Spatially resolved water content profiles from inverted time domain reflectometry signals

Abstract

[1] We present a method for extracting spatially resolved water content profiles q(x) from a two-wire time domain reflectometry (TDR) probe. The profile q(x) is represented in terms of the dielectric e r (x) and ohmic s(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.

Efficient reconstruction of dispersive dielectric profiles using time domain reflectometry (TDR)

“…Ramo et al, 1984). Our approach for numerically modeling TDR probes is essentially based on Oswald et al (2003). A transmission line is described by capacitance C , conductance G , inductance L and resistance R , all per unit length, respectively.…”

“…With a variable water content θ (x) along the probe the parameters G and C vary accordingly; L is assumed to be constant, because the materials' magnetic permeability equals µ 0 ; resistance R , caused by skin effect, is neglected in the current study. For extracting dielectric and ohmic profiles from measured TDR traces we use an iterative, globally optimizing approach based on Oswald et al (2003) in order to solve the non-linear, inverse, electromagnetic problem. The global optimization method uses genetic algorithms (GA) from a publicly available library Levine (1996).…”

“…To implement the excitation we employ the same approach used by Oswald et al (2003). We couple a resistive voltage source to the distributed transmission line.…”

“…A second phase of TDR development has targeted to deliver spatially resolved water content profiles along the TDR probe (Yanuka et al, 1988;Hook et al, 1992;Dasberg and Hopmans, 1992;Lundstedt and Ström, 1996;Norgren and He, 1996;Pereira, 1997;Todoroff et al, 1998;Feng Correspondence to: B. Oswald (benedikt.oswald@psi.ch) et al, 1999;Oswald, 2000;Oswald et al, 2003;Lin, 2003;Heimovaara et al, 2004;Schlaeger, 2005).…”

“…Our profile reconstruction approach is based on Oswald et al (2003). The non-linear inverse problem is solved iteratively with a transmission line solver to calculate TDR traces, based on a given profile of electric parameters.…”