Numerical modeling of the electromagnetic coupling effects for phase error correction in EIT borehole measurement Y Zhao1, E Zimmermann1, J A Huisman2, A Treichel2, B Wolters1, S van Waasen1, A Kemna3 1Central Institute ZEA-2 – Electronic Systems, Forschungszentrum Jülich GmbH, Germany 2Institute of Bio- and Geosciences (IBG-3), Forschungszentrum Jülich GmbH, Germany 3Department of Geodynamics and Geophysics , University of Bonn, Germany Yulong Zhao Dipl.- Ing. ZEA-2 Electronic Systems Forschungszentrum Jülich Tel: +49 2461 614323 Email: y.zhao@fz-juelich.de

Overview Introduction Objective of this work Inductive coupling effect Capacitive coupling effect Results Summary

„membrane“ polarization Introduction Spectral induced Polarization (SIP) of soils and rocks „membrane“ polarization electrical double layer Description by complex, frequency-dependent electrical conductivity Textual, hydraulic, and geochemical properties of soils and rocks could be characterized with SIP frequency [Hz] amplitude [Ωm] phase [mrad] (Kemna 2011)

Introduction Electrical Impedance Tomography (EIT) = SIP + imaging imaging at diverse frequencies f1 log f f2 f3 EIT SIP (Kemna 2011)

Objective of this work Accurate EIT-measurement for high frequencies with small phase error in field measurements loess 0.02 middle gravel middle sand aquifer fine gravel 0.002 middle gravel sand, gravel, clay fine sand clay 10 Hz 10 kHz Measured phase spectra of sediment samples from Krauthausen, Germany

Objective of this work Starting situation and objective EIT40 40 channels <1 mrad phase accuracy at 1kHz in laboratory measurement EIT40 - borehole measurement system correction of the phase errors due to inductive and capacitive effects from the cable for field application

Objective of this work Simplified circuit diagram of electrode modules shielding of cable shielding of wires ring electrodes 16.2 cm wire 1 wire 2 wire 3 wire 4 E1 E2 E3 E4 GND : relay switched to electrode : amplifier : relay switched to amplifier

Inductive coupling effect Inductive coupling between two wire pairs 1 2 4 3 r13 r24 r14 r23 II 𝑼 𝑰𝑰 B mutual inductance: 𝐿 II,I = 𝜇 0 𝑙 2𝜋 ln 𝑟 14 𝑟 23 𝑟 13 𝑟 24 = 𝐿 𝐼,𝐼𝐼 =𝑀 measured impedance: 𝑈 𝑀 𝜔 𝐼 𝐼 (𝜔) = 𝑍 𝑀 =𝑍 𝑜 𝜔 +𝑗𝜔𝑀(𝜔) : wire pair I/ loop I (current injection) :wire pair II/ loop II (voltage measurement) : injection current : magnetic field line

Inductive coupling effect The pole-pole calibration measurement EIT40 GND wire 1 to 8 ring electrode short-circuit line multicore cable The mutual impedance between the single current wire and the single potential wire instead of the wire pairs will be measured!

Inductive coupling effect The pole-pole matrix Z fn = [ ] 𝑍 1,2 𝑍 2,1 [ ] ⋯ 𝑍 1,7 𝑍 1,8 𝑍 2,7 𝑍 2,8 ⋮ ⋱ ⋮ 𝑍 7,1 𝑍 7,2 𝑍 8,1 𝑍 8,2 ⋯ [ ] 𝑍 7,8 𝑍 8,7 [ ] Z f1 = [ ] 𝑍 1,2 𝑍 2,1 [ ] ⋯ 𝑍 1,7 𝑍 1,8 𝑍 2,7 𝑍 2,8 ⋮ ⋱ ⋮ 𝑍 7,1 𝑍 7,2 𝑍 8,1 𝑍 8,2 ⋯ [ ] 𝑍 7,8 𝑍 8,7 [ ] ⋱ C1 C2 P 1 2, 3, 4, 5, 6, 7, 8 2 1, 3, 4, 5, 6, 7, 8 3 1, 2, 4, 5, 6, 7, 8 … 8 1, 2, 3, 4, 5, 6, 7 example: Z1234 = Z123-Z124 = (Z13 – Z23) – (Z14 – Z24) C1 C2 P1 P2 1 2 3 4

Capacitive coupling effect wires The capacitance between the shield and the environment is calculated with: 𝐶=2∙𝜋∙ 𝜀 0 ∙ 𝜀 𝑟 ∙ 𝑙 ln 𝑅 2 𝑅 1 insulator el. conductive shielding i +u R1 R2 currents in the soil PVC as insulator electrodes i The relative permittivity εr of PVC materials is also frequency-dependent. C* fitting with Cole-Cole is necessary -u : parasitic current : injection current : capacitor soil 𝜀 ∗ = 𝜀 0 − 𝜀 ∞ 1+ (𝑗𝜔 𝜏 0 ) 1−𝛼 + 𝜀 ∞

test measurement in a rain barrel with borehole logging tool Calculation of the admittance matrix and the transfer impedance due to the capacitive effect A B M N : electrodes : C at cable : C at rod : C at bottom test measurement in a rain barrel with borehole logging tool 2D- mesh of the rain barrel with integrated capacitances For each node with C: 𝑌 𝐶 𝑛,𝑛 =𝑗𝜔 𝐶 𝑛,𝑛 ∗ For the whole admittance matrix: 𝑌 𝐺 = 𝑌 𝑆 + 𝑌 𝐶 𝑛,𝑛 From 𝑌 𝐺 𝑈 = 𝐼 𝑍 𝑀,𝑁 = 𝑈 𝑀,𝑁 /𝐼

Results of the correction procedures comparison of Z, Zcr and Zc (Zcr = Z - jωM, ZC: modeled Z) at 10 kHz, Δϕ= 0.8 mrad

The first field demonstration (1D inversion at 1kHz) z = -9.7 m z = -2.5 m borehole with slices z = 0 m z = -2.7 m water

Summary A high phase accuracy of 0.8 mrad at 10 kHz in the test measurements has been obtained The correction procedures were successfully applied in real field measurements The same accuracy was achieved with the new pole-pole calibration Outlook Correction procedures for field measurements in two boreholes

Thank you for your attention!

References About SIP or EIT: Kemna et al. 2000 Complex resistivity tomography for environmental applications Chem. Eng. J. vol 77 pp 11 – 8 Binley et al. 2005 Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone Water Resour. Res. vol 41 p W12417 About the instruments: Zimmermann et al. 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 About the modeling and phase error correction: Zimmermann 2010 Phasengenaue Impedanzspektroskopie und - tomographie für geophysikalische Anwendungen (phD thesis.) Rheinischen Friedrich-Wilhelms-Universität Bonn Zhao et al. 2013 Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects Measurement Science and Technology vol 24 p 085005