The effects of neglecting displacement currents when studying transient wave propagation in the Earth

Diffusion approximations are often used to study the interaction of transient electromagnetic waves with the Earth. If a frequency-independent conductivity and permittivity are assumed, then neglecting the displacement currents in the Earth reduces the wave equation to the diffusion equation, which sometimes can be solved analytically using elementary special functions. We study the validity of the diffusion approximation for a transient electromagnetic plane wave obliquely incident on the Earth which is modeled as a conductive half-space. The limitations of the diffusion approximation are investigated by comparing the approximate diffusion results with "exact" solutions, which are computed using closed-form expressions for the transient fields. We find that the approximate diffusion fields violate causality and only yield accurate results at late times.