Multiple reflection and attenuation of time domain reflectometry pulses: Theoretical considerations for applications to soil and water

Abstract

The application of time domain reflectometry (TDR) to determine soil water content, using only the time axis of a TDR trace, has been widely investigated. Other interpretations from the TDR trace, such as the determination of electrical conductivity, make use of the amplitude or reflection coefficient values. These latter interpretations must take account of multiple reflections in the media. A multiple‐reflection algorithm is developed which takes account of primary reflection first, then provides for inclusion of higher‐order reflections as well. The algorithm is formulated to generate the TDR trace from a sequence of known dielectrics. The inverse case is analyzed where the dielectric constant of the layered medium is calculated from a measured TDR trace. The model allows for both conductive and nonconductive dielectrics. Experiments showed that the model is a reasonably good qualitative representation of the layered nonconductive media with a wide range of dielectric constants. There is insufficient information in a TDR trace to solve the conductive cases except for a single layer. From KCl solutions at two concentrations the experiments showed that instantaneous reflection and transmission are inadequate assumptions for conductive systems. This indicates the need for caution when applying the model to conductive media such as soils, especially where soil water content is not uniform.