Inversion of TDR signals -: revisited

In this study, we discuss the consistence of measured and calculated TDR traces. The calculated traces are solutions of a time domain reflectometry (TDR) forward solver, an algorithm for a computing the TDR trace for a given dielectric profile along a transmission line. An unambiguous and efficient forward solver is a prerequisite for a good solution of the inverse problem, i.e., to extract the spatial distribution of the dielectric properties along the transmission line from a TDR trace. To advance our understanding of TDR inversion, we proceeded in two steps: (1) design of a TDR head section with minimal disturbances on the signal and (2) searching for causes why measured and predicted TDR traces differ. Based on a first experiment with a three-rod TDR probe of 100 cm length, we demonstrated that our TDR forward solver-like others presented in literature-approximate the measured TDR traces apparently well but not precisely enough for signal inversion. In a second experiment, using a two-rod TDR probe of 70 cm length, we addressed the problem of non-parallel transmission lines. We found that the influence of a non-parallel installation is similar to an increase of the electrical conductivity in soil water but can be distinguished from this property. A third experiment reveals that lateral and longitudinal disturbances in the vicinity of a TDR probe are of minor importance. From the analysis of our experiments, we found that neither lateral disturbances nor non-parallel rods are responsible for the deviations between calculated and measured traces. This analysis showed us that structure in the sampled medium affects the shape of the TDR traces. Since minor deviations are essential for TDR-signal inversion, we need new concepts to handle the fuzziness between measurements and calculations.