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Mitglied der Helmholtz-Gemeinschaft Y. Zhao 1*, E. Zimmermann 1, J. A. Huisman 2, A. Treichel 2, B. Wolters 1, S. van Waasen 1, A. Kemna 3 1 Central Institute ZEA-2 – Electronic Systems, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany, 2 Institute of Bio- and Geosciences (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany 3 Applied Geophysics, Steinmann-Institute, Bonn University, 53115 Bonn, Germany *Corresponding author: y.zhao@fz-juelich.de 9. The Pole-Pole matrix Numerical correction of the phase error due to electromagnetic coupling effects in EIT borehole measurements 1. Introduction Spectral Electrical Impedance Tomography (EIT) allows obtaining images of the complex electrical conductivity for a broad frequency range (mHz to kHz). It has recently received increased interest in the field of near-surface geophysics and hydro-geophysics because of the relationships between complex electrical properties and hydrogeological and biogeochemical properties and processes observed in the laboratory with Spectral Induced Polarization (SIP) (see. e.g. Kemna et al. 2000; Hördt et al. 2007; Karaoulis et al. 2011; Flores Orozco et al. 2012). However, these laboratory results have also indicated that a high phase accuracy is required for surface and borehole EIT measurements because many soils and sediments are only weakly polarizable and show phase angles between 1 and 20 mrad only. In the case of borehole EIT measurements, long cables and electrode chains (>10 meters) are typically used, which leads to undesired inductive coupling between the electric loops for current injection and potential measurement and capacitive coupling between the electrically conductive cable shielding and the soil. Both coupling effects can cause large phase errors that have typically limited the frequency bandwidth of field EIT measurement to the mHz to Hz range. The aim of this study is i) to develop correction procedures for these coupling effects to extend the applicability of EIT to the kHz range and ii) to validate these corrections using controlled laboratory measurements and field measurements. In order to do so, the inductive coupling effect was modeled using electronic circuit models and the capacitive coupling effect was modeled by integrating discrete capacitances in the electrical forward model describing the EIT measurement process. 7. Model verification A B M N : electrodes : C at cable : C at rod : C at bottom 2D-mesh of the rain barrel with integrated capacitances (Zimmermann 2010) Electrode rod with 4 electrodes ρ tap water = 30 Ωm Z: original data, Z cr : inductive corrected, Z c : modeled impedance (Funded by the Federal Ministry of Education and Research grant 03G0743B) The correction methods for 1D EIT borehole measurements were successfully verified with measurements under controlled conditions in a water-filled rain barrel, where a high phase accuracy of 0.8 mrad in the frequency range up to 10 kHz was achieved. In a field demonstration using a 10 m borehole EIT chain with 8 electrodes with 1 m electrode separation, the corrections were also applied within a 1D inversion of the borehole EIT measurements. The results show that the correction methods increased the measurement accuracy considerably. The measured calibration data set of mutual inductances obtained for each individual electrode chain was combined with the numerically modeled mutual inductances to obtain the mutual inductance for each considered electrode configuration (e.g. cross-hole). The inductive correction has worked for a test measurement on the ground. The modeling of the capacitive effect will be verified by the pool measurement under controlled measurement conditions. 12. Conclusion & Outlook 1D borehole field measurement using electrode chain with 8 electrodes (1m electrode spacing) at test site Krauthausen, Germany 6. Rain barrel measurement 8. Field demonstration EIT40 GND wire 1 to 8 ring electrode short-circuit line multicore cable C1C2P 102, 3, 4, 5, 6, 7, 8 201, 3, 4, 5, 6, 7, 8 301, 2, 4, 5, 6, 7, 8 …… 801, 2, 3, 4, 5, 6, 7 Z1234 = Z2034-Z1034 = (Z204 – Z203) – (Z104 – Z103) = (Z 2,4 – Z 2,3 ) – (Z 1,4 – Z 1,3 ) C1 C2 P1 P2 1 2 3 4 example configuration: 10. Mutual inductance for cross-hole M cpm : obtained from the pole-pole matrix M gem : modeled with Neumann’s integral E7 E8 E15 E16 i u chain 1 chain 2 chain 1 chain 2 11. Comparison of calc. and meas. mutual impedances at 10 kHz, Δϕ = 0.8 mrad Test measurement on the ground: electrodes connected but not grounded E8E7 E6 E5E4 E3 E2E1 E16E15E14E13E12 E11 E10 E9 EIT40 electrode chain 1 electrode chain 2 5 m 1 m 2. EIT borehole field measurement A B M N electrode chain borehole EIT40 field B M N A A N B M A N B M A, B: current electrodes M, N: voltage electrodes : wires for current injection : wires for potential measurement case 1case 2 case 3 case 4 3. Inductive coupling in the cable 1 24 3 r 13 r 24 r 14 r 23 iIiI B : wire pair I/ loop I (current injection) : wire pair II/ loop II (voltage measurement) : electric current : magnetic field line The mutual inductance is calculated with simplified Neumann’s formula: Capacitive coupling between the cable shield and the conductive soil electrodes insulator el. conductive shielding soil currents in the soil i i +u -u wires : parasitic current : injection current : capacitor 4. Capacitive coupling 5. EIT40 system Zimmermann et al 2008 + Flores Orozco A, Kemna A, Oberdörster C, Zschornack L, Leven C, Dietrich P and Weiss H 2012 Delineation of subsurface hydrocarbon contamination at a former hydrogenation plant using spectral induced polarization imaging J. Contam. Hydrol. vol 136–137 pp 131-44 Hördt A, Blaschek R, Kemna A and Zisser N 2007 Hydraulic conductivity estimation from induced polarisation data at the field scale — the Krauthausen case history J. Appl. Geophys. vol 62 pp 33-46 Karaoulis M, Revil A, Werkema D D, Minsley B J, Woodruff W F and Kemna A 2011 Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach Geophys. J. Int. vol 187 pp 237-51 Kemna A, Binley A, Ramirez A and Daily W 2000 Complex resistivity tomography for environmental applications Chem. Eng. J. vol 77 pp 11 – 8 Zimmermann E, Kemna A, Berwix J, Glaas W and Vereecken H 2008 EIT measurement system with high phase accuracy for the imaging of spectral induced polarization properties of soils and sediments Meas. Sci. Technol. vol 19 p 094010 Zimmermann E 2010 Phasengenaue Impedanzspektroskopie und -tomographie für geophysikalische Anwendungen (Diss.) Rheinischen Friedrich-Wilhelms-Universität Bonn References Yulong Zhao Dipl.- Ing ZEA-2 Electronic Systems Forschungszentrum Jülich Tel: 02461 614323 Email: y.zhao@fz-juelich.de

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