Efficient reconstruction of dispersive dielectric profiles using time domain reflectometry (TDR)

We present a numerical model for time domain reflectometry (TDR) signal propagation in dispersive dielectric materials. The numerical probe model is terminated with a parallel circuit, consisting of an ohmic resistor and an ideal capacitance. We derive analytical approximations for the capacitance, the inductance and the conductance of three-wire probes. We couple the time domain model with global optimization in order to reconstruct water content profiles from TDR traces. For efficiently solving the inverse problem we use genetic algorithms combined with a hierarchical parameterization. We investigate the performance of the method by reconstructing synthetically generated profiles. The algorithm is then applied to retrieve dielectric profiles from TDR traces measured in the field. We succeed in reconstructing dielectric and ohmic profiles where conventional methods, based on travel time extraction, fail.