Efficient reconstruction of dispersive dielectric profiles using time domain reflectometry (TDR)

Abstract

Abstract. We present a numerical model for time domain reflectometry (TDR) signal propagation in dispersive dielectric materials. The numerical probe model is terminated with a parallel circuit, consisting of an ohmic resistor and an ideal capacitance. We derive analytical approximations for the capacitance, the inductance and the conductance of three-wire probes. We couple the time domain model with global optimization in order to reconstruct water content profiles from TDR traces. For efficiently solving the inverse problem we use genetic algorithms combined with a hierarchical parameterization. We investigate the performance of the method by reconstructing synthetically generated profiles. The algorithm is then applied to retrieve dielectric profiles from TDR traces measured in the field. We succeed in reconstructing dielectric and ohmic profiles where conventional methods, based on travel time extraction, fail.

Spatial time domain reflectometry and its application for the measurement of water content distributions along flat ribbon cables in a full‐scale levee model

“…Another possibility is to develop inversion algorithms based on a straightforward calculation of the wave propagation along the transmission line due to an incident voltage step. Here the response of the transmission line can be calculated either in the time domain [Lundstedt and Stroem, 1996;Lundstedt and He, 1996;Feng et al, 1999;Oswald, 2000;Todoroff and Lan Sun Luk, 2001;Lundstedt and Norgren, 2003;Rahman and Marklein, 2005;Greco, 2006] or in the frequency domain [Norgren and He, 1996;Heimovaara et al, 2004;Lambot et al, 2004;Leidenberger et al, 2006;Scheuermann and Huebner, 2009].…”

The Technical Challenges for Applying Unsaturated Soil Sensors to Conduct Laboratory-Scale Seepage Experiments

“…The outputs from the data logging system mentioned above are a series of TDR waveforms in the temporal sequence received from both ends of an FRC sensor. Many very successful instances have been demonstrated in previous literature of many studies [ 11 , 15 , 16 , 19 , 20 , 21 , 45 , 69 , 71 , 76 , 77 ]. Here, a perfect example is shown in Figure 15 a,b for demonstrating TDR waveforms detected at the bottom and top of a soil column during a one-step outflow test.…”

Application of Spatial Time Domain Reflectometry for Investigating Moisture Content Dynamics in Unsaturated Loamy Sand for Gravitational Drainage

“…For such a infinitesimal section, information on the surrounding soil and coating material properties can be extracted from the conductance (G) and capacitance (C) using inverse modeling of the telegraph equation [19,[38][39][40][41]. For instance, one version developed by Schlaeger [5] is selected to conduct the inverse analysis in this study.…”

“…According to the electrical circuit simplified in Figure 3a, the forward modeling telegraph equation can predict the TDR trace along a flat ribbon cable. Therefore, the finite difference method is applied to numerically solve these equations with boundary conditions exactly matching the physical sensor design to predict the TDR trace [38,[40][41][42]. To simplify the original telegraph equations for solving, Schlaeger transformed two first-order governing partial differential equations (PDE) into a single PDE in second-order as Equation ( 4):…”