On the effect of electrode finiteness in small-scale electrical resistivity imaging

Abstract

Electrical resistivity tomography (ERT) profiles including finite steel-rod electrodes have been widely used in assuming a surface-node current injection for inversion. This hypothesis was shown by others to be safe for ratios of electrode embedment to electrode spacing smaller than 20%. Relying on the conductive cell model (CCM), we took into account the complete electrodes in the DC forward problem. We found that an electrode effect is included in resistivity sections inverted with a surface point electrode model. Several synthetic examples indicated that this unwanted effect is particularly developed when the electrode spacing does not meet a double constraint from the characteristic size of a shallow heterogeneity and from the electrode embedment. This effect deserved correction. A point approximation for a finite electrode referred to as the equivalent electrode point (EEP) was sought by placing a point-source current in the ground along the electrode length. The appropriate EEP depth was the one for which the CCM and a buried point source minimized a systematic geometric error; i.e., the relative change of the geometric factors obtained with the CCM and with an EEP. An EEP placed at 73% of the electrode length was declared as a suitable point approximation for an electrode. Use of this point assumption for inversion remedied efficiently the electrode effect subject to conditions. More precisely, the electrode spacing should stay within a lower bound equal to twice the electrode embedment and an upper bound equal to the shallow heterogeneity characteristic size divided by 0.75. The interest of such a metrological appraisal of the suitable acquisition layout to be used on the field was illustrated by a small-scale ERT field survey. This case study permitted us to understand more reliably the impact from fires upon a centimetric shallow layer in a calcareous wall.