Current turn-off in an ungrounded horizontal loop: experiment and theory

An ungrounded horizontal loop, a common transmitter type in TEM surveys, makes up a system with distributed parameters with the earth under it. It can be simulated by an equivalent circuit with lumped parameters at late times and/or low frequencies, but at early times commensurate with the period of free current oscillations, the lumped circuit model fails to account for experimental data. At high frequencies and/or early times, the wire, in combination with the underlying earth, forms a transmission line in which current behaves according to the wave equation. This model allows calculating the current at any time and at any loop point with reference to the theory of long transmission lines. At early times, the loop self-responses depend on near-surface resistivity and environment and its primary magnetic field differs from that predicted by the classical theory of TEM surveys. Therefore, inversion of early-time rerponse in terms of the conventional TEM system model is meaningless. However, as illustrated with a loop shunted by a matching resistor, the loop model as a combination of two transmission lines enables the inversion of the early-time current response in terms of the line parameters and near-surface resistivity.