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.
Any measured gravity or magnetic field can be treated as a signal made up of a spectrum of spatial wavelengths — long wavelengths from deep, broad sources and short wavelengths from shallow, compact sources or cultural noise. When that continuous field is sampled at discrete stations, the sampling theorem (Nyquist criterion) requires the station interval Δx to satisfy Δx ≤ λmin/2, where λmin is the shortest wavelength present in the true field. If the interval is coarser than this, the short-wavelength energy is not merely lost — it is mis-recorded and reappears, folded back, as spurious LONGER-wavelength variation in the sampled data that was never really there. This folding-back is aliasing: a real short-wavelength anomaly and a fictitious long-wavelength one become indistinguishable once under-sampled, and no amount of processing after the fact can separate them because the information about which one was actually present is destroyed at the moment of sampling.
Because the shortest wavelength of interest is set by the shallowest, smallest target the survey is meant to resolve, aliasing forces station spacing and line spacing to be chosen from the TARGET, not from budget or logistics: a common rule of thumb is station spacing no coarser than about one target depth and line spacing no coarser than about twice the target depth, so that the anomaly's half-width (which scales with depth) is sampled at least twice. A survey designed with station spacing driven only by cost will alias any shallower/smaller feature than planned for into either noise or a misleading longer-wavelength "regional" appearance, corrupting later regional-residual separation (Question 9) and interpretation. The same logic applies across LINES: if line spacing is too coarse relative to the along-strike wavelength of a linear target (a dyke, a fault), the gridded/contoured map can show a spurious trend direction or miss the feature between lines entirely.
The same principle applies in time. Diurnal/tidal correction (Questions 2–3) assumes the temporal field varies smoothly and can be linearly interpolated between repeat-station ties; if the tie interval is too long relative to real short-period variation (geomagnetic micropulsations, a passing thunderstorm-induced field change, a brief magnetic sub-storm), that higher-frequency temporal signal aliases into the assumed-linear drift curve and is wrongly subtracted from — or wrongly left in — the station readings. Survey planning therefore also sets a maximum time between repeat ties (commonly 15–30 minutes) based on how active the temporal field is expected to be on the survey day, exactly mirroring the spatial Nyquist argument.
