Examination of the validity of the computed intermediate apparent resistivity points in the Wenner and offset Wenner configuration of sounding

Abstract

The Wenner and offset Wenner array is among the quite recent configurations used to assess and reduce the disturbing lateral effect in resistivity soundings. Even if this system could be considered as one of the most efficient configurations for this purpose so far, the restricted number of measuring points makes its vertical resolution limited. To fix this limitation, Barker found out a specific equation by which resistance values at points halfway between the actual measuring ones are computed without being measured. This aim was reached by combining expressions of electric potentials at various electrode spacings. For the same purpose, three other equations were worked out and tested. For a single sounding, resistance values were computed at intermediate points by the mean of these equations. Observational errors were also calculated using Barker’s formulae. The computed resistance values were found to be contaminated by these errors, in varying degrees to the extent that some of them were lacking reliability. Furthermore, at each electrode spacing, the differences between the interpolated and the assumed resistivity values on a straight line joining the actual measuring points were calculated. After normalizing these differences to their corresponding averages, the RMS of these normalized differences were computed for a set of soundings using the four equations. Finally, a comparison of the obtained results with the errors of measurements from the reliability of the computed resistance values was made. This comparison allowed classifying these equations from the reliability of the intermediate resistivity values perspective. In addition, Barker’s choice of one of these equations as the one that gives the most satisfactory results is justified.