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.
A buried body's magnetization is (for the purely induced case) parallel to the Earth's ambient field, whose direction at any location is set by the inclination, I (the dip angle of the field from horizontal) and the declination, D (the azimuth from true north). Because a dipole's field depends on the angle θ between the observation point and the dipole axis (Question 2), and because what is actually measured at surface is the projection of the total anomalous field onto the ambient-field direction (for a total-field magnetometer), the SAME buried body produces a completely different-looking surface anomaly depending on I and D. Near the magnetic pole (I ≈ 90°), magnetization is essentially vertical and the anomaly is a simple, symmetric positive "bullseye" centred directly over the body. Near the magnetic equator (I ≈ 0°), magnetization is horizontal and the anomaly becomes an asymmetric positive/negative couplet straddling the body, with the peak offset well away from the true source location. At intermediate latitudes the anomaly is a skewed, asymmetric shape whose peak is displaced from the source in the up-dip (equatorward) direction.
This location-dependent skewing means the position of the anomaly's maximum is generally NOT directly above the causative body except very near the magnetic poles, so naively picking the peak to locate a target, or comparing anomaly shapes across a survey spanning a range of latitudes, or correlating a magnetic map directly with a geological map (which shows true body position), can all be misleading unless the field-direction effect is removed first.
Reduction to the pole (RTP) is a Fourier-domain filter that mathematically transforms the observed anomaly into the anomaly the same body would produce if it were surveyed at the magnetic pole (I = 90°), collapsing the skewed shape back to a symmetric bullseye centred over the source. Strength: greatly simplifies qualitative interpretation and correlation with geological structure. Weakness: the filter's amplitude spectrum is unstable (division by near-zero terms) at low magnetic inclination, so RTP becomes noisy and unreliable near the magnetic equator; it also assumes uniform, purely induced magnetization in one known direction, so it distorts anomalies from bodies with significant remanent magnetization (high Koenigsberger ratio, Question 1) in an unpredictable direction.
Reduction to the equator (RTE) is the low-latitude analogue, transforming data to the equivalent equatorial-field anomaly shape; it is numerically better-behaved at low inclination than RTP but is used less often because a symmetric couplet is a less intuitive shape to interpret visually than a bullseye.
Pseudo-gravity transformation converts the magnetic field into the gravity field that a body of proportional density (via Poisson's relation) would produce, which removes the dipolar 1/r³ skew and directional dependence altogether and yields a smoother, more geologically intuitive map (useful for joint interpretation with real gravity data). Weakness: it inherits the same instability at low inclination and the same purely-induced-magnetization assumption as RTP, since it is derived from the RTP field.
Analytic signal / total gradient methods combine the horizontal and vertical gradients of the field in a way that is mathematically independent of the direction of magnetization altogether, so no assumption about I, D, or remanence direction is required. Strength: works even where the magnetization direction is unknown or remanence-dominated, and remains stable at low latitude. Weakness: it only reliably locates the source edges/centre and gives a rough depth estimate; it does not reproduce the full, correctly-shaped anomaly the way RTP does, so it is complementary to, not a full replacement for, RTP.
