Non Invasive Time Domain Reflectometry (TDR) may be used to estimate the volumetric
moisture content, θv, with depth for a variety of sample materials. The forward physical model is
couched in terms of a moment method where integration is performed over a descretized sample space
to estimate the measured propagation time tp down a pair of parallel transmission lines. We show that
the inverse solution to this, which recovers relative permittivity and thus θv, is greatly facilitated by a
simplification of the system geometry via, 1) realistically modeling the prior density of the sample,
2) using this prior with the inherent system symmetry to reduce the number of required discretization
cells, and 3) determining a physically meaningful reduction operator to allow a coarse discretization
mesh to be used. The observational equation is expressed in the Bayesian paradigm with the most
accurate and robust solution obtained using the Conditional Mean of the posterior distribution
constructed via a Monte Carlo method. Results of simulation show that the method is capable of
providing accurate estimates of the moisture density profile down to a depth of 100 mm with an error
of less than 4 %. Further, the reduction in the number of descretized cells required to accurately
estimate these profiles means that the inversion procedure is quick enough to enable the real time
application of the equipment, a fundamental requirement in the development.[Show full abstract]
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