Formulas in wenner and schlumberger configurations in ers?

In Electrical Resistivity Surveying (ERS), the Wenner and Schlumberger configurations are commonly used for measuring subsurface resistivity.

For the Wenner configuration, the apparent resistivity (( \rho_a )) is calculated using the formula: [ \rho_a = 2\pi a V/I ] where ( a ) is the electrode spacing, ( V ) is the measured potential difference, and ( I ) is the current applied.

In the Schlumberger configuration, the formula is similar but accounts for the larger distance between the outer electrodes: [ \rho_a = \frac{2\pi (AB)^2}{(AB - a)V/I} ] where ( AB ) is the distance between the outer electrodes and ( a ) is the distance between the inner electrodes. Both configurations help in interpreting subsurface resistivity variations.