04-Geol-B10 · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 04-Geol-B10-2 Electrical Methods, 2017-May. 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, about half an hour each".
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics, 2nd ed. (electrical properties of rocks ch.5; self-potential ch.6; induced polarization ch.9; resistivity ch.8; electromagnetic methods ch.7; magnetotellurics ch.10); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (resistivity arrays, EM systems, MT surveying, ch.8–9); Simpson & Bahr, Practical Magnetotellurics (MT instrumentation and robust/remote-reference processing, ch.2–6).
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.
Aliasing occurs whenever a continuously varying signal is sampled at a rate too coarse (in space or time) to capture its true variation: the Nyquist–Shannon sampling theorem states that a signal must be sampled at more than twice its highest significant frequency (or, spatially, more than twice per shortest wavelength present), or the under-sampled high-frequency content folds back and is mis-recorded as a false LOWER-frequency signal. It is a problem because an aliased dataset looks perfectly plausible — it does not obviously look like noise — yet it misrepresents the true field, and any interpretation (a modelled anomaly wavelength, a sounding depth, an inversion) built on it will be systematically wrong without any warning sign in the data itself.
A narrow, sub-vertical conductive dyke produces a sharp, narrow potential-field/EM anomaly whose "wavelength" is comparable to the dyke's width and depth. If station/line spacing is coarser than roughly half the anomaly's shortest significant wavelength (e.g. survey stations every 25 m over a dyke whose true anomaly is only ~20 m wide), the true peak may be missed entirely between stations, or the sampled points may be mis-assembled into a broader, smoother, mis-located false anomaly — classic spatial aliasing.
In an AC/EM survey energized at, say, a 60 Hz-adjacent frequency near strong power-line interference, or in a TDEM decay sampled with widely spaced time gates, the recorded transient/waveform can be aliased: 60 Hz power-line noise sampled below its own Nyquist rate (or beating against an instrument's sampling clock) can appear in the recovered data as a spurious low-frequency drift or oscillation that is easily mistaken for a real, slowly varying geological/EM decay signal rather than aliased line noise.
Spatially, station and line spacing must be chosen at or below half the shortest wavelength/feature size expected from the target (denser sampling for narrower/shallower targets), guided by a pre-survey estimate of target size and depth. Temporally, the data-acquisition sampling rate must exceed twice the highest frequency present in the true signal or in expected noise (an anti-alias low-pass analogue filter is applied before digitizing to remove content above the Nyquist frequency so it cannot fold back), and, for line noise specifically, synchronous/notch filtering or choosing a survey frequency well clear of 60 Hz and its harmonics avoids the problem at the source.
