Extreme sensitivity of crosshole electrical resistivity tomography measurements to geometric errors

The 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.