18-Geol-B10 · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 18-Geol-B10-1 Gravity and Magnetics Fields, 2019-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, drift and tidal correction ch.2; magnetometers, gradiometers and magnetic surveying ch.4–5; anomaly enhancement and interpretation throughout); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (survey design, temporal-variation correction, case-history applications ch.6 & 7); Blakely, Potential Theory in Gravity and Magnetic Applications (potential-field theory, derivative and Fourier-domain filters, regional-residual separation 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.
To first order the Earth's main field is that of a geocentric dipole tilted about 10° from the rotation axis; its behaviour is easiest to describe in terms of MAGNETIC latitude λm (latitude measured from the dipole's own equatorial plane). For a dipole field the total intensity and inclination both depend only on λm:
$$F(\lambda_m) = F_{eq}\sqrt{1+3\sin^{2}\lambda_m}, \qquad \tan I = 2\tan\lambda_m$$
where Feq is the field strength at the magnetic equator and I is inclination (the dip angle of the field vector below horizontal).
| Location | Total field F | Inclination I |
|---|---|---|
| Magnetic equator | ≈ 30,000–35,000 nT | 0° (horizontal) |
| North magnetic pole (Arctic Canada) | ≈ 55,000–60,000 nT | +90° (vertical, field points DOWN into the ground) |
| South magnetic pole (Antarctic margin) | ≈ 60,000–70,000 nT | −90° (vertical, field points UP out of the ground) |
The two poles are not exactly equal in intensity because the real field is not a perfect geocentric dipole: the southern polar region carries a somewhat stronger total field than the northern one, and the offset, non-axial part of the field is also why the geomagnetic poles are not antipodal. The dipole model nevertheless captures the dominant behaviour — a roughly two-fold rise in intensity from equator to either pole and a sign reversal of inclination between the northern and southern hemispheres.
The roughly two-fold increase in intensity from equator to pole follows directly from the √(1+3sin²λm) factor above: evaluating it at λm=0° and ±90° gives a factor-of-2 ratio (√1 vs √4), consistent with these typical field-strength ranges.
Magnetic declination, D, is the horizontal angle between geographic (true) north and magnetic north — the direction a compass needle actually points — measured positive EAST of true north. Declination arises because the geomagnetic pole is offset from the geographic pole and, more importantly, because the field's true, complex (non-dipole) structure and its ongoing secular variation cause the direction of the horizontal field component to vary substantially and irregularly from place to place and slowly drift with time at any one place, which is why every topographic map and compass survey must quote both the value AND the date to which it applies.
| Location (approximate) | Typical declination (2019) |
|---|---|
| Eastern Canada (e.g. Nova Scotia) | ≈ −17° (17° W) |
| Western Canada (e.g. British Columbia) | ≈ +15° to +18° (E) |
| Central USA / Mississippi valley | ≈ 0° (agonic line) |
| Western Australia | ≈ −1° to −3° (W) |
