An interpretation problem in electromagnetic prospecting is discussed. A flat earth in which the three electrical properties of material vary only with depth is subjected to an alternating inducing field produced by a dipole above the surface with axis perpendicular to the surface. Observations of the horizontal or of the vertical component of the magnetic intensity at the ground's surface are supposed to be available at all distances. From these observations solutions for the three unknown functions are developed. When the magnetic permeability is variable, the solutions for the permeability and dielectric functions require observations at two different frequencies. The conductivity function may be found from observations at a single frequency.It is shown that the horizontal and vertical components of the magnetic field intensity are mutually dependent in the region above the ground's surface; and formulae independent of the ground's characteristics are deduced for expressing H (sub rho ) (rho , z i ) in terms of H z (rho , z i ), and vice-versa. Here z = z i < or = h denotes a plane coincident with or above and parallel to, the earth's surface. Partial List of Notations, in Order of Use (Rationalized MKS units used throughout)

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