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.
The tilt angle (or tilt derivative) is a normalized edge-detection transform defined as
$$\theta_{tilt} = \tan^{-1}\!\left(\frac{\partial T/\partial z}{\sqrt{(\partial T/\partial x)^{2}+(\partial T/\partial y)^{2}}}\right)$$
where T is the (usually reduced-to-pole) total-field anomaly, ∂T/∂z is its VERTICAL derivative and the denominator is the magnitude of its HORIZONTAL gradient. Because it is an arctangent of a RATIO of two derivatives of the same field, the tilt angle is bounded between −90° and +90° regardless of the source's magnetization intensity or depth — it self-normalizes anomaly amplitude out of the display entirely.
A raw total-field map is dominated visually by its largest-amplitude anomalies, so smaller or deeper (hence weaker) sources of real geological interest can be invisible next to a single strong anomaly on the same colour scale. The tilt angle is applied specifically to REMOVE this amplitude dependence, so that subtle, low-amplitude anomalies from smaller, deeper or weakly magnetic sources are displayed with the same visual weight as strong, shallow, highly magnetic ones.
Because θtilt is bounded and self-normalized, weak and strong anomalies alike are rendered on the SAME scale, revealing subtle features that a linear total-field colour stretch would compress into an indistinguishable background. The transform is also a useful semi-quantitative EDGE and DEPTH tool: for many simple source geometries, the θtilt=0° contour sits directly over (or very close to) the edge of the causative body, and HALF the horizontal distance between the θtilt=+45° and θtilt=−45° contours estimates the depth to the top of the source (the "tilt-depth" rule: for a vertical contact at depth zc, θtilt=±45° occurs at a horizontal offset of exactly ±zc from the contact, so the two contours are 2zc apart). The transform therefore doubles as both an enhancement display and a first-pass interpretation aid.
Because the tilt angle involves taking derivatives of the field — a HIGH-PASS operation — it strongly amplifies high-wavenumber NOISE in the original data, so a noisy or under-sampled survey produces a visually "busy," speckled tilt-angle map with spurious zero-crossings that do not correspond to real geological edges; the input grid typically needs careful noise suppression or upward continuation before the transform is applied. The depth-estimation rule of thumb also assumes a simple, isolated, near-vertical-sided source; where anomalies from several nearby sources interfere, or the source has a dipping or irregular geometry, the zero-contour position and the ±45° half-separation depth rule can both be misleading.
