Three Dimensional Finite Difference Time Domain Modeling of Schumann Resonances On Earth and Other Planets of the Solar System

Open Access
Yang, Heng
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
October 30, 2007
Committee Members:
  • Victor P Pasko, Committee Chair
  • John David Mathews, Committee Member
  • Kultegin Aydin, Committee Member
  • Douglas Henry Werner, Committee Member
  • Michael T Lanagan, Committee Member
  • Schuamann resonances
  • FDTD
  • Lightning
  • Mars
  • ELF
  • Earth-ionosphere cavity
Resonance properties of the Earth-ionosphere cavity were predicted by W. O. Schumann in 1952. Since then observations of electromagnetic signals in the frequency range 1-500 Hz have become a powerful tool for variety of remote sensing applications, which in recent years included studies of thunderstorm related transient luminous events in the middle atmosphere and related lightning discharges. In this thesis, a three dimensional Finite Difference Time Domain (FDTD) model is developed to study the propagation of the extremely low frequency (ELF) waves in the Earth-ionosphere cavity and in similar cavities on other celestial bodies of the Solar System. A comparison of the results from this FDTD model with a set of classical eigenfrequency ($f_n$) and quality factor ($Q_n$) solutions for laterally uniform spherically symmetric Earth-ionosphere cavity and with recent observations of Schumann resonance (SR) during solar proton events (SPEs) and X-ray bursts is provided. The FDTD $f_n$ and $Q_n$ solutions for the uniform cavity appear to be in excellent agreement (within several $\%$) with well-known experimental results documented in the literature. The related analysis indicates that the frequency of the first SR mode decreases during SPEs and increases during X-ray bursts by a fraction of a Hz, in agreement with physical arguments presented in previously published literature and with observations. The FDTD model is extended to include the effects of the geomagnetic field on SR parameters. A higher penetration height of SR electric and magnetic components is found with the presence of the geomagnetic field. In a realistic cavity, the conductivity distribution is not laterally uniform and spherically symmetric, but varies with local time and seasons reflecting related variations in the effects of solar radiation on the conductivity of the lower ionosphere. The global lightning activity in the three main areas (Africa, South-East Asia, and South America) also has diurnal and seasonal variation patterns, which manifest themselves in the diurnal and seasonal variations of SR parameters. In this thesis, the FDTD model is used to account for the realistic cavity at different local time and seasons using asymmetric conductivity profiles derived from International Reference Ionosphere (IRI) model. The FDTD results are compared with observational data in the available literature. The influence of the diurnal and seasonal conductivity variation, the global lightning activity, and the positions of the observation stations on the SR parameters are discussed. Another important factor influencing the SR power is related to the shifts of the global thunderstorm regions due to the El Ni~{n}o and La Ni~{n}a phenomena. Due to the different spatial field distributions of SR electric and magnetic components in the Earth-ionosphere cavity, the different power variation patterns are clearly observed in the electric and magnetic components with the motion of the thunderstorm center in our FDTD results. A new method is proposed to detect the shifts of the thunderstorm regions related to the El Ni~{n}o and La Ni~{n}a phenomena using a combination of electric and magnetic components of Schumann resonances at a single station. In recent years, there has been an increasing interest in the exploration of the other planets in the Solar System. On January 14, 2005, HUYGENS probe landed on Titan, and started exploration of this largest moon of Saturn. One of multiple missions of HUYGENS probe is to find if there are lightning discharges in the Titan’s atmosphere. It is believed that conducting properties of the Titan’s atmosphere are favorable for the formation of the cavity for propagation of electromagnetic waves, so the existence of SR will give a support for the existence of the electrical discharges in the lower atmosphere on Titan. SR parameters are also useful in the study of the electromagnetic properties of Titan’s lower ionosphere. Several papers have recently been published in the refereed literature, which discuss SR parameters on Titan. In this thesis, the 3D FDTD model is used to predict the SR frequencies and Q-factors on Titan. The FDTD results are also compared with those obtained by other analytical and numerical techniques reported in the previously published papers. Besides Titan, we also discuss SR on other planets, specifically Mars and Venus. The atmospheric conductivity profiles for these studies are derived from the previously reported ionospheric models for these planets.