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.
Any measured gravity or magnetic anomaly is a superposition of a broad, smoothly varying regional component — contributed by deep or laterally extensive geological structure such as basement topography or crustal-scale density/susceptibility variation — and a narrower residual (or local) component contributed by the shallower, smaller feature actually being investigated. Regional-residual separation is the process of estimating and removing the regional component so the residual, which carries the target signal, can be reliably mapped and interpreted. It is necessary because exploration and engineering targets are almost always local features superimposed on a regional trend that is comparable to, or larger in amplitude than, the target's own anomaly; without removing it, the target signal is masked, distorted in shape, or mis-located, and cannot be reliably inverted for depth or size.
A low-order polynomial surface z = f(x,y) is fit to the observed, gridded field by least squares and taken to represent the smoothly varying regional. A first-order surface is a plane, z = a + bx + cy; a second-order surface adds curvature, z = a + bx + cy + dx² + exy + fy²; the coefficients a, b, c, ... are found by minimizing the sum of squared differences between the fitted surface and every observed grid value. The fitted regional surface is then subtracted point-by-point from the observed field, leaving the residual grid, which is contoured and interpreted as the local (target) anomaly. The polynomial order is chosen to match the expected complexity and spatial scale of the true regional: too low an order leaves regional structure behind in the "residual" (under-fitting), while too high an order lets the fitted surface bend to follow part of the true local anomaly as well, artificially suppressing it — a well-known failure mode called regional leakage — so the order is usually chosen as the lowest that adequately captures the broad-scale trend seen away from the target of interest.
Related techniques achieve the same separation by filtering rather than curve-fitting: wavenumber-domain low-pass filtering isolates the regional (long-wavelength) content directly, with its high-pass complement giving the residual; and upward continuation — mathematically continuing the field to a higher observation elevation — attenuates short-wavelength (shallow-source) content faster than long-wavelength (deep/regional) content, so subtracting the upward-continued field from the original observed field also yields an approximate residual.
