Estimation of the error made in Pole–Dipole Electrical Resistivity Tomography depending on the location of the remote electrode: Modeling and field study

Abstract

Abstract Objective The objective was to estimate the error made in Electrical Resistivity Tomography (ERT) when Pole–Dipole array (PD) is used, as a function of the location of the remote electrode. Methods First, we carried out a parametrical analysis to quantify the error in the geometrical factor and in the apparent resistivity using analytical calculation and numerical model based on the general moment method. Then, the influence of the remote electrode location was studied considering PsPD (Pseudo-Pole–Dipole i.e. when the exact location of the remote electrode is used even when finite) in comparison to PDbias (Pole–Dipole bias i.e. remote electrode is considered at infinity even when finite). Anomaly Effect (AE) with new consideration of the averaged mean resistivity value was used for the illustration, results with L1 and L2-norms were compared and Forward/Reverse measurements were considered. Results First results showed that for the geometrical factor, a minimum Q (the remote distance divided by the half of the distance between the first and the last in-line electrodes) value of 5 at least is needed while for the apparent resistivity, a minimum of Q value between 2 and 5 would be sufficient if α = 100° (angle between the line BO – joining the remote electrode and the center of all in-line electrodes – and the line joining all in-line electrodes). A spread α value around 100° gave the weakest error. Angle α around 30° was identified as giving homogeneous spread error between PsPD and PDbias data treatments. For α ~ 140°, the error made when the true coordinates of the remote electrode is not informed is higher near layer's interface if L1-norm is used. Whereas this error is more visible in deep level if L2-norm is used. Finally, experimental results showed the influence of the location of the remote electrode when “Forward” measurements are completed by “Reverse” ones. Conclusion Depending on in-situ conditions, the accessibility of ideal remote electrode is not always satisfactory. Our study has given an overview of the error which can be made depending on the location of the remote electrode when Pole–Dipole array is chosen. Considering valuable results obtained by other authors with this array in the literature, this drawback is counterbalanced by other advantages of this array with respect to others which do not need a remote electrode. Practice implications PsPD cannot be substituted with PDbias, then, it is always preferable to consider the true coordinates of the remote electrode for data treatment either for apparent resistivity or for interpreted ones, this information is also needed by Res2Dinv to compute the 3D electrical potential. Q value equal or higher than 5 is ideally to be preferred and if an angle of 100° is not possible, a value of 30° will be used for “Forward” measurement and completed with Reverse one using the same location of the remote electrode.