Question 4 of 10: Resistivity Survey Arrays — Configuration, Strengths/Weaknesses, and a Case History

Question 4: Resistivity Survey Arrays — Configuration, Strengths/Weaknesses, and a Case History (16.66% of paper)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Wenner array. Four collinear electrodes A-M-N-B equally spaced by $a$ (current electrodes A/B outermost, potential electrodes M/N innermost); the whole four-electrode set is expanded about a fixed centre point for vertical sounding, or the whole set translated along a line at fixed $a$ for horizontal profiling. Geometric factor $k=2\pi a$, so $\rho_a=k\cdot V/I$. Strengths: strong signal-to-noise (good vertical resolution, simple geometric factor). Weaknesses: requires moving all four electrodes for every reading (slow in the field) and has relatively poor lateral/horizontal resolution compared with a dipole array.

Schlumberger array. Also collinear A-M-N-B, but M/N stay closely and fixedly spaced near the centre while A/B are expanded outward in larger steps for sounding; occasionally M/N are also repositioned when the signal becomes too small. Strengths: fewer electrode moves per sounding than Wenner (faster), good depth resolution for vertical electrical sounding (VES). Weaknesses: requires a sensitive voltmeter as A-B spacing grows large relative to M-N (weak signal at MN), and is primarily a 1-D sounding tool rather than a mapping array.

Dipole–dipole array. Two independent, closely-spaced dipole pairs (current dipole A-B, potential dipole M-N) separated by a variable multiple $n$ of the dipole length $a$; the current dipole is stepped along the line and, for each position, readings are taken at increasing $n$ to build a pseudosection. Strengths: excellent lateral resolution, good for 2-D mapping/pseudosections, well suited to IP surveying (current and potential circuits are physically separated, reducing electromagnetic coupling). Weaknesses: weaker signal at large $n$ (both geometric spreading and increasing electrode separation), more sensitive to near-surface lateral resistivity variations (noisier pseudosections) than Wenner.

Case history. A Wenner/dipole-dipole 2-D resistivity survey to map a buried, unlined waste disposal trench and assess leachate migration: a 200 m line with 5 m electrode spacing (giving investigation depth of roughly 30–40 m with a multi-electrode 2-D system), current injected at 1–5 mA via a multi-electrode switching unit, dipole-dipole array used for the main 2-D imaging (better lateral resolution to delineate the trench edges) cross-checked with a Wenner sounding at one location for a 1-D depth control.

Processing, display and interpretation. Apparent resistivity values from each electrode combination are first quality-controlled (removing obviously noisy/contact-resistance-affected readings), assembled into a pseudosection (apparent resistivity plotted at the midpoint/pseudo-depth of each reading), and then inverted using a 2-D smooth-model or layered inversion (e.g. finite-element forward modelling with regularized least-squares inversion) to produce a true resistivity cross-section. The interpreter looks for a low-resistivity anomaly (elevated conductivity from leachate-saturated, ionic pore fluid) coincident with the mapped trench footprint, and compares its lateral extent against the anomaly boundary to infer a leachate migration plume beyond the trench's known limits.