A Stochastic Analysis of Cross-Hole Ground-Penetrating Rada Zero-Offset Profiles for Subsurface Characterization

Cross-hole ground-penetrating radar (GPR) zero-offset profiling (ZOP) is a well-established technique for the measurement of the one-dimensional (1-D) vertical distribution of soil dielectric permittivity and has often been used in time-lapse mode for the monitoring of natural or man-made infiltration and soil moisture redistribution processes in the vadose zone. However, in spite of its widespread use, the quantitative interpretation of ZOPs in terms of dielectric permittivity profiles is known to be fraught with difficulties. Often a simplified approach is adopted that translates directly ZOP travel times into electromagnetic (EM) velocities and these, in turn, into dielectric permittivities and soil volumetric moisture content. This approach is known to lead to over-smoothed moisture content profiles, which are a consequence of the ZOP measurement scale, controlled by critical refractions along fast layers and averaging effects within the first Fresnel zone. Such smooth profiles are not necessarily compatible with the true soil moisture content that should be reproduced by water flow models. In this paper we present a stochastic inversion approach that aims at solving these issues. The approach is based on a forward stochastic simulation that generates the expected travel times by means of a two-dimensional (2-D) full waveform modeling, thus reproducing all physical processes that contribute to profile smoothing. We first assess the robustness of this approach on synthetic data, where the true dielectric permittivity profile is known. Then we apply the technique to two different case studies, where the results of the proposed technique show supporting evidence from independent information on the sites' stratigraphy. The proposed approach proves to be capable of reconstructing sharp dielectric profiles, in addition to assigning relevant uncertainty bounds derived from the expected errors in travel time picking. These results may prove very useful in a correct assessment of the hydrological implications of the measured dielectric permittivity, and thus moisture content, profile.