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 Bouguer slab correction removes the attraction of an assumed infinite, flat horizontal slab of rock of density ρ and thickness h (the station's height above datum), BC = 2πGρh, subtracted from the observed reading to reduce it to datum. This idealization is exact only where topography really is flat and horizontal around the station; real topography (a nearby hill or valley) departs from the flat slab and introduces an error that the terrain (topographic) correction must separately remove.
The nearby hill's mass rises above the station's own elevation, so it lies entirely outside the flat slab the Bouguer formula assumes (that slab only extends up to the station's height). This extra mass attracts the gravimeter's test mass toward itself — up and to the side — and the UPWARD component of that attraction directly opposes true (downward) gravity, so the raw reading recorded at the station is smaller than it would be in the absence of the hill. Since the standard Bouguer slab correction does not know about, and cannot remove, an effect from mass ABOVE the station elevation, the Bouguer-corrected value inherits this reduction and reads too low.
Here the flat Bouguer slab implicitly assumes rock is present at the station's own elevation extending outward in all directions — including over the valley, where in reality that rock is absent. If that missing rock WERE present, its attraction on the station (located down and to the side of the station, since it is below station elevation) would have a downward component, adding to the measured gravity. Because it is absent, the raw reading is smaller than the ideal flat-slab formula assumes, and the standard Bouguer reduction — again, blind to nearby relief — passes this deficit straight through, so the corrected value again reads too low.
Although the physical cause is opposite in each case (excess mass above the station vs. missing mass below/beside it), both effects reduce the raw reading below what the idealized flat slab predicts, so in BOTH cases the terrain (topographic) correction that must be applied on top of the Bouguer slab correction is positive — it always adds to, never subtracts from, the Bouguer-corrected value. This is the well-known result that the terrain correction is always positive, regardless of whether the surrounding relief is a hill or a valley.
