Frequency Dependence of the Soil Electromagnetic Properties Derived from Ground-Penetrating Radar Signal Inversion

The accuracy at which the subsurface electromagnetic properties can be identified from full wave inversion of ground penetrating radar (GPR) signals relies on the appropriateness of the model describing their frequency dependence. In this paper, we focus on the characterization of the frequency dependence of the dielectric permittivity and electric conductivity of a sandy soil subject to different water contents from inversion of GPR measurements. Based on previous studies of Lambot et al. the methodology relies on an ultrawide band (UWB) stepped-frequency continuous-wave (SFCW) radar combined with an off-ground monostatic transverse electromagnetic (TEM) horn antenna. Forward modeling of the radar signal is based on linear system transfer functions for describing the antenna, and on the exact solution of Maxwell's equations for wave propagation in a horizontally multilayered medium representing the subsurface. Model inversion, formulated by the classical least-squares problem, is carried out iteratively using advanced global optimization techniques. The frequency dependence of the electromagnetic properties of the sandy soil is characterized by performing inversions of the radar signal in different and subsequent limited frequency bands, in which the electromagnetic parameters are assumed to be constant. We observed that over the entire frequency band considered in this study (1-3 GHz), the dielectric permittivity of the sand remains constant with frequency, whatever the water content is. In contrast, the electric conductivity increases significantly from 1GHz to 3 GHz, and this effect increases with water content. The frequency dependence of the electric conductivity may be adequately described using a simple linear relationship. This approach is advantageous since it limits the number of parameters to be optimized in the inverse modeling procedure.