Asymptotic expansions may be derived for transient electromagnetic (EM) fields. The expansions are valid when σμ0l2/t is less than about 0.1. Here l, σ, μ0, and t are the respective lengths, conductivities, permeabilities of free space and time.
Cases for which asymptotic expansions are presented include (1) layered grounds, (2) axisymmetric structure, and (3) two-dimensional (2-D) structures.
In all cases the transient voltage eventually approaches that of the host medium alone, the ratio of anomalous response to the half-space response being proportional to 1/tv. Here v is equal to 0.5 for layered structures and 1.0 for 2-D or 3-D structures.