In the present work the variation in ionospheric height observed during the dawn or dusk hours is used to develop an electromagnetic imaging system for extremely low frequencies (ELF). The description concerns the mathematical principles of the proposed method rather than a realistic implementation of the technique. The scattering of ELF waves emanating from a point source on the Earth surface by a cylindrical underground formation is studied analytically with use of a Green's function method. The ionospheric discontinuity is treated with the help of mode matching technique and the subterranean scatterer by application of the method of auxiliary sources. Numerical results are presented and discussed for several cases.