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Using a finite-difference method, the surface magnetic fields of a harmonic vertical magnetic dipole buried in a laterally inhomogeneous earth are computed. The geoelectric section consists of a homogeneous half space in which a cylindrical conductor of square cross section is embedded. Results are presented in terms of the magnetic field polarization ellipse parameters, with particular attention being paid to the ellipticities in the horizontal and vertical planes. These are shown by means of equicontour maps in the surface plane, and promise to be quite useful in the detection and mapping of subsurface conductivity zones. With reference to buried-source location methods, it is shown that the source location error, as derived from the tilt angle of the vertical polarization ellipse (measured at the surface) is quite small. Finally, some suggestions are made on field procedures, which may enable on-site corrections to apparent locations to be made without knowledge of the subsurface conductivity structure