04-Geol-B10 · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 04-Geol-B10-1 Gravity and Magnetic Fields, 2017-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, gravity reduction and terrain correction ch.2; magnetometers and magnetic surveying ch.4–5; anomaly interpretation throughout); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (survey design, diurnal correction, case-history applications ch.6 & 7); Blakely, Potential Theory in Gravity and Magnetic Applications (potential-field theory, Fourier-domain filters, reduction-to-pole, non-uniqueness ch.2, 5, 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.
The physical property that controls the gravity method is bulk density, ρ (kg/m³ or g/cm³), because the measured quantity — the vertical component of the gravitational attraction of a subsurface mass — is directly proportional to the density of that mass relative to its surroundings (Question 6 develops this further for the sign of the anomaly).
The standard laboratory technique is the Archimedes immersion method. The sample is first weighed dry in air, Wair, then weighed suspended and fully submerged in water, Wwater. The loss of weight on immersion equals the weight of water displaced, so the sample's bulk volume is V = (Wair − Wwater)/(ρwaterg), and its bulk density follows as ρ = Wair/(Vg) = ρwater·Wair/(Wair−Wwater). Porous samples are first sealed (dipped in paraffin wax or wrapped) or saturated under vacuum before weighing, so that water does not infiltrate the pore space during the immersion step and bias the displaced-volume measurement.
The method is fast, cheap, requires only a balance and a beaker of water, and is non-destructive, so large numbers of core or hand samples can be measured routinely, and the same samples can afterwards be used for petrographic or geochemical work. Its principal weakness is representativeness rather than precision: a small hand sample may not capture the bulk in-situ density of the rock mass, particularly where the rock is fractured, vesicular, or has variable porosity/moisture saturation at outcrop scale — a dry, sealed lab sample of a normally water-saturated sandstone, for instance, understates its true field density. Weathered or friable samples can also lose material during handling, and a single hand sample cannot capture density heterogeneity across a lithologic unit, so lab measurements are best combined with downhole density logging or regional rock-property compilations for survey design and modelling.
| Material | Type | Typical density (g/cm³) |
|---|---|---|
| Granite | Rock (felsic intrusive) | 2.5–2.7 |
| Basalt | Rock (mafic extrusive) | 2.7–3.1 |
| Quartz | Mineral | 2.65 |
| Magnetite | Mineral | 5.0–5.2 |
For comparison, two examples of buried material relevant to engineering geophysics: an air-filled karst cavity or old mine working is effectively 0 g/cm³, and loose, uncompacted landfill waste is typically 1.0–1.5 g/cm³, both strongly negative-density-contrast targets against normal bedrock or soil (Question 6).
