Spatially resolved water content profiles from inverted time domain reflectometry signals

Abstract

We present a method for extracting spatially resolved water content profiles θ( x ) from a two‐wire time domain reflectometry (TDR) probe. The profile θ( x ) is represented in terms of the dielectric ε r ( x ) and ohmic σ( x ) properties in the longitudinal direction of the TDR probe. We solve the inverse problem iteratively by combining a one‐dimensional time domain solution of the transmission line equations and a genetic optimization method. The method is capable of finding the global optimum in a complicated error landscape without initial assumptions, except physically reasonable limits. The method utilizes both the position and the magnitude of the TDR signal. We analyze water content profiles from laboratory measurements and demonstrate that the achievable spatial resolution can be made as low as 2 cm and even smaller. The present implementation of the numerical code demonstrates the practical feasibility of spatially resolved water content profiles.