Wave propagation at the bottom of the electromagnetic spectrum (below 300 kHz) in the Earth-ionosphere system is a problem having a rich history of theoretical investigation extending over many decades. Propagation within this system involves complex interactions of electromagnetic waves with the lithosphere, oceans, and ionosphere, leading to resonances that involve literally the entire planet Earth. Currently, electromagnetic phenomena below 300 kHz form the physics basis of remote-sensing investigations of lightning and sprites, global temperature change, subsurface structures, submarine communications, and potential earthquake precursors.

This dissertation addresses the application of the finite-difference time-domain (FDTD) algorithm to model impulsive electromagnetic wave propagation within the global Earth-ionosphere cavity at frequencies below 30 kHz. Two generations of numerical models are presented: a latitude-longitude grid-cell arrangement, and a geodesic grid-cell arrangement. Both types of models extend from 100 km below sea level to an altitude of 100 km, and enable a direct, full-vector, 3-D time-domain Maxwell's equations calculation of electromagnetic wave propagation due to an arbitrary excitation. Furthermore, they can account for arbitrary horizontal as well as vertical geometrical and electrical inhomogeneities and anisotropies of the ionosphere, lithosphere, oceans, and Earth's magnetic field. First, the models are verified by comparing the FDTD-calculated daytime ELF propagation attenuation with data reported in the literature. Next, four example applications are provided: (1) an investigation of hypothesized preseismic electromagnetic phenomena; (2) the development of a novel subsurface radar designed to sense the presence of major oil deposits; (3) the development of a novel radar for locating and characterizing localized ionospheric anomalies within 100 km of the Earth's surface; and (4) the development of a gyrotropic ionosphere plasma model for studying electromagnetic radiation from lightning and sprites.