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. Howevet, 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 testet and coaxial cable. The model was validated by comparison of the measured spectra of properly terminated coaxial cable with the theoretical values, and the accutacy of the model was studied by the comparison of the estimated complex dielectric petmittivity 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 watet 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 petmittivity at low frequency range. The lowest frequency of 30 MHz was used to estimate soil complex dielecttic petmittivity. The teal parts of the estimated soil dielectric permittivity were close to the appatent dielectric petmittivity determined by travel time analysis (TTA). The soil bulk EC calculated from the imaginaty parts of the estimated soil dielecttic petmittivity was close to the measured values.