Resolution depths for some transmitter-receiver configurations

Equivalent dipole polarizability matrices and equivalent dipole location are a convenient way to interpret magnetic field data due to currents induced in isolated conductive objects. The uncertainties in polarizability estimates and in the equivalent dipole location provide a quantitative measure of the performance of different configurations of transmitters and receivers. In another paper, we estimate these uncertainties using a linearized inversion. For many systems, consisting of one or more rectangular loop transmitters and a number of dipole receivers, sited on a horizontal grid, equivalent dipole depth is determined to 10% accuracy to depths approximately 20% deeper than the depths at which polarizability matrix elements can be determined to the same precision. Systems that have a lower product of rms polarizability uncertainty and square root of their number of transmitter-receiver pairs are considered more effective for the number of transmitter-receiver pairs. Among the systems studied, a system with three orthogonal transmitter loops and a three-component receiver is the most effective, for objects shallower than 0.6 times the instrument siting grid spacing, yielding an rms polarizability uncertainty 0.04 times that of a single-transmitter single-receiver system. At intermediate depths, a system with two vertical component receivers on the diagonal of a square horizontal transmitter loop is most effective for its number of transmitter-receiver pairs, yielding an rms polarizability uncertainty 0.07 times that of a single receiver system. At depths greater than 2.5 times, the siting grid spacing a three-orthogonal loop transmitter with a single vertical component receiver is about the most effective for its number of transmitter-receiver pairs, yielding an rms polarizability uncertainty 0.08 times that of a single-transmitter system.