04-Geol-B10 · May 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-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".
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, Fourier-domain filters, reduction-to-pole ch.2, 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 proton-precession magnetometer measures total field magnitude using nuclear magnetic resonance in a hydrogen-rich fluid (e.g. kerosene or water) held in a sensor coil. In the polarizing phase, a strong DC current is passed through the coil, generating a magnetic field roughly 100 times the Earth's field; this aligns (polarizes) the magnetic moments of the hydrogen protons, whose spins otherwise precess about the ambient field but are randomly oriented in azimuth. The polarizing current is then abruptly switched off. Freed from the strong artificial field, the proton spins precess about the (now dominant) ambient Earth's field like a spinning top precessing about gravity, at the Larmor frequency:
$$f = \dfrac{\gamma_p}{2\pi}\,B$$
where γp is the proton's gyromagnetic ratio (a precisely known atomic constant) and B is the total ambient field magnitude. This coherent precession induces a small, decaying AC voltage in the same coil (now used as a receiver), whose frequency is measured very precisely (protons precess at about 42.6 Hz per 1000 nT) and converted directly to B through the known constant γp. Because the reading depends only on a frequency measurement against an atomic constant, no orientation of the sensor is needed (it measures scalar total field, not a vector component) and the instrument needs no field calibration — it is inherently absolute.
A gradiometer uses two (or more) magnetic sensors mounted on a fixed, known baseline (vertically or horizontally separated, typically 0.5–2 m) and outputs the difference between the two simultaneous readings divided by the separation — i.e. it measures the spatial gradient of the field rather than the field itself.
Advantages: because both sensors experience essentially the same diurnal variation and regional field at the same instant, subtracting them cancels the time-varying diurnal field and much of the regional field automatically, removing the need for a base station and its associated corrections; the gradient signal also falls off faster with depth than the total field itself, which sharpens and better resolves small, shallow targets and improves lateral resolution/separation of closely spaced sources.
Disadvantages: the same faster fall-off with distance that sharpens shallow targets makes the gradiometer comparatively insensitive to deep sources, so it is a poor tool for regional/deep exploration; the gradient (a small difference of two similar large numbers over a short baseline) is intrinsically noisier and more sensitive to small sensor mis-orientation, mis-levelling or timing error between the two sensors than a single total-field reading; and the instrumentation (two synchronized, closely matched sensors on a rigid boom) is more costly and less convenient to deploy, especially over rough terrain.
