05-Geol-B10 · December 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 04-Geol-B10-1 Gravity and Magnetic Fields, 2016-Dec. Closed book; no calculator permitted. All ten questions require an answer in essay format, with diagrams used wherever appropriate. The exam instructs "choose six (6) of the following ten (10) questions, the first six as they appear in the answer book will be marked, each of equal value".
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics, 2nd ed. (physical properties ch.2 & 5; gravimeters and gravity reduction ch.2; magnetometers and magnetic surveying ch.4–5; forward/inverse modelling throughout); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (survey design, data processing and interpretation workflow ch.6 & 7); Blakely, Potential Theory in Gravity and Magnetic Applications (potential-field theory, uniqueness/equivalent sources ch.5, Fourier-domain filters ch.9 & 12).
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.
A well-documented class of engineering-geophysics case history is the microgravity survey used to detect a suspected sinkhole cavity, abandoned mine working, or karst void beneath a proposed foundation, highway, or pipeline corridor. Such investigations are routinely reported in the engineering-geophysics literature (e.g. Telford, Geldart & Sheriff and Kearey, Brooks & Hill both discuss this application class) as a standard use of high-precision ("microgravity") gravity surveying in site investigation.
A cavity or void — whether air-filled or water-filled — represents a large, unambiguous NEGATIVE density contrast against the surrounding rock or soil, which gravity senses directly and quantitatively. Ground-penetrating radar is often defeated by conductive overburden (clay, saturated soil) that attenuates the radar signal before it reaches the target depth, and resistivity surveys can be complicated by 3-D near-surface conductivity heterogeneity unrelated to the void. Microgravity is comparatively immune to these near-surface conductivity/permittivity complications and provides a direct, physically interpretable density-contrast measurement well suited to a quantitative engineering risk assessment.
Because the target residual anomaly from a small, shallow void can be only tens of microgal, the survey uses a dense station grid (spacing much smaller than the expected cavity depth/diameter) with very high-precision levelling — elevation control to millimetres, since a 1 mm elevation error corresponds to about 0.0003 mGal via the free-air correction, which matters at this signal level — and short, frequent loop closures to control drift and tide as described in Question 3. Because engineering sites are often close to structures, culverts and made ground, a careful terrain correction (and sometimes a "building correction" for nearby structural mass) is required.
The full standard reduction chain — tide, drift, latitude, free-air, Bouguer, and terrain corrections — is applied to obtain the Bouguer (or complete Bouguer) anomaly, after which regional-residual separation (Question 9) isolates the local void signature from the broader density trend of the site geology. The residual anomaly is then forward-modelled, typically as a sphere or horizontal cylinder of an assumed density contrast, to estimate plausible void depth and size, or a formal (regularized) inversion is run for a fuller 2-D/3-D density model.
Microgravity void detection has an inherently low resolving power for pinpointing exact void geometry — depth, size and density contrast trade off against one another in the forward/inverse model, a direct instance of the non-uniqueness discussed in Question 10 — so the modelled void geometry is never unique from gravity data alone. The survey can also be slow and labour-intensive (station-by-station precision levelling) compared with faster geophysical alternatives, and ambient/cultural noise from traffic and nearby structures can be significant at engineering sites. A repeat survey could be improved by tighter station spacing over any anomaly of interest, by adding gravity gradiometry (Question 5) for sharper shallow resolution, and by integrating complementary methods (GPR, resistivity, or a confirmatory borehole) to constrain the void's geometry independently and reduce the non-uniqueness that gravity alone cannot resolve.
