Two smoke rings or one? The transient electromagnetic response of a buried loop

Summary The transient electromagnetic 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 downwards and outwards 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 transient electromagnetic prospecting systems are placed in mine tunnels or horizontal boreholes. In this abstract we examine the transient electromagnetic response of a wire loop buried within a conductive halfspace. Expressions are derived for the azimuthal electric field and corresponding vertical and radial magnetic fields. Results show that when the loop is far from the earth-air interface, a single smoke ring system diffuses radially outwards from the loop, as opposed to two loops travelling up and down in the vertical directions (as we previously expected). As the loop burial depth decreases, 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, add a vertical direction to the field diffusion. At late times, the field behaviour 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 suggest that it is the effect of the interface which produces the downward migration of a smoke ring system, while the outward migration is mainly generated by the primary field.