The surface impedance matrix is calculated for a realistic model of the lower ionosphere under both daytime and nighttime conditions. For ELF, this impedance is almost independent of angle of incidence and therefore may be used to characterize the outer surface of the hypothetical earth-ionosphere cavity. A solution is carried through for a ring magnetic source which includes, as a special case, excitation by a vertical electric dipole at the earth's surface. Extensive numerical results are given first for a constant surface impedance. They illustrate many important features such as the dependence of the apparent resonant frequencies on the relative location of source and observer. The calculations are then extended to include an idealized day/night hemispheric model that demonstrates significant coupling between cavity modes with a resultant lowering of cavity Q's. The calculated results are discussed in relation to experimental data observed by other workers.