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Determination of the spatial TDR-sensor characteristics in strong dispersive subsoil using 3D-FEM frequency domain simulations in combination with microwave dielectric spectroscopy

Norman Wagner, Eberhard Trinks and Klaus Kupfer

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The spatial sensor characteristics of a 6 cm TDR flat band cable sensor section was simulated with finite element modelling (high frequency structure simulator—HFSS) under certain conditions: (i) in direct contact with the surrounding material (air, water of different salinities, different synthetic and natural soils (sand–silt–clay mixtures)), (ii) with consideration of a defined gap of different size filled with air or water and (iii) the cable sensor pressed at a borehole-wall. The complex dielectric permittivity εsstarf(ω, τi) or complex electrical conductivity σsstarf(ω, τi) = iωεsstarf(ω, τi) of the investigated saturated and unsaturated soils was examined in the frequency range 50 MHz–20 GHz at room temperature and atmospheric pressure with a HP8720D-network analyser. Three soil-specific relaxation processes are assumed to act in the investigated frequency–temperature–pressure range: one primary α-process (main water relaxation) and two secondary (α', β)-processes due to clay–water–ion interactions (bound water relaxation and the Maxwell–Wagner effect). The dielectric relaxation behaviour of every process is described with the use of a simple fractional relaxation model. 3D finite element simulation is performed with a λ/3 based adaptive mesh refinement at a solution frequency of 1 MHz, 10 MHz, 0.1 GHz, 1 GHz and 12.5 GHz. The electromagnetic field distribution, S-parameter and step responses were examined. The simulation adequately reproduces the spatial and temporal electrical and magnetic field distribution. High-lossy soils cause, as a function of increasing gravimetric water content and bulk density, an increase in TDR signal rise time as well as a strong absorption of multiple reflections. An air or water gap works as a quasi-waveguide, i.e. the influence of the surrounding medium is strongly reduced. Appropriate TDR-travel-time distortions can be quantified.


PACS

91.60.Pn Magnetic and electric properties; environmental magnetism

77.22.Gm Dielectric loss and relaxation

77.22.Ch Permittivity (dielectric function)

Subjects

Condensed matter: electrical, magnetic and optical

Environmental and Earth science

Dates

Issue 4 (April 2007)

Received 9 May 2006, in final form 17 July 2006

Published 27 February 2007



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