Apparent electrical conductivity integrated from layered soil profiles

Time domain reflectometry (TDR) trace analysis aims at extracting the water content profile, along TDR probes. This can be done by applying a TDR forward solver inversely. Thus, TDR-trace inversion is basically an optimization problem. As in any optimization procedure, it is worthwhile to include as much a priori information as possible about the problem to be solved. In this study, we discuss the feasibility to use the apparent electrical conductivity as constraint for the TDR inversion. The resistors-in-parallel circuit can be used to integrate a multislice soil model to obtain the apparent electrical conductivity. We apply additionally Archie's law to link the water content of a particular slice with its electrical conductivity. We compare the results from this approach with measured TDR traces and show that the problem is solved exactly. Finally, we address the thin-layer issue because thin layers with a high permittivity contrast result in a delay of the run time of an electromagnetic pulse. We test numerically whether a similar behavior can be observed for a thin layered electrical conductivity profile. Our results show that the thickness of the soil layer with respect to electrical conductivity has no effect on the apparent electrical conductivity. We conclude that the apparent electrical conductivity is appropriate as boundary condition in TDR inversion as long as a procedure is known to convert the water content of a slice to its electrical conductivity