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.

Determination of local phase holdups in airlift reactors by means of time‐domain‐reflectometry

“…[4] and Yanuka et al [5]. Topp and Davis [3] have compared TDR and gravimetric measurements and found similar accuracy.…”

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

“…Early realizations of the method delivered a single water content θ from a TDR trace (Birchak et al, 1974;Topp et al, 1980Topp et al, , 1982aTopp and Davis, 1985;Dasberg and Dalton, 1985). A second phase of TDR development has targeted to deliver spatially resolved water content profiles along the TDR probe (Yanuka et al, 1988;Hook et al, 1992;Dasberg and Hopmans, 1992;Lundstedt and Ström, 1996;Norgren and He, 1996;Pereira, 1997;Todoroff et al, 1998;Feng Correspondence to: B. Oswald (benedikt.oswald@psi.ch) et al, 1999;Oswald, 2000;Oswald et al, 2003;Lin, 2003;Heimovaara et al, 2004;Schlaeger, 2005).…”

Spatially resolved water content profiles from inverted time domain reflectometry signals

“…His approach is based on specific assumptions which allow to simplify the differential equation, e.g., a slowly varying impedance profile, the validity of which may be limited in the general case. Todoroff et al [1998] also use an approach based on a decomposition of forward and back traveling partial waves in the time domain, similar to Yanuka et al [1988], but implement a genetic algorithm for the reconstruction of the water content profile. Feng et al [1999] investigated a frequency domain approach to discriminate transitions between wet and dry sections.…”

“…Yanuka et al [1988] model spatially variable water content profiles using a linear superposition of forward and 1992] employed diodes for the discrimination of different sections of the TDR probe. Pereira Dos Santos [1997] solves the inverse problem using an integral transform technique based on a simplified version of Ricatti's differential equation.…”