## 1. Introduction

[2] The Earth can be regarded as a nearly conducting sphere, wrapped in a thin dielectric atmosphere that extends up to the ionosphere, where the conductivity is also substantial. Atmospheric electric discharges generate broadband electromagnetic waves that propagate between the surface and the ionosphere. These two layers define the surface-ionosphere cavity, which supports two types of electromagnetic modes: (i) longitudinal modes corresponding to global, quasi-horizontal wave propagation around the globe and (ii) transverse modes related to local, quasi-vertical propagation between the surface and the ionosphere, as described by *Nickolaenko and Hayakawa* [2002]. In this work, we discuss the longitudinal modes only. Random lightning strokes with spatial probability distribution peaking over the continents, particularly in the low latitude regions, induce development of standing waves whose wavelength is related to the radius of the cavity. This phenomenon, known as Schumann resonance, develops when the average equatorial circumference is approximately equal to an integral number of wavelengths of the electromagnetic waves.

[3] For a thin, lossless cavity, the Schumann resonance eigenfrequencies, *ω*_{n}, are approximately given by

where *c* is the velocity of light in free space, *R* is the Earth radius, and *n* = 1, 2, 3,… is the corresponding eigenmode [*Schumann*, 1952]. When more elaborate conditions are considered, namely losses in the cavity and variability of the upper boundary due to atmospheric conductivity and ionospheric dynamics, the eigenfrequencies are slightly lower [*Balser and Wagner*, 1960]. The average frequencies of the five lowest eigenmodes are, approximately, 7.8, 14.3, 20.8, 27.3, and 33.8 Hz, which fall in the Extremely Low Frequency (ELF) range [e.g., *Nickolaenko and Hayakawa*, 2002]. The corresponding Q-factors are Q ∼ 5 and provide estimates of wave propagation conditions in the cavity. The Q-factor is commonly defined as the ratio of the accumulated field power to the power lost in the oscillation period. The ELF wave attenuation can be computed from the Q-factor of the cavity, which can be approximated by *Q*_{n} ≈ *f*_{n}/Δ*f*_{n}, where Δ*f*_{n} is the full width at half maximum of peak *n*.

[4] Schumann resonances have been used to investigate multiple phenomena related to the surface-ionosphere cavity, namely electromagnetic sources, properties of the medium, and boundary conditions. Since lightning is the major source of electromagnetic radiation in the ELF range, Schumann resonances are used to study the daily and seasonal variability of lightning in the cavity [e.g., *Balser and Wagner*, 1960; *Sentman*, 1995; *Nickolaenko and Hayakawa*, 2002] as well as other phenomena such as tropospheric water vapor, aerosol distributions, transient luminous events, and solar flares and geomagnetic storms [e.g., *Reid*, 1986; *Williams*, 1992; *Boccippio et al.*, 1995; *Price*, 2000].