Skip to main content
SpringerLink
Log in

Model Waveforms of Slow-Tail Sferics

  • Published:
Radiophysics and Quantum Electronics Aims and scope

We simulate numerically the propagation of slow-tail sferics, which occupy a wide frequency band from 1 Hz to 10 kHz, in the spherical Earth–ionosphere cavity. The TM wave generated by a vertical lightning discharge is considered. Classic engineering models of a lightning stroke are employed. The calculations use the Williams stroke model as the field source. We assume that the upper boundary of the cavity is an isotropic horizontally stratified ionosphere, and the conductivity of each layer depends on its altitude. The day and night-time models of the vertical conductivity profile, which were used for correct description of the global electromagnetic (Schumann) resonance, are employed. The frequency dependence of the complex propagation constants of the zero- and first-order modes was found by using the full-wave solution in the form of the Riccati equation. The roots of this equation are the eigenvalues of the problem, which are found by iterations. Complex spectra of vertical electric and horizontal magnetic fields are constructed in the form of a series of modes with known propagation constants. Various source-to-observer distances in the day and night-time cavities are considered. The Fourier transform is applied to the complex field spectra to find the waveforms of the sferics. The model data allowed us to obtain the calibration curves for estimating the source-to-observer distance from the delay between the ELF slow tail and the VLF precursor. It is shown that the calibration curves are coincident for the day and night-time propagation conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. R. Wait, Proc. IRE, 45, 760–768 (1957). https://doi.org/10.1109/JRPROC.1957.278469

    Article  Google Scholar 

  2. J. R. Wait, J. Geophys. Res., 65, No. 7, 1939–1946 (1960). https://doi.org/10.1029/JZ065i007p01939

    Article  ADS  Google Scholar 

  3. J. R. Wait, Electromagnetic Waves in Stratified Media, Pergamon Press, Oxford (1970).

    MATH  Google Scholar 

  4. K. Sao, M. Yamashita, S. Tanahashi, and W. I. Taylor, J. Atmos. Terr. Phys., 32, No. 6, 1147–1151 (1970). https://doi.org/10.1016/0021-9169(70)90126-1

    Article  ADS  Google Scholar 

  5. Ya. L. Al’pert, Propagation of Electromagnetic Waves in the Ionosphere [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  6. R. Barr, in: J. A. Holtet, ed., ELF–VLF Radio Wave Propagation, D. Reidel Publ. Co., Dordrecht–Boston (1974), pp. 225–231.

  7. M. Yamashita, J. Atmos. Terr. Phys., 40, No. 2, 151–153 (1978). https://doi.org/10.1016/0021-9169(78)90019-3

    Article  ADS  Google Scholar 

  8. S. Yano, T. Ogawa, H. Hagino, and M. Masuhiro, J. Atmos. Electr., 14, 129–138 (1994).

    Google Scholar 

  9. H. Volland, in: Handbook of Atmospheric Electrodynamics, Vol. 2, CRC Press, Boca Raton (1995), pp. 65–94.

  10. M. Hayakawa, K. Ohta, S. Shimakura, and K. Baba, J. Atmos. Terr. Phys., 57, No. 5, 467–477 (1995). https://doi.org/10.1016/0021-9169(94)00074-X

    Article  ADS  Google Scholar 

  11. C. Mackay and A. C. Fraser-Smith, Radio Sci., 45, No. 5, RS5010 (2010). https://doi.org/10.1029/2010RS004405

    Article  ADS  Google Scholar 

  12. A. I. Sukhorukov, Ann. Geophys., 14, No. 1, 33–41 (1996). https://doi.org/10.1007/s00585-996-0033-7

    Article  ADS  Google Scholar 

  13. T. Ogawa and M. Komatsu, Radio Sci., 42, No. 2, RS2S18 (2007). https://doi.org/10.1029/2006RS003493

    Article  Google Scholar 

  14. T. Ogawa and M. Komatsu, Atmos. Res., 91, Nos. 2–4, 538–545 (2009). https://doi.org/10.1016/j.atmosres.2008.04.013

    Article  Google Scholar 

  15. A. P. Nickolaenko, M. Hayakawa, T. Ogawa, and M. Komatsu, Radio Sci., 43, No. 4, RS4014 (2008). https://doi.org/10.1029/2008RS003838

    Article  ADS  Google Scholar 

  16. A. P. Nickolaenko and M. Hayakawa, Resonances in the Earth–Ionosphere Cavity, Kluwer Academic Publishers, Dordrecht–Boston–London (2002).

  17. A. Nickolaenko and M. Hayakawa, Schumann Resonance for Tyros: Essentials of Global Electromagnetic Resonance in the Earth–Ionosphere Cavity, Springer, Tokyo–Heidelberg–New York–Dordrecht–London (2014). https://doi.org/10.1007/978-4-431-54358-9

  18. R. Barr, D. L. Jones, and C. J. Rodger, J. Atmos. Terr. Phys., 62, No. 17–18, 1689–1718 (2000). https://doi.org/10.1016/S1364-6826(00)00121-8

    Article  ADS  Google Scholar 

  19. K. G. Budden, The Waveguide Mode Theory of Wave Propagation, Logos Press, London (1961).

    Google Scholar 

  20. J. Galejs, Terrestrial Propagation of Long Electromagnetic Waves, Pergamon Press, New York (1972).

    Google Scholar 

  21. P. E. Krasnushkin and V. N. Fedorov, Geomagn. Aéron., 12, No. 1, 18–29 (1972).

    Google Scholar 

  22. G. I. Makarov, V. V. Novikov, and S. T. Rybachek, Electromagnetic Waves Propagation over the Earth’s Surface, Vol. 1 [in Russian], Nauka, Moscow (1991).

  23. G. I. Makarov, V. V. Novikov, and S. T. Rybachek, Propagation of Electromagnetic Waves over the Earth’s Surface, Vol. 2 [in Russian], Nauka, Moscow (1994).

  24. G. I. Makarov and V. V. Novikov, in: Problems of Diffraction and Propagation of Radio Waves [in Russian], No. 28, Leningrad State University, Leningrad (2000), pp. 18–58.

  25. V. A. Rafalsky, A. V. Shvets, and M. Hayakawa, J. Atmos. Terr. Phys., 57, No. 11, 1255–1261 (1995). https://doi.org/10.1016/0021-9169(95)00011-P

    Article  ADS  Google Scholar 

  26. E. M. Hünninen and Yu. P. Galuk, in: Problems of Diffraction and Propagation of Radio Waves, No. 11, Leningrad State University, Leningrad (1972), pp. 109–120.

  27. P. V. Bliokh, Yu. P. Galuk, E. M. Hünninen, et al., Radiophys. Quantum Electron., 20, No. 4, 339–345 (1977). https://doi.org/10.1007/BF01033918501-509

    Article  ADS  Google Scholar 

  28. A. P. Nickolaenko, Yu. P. Galuk, and M. Hayakawa, Radiofiz. Élektron., 6, No. 3, 30–37 (2015).

    Article  Google Scholar 

  29. Yu. P. Galuk, A. P. Nickolaenko, and M. Hayakawa, Radiofiz. Élektron., 6, No. 2, 41–47 (2015).

    Google Scholar 

  30. A. P. Nickolaenko, Yu. P. Galuk, and M. Hayakawa, SpringerPlus, 5, 108 (2016). https://doi.org/10.1186/s40064-016-1742-3

    Article  Google Scholar 

  31. A. P. Nickolaenko, Yu. P. Galuk, and M. Hayakawa, in: A. Reimer, ed., Horizons in World Physics, Vol. 288, NOVA Sci. Publishers, New York (2017), pp. 105–128.

    Google Scholar 

  32. H. J. Zhou, M. Hayakawa, Yu. P. Galuk, and A. P. Nickolaenko, Sun and Geosphere, 11, No. 1, 5–15 (2016).

    Google Scholar 

  33. I. G. Kudintseva, A. P. Nickolaenko, M. J. Rycroft, and A. Odzimek, Ann. Geophys., 59, No. 5, A0545 (2016). https://doi.org/10.4401/ag-6870

    Article  Google Scholar 

  34. C. Greifinger and P. Greifinger, Radio Sci., 13, No. 5, 831–837 (1978). https://doi.org/10.1029/RS013i005p0083113

    Article  ADS  Google Scholar 

  35. K. G. Budden and M. Eve, Proc. Roy. Soc., A342, No. 1629, 175–190, London (1975). https://doi.org/10.1098/rspa.1975.0019

  36. Yu. P. Galuk, E. M. Hünninen, and S. Yu. Fesenko, in: Problems of Diffraction and Propagation of Radio Waves [in Russian], No. 16, Leningrad State University, Leningrad (1978), pp. 188–194.

  37. T. I. Bichutskaya, Problems of Diffraction and Propagation of Radio Waves [in Russian], No. 22, Leningrad State University, Leningrad (1978), pp. 114–123.

  38. P. V. Bliokh, A. P. Nickolaenko, and Yu. F. Filippov, Global Electromagnetic Resonances in the Earth–Ionosphere Cavity [in Russian], Naukova Dumka, Kiev (1977).

  39. D. J. Boccippio, E. R. Williams, S. J. Heckman, et al., Science, 269, No. 5227, 1088–1091 (1995). https://doi.org/10.1126/science.269.5227.1088

    Article  ADS  Google Scholar 

  40. E. Huang, E. Williams, R. Boldi, et al., J. Geophys. Res., 104, No. D14, 16943–16964 (1999). https://doi.org/10.1029/1999JD900139

    Article  ADS  Google Scholar 

  41. A. V. Shvets, A. P. Nickolaenko, A. V. Koloskov, et al., Ukrainian Antarctic J., No. 1 (18), 116–127 (2019).

Download references

Author information

Authors and Affiliations

  1. A. Ya.Usikov Institute of Radiophysics and Electronics of the Ukrainean National Academy of Sciences, Kharkov, Ukraine

    A. P. Nickolaenko

  2. St. Petersburg State University, St. Petersburg, Russia

    Yu. P. Galuk

  3. Hayakawa Institute of Seismo Electromagnetics Co. Ltd., University of Electro-Communications Alliance Center, Chofu, Japan

    M. Hayakawa

  4. University of Electro-Communications, Advanced Wireless and Communications Research Center, Chofu, Japan

    M. Hayakawa

  5. V.N. Karazin National University, Kharkov, Ukraine

    I. G. Kudintseva

Authors
  1. A. P. Nickolaenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. P. Galuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Hayakawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. I. G. Kudintseva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. P. Nickolaenko.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 64, No. 6, pp. 445–457, June 2021. Russian DOI: 10.52452/00213462_2021_64_06_445

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nickolaenko, A.P., Galuk, Y.P., Hayakawa, M. et al. Model Waveforms of Slow-Tail Sferics. Radiophys Quantum El 64, 401–411 (2021). https://doi.org/10.1007/s11141-022-10142-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-022-10142-x

Search

Navigation