• Українська
  • English
  • Русский
ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

COMPARISON OF EXACT AND APPROXIMATE SOLUTIONS OF THE SCHUMANN RESONANCE PROBLEM FOR THE KNEE CONDUCTIVITY PROFILE

heading: 
RADIOWAVE PROPAGATION, RADIOLOCATION AND REMOTE SENSING
Galuk, YP, Nickolaenko, AP, Hayakawa, M
Organization: 

Sankt-Petersburg State University
35, University Avenue., St. Petersburg, Peterhof 198504, Russia
E-mail: galyuck@paloma.spbu.ru

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: sasha@ire.kharkov.ua

Institute Hayakawa, the seismic company electromagnetism,
Incubation Center 508 Telecommunication University,
Chofugaoka 1-5-1, Chofu, Tokyo 182-8585, Japan
E-mail: hayakawa@hi-seismo-em.jp
https://doi.org/10.15407/rej2015.02.040
Language: russian
Abstract: 

The rapid development of computer technology allows for the direct numerical solution of the electromagnetic resonance problem in the Earth–ionosphere cavity. Either the two-dimensional telegraph equations (2DTU) or the finite element method in the time domain (FDTD) techniques are used. The direct solutions apply the same models of the conductivity profile of atmosphere as those applied in ordinary solutions. However, it is forgotten that these profiles are nothing else, but a convenient interpretation for the approximate heuristic relations for deriving the propgation constant. Since the full wave solution of the electromagnetic problem for such a profile does not coincide with the aproximate one, the direct numerical solutions must also deviate from the heuristic one. We apply the knee conductivity profile in the rigorous full wave solution and in the approximate solution and evaluate their devations
Keywords: global electromagnetic resonance, rigorous and approximate solutions, the knee profile

Manuscript submitted 05.03.2015
PACS     93.85.Pq, 94.20.Ws, 94.20.Cf
Radiofiz. elektron. 2015, 20(2): 40-47
Full text  (PDF)

References: 
  1. Kirillov, V. V., 1993. Parameters of the Earth-ionosphere waveguide at extremely low frequencies, Problemy difraktsii i rasprostraneniya radiovoln. 25, pp. 35–52 (in Russian).
  2. Kirillov, V. V., Kopeykin, V. N. and Mushtak, V. C., 1997. ELF electromagnetic waves within the Earth-ionosphere waveguide. Geomagnetizm i Aeronomiya. 37(3), pp. 114–120 (in Russian).
  3. Kirillov, V. V., 1996. A two-dimensional theory of propagation of ELF electromagnetic waves within the Earth-ionosphere waveguide. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 39(12), pp. 1103–1112 (in Russian).
  4. Kirillov, V. V. and Kopeykin, V. N., 2002. Solving a two-dimensional telegraph equation with anisotropic parameters. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 45(12), pp. 1011–1024 (in Russian).
  5. Pechony, O. and Price, C., 2004. Schumann resonance parameters calculated with a partially uniform knee model on Earth, Venus, Mars, and Titan. Radio Sci. 39(5), pp. RS5007 (10 р.).
  6. Pechony, O., 2007. Modeling and Simulations of Schumann Resonance Parameters Observed at the Mitzpe Ramon Field Station. PhD. thesis ed. Tel-Aviv University, Tel-Aviv.
  7. Ando, Y., Shvets, A. V. and Nickolaenko, A. P., 2005. Finite difference analyses of Schumann resonance and reconstruction of lightning distribution. Radio Sci. 40(2), pp. RS2002 (17 p.).
  8. Morente, J. A., Portí, J. A., Besser, B. P., Salinas, A., Lichtenegger, H. I. M., Navarro, E. A. and Molina-Cuberos, G. J., 2002. A numerical simulation of Earth’s electromagnetic cavity with the Transmission Line Matrix method: Schumann resonances. J. Geophys. Res. 108(A5), pp. 1195 (11 p.).
  9. Yang, H. and Pasko, V. P., 2007. Power variations of Schumann resonances related to El Nino and La Nina phenomena, Geophys. Res. Lett. 34(11), pp. L11102 (5 p.).
  10. Yang, H. and Pasko, V. P., 2005. Three-dimensional finite-difference time domain modeling of the Earth-ionosphere cavity resonances. Geophys. Res. Lett. 32(3), pp. L03114 (4 p.).
  11. Yang, H., Pasko, V. P. and Yair, Y., 2006. Three-dimensional finite difference time-domain modeling of the Schumann resonance parameters on Titan, Venus, and Mars. Radio Sci. 41(2), pp. RS2S03 (10 p.).
  12. Molina-Cuberos, G. J., Morente, J. A., Besser, B. P., Portí, J., Lichtenegger, H., Schwingenschuh, K., Salinas, A. and Margineda, J., 2006. Schumann resonances as a tool to study the lower ionospheric structure of Mars. Radio. Sci. 41(1), pp. RS1003 (8 p.).
  13. Toledo‐Redondo, S., Salinas, A., Portí, J., Morente, J. A., Fornieles, J., Méndez, A., Galindo‐Zaldívar, J., Pedrera, A., Ruiz‐Constán, A., Anahnah, F., 2010. Study of Schumann resonances based on magnetotelluric records from the western Mediterranean and Antarctica. J. Geophys. Res. 115(D22), pp. 114–124.DOI: https://doi.org/10.1029/2010JD014316
  14. Toledo-Redondo, S., Salinas, A., Morente-Molinera, J. A., Méndez, A., Fornieles, J., Portí, J., Morente, J. A., 2013. Parallel 3D-TLM algorithm for simulation of the Earth-ionosphere cavity. J. Comput. Phys. 236, pp. 367–379.DOI: https://doi.org/10.1016/j.jcp.2012.10.047
  15. Nickolaenko, A. P. and Hayakawa, M., 2002. Resonances in the Earth-ionosphere cavity. Dordrecht-Boston-L.: Kluwer Academic Publ.
  16. Nickolaenko, A. P. and Hayakawa, M., 2014. Schumann resonance for tyros (Essentials of Global Electromagnetic Resonance in the Earth–Ionosphere Cavity). Tokyo-Heidelberg-N. Y.-Dordrecht-L.: Springer. Ser. XI. Springer Geophys.
  17. Ishaq, M. and Jones Ll. D., 1977. Method of obtaining radio wave propagation parameters for the Earth–ionosphere duct at ELF. Electron. Lett. 13(2), pp. 254–255.DOI: https://doi.org/10.1049/el:19770184
  18. Nickolaenko, A. P. and Rabinowicz, L. M., 1982. Possible global electromagnetic resonances on the planets of Solar system. Cosmic Res. 20(1), pp. 67–71.
  19. Nickolaenko, A. P. and Rabinowicz, L. M., 1987. On the applicability of extremely low frequency global resonances in the studies of lightning activity at Venus. Cosmic Res. 25(2), pp. 301–306.
  20. Sentman, D. D., 1990. Electrical conductivity of Jupiter Shallow interior and the formation of a resonant planetary-ionospheric cavity. ICARUS. 88(1), pp. 73–86.DOI: https://doi.org/10.1016/0019-1035(90)90177-B
  21. Bliokh, P. V., Nickolaenko, A. P., and Filippov, Yu. F., 1980. Schumann resonances in the Earth-ionosphere cavity. New York, London, Paris: Peter Perigrinus.
  22. Wait, J. R., 1970. Electromagnetic Waves in Stratified Media. Oxford, N. Y.-Toronto: Pergamon Press.
  23. Hynninen, E. M. and Galuk, Yu. P., 1972. Field of a vertical electric dipole over the spherical Earth with a non-uniform in height ionosphere. Problemy difraktsii i rasprostraneniya radiovoln. 11, pp. 109–120 (in Russian).
  24. Bliokh, P. V., Galuk, Yu. P., Hynninen, E. M, Nickolaenko, A. P. and Rabinowicz, L. M., 1977. On the resonance phenomena in the Earth–ionosphere cavity. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 20(4), pp. 501–509 (in Russian).
  25. Galuk, Yu. P. and Ivanov, V. I., 1978. Finding the propagation characteristics of VLF fields in the Earth – non-uniform along the height anisotropic ionosphere. Problemy difraktsii i rasprostraneniya radiovoln. 16, pp. 148–153 (in Russian).
  26. Greifinger, C. and Greifinger, P., 1978. Approximate method for determining ELF eigenvalues in the Earth-ionosphere waveguide. Radio Sci. 13, pp. 831-837.DOI: https://doi.org/10.1029/RS013i005p00831
  27. Wait, J. R. and Spies, K. P., 1964. Characteristics of the Earth–ionosphere waveguide for VLF radio waves. [pdf] U. S. Department of Commerce. National Bureau of Standards. NBS Technical Note N 300. Available from: http://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote300.pdf
  28. Cole, R. K. and Pierce, E. T., 1965. Electrification in the Earth’s atmosphere from altitudes between 0 and 100 kilometers, J. Geophys. Res. 70(11), pp. 2735-2749.DOI: https://doi.org/10.1029/JZ070i012p02735
  29. Sentman, D. D., 1990. Approximate Schumann resonance parameters for two-scale-height ionosphere. J. Atmos. Terr. Phys. 52(1), pp. 35-46.DOI: https://doi.org/10.1016/0021-9169(90)90113-2
  30. Fullekrug, M., 2000. Dispersion relation for spherical electromagnetic resonances in the atmosphere. Phys. Lett. A. 275(1), pp. 80–89.DOI: https://doi.org/10.1016/S0375-9601(00)00549-1
  31. Mushtak, V. C. and Williams, E., 2002. Propagation parameters for uniform models of the Earth-ionosphere waveguide. J. Atmos. Solar-Terr. Phys. 64(18), pp. 1989–2001.DOI: https://doi.org/10.1016/S1364-6826(02)00222-5
  32. Greifinger, P. S., Mushtak, V. C. and Williams, E. R., 2007. On modeling the lower characteristic ELF altitude from aeronomical data. Radio Sci. 42(2), pp. RS2S12 (12 р.).
  33. Jones, D. Ll. and Knott, M., 2003. The full wave solution and computations of the electromagnetic resonance in the Earth–ionosphere cavity. In: V. M. Yakovenko, ed. 2003. Radiofizika i elektronika. Kharkov: IRE NAS of Ukraine Publ. 8(1), pp. 55–66 (in Russian).
  34. Williams, E. R., Mushtak, V. C. and Nickolaenko, A. P., 2006. Distinguishing ionospheric models using Schumann resonance spectra. J. Geophys. Res. 111, pp. D16107 (12 p.).
  35. Shvets, A. V., Hobara, Y., and Hayakawa, M., 2010. Variations of the global lightning distribution revealed from three station Schumann resonance measurements. J. Geophys. Res. 115, pp. A12316 (15 p.).
  36. Shvets, A. V. and Hayakawa, M., 2011. Global lightning activity on the basis of inversions of natural elf electromagnetic data observed at multiple stations around the world. Surv. Geophys. 32(6), p. 705–732.DOI: https://doi.org/10.1007/s10712-011-9135-1