05-Geol-B10 · December 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-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 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, uniqueness/equivalent sources ch.5, Fourier-domain filters ch.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 first vertical derivative (VD, ∂T/∂z) is computed in the wavenumber domain by multiplying the Fourier transform of the total field by |k| — a linear high-pass filter. Advantages: it sharpens and resolves closely spaced or shallow sources by enhancing short-wavelength (near-surface) anomalies and suppressing long-wavelength regional signal, effectively performing much of the regional-residual separation (Question 9) as part of the enhancement step. Disadvantages: differentiation strongly amplifies high-frequency noise, so VD requires good data quality/gridding; and, being a directional derivative of the total field, its sign and anomaly shape still depend on the ambient field's inclination/declination and on the body's magnetization direction, so VD anomalies remain skewed at non-polar magnetic latitudes and complicated by remanence — the same interpretational ambiguity as the total field itself, only sharper.
The analytic signal amplitude (ASA) combines all three orthogonal field gradients in quadrature, |AS| = √[(∂T/∂x)² + (∂T/∂y)² + (∂T/∂z)²]. Advantages: this combination is INDEPENDENT of the direction of magnetization and of the ambient field's inclination/declination, so ASA peaks directly over (or at the edges of) the causative body regardless of whether the source is purely induced, remanence-dominated, or surveyed at a low magnetic latitude where total-field anomalies are heavily skewed — its major practical advantage. Disadvantages: ASA is always positive, discarding the sign/polarity information the VD retains, which reduces information useful for basic source-type discrimination; it tends to broaden and merge anomalies from closely spaced sources compared with VD; and, like VD, it amplifies high-frequency noise and needs good data quality.
Vertical derivative more appropriate: resolving two closely spaced, parallel thin dykes surveyed at moderate-to-high magnetic latitude in a shield terrane where remanence is minor and known — here preserving amplitude and sign helps separate the two individual dyke traces, which ASA would tend to smear together. Analytic signal amplitude more appropriate: outlining the edges of a magnetite-skarn body known or suspected to carry significant remanent magnetization, or any survey conducted near the magnetic equator where total-field/VD anomalies are strongly skewed and difficult to associate directly with the causative body's true location — ASA gives a direction-independent, reliably centred target outline in both situations.
