Currently, in geophysics, there is growing interest about the deep layers of the Earth. Information about these layers may be obtained from analysis of the electromagnetic' field at relatively low frequencies. Low-frequency antennas are usually very cumbersome. One aim is creation of an antenna that would be effective at low frequencies and compact enough. To do this, electromagnetic fields of ground-based sources in the presence of a plasma coating are studied. Such problems for the well-conducting Earth's surface are solved approximately using the equivalent theorem. This makes it possible to find the field at any distance from the source, including the Earth's surface. For a coating in the form of a two-layer plasma semispheroid, the solution is looked for in spheroidal functions attracting the theorem of addition. The influence of a plasma coating of high curvature is analyzed in the quasi-static approximation.
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