04-Geol-B10 · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 04-Geol-B10-1 Gravity and Magnetic Fields, 2017-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 and terrain correction ch.2; magnetometers and magnetic surveying ch.4–5; anomaly interpretation throughout); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (survey design, diurnal correction, case-history applications ch.6 & 7); Blakely, Potential Theory in Gravity and Magnetic Applications (potential-field theory, Fourier-domain filters, reduction-to-pole, non-uniqueness ch.2, 5, 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.
A sun-shaded (or "sun-angle", "hill-shaded") image applies an artificial oblique illumination to a gridded gravity or magnetic dataset, exactly as a hillshade is computed from a topographic digital elevation model: the grid is treated as a synthetic surface, and a simulated light source at a chosen azimuth and elevation angle is used to compute apparent shading (brighter where the "surface" slopes toward the light, darker where it slopes away), producing a shaded-relief-style rendering of what is really a geophysical field, not real topography.
The shading creates strong local contrast (highlight/shadow) along even very subtle gradients in the field that would be nearly invisible on a standard colour or contour map, dramatically enhancing the visibility of short-wavelength, high-frequency texture and LINEAR trends — faults, fracture sets, dyke swarms, lithological contacts — that align across many grid cells and so produce a coherent shadow/highlight pattern, effectively acting as a form of edge and fabric enhancement without any numerical filtering of the data values themselves.
The technique is cheap and fast to compute, requires no assumptions about magnetization direction or density, works on any gridded field, and multiple illumination azimuths can be generated quickly to explore fabric in different orientations. Its principal disadvantage is a strong directional bias: linear features oriented PARALLEL to the illumination azimuth cast no shadow and are suppressed or invisible, so a single sun-angle image can miss real structure and must be paired with at least one other azimuth (commonly orthogonal) to characterize the full fabric. It is also purely a QUALITATIVE visualization aid — it enhances the visual appearance of gradients but does not itself produce any quantitative measure (depth, physical property, edge location) that can be extracted from the image alone, and an inexperienced interpreter can over-read shading artefacts (grid noise, interpolation artefacts) as genuine geological lineaments.
The horizontal and vertical derivatives (first or second order) sharpen the response of shallow sources and steepen edges but simultaneously amplify high-frequency noise, requiring care with data quality. The analytic signal (Question 7) produces a magnetization-direction-independent measure that peaks over source edges regardless of remanence, useful where magnetization direction is uncertain. The tilt derivative (arctan of the vertical derivative over the horizontal gradient magnitude) is self-normalizing, giving comparably strong edge responses over both weak and strong sources, which a raw derivative does not. Upward continuation suppresses shallow noise and near-surface texture to emphasize deeper, regional sources, at the cost of resolution. Horizontal gradient magnitude peaks directly over density/susceptibility contacts, giving a direct, quantitative edge-location tool. All derivative-based filters share the general trade-off that boosting high-wavenumber content for enhancement also boosts high-wavenumber NOISE, so the choice and order of filter must be balanced against the data's actual signal-to-noise ratio, and none of these qualitative/semi-quantitative enhancements substitutes for true forward or inverse modelling (Question 10) when an actual physical-property model is required.
