On smoke rings produced by a loop buried in a conductive half-space

The transient electromagnetic (TEM) response of a wire loop at the surface of the earth has been studied in detail for several decades. When current in the loop is rapidly switched off, an identical system of current, commonly referred to as a "smoke ring," is induced in the conductive subsurface and diffuses downward and outward into the earth. What has not been studied as thoroughly is the response of a loop buried within a conductive medium, as might be the case in the marine environment or when TEM prospecting systems are placed in mine tunnels or horizontal boreholes. We have examined the TEM response of a horizontal wire loop buried within a conductive half-space. Expressions were derived for the azimuthal electric field and corresponding vertical and radial magnetic fields. Our results showed that when the loop is far from the earth-air interface, a single smoke ring system diffuses radially outward from the transmitter, while the electric field and corresponding current density decays away in the vertical direction. As the loop approaches the interface, the smoke ring system diffuses radially at early times, but gradually, the complex image of the loop in the air produces a system of secondary azimuthal electric fields, which, when combined with the primary field, adds a vertical component to the field diffusion. At late times, the field behavior reduces to the well-known surface case and the maximum current system diffuses downward at a constant angle of 26 degrees with respect to the plane of the loop. We concluded that it was the effect of the interface that produces the downward migration of a smoke ring system, whereas the outward migration is mainly generated by the primary field.