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Use of the zonal harmonic series for obtaining numerical solutions to electromagnetic boundary value problems
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Details:
  • Personal Authors:
    Lewis, Richard L.
  • Conference Authors:
    Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
  • Description:
    This is a discussion of the application of the zonal harmonic series to problems involving dipole sources in the vicinity of spherical boundaries. The application of a formal zonal-harmonic series solution to directly obtain numerical results involves two distinct problems: namely, the convergence of the series solution and the accurate calculation of the special functions involved in the series solution. Some interesting techniques will be introduced which help to improve the convergence properties of the series solution.

  • Document Type:
    Book Chapter
  • Collection(s):
    National Institute for Occupational Safety and Health
  • Main Document Checksum:
  • Supporting Files:
    No Additional Files
    1. Theory of the propagation of UHF radio waves in coal mine tunnels
      Personal Author:
      Emslie, Alfred G.; Lagace, Robert L.; Strong, Peter F.;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 38-48
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      This paper is concerned with the theoretical study of UHF radio communication in coal mines, with particular reference to the rate of loss of signal strength along a tunnel, and from one tunnel to another around a comer. Of prime interest are the nat...
      File Type:
      Filetype[PDF - 500.48 KB]
    2. A discussion on the three-dimensional boundary value problem for electromagnetic fields
      Personal Author:
      Rankin, David
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 92-94
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      Three -dimensional boundary value problems are difficult to solve. Indeed, while the separation of the scalar wave equation can be effected in 11 different coordinate systems, an analytic solution requires that the boundaries, both external and inter...
      File Type:
      Filetype[PDF - 123.86 KB]
    3. Objectives and constraints of through-the-earth electromagnetic communication systems
      Personal Author:
      Parkinson, Howard E.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 1-8
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      In 1969, new coal mine health and safety legislation was enacted in the United States. As a result of this legislation, the Department of Interior, Bureau of Mines has carried out communications research aimed at developing whole mine communications ...
      File Type:
      Filetype[PDF - 502.00 KB]
    4. Feasibility of a radiocommunication in mine galleries by means of a coaxial cable having a high coupling impedance
      Personal Author:
      Fontaine, J.; Demoulin, B.; Degauque, P.; Gabillard, R.;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 130-139
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      To realize a radiowave communication along mine galleries a few kilometers long without repeater, we show that it is possible to use a coaxial cable bearing an important surface transfer impedance like a transmission line with an inductive coupling t...
      File Type:
      Filetype[PDF - 326.47 KB]
    5. State of knowledge of analytical techniques for thru-the-earth electromagnetic wave problems relevant to mine rescue
      Personal Author:
      Wait, James R.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 9-14
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      It is the purpose of this paper to review theoretical model concepts in through- the -earth transmission of electromagnetic waves. While the subject is very broad in its defined scope, we will be conscious of the specific applications to mine rescue ...
      File Type:
      Filetype[PDF - 232.46 KB]
    6. An underground electromagnetic sounder experiment
      Personal Author:
      Dolphin, Lambert; Bollen, Robert; Oetzel, George;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 168
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      An electromagnetic sounder developed for an archaeological application in Egypt has been successfully tested in a California dolomite mine. Chambers in the mine 100 to 130 feet from the surface gave intense, well-defined echoes consistent with an ave...
      File Type:
      Filetype[PDF - 31.08 KB]
    7. Performance of manpack electromagnetic location equipment in trapped miner location tests
      Personal Author:
      Farstad, Arnold J.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 62-72
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      The use of radio signals for underground communications was considered as early as the mid-1920's [1] - [4] . However, early experiments did not produce promising results with the type of equipment that was available then [5] . With advancements in s...
      File Type:
      Filetype[PDF - 1010.41 KB]
    8. Electromagnetic field solutions for infinite and finite cables for conducting half-space models- both frequency - and time-domain
      Personal Author:
      Hill, D. A.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 15-19
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      Introduction The fields of an infinite line source in the presence of a conducting half-space have been examined by Wait and Spies (1971). In any real communication link using a current-carrying cable for the transmitting antenna, the cable is of fin...
      File Type:
      Filetype[PDF - 104.72 KB]
    9. Spectrum measurements of electromagnetic-noise in coal mines;
      Personal Author:
      Bensema, W. D.; Adams, J. W.;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 151-155
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      A portable, multichannel battery-operated mine-permissible measurement system was developed to measure the rms magnetic-field noise spectrum in the frequency range from 100 Hz to 375 kHz. During each measurement, the entire spectrum is measured simul...
      File Type:
      Filetype[PDF - 231.00 KB]
    10. Fields of a magnetic dipole excited buried cylinder
      Personal Author:
      Howard, Allen Q., Jr.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 73-80
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      An approximate solution to the electromagnetic boundary value problem consisting of a horizontal cylindrical conductor buried in a lossy half-space and excited by an arbitrarily oriented magnetic dipole is found using an iterative perturbation techni...
      File Type:
      Filetype[PDF - 234.53 KB]
    11. Reply to: "A Discussion on the three-dimensional boundary value problem for electromagnetic field" by D. Rankin
      Personal Author:
      Jones, F. W.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 95-97
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      I do not regard the criticism by Rankin of my work as valid or even meaningful. I strongly reject the assertion by Rankin that my results are invalid. As stated in my paper, the equation to solve (in e. m.u. ) is: [ ] where n2 =4 ??? . This may be re...
      File Type:
      Filetype[PDF - 100.72 KB]
    12. The electromagnetic response of a buried sphere for buried dipole excitation 
      Personal Author:
      Hill, D. A.; Wait, J. R.;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 81-85
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      The feasibility of locating a buried vertical magnetic dipole source (horizontal loop) from surface measurements of the vertical and horizontal magnetic field components has been investigated by Wait (1971). , For sufficiently low frequencies, the ma...
      File Type:
      Filetype[PDF - 186.51 KB]
    13. Subsurface applications of periodic electromagnetic video pulse signals 
      Personal Author:
      Moffatt, David L.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 112-120
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      Considerable current interest is evident[l,2] in the use of transient electromagnetic methods for subsurface remote sensing. A transient method is discussed which uses a periodic video-type pulse containing a wide frequency range. A video pulse is us...
      File Type:
      Filetype[PDF - 354.63 KB]
    14. Summary report on electromagnetic noise measurement program
      Personal Author:
      Adams, John W.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 169
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      The present status of the National Bureau of Standards program is that many magnetic tapes of analog data have been recorded in four major mines. Each mine uses different types of equipment. In addition, some surface measurements of noise have been m...
      File Type:
      Filetype[PDF - 37.61 KB]
    15. Summary report of electromagnetic location techniques working group 
      Personal Author:
      Farstad, Arnold J.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 171-177
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      The Location Group conversed in the Petroleum Room of the Green Center with the purpose of addressing the following list of topics in light of the Bureau of Mines' requirements for detecting and locating trapped miners by electromagnetic methods. The...
      File Type:
      Filetype[PDF - 288.74 KB]
    16. Admittance and effective height of buried antennas
      Personal Author:
      Franceschetti, Giorgio
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 162-167
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      Explicit expressions are presented for the input admittance and effective height of several buried metal antennas, namely: (i) prolate spheroidal; (ii) spherical; (iii) oblate spheroidal; (iv) parallel plate; (v) parallel plate with protruding dielec...
      File Type:
      Filetype[PDF - 27.45 KB]
    17. The perturbation of alternating electromagnetic fields by three-dimensional bodies
      Personal Author:
      Jones, F. W.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 86-91
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      The perturbation of alternating electromagnetic fields by three-dimensional structures is considered. The general model is that of a semi-infinite conducting half -space which consists of regions of different conductivities. A numerical method is use...
      File Type:
      Filetype[PDF - 143.65 KB]
    18. Electromagnetic survey method applicable to underground quarries; proceedings of thru-the-earth electromagnetics workshop
      Personal Author:
      Gabillard, R.; Dubus, J. P.; Cherpereel, F.;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 121-129
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      We present an electromagnetic method taken from the well known radiogoniometer that allows us to locate at the surface of the ground the vertical axis of a magnetic antenna transmitter buried at a depth h in the earth. The method and the equipment ac...
      File Type:
      Filetype[PDF - 739.67 KB]
    19. Electromagnetic transmission and detection at deep depths
      Personal Author:
      Starkey, D. B.
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 140-148
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      nvestigation into the expressions of the field produced by a loop over a conducting half space or in an infinite conducting half space are well documented. Reasonably complex descriptions of the effects of stratification also are reported. However, a...
      File Type:
      Filetype[PDF - 273.87 KB]
    20. Experimental comparison of buried and elevated ELF transmitting antennas
      Personal Author:
      Bannister, Peter R.; Williams, Frederick J.; Katan, J. Robert; Ball, John R.;
      Conference Author:
      Thru-the-Earth-Electromagnetics Workshop (1973 : Colorado School of Mines)
      Published:
      1973
      Source:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines, p. 162-167
      Series:
      Proceedings of Thru-the-Earth Electromagnetics, August 15-17,1973, Colorado School of Mines
      Description:
      During the last week in March and the first week in April, 1973, the Naval Underwater Systems Center measured the 76 Hz magnetic field strength (in Wisconsin and Texas) produced by both the elevated and (newly installed) buried Wisconsin Test Facilit...
      File Type:
      Filetype[PDF - 249.63 KB]
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