Three-dimensional effects causing artifacts in two-dimensional, cross-borehole, electrical imaging

Abstract

Summary Cross-borehole electrical resistance tomography (ERT) experiments utilize downhole electrodes, typically placed in a borehole filled with material of contrasting resistivity to the host rock. The circular geometry of the boreholes is three-dimensional, and inversion routines are typically two-dimensional. Because of the resistivity contrast, artifacts in the form of borehole inversion effects develop in the resistivity images. Other 3D effects resulting in inversion artifacts are shadow effects caused by use of a 2D code to invert data from a 3D body located outside the image plane. In both cases the inversion model misrepresents the spatial change in voltages as a corresponding spatial change in resistivity. Borehole inversion effects and shadow effects result as the forward solver attempts to resolve the discrepancy in the voltages for numerous electrode pairs into a meaningful resistivity distribution. Borehole inversion effects are shown to be related to the resistivity contrast between the borehole fill and the host medium, and to borehole diameter. Borehole inversion effects do not materialize with small diameter boreholes (e.g. ⩽0.1 m) when the fill resistivity contrast is one order of magnitude or less; however, a borehole fill resistivity contrast of two orders of magnitude causes artifacts in the form of sheaths near the boreholes, and a conductive artifact between the boreholes. Larger diameter borehole (e.g. 0.2 m) induce significant borehole inversion effects with as little as one order of magnitude fill resistivity contrast. The general resistivity patterns are similar for the borehole inversion effects. However, the artifacts are amplified as resistivity contrast and/or borehole diameter increase. These results are significant because borehole inversion effects may mask a target heterogeneity or an artifact may be confused for an anomaly resulting in improper actions for site characterizations or remediation strategies. Suggestions of best practices for experimental design to prevent or minimize borehole inversion effects include: minimizing borehole diameter, minimizing borehole fill resistivity contrast, measuring and inputting the resistivity of the borehole fill/water into the model, and inverting changes in resistivity for time-lapse ERT data. Shadow effects are shown to be related directly to the distance of the target heterogeneity out of the image plane. Our results show that shadow effects become insignificant when the target is between 3 and 5 m outside the 10-m wide image plane. Because the size of the target and resistivity contrast of the target to the host rock are site-specific variables, the actual distance at which shadow effects become insignificant will vary from site to site. To reduce misinterpretations by shadow effects reduce the dipole length of the four electrode measurements and supplement data from other well pairs and/or other methods.