Extreme sensitivity of crosshole electrical resistivity tomography measurements to geometric errors

Abstract

S U M M A R YThe effects of geometric errors on crosshole resistivity data are investigated using analytical methods. Geometric errors are systematic and can occur due to uncertainties in the individual electrode positions, the vertical spacing between electrodes in the same borehole, or the vertical offset between electrodes in opposite boreholes. An estimate of the sensitivity to geometric error is calculated for each of two generic types of four-electrode crosshole configuration: current flow and potential difference crosshole (XH) and in-hole (IH). It is found that XH configurations are not particularly sensitive to geometric error unless the boreholes are closely spaced on the scale of the vertical separation of the current and potential electrodes. However, extremely sensitive IH configurations are shown to exist for any borehole separation. Therefore, it is recommended that XH configurations be used in preference to IH schemes. The effects of geometric error are demonstrated using real XH data from a closely spaced line of boreholes designed to monitor bioremediation of chlorinated solvents at an industrial site. A small fraction of the data had physically unrealistic apparent resistivities, which were either negative or unexpectedly large. However by filtering out configurations with high sensitivities to geometric error, all of the suspect data were removed. This filtering also significantly improved the convergence between the predicted and the measured resistivities when the data were inverted. In addition to systematic geometric errors, the measured data also exhibit a high level of random noise. Despite this, the resulting inverted images correspond reasonably closely with the known geology and nearby cone penetrometer resistivity profiles.

Computation of optimized arrays for 3-D electrical imaging surveys

“…Research is currently being carried on using the 3-D array optimization algorithm for surveys with subsurface electrodes using conventional vertical boreholes (Wilkinson et al 2008), as well as along horizontal lines of subsurface electrodes (Harro & Kruse 2013). As these surveys involve electrodes on different lines, it will also be necessary to use the geometric factor relative error to filter out potentially unstable arrays.…”

“…Wilkinson et al (2008) found that for cross-borehole surveys it was necessary to set a limit on the sensitivity of the array geometric factor to errors in the position of the electrodes as well to remove arrays that are likely to be unstable. As 3-D surveys involve cross-line measurements, we also use this method.…”

“…Following Wilkinson et al (2008), we use a value of 5 m −1 as the cut-off factor when the unit electrode spacing is 1 m, which gives a maximum R E of 5 per cent for a 1 cm uncertainty in electrode position.…”

Optimized arrays for 2D cross‐borehole electrical tomography surveys

“…In these experiments, the distance between adjacent electrodes in the tank setup was only 0.05 meter (50 mm). Small errors in the positions of the electrodes and their finite sizes can have significant effects on the results for certain cross-borehole configurations (Wilkinson et al 2008). To minimize these geometric errors, the electrodes were mounted on rigid rods and anchored to fixed points on the base of the tank.…”

Imaging Seawater Intrusion in Coastal Zone of Kavala (N. Greece) With Electrical Resistivity Tomography

“…Among them, the Electrical Resistivity Tomography (ERT) is considered as one the most efficient techniques in imaging such properties and processes associated to subsurface geoelectrical structure (Daily et al, 1992;Park, 1998;Muller et al, 2003;Singha and Gorelick, 2005;Mohnke et al, 2006;Nguyen et al, 2009). In order to eliminate limitations of resolution decrease with increasing depth of investigation, ERT techniques based on variations of borehole, surface-to-borehole and cross-hole measurements, have been proposed (Asch and Morrison, 1989;Daily and Owen, 1991;Slater et al, 2000;Zhou and Greenhalgh, 2000;Friedel et al, 2004;Marescot et al, 2002;Tsourlos et al, 2004Tsourlos et al, , 2005Wilkinson et al, 2008). Along with spatial, ways for time resolution extent with time-lapse techniques, have been reported to literature (Tsourlos et al, 2003(Tsourlos et al, , 2005Oldenborger et al, 2007).…”