Time-domain study of half-space transmission problem with vertical and horizontal dipoles

The paper deals with the transient fields transmitted through the interface between the air and ground. Excitation for the electromagnetic fields is produced by a vertically or horizontally oriented impulsive dipole, which may be electric or magnetic. However, only electric sources are discussed, because the analog results for magnetic sources are obtained easily through the duality transform. The ground medium has arbitrary permittivity and permeability, but it is restricted to lossless, i.e. the conductivity is assumed to be zero. In this study simple integral expressions are derived for the time-dependent Hertz vector in the ground from which the propagating transient fields can be obtained through differentiation. In certain specific cases some components of electric or magnetic field have a closed-form solution in terms of elementary functions. All the nontrivial solutions of this type in the ground medium are given