A fast TDR-inversion technique for the reconstruction of spatial soil moisture content

Spatial moisture distribution in natural soil or other material is a valuably information for many applications. Standard measurement techniques give only mean or punctual results. Therefore a new inversion algorithm has been developed to derive moisture profiles along single TDR sensor-probes. The algorithm uses the full information content of TDR reflection data measured from one or both sides of an embedded probe. The system consisting of sensor probe and surrounded soil can be interpreted as a nonuniform transmission-line. The algorithm is based on the telegraph equations for nonuniform transmission-lines and an optimization approach to reconstruct the distribution of the capacitance and effective conductance along the transmission-line with high spatial resolution. The capacitance distribution can be converted into permittivity and water content by means of a capacitance model and dielectric mixing rules. Numerical investigations have been carried out to verify the accuracy of the inversion algorithm. Single- and double-sided time-domain reflection data were used to determine the capacitance and effective conductance profiles of lossless and lossy materials. The results show that single-sided reflection data are sufficient for lossless (or low-loss) cases. In case of lossy material two independent reflection measurements are required to reconstruct a reliable capacitance profile. The inclusion of an additional effective conductivity profile leads to an improved capacitance profile. The algorithm converges very fast and yields a capacitance profile within a sufficiently short time. The additional transformation to the water content requires no significant calculation time.