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.
Electrical conductivity ($\sigma$) is the constant of proportionality between the current density $J$ that flows through a material and the electric field $E$ driving it, the point form of Ohm's law:
$$J=\sigma E$$
with SI units of siemens per metre (S/m). Physically it measures how readily a material passes electric current — a bulk property that, in rocks, is controlled far more by porosity, pore-fluid salinity and clay content than by the conductivity of the constituent minerals themselves (most rock-forming silicates are near-insulators).
Typical values. Unweathered crystalline rock (granite, gneiss, unfractured basalt) is highly resistive, $\sigma\approx10^{-5}$–$10^{-3}$ S/m. Porous sedimentary rock (sandstone, limestone) spans a wide range, $\sigma\approx10^{-3}$–$10^{-1}$ S/m, controlled by Archie's-law porosity and pore-water salinity. Clay and shale are among the most conductive common earth materials, $\sigma\approx0.05$–$1$ S/m, because clay minerals conduct via surface (cation-exchange) conduction along hydrated interlayer cations in addition to any pore fluid. Saline groundwater and seawater are highly conductive, $\sigma$ up to several S/m. Massive sulphide ore and graphite are the most conductive geological materials encountered, approaching metallic conduction, $\sigma\gg1$ S/m. Dry sand, permafrost and glacial ice sit at the resistive end, $\sigma<10^{-3}$ S/m. For geotechnical work, buried metallic infrastructure (pipes, drums, rebar) is effectively a near-perfect conductor, orders of magnitude above any natural geological material.
Conductivity vs. resistivity. Resistivity $\rho$ is simply the reciprocal, $\rho=1/\sigma$ (units $\Omega\cdot$m) — the same physical property expressed the other way round. The choice of convention follows the method: the DC resistivity method directly measures a voltage/current ratio and multiplies by a purely geometric array factor to obtain $\rho_a$, so resistivity is the natural unit for that method; the electromagnetic (EM) method instead responds to induced (eddy) currents whose magnitude scales more directly and, at low induction number, linearly with $\sigma$, so EM instruments (e.g. Slingram/ground conductivity meters, airborne EM) conventionally output apparent conductivity (mS/m) rather than forcing every reading through a reciprocal.
Conductance. Conductance is a distinct, third quantity — the integrated conductivity of a layer of thickness $t$:
$$S=\sigma t=\dfrac{t}{\rho}$$
with units of siemens (S), not S/m — a genuine conductance, not a per-length property. Conductance matters because for a layer that is thin compared with the depths of investigation involved, DC resistivity and EM surveys cannot resolve $\sigma$ and $t$ independently — only their product $S$ is recoverable (the thin-sheet, or "S-equivalence", principle). A thin, highly conductive clay aquitard or graphitic shear zone is therefore usually characterized, and surveys targeting it are designed and interpreted, in terms of its conductance rather than an attempted separate $\sigma$ and $t$.
Why all three matter. Resistivity is the parameter Ohm's law and the DC method deliver directly, and it is the quantity geological interpretation (Archie's law porosity/saturation, lithology discrimination) is conventionally built around. Conductivity is the natural EM-method quantity, sums intuitively for layered or anisotropic media (bulk conductivity of parallel layers is a thickness-weighted average of $\sigma$), and is what most modern airborne/ground EM systems report. Conductance governs the detectability and resolvability of thin conductive targets regardless of which method is used, and is the actual resolved parameter whenever $\sigma$ and $t$ trade off against one another — so a geophysicist fluent in all three can move correctly between a DC sounding, an EM conductivity map and a thin-layer exploration target without confusing what each number really represents.
