The electromagnetic response of a buried sphere for buried dipole excitation.
Proceedings of Thru-the-Earth Electromagnetics Workshop, August 15-17, 1973, Colorado School of Mines, Golden, Colorado. Geyer RG, ed., Pittsburgh, PA: U.S. Department of the Interior, Bureau of Mines, Grant G0133023, 1973 Dec; :81-85
The feasibility of locating a buried vertical magnetic dipole source (horizontal loop) from surface measurements of the vertical and horizontal magnetic field components has been investigated by Wait (1971). For sufficiently low frequencies, the magnetic fields have a simple static-like behavior, and a single observation of the ratio and relative phases of the vertical and horizontal field components is sufficient for location when the earth is homogeneous. However, when inhomogenieties are present, the surface fields will be modified, and source location may be more difficult. In order to obtain a quantitative idea of the surface field modifications, we consider a spherical conducting zone as a perturbation to the homogeneous half-space. A rigorous solution for the buried sphere problem has been formulated by D'Yakanov (1959). Unfortunately, his solution is restricted to azimuthally symmetric excitation, and even then the solution is not in a convenient computational form. However, if the sphere is electrically small and is located at a sufficient distance from both the dipole source and the interface, the scattered fields can be identified as the secondary fields of induced dipole moments. The latter are equal to the product of the incident fields and the polarizabilities of the sphere. The details of the approach are given by Hill and Wait (1973). Wait (1968) has used this induced dipole moment approach for scattering by a small sphere above a conducting half-space. The method has the advantage that it is easily generalized to scatterers of other shapes for which both the electric and magnetic polarizabilities are known, such as spheroids (Van de Hulst, 1957). This concept has also been considered by Ward (1967) in the context of electromagnetic detection of massive sulfide ore bodies from airborne platforms. A computer program was written to calculate the magnitude and phase of the ratio of the vertical and horizontal magnetic field components at the earth's surface. These are the measurable quantities which Wait (1971) has suggested for location of the vertical magnetic dipole source. For spheres of radius less than .2 times the source depth, the change in surface fields are found to be insignificant. For a sphere of radius .3 times the source depth located at half the source depth, some noticeable changes in the surface fields begin to occur. However, resultant errors in source location should still be small. Larger errors can be expected when the sphere is either larger or closer to the source or interface, but the simplified theory presented here is not valid under such conditions. The study of such cases is a worthwhile extension.
Mining-industry; Mining-equipment; Underground-mining; Radio-waves; Electromagnetic-energy; Electromagnetic-fields; Electromagnetic-wave-transmission
Proceedings of Thru-the-Earth Electromagnetics Workshop, August 15-17, 1973, Colorado School of Mines, Golden, Colorado
Department of Commerce, Institute for Telecommunication Sciences, Office of Telecommunications