Reducing the Complexity of Inverse Analysis of Time Domain Reflectometry Waveforms

Inverse analysis of time domain reflectometry (TDR) waveform in the frequency domain is important in measuring complex dielectric permittivity of soils. However, for widely used probes designed as impedance mismatching and nonseparable connection between probe head and coaxial cable, none of the available models can be used for the inverse analysis. The objective of this study was to derive a model which is applicable for this specific type of probes. A two-section (probe head and probe rods) model was derived from the full model of Feng et al. (1999) by reducing its complexity on the basis of the matching design of cable tester and coaxial cable. The model was validated by comparison of the measured spectra of properly terminated coaxial cable with the theoretical values, and the accuracy of the model was studied by the comparison of the estimated complex dielectric permittivity of ethanol by the model with those measured by the network analyzer method. This model was applied to a silt loam soil under different levels of water content and electrical conductivity (EC). The results showed that the two-section model was applicable for this specific type of probes to measure complex dielectric permittivity at low frequency range. The lowest frequency of 30 MHz was used to estimate soil complex dielectric permittivity. The real parts of the estimated soil dielectric permittivity were close to the apparent dielectric permittivity determined by travel time analysis (TTA). The soil bulk EC calculated from the imaginary parts of the estimated soil dielectric permittivity was close to the measured values.