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.
Computed in the wavenumber domain by multiplying the Fourier transform of the grid by |k| (equivalent to differentiating with respect to depth/height), the first vertical derivative sharpens anomalies, narrows their width so that closely spaced sources are better separated, and shifts the anomaly peak to sit more directly over steeply dipping or near-vertical edges. It assists interpretation by improving resolution of shallow, near-surface features and structural trends (faults, contacts, dykes), but hinders it by strongly amplifying high-wavenumber noise, so it requires reasonably clean, well-gridded data and is less useful for identifying deep, broad (regional) sources, which it suppresses.
This filter mathematically recomputes the field as though it had been measured at a greater height above the source (multiplying the Fourier transform by e-2π|k|Δz), which preferentially attenuates short-wavelength (shallow-source, high-wavenumber) signal relative to long-wavelength (deep-source, regional) signal. It assists interpretation by isolating the regional/deep-source trend for regional-residual separation and by acting as a natural, physically-based low-pass noise filter. It hinders interpretation of shallow targets, since it is precisely those anomalies that it removes.
The inverse operation, multiplying by e+2π|k|Δz, projects the field closer to the source, sharpening and amplifying shallow anomalies and improving resolution of near-surface targets. It assists interpretation of shallow sources by boosting their relative signal, but it is the most noise-sensitive of all the standard filters (it amplifies high wavenumbers exponentially) and becomes numerically unstable if continued past the depth of the source itself, so it hinders interpretation whenever the data are noisy or the continuation distance is not well constrained.
Defined as the arctangent of the vertical derivative divided by the total horizontal derivative, tilt = arctan(∂F/∂z ÷ |∇hF|), the tilt derivative is self-normalizing: its value is bounded between ±90° regardless of anomaly amplitude, and its zero-contour sits almost exactly over the edge of a vertical-sided source. It strongly assists interpretation because both weak, deep anomalies and strong, shallow anomalies appear with comparable, mappable amplitude on the same display (unlike a raw derivative, which is dominated by the strongest anomalies), making it excellent for structural/lineament mapping across an area with widely varying anomaly strength. It can hinder quantitative work, however, since the amplitude no longer carries direct information about the source's physical property or depth once it has been normalized away.
The gridded surface is illuminated computationally from a chosen azimuth and elevation as though it were topographic relief, producing shadow-and-highlight shading that dramatically emphasizes subtle gradients and lineaments trending across the illumination direction. It assists visual (qualitative) recognition of faults, fabric and structural trends, especially subtle ones invisible on a plain contour or colour map, but it hinders interpretation by suppressing features that trend parallel to the illumination azimuth (they cast no shadow) and by not preserving true anomaly amplitude, so it must always be used alongside, not instead of, a conventional colour/contour map, and often with more than one illumination azimuth to avoid missing trend-parallel structure.
