computational speed. The full-wave models required 1157 s to simulate on an 8-core Intel E5620. On the same machine, the hybrid model required only 10.7 s, providing a runtime reduction factor of 110.

Finally, to further demonstrate the power of the hybrid approach, a TL break (1-cm section removed), simulating a mine collapse, was introduced into the communication network, represented by a red “X” in

The hybrid approach was shown to significantly improve computational efficiency while simultaneously providing a high degree of precision. First, TLs making a T-intersection placed in free space were verified. Then, geometries that utilize earth materials as a current return path were approximated using D’Amore’s method. From this approximation, appropriate TL equations were implemented into both above earth and coal mine tunnel hybrid models, which were validated through comparisons with full-wave simulations. With these basic tools, it was demonstrated that full-scale coal mine communication networks can be constructed and optimized both for daily operations as well as emergency communications and tracking. Future work will include comparing the outlined design techniques and optimized coal mine communication networks with measurements to further verify the accuracy of the hybrid method. It will also be important to extend the hybrid approach to accommodate multimodal/multiconductor TLs. The combined methods of numerical and analytic modeling with measurements should provide a powerful engineering package for future system design.

The findings and conclusions in this paper are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health (NIOSH). Mention of any company name or product does not constitute endorsement by NIOSH.

This work was supported in part by the Centers for Disease Control and Prevention contract number 200-2010-36317.

He is a Research Assistant with the Computational Electromagnetics and Antennas Research Lab. His research interests include computational electromagnetics, metamaterials, geoelectromagnetics, and nanoelectromagnetics.

He is a Graduate Research Assistant for Dr. Werner with the Computational Electromagnetics and Antennas Research Lab. His research interests include nanotechnology, antenna engineering, metamaterials, and computational electromagnetics.

Mr. Sieber is a member of the Tau Beta Pi and Phi Kappa Phi honor societies and has served as the UWM-IEEE student chapter president.

He is an Acting Team Leader with the National Institute for Occupational Safety and Health (NIOSH). Prior to NIOSH, he worked in the industry investigating methods of improved spectrum management for the military. Previous to that, he was with the Los Alamos National Lab, developing applications of applied superconductors. His primary research focuses on wireless communications and electronic tracking. In particular, he is experimentally and theoretically investigating the mechanisms controlling path loss in underground coal mining applications. System frequency bands of interest include extremely low frequency, medium frequency, and ultrahigh frequency.

He is a Senior Service Fellow with the National Institute for Occupational Safety and Health. Previously, he was a Senior Software Engineer with Analog Devices, Inc. (ADI). Prior to ADI, he was an Instructor with the Department of Electrical and Automation Engineering, China University of Mining and Technology. His primary research interests are in underground communications and tracking and proximity detection. In particular, he is currently focused on investigating medium-frequency propagation characteristics in underground mines, modeling of magnetic field distribution, and precise locating architecture of magnetic proximity detection systems.

Dr. Li received the First Prize Paper Award and the Prize Paper Award in 1995 and 2000, both shared with Dr. J. Kohler, from the IEEE.

She is a Professor with the Pennsylvania State University College of Engineering, University Park, PA, USA. Her primary research focuses are in the area of electromagnetics, including fractal antenna engineering and the application of genetic algorithms in electromagnetics.

Ms. Werner received the Best Paper Award from the Applied Computational Electromagnetics Society in 1993. She is a member of the Tau Beta Pi National Engineering Honor Society, the Eta Kappa Nu National Electrical Engineering Honor Society, and the Sigma Xi National Research Honor Society.

He holds the John L. and Genevieve H. McCain Chair Professorship in the Pennsylvania State University Department of Electrical Engineering. He is the Director of the Computational Electromagnetics and Antennas Research Lab (

Dr. Werner was presented with the 1993 Applied Computational Electromagnetics Society (ACES) Best Paper Award and was also a recipient of the 1993 International Union of Radio Science (URSI) Young Scientist Award. In 1994, he received the Pennsylvania State University Applied Research Laboratory Outstanding Publication Award. He was a coauthor (with one of his graduate students) of a paper published in the IEEE Transactions on Antennas and Propagation that received the 2006 R. W. P. King Award. In 2011, he received the inaugural IEEE Antennas and Propagation Society Edward E. Altshuler Prize Paper Award. He has also received several Letters of Commendation from the Pennsylvania State University Department of Electrical Engineering for outstanding teaching and research. He is a former Associate Editor of

The approximation used for single-wire configurations with an earth return, which has been implemented here in the hybrid approach, was reported in 1996 by D’Amore and Sarto [

_{int} is the wire’s internal impedance, whereas _{1} and _{2} are the small argument, logarithmic approximations for the associated Sommerfeld integrals given by

Here, _{0} and _{g}^{2} + ^{2})^{1/2}, where

Note that the propagation constant, i.e.,

Comparison of a strictly full-wave model to a hybrid model using both full-wave regions and TL equations.

(a) Example geometry constructed to determine the full-wave sections required to accurately calculate power transfer from T_{x} to R_{x}. (b) Required length of full-wave (moment method) section to accurately couple EM energy from a small antenna element to the twin lead TL shown in (a).

(a) Geometry of a T-intersection full-wave and hybrid model comparison using open, shorted, and matched terminations. (b) Currents calculated using equivalent full-wave and hybrid models. The calculated current magnitudes were normalized to the source current.

(a) Geometry of a 27 _{0} long TL (i.e., 16.2 km) placed between two parallel boundaries of lossy earth used to test the hybrid model subject to environmental loading. (b) Current magnitudes and phases calculated on the R_{x} TL section were compared between full-wave and hybrid models for shorted and open terminations.

Geometry of single wire above lossy earth and free-space boundary.

(a) Geometry: 1-mm-radius wire placed 20 cm above lossy earth return. (b) Currents for full-wave and hybrid models were calculated and are compared for both shorted and open terminations.

(a) Geometry: wire placed above a lossy earth return. (b) Geometry: wire placed above a mine tunnel floor. (c) Side view of a mine tunnel hybrid model with a wire positioned 50 cm above a mine floor.

Currents for full-wave and hybrid models were calculated and are compared for both shorted and open terminations and two different return path conductivities.

Large TL network used to demonstrate the feasibility of performing large-scale optimizations by utilizing the hybrid approach. The optimization protocol was to simultaneously maximize power transfer from T_{x} to three different receivers by implementing open and shorted terminations at each node and end load.

Map of mining area showing room-and-pillar layout.

(a) Geometry for optimization problem using the hybrid approach. A network of single conductors is constructed and optimized for minimum SWR on the segments nearest to the transmitter and receiving antennas. Optimization is performed by varying the length of grounding rods at the end of each open segment. (b) Top: Current comparison for optimized hybrid and full-wave models. Bottom: Current comparison for hybrid and full-wave models after a line break was introduced. The TL section corresponding to R_{x1} is located after the TL break, as is evident in the relatively small current magnitudes.