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

Abstract

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

“…However, the main problem with the application of these theoretical approaches to borehole EIT measurements is the need to know the position of adjacent wires in borehole electrode chains with sufficient accuracy. In previous work, we solved this problem for measurements with a single borehole electrode chain using a method based on calibration measurements (Zhao et al 2013). This calibration must be done only once because it does not depend on the cable layout of the field measurement.…”

“…The electrode modules are connected to an adapter box close to the EIT data acquisition system using a 25 m long multicore cable that consists of 16 shielded, twisted wire pairs. To ensure a good electrical contact with the surrounding medium, we used brass ring electrodes with a diameter of 42 mm and a height of 10 mm (Zhao et al 2013).…”

“…Because of the small distances between the wires and the parasitic eddy currents in the shield of the electrode chain, it is very difficult to calculate the inductance M from the geometry for borehole EIT measurements with current injection and potential measurement in a single borehole chain (figure 1(a)). However, it is possible to use calibration measurements to remove the inductive coupling for this case since the wires are fixed inside one multicore cable (Zhao et al 2013). For the second case, the inductance now also depends on the layout of the two multicore electrode chains at the Earth's surface, which obviously varies with the measurement location and depends on the position of the EIT system relative to that of the boreholes.…”

“…Wagner 1914, Felger andBassewitz 1986). Therefore, we used the Cole-Cole model (Cole and Cole 1941) to describe the complex dielectric permittivity using ε s = 4.79, ε ∞ = 3.36, τ = 2.8 × 10 −5 s and α = 0.54 (Zhao et al 2013). This calculation is used to determine the capacitance of cable parts which are located in the water inside the borehole.…”

“…Furthermore the capacitances of the integrated amplifiers inside the electrode modules are considered. For more details about the calculation of these capacitances we refer to Zhao et al (2013).…”