1. 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:

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

3. „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)

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

5. 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

6. 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

7. 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

8. 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

9. 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!

10. 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

11. 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 ∞

12. 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

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

14. 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

15. 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

16. Thank you for your attention!

17. References About SIP or EIT:
Kemna et al Complex resistivity tomography for environmental applications Chem. Eng. J. vol 77 pp 11 – 8
Binley et al 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 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
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 Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects Measurement Science and Technology vol 24 p