The laterally inhomogeneous anisotropic ionosphere is represented by a changing ionospheric surface impedance. The fields across such discontinuities can be estimated by computing the propagation characteristics on the various segments as in a homogeneous environment and by applying the resulting propagation parameters to the appropriate segments of the path. For fields observed across a day-to-night boundary, the resulting error is of the order of one percent. The effects of more localized ionospheric perturbations depend on their azimuthal and transverse extent. In the lower ELF range, areas with transverse dimensions of one to two thousand kilometers affect the propagation path across the perturbation to about the same extent as a propagation path tangential to the periphery of the perturbed region.