A new computational technique for processing transmission-line measurements to determine dispersive dielectric properties

Dielectric relaxation behavior of Callovo‐Oxfordian clay rock: A hydraulic‐mechanical‐electromagnetic coupling approach

“…A further approach to obtain the frequency‐dependent permittivity is an inverse modeling technique based on the numerical calculation of the appropriate S parameters with a forward model (mostly TEM based) of the used coaxial transmission line cell in combination with a Debye‐type relaxation function [ Oswald et al , ], a broadband transfer function (CCPM) [ Wagner et al , ; ] or a generalized dielectric relaxation model (GDR) [ Wagner et al , ; ]: with high‐frequency limit of permittivity ϵ ∞ , relaxation strength Δ ϵ k , relaxation time τ k as well as stretching exponents 0≤ a k , b k ≤1 of the k th process and apparent direct current electrical conductivity σ DC . The technique can be used in equivalence to the BJI approach with measured S parameters separately or simultaneously.…”

“…Consequently, the open-ended coaxial probe method is more suited for liquids and homogeneous fine-grained materials than for hard rock samples. Studies by Folgero [1998], Shang et al [1999], Rowe et al [2001], Oswald et al [2006], Wagner et al [2011a], Siggins et al [2011], andBohleber et al [2012] describe two-port coaxial transmission line technique to investigate complex permittivity of soil. In Lauer et al [2012], a new technique was introduced to measure broadband dielectric spectra of undisturbed samples which was extended in Wagner and Lauer [2012] to simultaneously determine the dielectric relaxation behavior and soil water characteristic curve.…”

TDR response properties and their use in the estimation of soil permittivity

“…In the last years, great efforts have been spent on the modeling of TDR measurement systems and on methods to solve the inverse problem of estimating the permittivity from reflection responses (e.g., see [2], [3], [4], [5], [6] and references therein). In contrast, relatively little effort has been spent to study the properties of TDR waveforms and their influence on the estimation of the permittivity.…”

Time-Domain Reflectometry (TDR) Technique for the Estimation of Soil Permittivity

“…If the assumption is made that the imaginary part of the complex electrical permittivity is small compared to the real part, only the real part of permittivity changes with soil water content, and if the real part is close to the apparent dielectric permittivity K a (effective bulk permittivity), then water content can be evaluated by means of empirical formulas based on known value of K a Topp et al, 1980). Evaluation of the dielectric permittivity of a medium from its reflection response is an inverse problem in which the medium propagation behavior is used to infer its constitutive relations (Feng et al, 1999;Heimovaara, 1994;Lin, 2003;Oswald et al, 2006). Owing to this application, over the past twenty years great efforts have been spent on the calibration of the TDR system, i.e.…”

“…Owing to this application, over the past twenty years great efforts have been spent on the calibration of the TDR system, i.e. the relationship between apparent dielectric permittivity and soil water content (Hansson & Lundin, 2006;Roth et al, 1990;Topp et al, 1980), on the design and testing of various type of probes (Canone et al, 2009;Evett et al, 2006;Robinson et al, 2005); and on the methods to solve the inverse problem of estimating permittivity from reflection responses (Heimovaara, 1994;Oswald et al, 2006). Regardless of the inversion method used, the model of the measurement system (relating measured waveforms to the unknown permittivity to be estimated) is the instrument enabling the permittivity estimation from the reflection response.…”