Optimizing receiver configurations for resolution of equivalent dipole polarizabilities in situ

Equivalent dipole polarizabilities are a succinct way to summarize the inductive response of an isolated conductive body at distances greater than the scale of the body. At any time lag or frequency, an equivalent dipole polarizability response is comprised of nine parameters: six specifying an equivalent dipole polarizability matrix (which is symmetric) and three specifying the apparent location of the body center. Smith and Morrison have given equations for calculating uncertainties in equivalent dipole polarizability and position based on analysis of an iterative linearized inversion. Here, the root mean squared uncertainty in polarizability is weighted and summed over a number of control points and minimized using an evolutionary algorithm for a number of instrument designs. Three families of designs are presented: single-transmitter systems for use on a two-dimensional grid of positions with negligible error in relative instrument location, two-transmitter systems for use on a line of positions with negligible error in relative instrument location, and three-transmitter systems for stand alone use. Results for the one- and two-transmitter systems are strongly degraded by errors in instrument position, whereas the three-transmitter systems are insensitive to instrument positioning errors.