Question

A Wenner resistivity survey was performed with a spacing of 15 m between the current electrodes. Potential difference values of \(-25\ \text{mV}\) and \(225\ \text{mV}\) were measured before and after injecting \(100\ \text{mA}\) current into the ground. The apparent resistivity in \(\Omega\cdot\text{m}\) after correcting for the self-potential effect is:

• A. 78.5
• B. 62.8
• C. 188.5
• D. 235.6

Hint:

In Wenner configuration, the \emph{adjacent} electrode spacing is \(a\), while the current-electrode separation is \(3a\). Always correct the measured potential for self-potential before using \(\rho_a = 2\pi a\,\Delta V/I\).

Answer 1

The Correct Option is A

Step 1: Correct the measured potential.
Self-potential (before current) \(= -25\ \text{mV}\); measured after current \(= 225\ \text{mV}\).
\(\Delta V = 225 - (-25) = 250\ \text{mV} = 0.25\ \text{V}.\) Step 2: Determine Wenner spacing \(a\).
In a Wenner array, the distance between the current electrodes is \(AB = 3a\).
Given \(AB = 15\ \text{m}\Rightarrow a = 15/3 = 5\ \text{m}.\) Step 3: Compute apparent resistivity.
For Wenner array, \(\rho_a = 2\pi a\,\dfrac{\Delta V}{I}\).
With \(a=5\ \text{m}\), \(I=100\ \text{mA}=0.1\ \text{A}\): \[ \rho_a = 2\pi(5)\,\frac{0.25}{0.1} = 2\pi(5)\times 2.5 = 2\pi(12.5) \approx 78.5\ \Omega\cdot\text{m}. \] \[ \boxed{78.5\ \Omega\cdot\text{m}} \]