18-Geol-A7 Applied Geophysics · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2018 — 18-Geol-A7 Applied Geophysics. Three-hour, closed-book exam; approved Casio or Sharp calculator permitted. The paper offers a choice of six of the following ten questions, each worth 16.66% of the total mark, and every question requires an essay-format answer — this is a genuinely all-essay sitting with no numeric data, formula sheet, or figure supplied in the source. All ten questions are answered below so the set stands as a complete study resource for choose-N-of-M exams.
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics (2nd ed.) — the primary reference for every method touched in this paper (electrical/EM methods, seismic refraction/reflection, radiometrics, magnetics, gravity, well logging); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration (3rd ed.) — survey design, array geometry, data acquisition and processing; Blakely, Potential Theory in Gravity and Magnetic Applications — magnetic-mineral behaviour and gravity reduction (Q5, Q7); Selley & Sonnenberg, Elements of Petroleum Geology — well-logging tool context (Q8).
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 configuration. The Wenner array uses four collinear, equally-spaced electrodes: two outer current electrodes (A, B) inject a known current $I$ into the ground, and two inner potential electrodes (M, N) measure the resulting voltage $\Delta V$. All four electrodes share the same spacing $a$ (A–M = M–N = N–B = $a$).
Sounding vs. profiling. A sounding (vertical electrical sounding, VES) probes how resistivity changes with depth at one location: the whole array is symmetrically expanded about a fixed centre point, increasing $a$ in steps, so that progressively larger spacings sense progressively greater depths, producing a resistivity-vs-depth curve at that one site. A profiling survey instead maps lateral resistivity change at roughly one investigation depth: the spacing $a$ is held fixed and the entire array is moved, as a rigid unit, along a line at regular intervals, producing a resistivity profile along the traverse.
Apparent resistivity formula. For the Wenner configuration the geometric factor is $K=2\pi a$, so
$$\rho_a=2\pi a\,\dfrac{\Delta V}{I}$$
where $\Delta V/I$ is the measured resistance and $2\pi a$ converts that resistance into an apparent resistivity by accounting purely for the array's geometry.
True vs. apparent resistivity. The resistivity $\rho$ of a rock is an intrinsic material property (a function of porosity, pore-fluid salinity and clay content) that would be measured if the current flowed through a uniform, homogeneous half-space. Real ground is never homogeneous, so the quantity $\rho_a$ that comes directly out of the formula above is not the true resistivity of any single layer — it is a weighted average of the resistivities of every layer/body the current actually passed through, computed as if the ground were homogeneous. Recovering the true layered (or 2-D/3-D) resistivity distribution from a set of apparent-resistivity readings requires inversion; $\rho_a$ is only ever the raw field observation, not the interpreted answer.
Processing and interpreting a profile. Field readings are first quality-controlled (repeat/reciprocal readings to flag noisy contacts or electrode-placement errors, and near-surface inhomogeneities that can produce spurious spikes). Apparent resistivities are then computed with the array's geometric factor and assembled into a profile (1-D) or, if several spacings were also acquired at each station, a pseudosection (2-D). The data are then inverted (least-squares or smoothness-constrained 2-D/3-D inversion) to recover a true-resistivity model of the subsurface, and the resulting model is finally correlated with any available geological control (outcrop mapping, borehole logs) to interpret the resistivity contrasts in terms of lithology, structure, or the target of interest (e.g. a conductive fault zone, a resistive intrusion, the water table).
