Andrea Treichel

Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects

Electrical impedance tomography (EIT) is gaining importance in the field of geophysics and there is increasing interest for accurate borehole EIT measurements in a broad frequency range (mHz to kHz) in order to study subsurface properties. To characterize weakly polarizable soils and sediments with EIT, high phase accuracy is required. Typically, long electrode cables are used for borehole measurements. However, this may lead to undesired electromagnetic coupling effects associated with the inductive coupling between the double wire pairs for current injection and potential measurement and the capacitive coupling between the electrically conductive shield of the cable and the electrically conductive environment surrounding the electrode cables. Depending on the electrical properties of the subsurface and the measured transfer impedances, both coupling effects can cause large phase errors that have typically limited the frequency bandwidth of field EIT measurements to the mHz to Hz range. The aim of this paper is to develop numerical corrections for these phase errors. To this end, 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. The correction methods 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. The corrections were also applied to field EIT measurements made using a 25 m long EIT borehole chain with eight electrodes and an electrode separation of 1 m. The results of a 1D inversion of these measurements showed that the correction methods increased the measurement accuracy considerably. It was concluded that the proposed correction methods enlarge the bandwidth of the field EIT measurement system, and that accurate EIT measurements can now be made in the mHz to kHz frequency range. This increased accuracy in the kHz range will allow a more accurate field characterization of the complex electrical conductivity of soils and sediments, which may lead to the improved estimation of saturated hydraulic conductivity from electrical properties. Although the correction methods have been developed for a custom-made EIT system, they also have potential to improve the phase accuracy of EIT measurements made with commercial systems relying on multicore cables.

Phase correction of electromagnetic coupling effects in cross-borehole EIT measurements

Borehole EIT measurements in a broad frequency range (mHz to kHz) are used to study subsurface geophysical properties. However, accurate measurements have long been difficult because the required long electric cables introduce undesired inductive and capacitive coupling effects. Recently, it has been shown that such effects can successfully be corrected in the case of single-borehole measurements. The aim of this paper is to extend the previously developed correction procedure for inductive coupling during EIT measurements in a single borehole to cross-borehole EIT measurements with multiple borehole electrode chains. In order to accelerate and simplify the previously developed correction procedure for inductive coupling, a pole–pole matrix of mutual inductances is defined. This consists of the inductances of each individual chain obtained from calibration measurements and the inductances between two chains calculated from the known cable positions using numerical modelling. The new correction procedure is successfully verified with measurements in a water-filled pool under controlled conditions where the errors introduced by capacitive coupling were well-defined and could be estimated by FEM forward modelling. In addition, EIT field measurements demonstrate that the correction methods increase the phase accuracy considerably. Overall, the phase accuracy of cross-hole EIT measurements after correction of inductive and capacitive coupling is improved to better than 1 mrad up to a frequency of 1 kHz, which substantially improves our ability to characterize the frequency-dependent complex electrical resistivity of weakly polarizable soils and sediments in situ.

Broadband Electrical Impedance Tomography for Subsurface Characterization Using Improved Corrections of Electromagnetic Coupling and Spectral Regularization

The low-frequency complex electrical conductivity in the mHz to kHz range has been shown to enable an improved textural, hydraulic, and biogeochemical characterization of the subsurface using electrical impedance spectroscopy (EIS) methods. Principally, these results can be transferred to the field using electrical impedance tomography (EIT). However, the required accuracy of 1 mrad in the phase measurements is difficult to achieve for a broad frequency bandwidth because of electromagnetic (EM) coupling effects at high frequencies and the lack of inversion schemes that consider the spectral nature of the complex electrical conductivity. Here, we overcome these deficiencies by (i) extending the standard spatial-smoothness constraint in EIT to the frequency dimension, thus enforcing smooth spectral signatures, and (ii) implementing an advanced EM coupling removal procedure using a newly formulated forward electrical model and calibration measurements. Both methodological advances are independently validated, and the improved imaging capability of the overall methodology with respect to spectral electrical properties is demonstrated using borehole EIT measurements in a heterogeneous aquifer. The developed procedures represent a significant step forward towards broadband EIT, allowing transferring the considerable diagnostic potential of EIS in the mHz to kHz range to geophysical imaging applications at the field scale for improved subsurface characterization.

Numerical modeling of the electromagnetic coupling effects for phase error correction in EIT borehole measurement

Electrical Impedance Tomography (EIT) applications in geophysics require long electrode chains (25 m) for current injection and potential measurements. Undesired inductive coupling between the wire loops for current injection and potential measurement and capacitive coupling between the cable shield and the soil strongly decrease the phase accuracy of such measurements for frequencies above 100 Hz. Therefore, the bandwidth of EIT field measurements is typically limited to the mHz to Hz range. To overcome this limitation, we derived correction procedures for inductive and capacitive coupling by combining numerical modeling with calibration measurements. The correction procedures were verified with test measurements, where a phase accuracy better than 1 mrad at 10 kHz was achieved.