The generalized solution of the scattering of electromagnetic fields by an n-layer earth in the presence of oscillating magnetic dipoles carrying harmonic currents has been obtained. The solutions are valid for all frequency ranges and for arbitrary parameters of the n-layer earth. The results have been expressed in terms of six infinite integrals, four of which depend on the transverse electric modes and the rest on the transverse magnetic modes. These solutions have been used to obtain the generalized expressions for the mutual coupling ratios for five coil systems, most often used in the geophysical industry.Using the solutions, a study has been made on the relative performance of the five coil systems for mapping permafrost terrains by multifrequency techniques, assuming the earth to be a homogeneous lossy dielectric, which may be a valid model in winter. It has been observed that the responses in all five coil systems are quite similar, but the magnitude of the response is largest in the horizontal coplanar system. A graphical technique of obtaining the resistivity and dielectric constant of the ground from the mutual coupling ratios has also been described. The results would be useful for designing portable multifrequency e.m. dipole systems for the detection and delineation of permafrost at high latitudes. The inclined, parallel, null-coupled system comes next in order of preference for the mapping of permafrost terrain, followed by the vertical coplanar and the perpendicular systems.