Modeling ground-penetrating radar wave propagation and reflection with the Jonscher parameterization

As in seismic surveys, forward modeling is essential to the geological interpretation of georadar data. Because a radar signal is broad band, modeling radar waves in a realistic medium requires knowing the frequency dependence of the effective dielectric permittivity of rocks. Various models can be found in the literature. With the support of laboratory measurements carried out on various rock samples, the complex effective dielectric permittivity describing polarization and conduction effects can be modeled by the Jonscher law. In the megahertz range, the Jonscher parameterization involves only three real, constant parameters that are characteristic of the investigated media. Radar plane waves propagating in 1-D models are generated and compared to field data recorded in transmission mode for different frequencies, distances, and geological formations. The signal distortion from propagation is emphasized. Quality factors are calculated and found to be compatible with the propagation in real media. Reflection coefficients are written using the Jonscher relation. Two cases are illustrated: reflection from a halfspace and reflection from a thin layer. From the study of the influence of frequency, reflection modes, electric properties of rocks, and layer thickness, it can be concluded that reflection phenomena, like propagation phenomena, lead to phase shifts and frequency content variations. Thus, processing based on the assumption of stationary wavelets is not suitable for georadar signals, even in low-loss media.