Dyrda, M., Kulak, A., Mlynarczyk, J., and Ostrowski, M.: Novel analysis of a
sudden ionospheric disturbance using Schumann resonance measurements, J.
Geophys. Res.-Space, 120, 2255–2262, https://doi.org/10.1002/2014JA020854, 2015.
Galejs, J.: Terrestrial Propagation of Long Electromagnetic Waves, edited by: Cullen, A. L., Fock, V. A., and Wait, J. R., Pergamon,
New York, ISBN 978-14-8315-956-0, 1972.
Hayakawa, M. and Otsuyama, T.: FDTD analysis of ELF wave propagation in
inhomogeneous subionospheric waveguide models, Appl. Computational
Electromagnetics Soc. J., 17, 239–244, 2002.
Holland, R.: THREDS: A finite-difference time-domain EMP code in 3D
spherical coordinates, IEEE T. Nucl. Sci., NS-30, 4592–4595,
1983.
Hu, W. and Cummer, S. A.: An FDTD model for low and high altitude
lightning-generated EM fields, IEEE T. Antennas Propag., 54,
1513–1522, 2006.
Kirillov, V. V.: Parameters of the earth-ionosphere waveguide at ELF, Probl. Diffr. Wave Propagat., 25, 1993 (in
Russian).
Kudintseva, I. G., Nickolaenko, A. P., Rycroft, M. J., and Odzimek, A.: AC and
DC global electric circuit properties and the height profile of atmospheric
conductivity, Ann. Geophys., 25, 35–52, 2016.
Kulak, A. and Mlynarczyk, J.: A new technique for reconstruction of the
current moment waveform related to a gigantic jet from the magnetic field
component recorded by an ELF station, Radio Sci., 46, RS2016, https://doi.org/10.1029/2010RS004475, 2011.
Kulak, A. and Mlynarczyk, J.: ELF Propagation Parameters for the
Ground-Ionosphere Waveguide With Finite Ground Conductivity, IEEE T.
Antennas Propag., 61, 2269–2275, https://doi.org/10.1109/TAP.2012.2227445, 2013.
Kulak, A., Zieba, S., Micek, S., and Nieckarz, Z.: Solar variations in extremely
low frequency propagation parameters: 1. A two-dimensional telegraph
equation (TDTE) model of ELF propagation and fundamental parameters of
Schumann resonances, J. Geophys. Res.-Space, 108, 1270, https://doi.org/10.1029/2002JA009304, 2003.
Kulak, A., Mlynarczyk, J., Zieba, S., Micek, S., and Nieckarz, Z.: Studies of
ELF propagation in the spherical shell cavity using a field decomposition
method based on asymmetry of Schumann resonance curves, J. Geophys. Res.,
111, A10304, https://doi.org/10.1029/2005JA011429, 2006.
Kulak, A., Nieckarz, Z., and Zieba, S.: Analytical description of ELF
transients produced by cloud to ground lightning discharges, J. Geophys.
Res., 115, D19104, https://doi.org/10.1029/2009JD013033, 2010.
Kulak, A., Kubisz, J., Klucjasz, S., Michalec, A., Mlynarczyk, J., Nieckarz,
Z., Ostrowski, M., and Zieba, S.: Extremely low frequency electromagnetic field
measurements at the Hylaty station and methodology of signal analysis, Radio
Sci., 49, 361–370, 2014.
Lehtinen, N. G. and Inan, U. S.: Radiation of ELF/VLF waves by harmonically
varying currents into a stratified ionosphere with application to radiation
by a modulated electrojet, J. Geophys. Res., 113, A06301, https://doi.org/10.1029/2007JA012911, 2008.
Lehtinen, N. G. and Inan, U. S.: Full-wave modeling of transionospheric
propagation of VLF waves, Geophys. Res. Lett., 36, L03104, https://doi.org/10.1029/2008GL036535, 2009.
Li, D., Zhang, Q., Liu, T., and Wang, Z.: Validation of the Cooray-Rubinstein
(C-R) formula for a rough ground surface by using three-dimensional (3-D)
FDTD, J. Geophys. Res.-Atmos., 118, 12749–12754, 2013.
Li, D., Zhang, Q., Wang, Z., and Liu, T.: Computation of lightning horizontal
field over the two-dimensional rough ground by using the three-dimensional
FDTD, IEEE T. Electroman. Compat., 56, 143–148, 2014.
Li, D., Azadifar, M., Rachidi, F., Rubinstein, M., Paolone, M., Pavanello,
D., Metz, S., Zhang, Q., and Wang, Z.: On lightning electromagnetic field
propagation along an irregular terrain, IEEE T. Electroman. Compat.,
58, 161–171, 2016.
Li, D., Luque, A., Rachidi, F., Rubinstein, M., Azadifar, M., Diendorfer,
G., and Pichler, H.: The propagation effects of lightning electromagnetic fields
over mountainous terrain in the earth-Ionosphere waveguide, J. Geophys. Res.-Atmos., 124, 14198–14219, 2019.
Marchenko, V., Kulak, A., and Mlynarczyk, J.: The software code for Finite-Difference Time-Domain (FDTD) simulations used in the paper “Finite-difference time-domain analysis of ELF radio wave propagation in the spherical Earth-ionosphere waveguide and its validation based on analytical solutions”, Zenodo [code], https://doi.org/10.5281/zenodo.6628335, 2022a.
Marchenko, V., Kulak, A., and Mlynarczyk, J.: The conductivity profile of Earth-ionosphere cavity used in the paper “Finite-difference time-domain analysis of ELF radio wave propagation in the spherical Earth-ionosphere waveguide and its validation based on analytical solutions”, Zenodo [data set], https://doi.org/10.5281/zenodo.6628304, 2022b.
Marshall, R. A.: An improved model of the lightning electromagnetic field
interaction with the D-region ionosphere, J. Geophys. Res., 117, A03316, https://doi.org/10.1029/2011JA017408,
2012.
Mlynarczyk, J., Kulak, A., Popek, M., Iwanski, R., Klucjasz, S., and Kubisz, J.:
An analysis of TLE-associated discharges using the data recorded by a new
broadband ELF receiver, XVI International Conference on Atmospheric
Electricity, 17–22 June 2018, Nara city, Nara, Japan, 2018.
Morente, J. A., Molina-Cuberos, G. J., Porti, J. A., Besser, B. P., Salinas,
A., Schwingenschuch, K., and Lichtenegger, H.: A numerical simulation of
Earth's electromagnetic cavity with the Transmission Line Matrix method:
Schumann resonances, J. Geophys. Res., 108, 1195, https://doi.org/10.1029/2002JA009779, 2003.
Mushtak, C. and Williams, E. R.: ELF propagation parameters for uniform
models of the Earth-ionosphere waveguide, J. Atmos. Sol.-Terr.
Phy., 64, 1989–2001, 2002.
Navarro, E. A., Soriano, A., Morente, J. A., and Porti, J. A.: A finite
difference time domain model for the Titan ionosphere Schumann resonances,
Radio Sci., 42, RS2S04, https://doi.org/10.1029/2006RS003490, 2007.
Navarro, E. A., Soriano, A., Morente, J. A., and Porti, J. A.: Numerical
analysis of ionosphere disturbances and Schumann mode splitting in the
Earth-ionosphere cavity, J. Geophys. Res., 113, A09301, https://doi.org/10.1029/2008JA013143, 2008.
Nickolaenko, A. P., Galuk, Y. P., and Hayakawa, M.: Vertical profile of
atmospheric conductivity that matches Schumann resonance observations,
SpringerPlus, 5, 108, https://doi.org/10.1186/s40064-016-1742-3, 2016.
Nickolaenko, A. P., Galuk, Y. P., Hayakawa, M., and Kudintseva, I. G.: Model
sub-ionospheric ELF – VLF pulses, J. Atmos. Sol.-Terr. Phy., 223, 105726, https://doi.org/10.1016/j.jastp.2021.105726, 2021.
Ogawa, T., Tanaka, Y., Yasuhara, M., Fraser-Smith, A. C., and Gendrin, R.: Worldwide simultaneity of occurrence of a Q-type ELF burst in the Schumann
resonance frequency range, J. Geomagn. Geoelectr., 19,
377–384, 1967.
Otsuyama, T., Sakuma, D., and Hayakawa, M.: FDTD analysis of ELF wave
propagation and Schumann resonances for a subionospheric waveguide model,
Radio Sci., 38, 1103, https://doi.org/10.1029/2002RS002752, 2003.
Qin, Z., Cummer, S. A., Chen, M., Lyu, F., and Du, Y.: A Comparative Study of the
Ray Theory Model With the Finite Difference Time Domain Model for Lightning
Sferic Transmission in Earth-Ionosphere Waveguide, J. Geophys. Res.-Atmos., 124, 3335–3349, https://doi.org/10.1029/2018JD029440, 2019.
Prácser, E., Bozóki, T., Sátori, G., Williams, E., Guha, A., and
Yu, H.: Reconstruction of Global Lightning Activity Based on Schumann
Resonance Measurements: Model Description and Synthetic Tests, Radio
Sci., 54, 254–267, 2019.
Rakov, V.: Lightning Return Stroke Speed, Journal of Lightning Research,
1, 80–89, 2007.
Samimi, B., Nguyen, T., and Simpson, J. J.: Recent FDTD Advances for
Electromagnetic Wave Propagation in the Ionosphere, Chap. 4, in:
Computational Electromagnetic Methods and Applications, edited by: Yu, W., Artech,
Norwood, MA, ISBN 978-16-0807-896-7, 2015.
Simpson, J. J. and Taflove, A.: Two-dimensional FDTD model of antipodal ELF
propagation and Schumann resonance of the Earth, IEEE Antenn. Wirel.
Pr., 1, 53–56, 2002.
Soriano, A., Navarro, E. A., Morente, J. A., and Porti, J. A.: A numerical
study of the Schumann resonances in Mars with the FDTD method, J. Geophys.
Res., 112, A06311, https://doi.org/10.1029/2007JA012281, 2007.
Suzuki, Y., Araki, S., Baba, Y., Tsuboi, T., Okabe, S., and Rakov, V.: An FDTD
Study of Errors in Magnetic Direction Finding of Lightning Due to the
Presence of Conducting Structure Near the Field Measuring Station,
Atmosphere, 7, 92, https://doi.org/10.3390/atmos7070092, 2016.
Toledo-Redondo, S., Salinas, A., Fornieles, J., Porti, J., and Lichtenegger,
H. I. M.: Full 3-D TLM simulations of the Earth-ionosphere cavity: Effect of
conductivity on the Schumann resonances, J. Geophys. Res.-Space,
121, 5579–5593, 2016.
Yang, H. and Pasko, V. P.: Three-dimensional finite-difference time-domain
modeling of the Earth-ionosphere cavity resonances, Geophys. Res. Lett.,
32, L03114, https://doi.org/10.1029/2004GL021343, 2005.
Yang, H., Pasko, V. P., and Yair, Y.: Three-dimensional finite difference
time domain modeling of the Schumann resonance parameters on Titan, Venus,
and Mars, Radio Sci., 41, RS2S03, https://doi.org/10.1029/2005RS003431, 2006.
Yu, Y., Niu, J., and Simpson, J. J.: A 3-D global Earth-ionosphere FDTD model
including an anisotropic magnetized plasma ionosphere, IEEE T. Antennas
Propag., 60, 3246–3256, 2012.
Zhang, Q., Li, D., Zhang, Y., Gao, J., and Wang, Z.: On the accuracy of Wait's
formula along a mixed propagation path within 1 km from the lightning
channel, IEEE T. Electroman. Compat., 54, 1042–1047, 2012a.
Zhang, Q., Li, D., Fan, Y., Zhang, Y., and Gao, J.: Examination of the
Cooray-Rubinstein (C-R) formula for a mixed propagation path by using FDTD,
J. Geophys. Res.-Atmos., 117, D15309, https://doi.org/10.1029/2011JD017331, 2012b.
