The electromagnetic response of a buried sphere for buried dipole excitation 
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The electromagnetic response of a buried sphere for buried dipole excitation 

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      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 homo- geneous 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).
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