Effect of electrode shape on grounding resistances - Part 1: The focus-one protocol

Electrode grounding resistance is a major factor affecting measurement quality in electric resistivity tomography (ERT) measurements for cryospheric applications. Still, little information is available on grounding resistances in the geophysical literature, mainly because it is difficult to measure. The focus-one protocol is a new method for estimating single electrode grounding resistances by measuring the resistance between a single electrode in an ERT array and all the remaining electrodes connected in parallel. For large arrays, the measured resistance is dominated by the grounding resistance of the electrode under test, the focus electrode. We have developed an equivalent circuit model formulation for the resistance measured when applying the focus-one protocol. Our model depends on the individual grounding resistances of the electrodes of the array, the mutual resistances between electrodes, and the instrument input impedance. Using analytical formulations for the potentials around prolate and oblate spheroidal electrode models (as approximations for rod and plate electrodes), we have investigated the performance and accuracy of the focus-one protocol in estimating single-electrode grounding resistances. We also found that the focus-one protocol provided accurate estimations of electrode grounding resistances to within ±7% for arrays of 30 electrodes or more when the ratio of instrument input impedance to the half-space resistivity was 1000 m⁻¹ or more. The focus-one protocol was of high practical value in field operations because it helped to optimize array installation, electrode design, and placement. The measured grounding resistances may also be included in future inversion schemes to improve data interpretation under difficult environmental conditions such as those encountered in cryospheric applications.