## 1. Introduction

[2] The Earth and other celestial bodies with electric conductivity starting from low values near the surface and increasing with height, form an electromagnetic cavity for waves propagating in the extremely low frequency (ELF) range between the surface and the ionized layer. If the atmosphere between both conductive layers is not excessively dissipative, global lightning activity excites the resonant frequencies for the cavity, also called Schumann's resonances. These resonance frequencies were predicted by *Schumann* [1952] and detected by *Balser and Wagner* [1960]. Nowadays, there is renewed interest for the phenomenon of Schumann resonances mainly for two fundamental reasons: first, a clear correlation between annual variations of the first Schumann resonance intensity and the tropical temperature over a 6-year span, which suggests the possibility of using these frequencies as a global thermometer for the tropics of the Earth [*Williams*, 1992]. Second, to explore terrestrial-like electrical activity in other celestial bodies such as Mars [*Schwingenschuh et al.*, 2001] and the Saturnian moon, Titan [*Fulchignoni et al.*, 1997].

[3] Schumann resonance frequencies are lower than expected for an ideal cavity, i.e., two concentric layers of infinite conductivity filled by a lossless dielectric medium [*Jackson*, 1999], since Joule dissipation associated with the finite conductivity of the atmosphere makes the real system resonate at lower frequencies than a lossless system with an almost perfectly dielectric atmosphere. Therefore in order to obtain results close to experimental values, this loss of ideality in the dielectric behavior must be accounted for. As a consequence of considering ground and atmospheric conductivity, the exact analytical study of the electromagnetic system becomes unfeasible. Thus the use of strong mathematical approximations or the numerical analysis of the system is required.

[4] In the last few decades, a growing interest in numerical analysis and the design of complex systems has emerged, since it offers greater flexibility, easier diagnostics, lower costs, and rapid evaluation of alternatives when compared to conventional analytical or experimental studies. Once an adequate numerical model is available, it can be used to complement experimental work by numerical simulation of the complex interactions that take place in physical experiments and systems. Transmission Line Matrix (TLM) is a numerical method that models electromagnetic field phenomena by means of circuit concepts and has been successfully used in the simulation of especially complex electromagnetic systems [*Christopoulos*, 1997; *Portí et al.*, 1998a].

[5] In this paper, a numerical modeling of the natural cavity formed by the Earth's surface and the lower ionosphere is carried out by means of the TLM method. The results obtained are compared to the widely accepted two-scale-height ionospheric model [*Greifinger and Greifinger*, 1978; *Sentman*, 1990], a good correlation between them being observed. Numerical values for Schumann resonance frequencies are very close to the experimental ones, enabling us to affirm that this numerical tool is useful in predicting the Schumann frequencies of other planets or moons without making it necessary to fit the conductivity profile to a two-layer model. Finally, shifts in the Schumann resonance frequencies due to a sudden increase in the conductivity at a pole, caused by high-energy particle precipitation emitted from the Sun in conjunction with solar flares, have also been numerically modeled and compared with experimental resonances [*Schlegel and Füllekrug*, 1999]. A slight increase in the first Schumann resonance frequency is observed, which is related to a reduction in the electromagnetic cavity dimensions, since an increase in the electric conductivity is equivalent to a descent in the upper boundary of the Earth-ionosphere cavity.