Apparent resistivity from a resistivity survey depends on the electrode array geometry through a geometric factor: for the Wenner array (equal spacing 'a'), ρa = 2πa(ΔV/I); for the Schlumberger array, ρa = π[(AB/2)²−(MN/2)²]/MN × (ΔV/I). Since apparent resistivity for a given subsurface (homogeneous ground) is the same physical quantity regardless of array type, equating the two expressions allows solving for the unknown potential difference in the second array configuration.
First compute the true (apparent) resistivity from the Wenner measurement: ρa = 2πa(ΔV/I) = 2π(10)(0.010V/1.0A) = 2π(10)(0.01) = 0.6283 Ω·m. For the Schlumberger array with...
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