18-Geol-A7 Applied Geophysics · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2019 — 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 (physical properties, gravity, magnetics, electrical/EM methods, seismic refraction/reflection, radiometrics, well logging, magnetotellurics); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration (3rd ed.) — survey design, array geometry, data acquisition, processing and display; Blakely, Potential Theory in Gravity and Magnetic Applications — potential-field survey design and reduction (Q2); Selley & Sonnenberg, Elements of Petroleum Geology — well-logging tool context (Q7).
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.
Target and geological setting. A representative gravity target is a shallow karst cavity or abandoned mine void beneath a proposed building or highway alignment — a common geotechnical hazard-detection problem in carbonate or historically mined terrain. The setting is typically flat-lying to gently rolling ground with a thin soil/overburden cover over limestone or old workings, so terrain corrections are modest but not negligible.
Physical property contrast. An air-filled or rubble-filled void has $\rho\approx0$–$1.8\,\text{g/cm}^3$ against a limestone host of $\rho\approx2.6\,\text{g/cm}^3$, giving a density contrast $\Delta\rho\approx-0.8$ to $-2.6\,\text{g/cm}^3$ — a strong, negative (mass-deficient) anomaly.
Signal and noise levels. For a void of radius $r$ at depth $z$, the microgravity anomaly (spherical approximation) at horizontal offset $x$ is $g(x)=\dfrac{4}{3}\pi G r^3\Delta\rho\,\dfrac{z}{(x^2+z^2)^{3/2}}$, peaking directly above the centre at $g_{max}=\tfrac{4}{3}\pi G r^3\Delta\rho/z^2$; for a 3 m-radius void centred 6 m deep this gives a peak anomaly of roughly 17–55 μGal across the rubble-filled to air-filled contrast range — a few tens of microgals — small, so a microgravity survey needs a gravimeter reading to $\pm5$–$10\,\mu\text{Gal}$ repeatability. Noise sources at this level include instrument drift (corrected with repeat base-station ties every 1–2 hours), tares (sudden jumps, discarded and re-tied), tidal variation (computed and removed), and — critically at microgal precision — elevation error: a 1 cm error in station elevation produces roughly a 3 μGal free-air error, so station elevations must be surveyed to sub-centimetre accuracy (RTK GPS or differential levelling), not read off a topographic map.
Wavelength and station spacing. The anomaly's half-width scales with target depth (for a sphere the half-maximum offset is $x_{1/2}\approx0.77z$, about 4.6 m here), so a 6 m-deep void produces an anomaly only about 10 m wide. To sample this without aliasing, the station spacing must be a fraction of the target depth — here roughly 1–2 m — on a tight grid, not the tens-of-metres spacing adequate for a regional gravity survey of a much larger, deeper target (e.g. a basin or intrusion).
Acquisition procedure. Lay out a dense grid (1–2 m station spacing) over the suspect area with a looped base-station tie every 60–90 minutes for drift/tare control; survey each station's elevation and position to sub-centimetre accuracy; apply latitude, free-air, Bouguer and terrain corrections (the last significant if the ground surface itself is irregular) to obtain the complete Bouguer anomaly; then apply a regional/residual separation (e.g. polynomial trend removal or upward continuation) to isolate the shallow, short-wavelength void signature from the broader regional geological trend before contouring and interpreting.
