Question 4 of 10: Downhole Resistivity Survey Arrays

Question 4: Downhole Resistivity Survey Arrays (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.

Array 1 — single-hole normal (resistivity) log. A four-electrode sonde is run down one borehole on a wireline: a current electrode ($A$) on the sonde and a distant "infinite" return electrode ($B$) at the surface inject current, while a potential electrode ($M$) on the sonde, paired with a distant reference potential electrode ($N$) at the surface, measures the resulting voltage. The current-potential electrode spacing ("normal" spacing, commonly a 0.4 m "short normal" and a 1.6 m "long normal") is fixed on the sonde, and the whole sonde is winched continuously up (or down) the hole, logging apparent resistivity, $\rho_a=k\cdot V/I$ with a spacing-dependent geometric factor $k$, as a continuous function of depth. Strengths: simple, robust, gives a continuous high-vertical-resolution log directly comparable to surface array theory; short- and long-normal logs run together give a crude measure of invasion (contrast between the two investigation depths). Weaknesses: only samples the rock immediately around the single hole (no lateral coverage away from it), and resolution/depth of investigation are coupled to the fixed normal spacing (cannot be adjusted mid-survey).

Array 2 — cross-hole (borehole-to-borehole) resistivity tomography. Current and potential electrodes are distributed along strings in two (or more) boreholes bracketing a target zone (optionally combined with surface electrodes for extra ray coverage); current is injected between an electrode pair chosen from different holes (or hole-to-surface) and potential is measured at many other electrode pairs, and the transmitter/receiver electrode pair is systematically stepped through essentially all combinations across the electrode strings ("all combinations" or a chosen data-collection sequence), building a dense set of apparent-resistivity measurements that sample the volume between the holes from many different ray paths and angles. Strengths: images the resistivity structure BETWEEN boreholes (not just around one hole), so it can detect and geometrically locate a target (fracture zone, contamination plume, ore lens) that neither hole itself intersects. Weaknesses: requires at least two existing boreholes (higher cost, only applicable once drilling is underway), acquisition is slow (very large number of electrode combinations), and inversion is more strongly non-unique than a simple 1-D sounding, particularly for structure outside the direct line between the holes.

Case history. A cross-hole resistivity tomography survey between two 40 m deep, 30 m apart boreholes to characterize a suspected clay-filled fault zone for a proposed underground excavation: 20 electrodes at 2 m spacing in each hole, current injected at roughly 20–100 mA, several thousand four-electrode readings collected over the full combination set, and single-hole normal logs (0.4 m/1.6 m spacing) run in both holes first to establish a 1-D baseline for the tomographic inversion's starting model.

Processing, display and interpretation. Single-hole normal-log data are displayed directly as a resistivity-vs-depth log and interpreted lithologically (low resistivity for clay/shale/saturated fracture zones, higher resistivity for competent, low-porosity rock). Cross-hole tomography data are first quality-controlled (removing readings with poor electrode contact/reciprocal-error checks), then inverted using a 2-D or 3-D finite-element/finite-difference regularized least-squares inversion (analogous in principle to surface 2-D resistivity inversion, but with a genuinely 2-D or 3-D ray/sensitivity geometry rather than a surface-only footprint) to produce a resistivity cross-section or volume between the holes, which the interpreter then examines for a low-resistivity zone consistent with the suspected clay-filled fault, cross-checked directly against the two single-hole logs at the borehole locations as ground truth.