A 1D inversion for non-invasive time domain reflectometry

Time domain reflectometry may be used to non-invasively determine volumetric θv moisture content within various sample materials. For many practical applications, however (e.g. soil, pavement and concrete), the water distribution can be realistically described as being plane stratified. This leads to the possibility of decreasing the number of equations and unknowns in the system equation that describes the interaction of the transmission line's electric fields with the sample dielectric. Since the required solution is an inverse of the system equation, iteration must be performed and such a reduction in equation complexity becomes critical. The general form of the system equation, either before or after the stratification adjustment, is not readily amenable to the standard forms of optimization (e.g. steepest descent, conjugate gradient) so a Monte Carlo method is used with pre-computed values to mitigate against the usual speed problems associated with these methods. Simulation of the physical process shows that this technique provides a good estimate of θv provided that a suitable prior density is given. It is shown that this inversion is fast enough to allow real-time operational use of the TDR and can also provide a good measure of the individual error associated with each estimate