18-Geol-B10 · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 18-Geol-B10-1 Gravity and Magnetics Fields, 2019-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, drift and tidal correction ch.2; magnetometers, gradiometers and magnetic surveying ch.4–5; anomaly enhancement and interpretation throughout); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (survey design, temporal-variation correction, case-history applications ch.6 & 7); Blakely, Potential Theory in Gravity and Magnetic Applications (potential-field theory, derivative and Fourier-domain filters, regional-residual separation 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.
An observed potential-field anomaly (gravity or magnetic) at any point is the SUPERPOSITION of the fields of ALL subsurface sources, at every depth. Regional–residual separation is the process of decomposing that observed field into a smoothly-varying regional component, attributed to broad, deep or distant sources (regional geological structure, crustal-scale density/susceptibility variation), and a shorter-wavelength residual component, attributed to the shallower, more localized sources actually of interest (an ore body, a cavity, a fault). It is necessary because the regional field, though geologically real, is not the target of the investigation and its amplitude can be comparable to or larger than the local anomaly, so without removing it the local target's shape, amplitude and even its presence can be misread.
Graphical/manual smoothing: an experienced interpreter draws a smooth regional trend by eye through a profile or map, guided by known regional geology; simple but SUBJECTIVE and difficult to reproduce. Polynomial trend-surface fitting: a low-order (typically 1st–3rd degree) polynomial surface is fitted to the whole grid by least squares; the fitted surface is taken as the regional and the fit residuals as the local anomaly — objective and repeatable, but the chosen polynomial order strongly affects the result and a real local high or low near the map edge can bias the fit. Moving-average / spatial filtering: the regional is estimated as a spatial low-pass (running-average) filter of the grid over a window comparable to or larger than the target's expected wavelength; the residual is the original grid minus this smoothed version — equivalent in spirit to a wavenumber (Fourier) high-pass filter, and indeed can be implemented directly in the FREQUENCY domain by suppressing the lowest wavenumbers. Upward continuation: mathematically projecting the observed field to a higher elevation attenuates short-wavelength (shallow-source) content faster than long-wavelength (deep-source) content, so the upward-continued field approximates the regional directly, and can then be subtracted from the original (observed-level) field to isolate the residual. Second vertical derivative: taking the second vertical derivative of the field strongly enhances short-wavelength content and suppresses the regional automatically, at the cost of amplifying noise, similar in spirit to the tilt-derivative approach of Question 7.
All of these methods assume that regional and local sources occupy genuinely DIFFERENT characteristic depths (and hence different characteristic wavelengths in their surface anomalies), so that a spatial-frequency-based separation is geologically meaningful rather than arbitrary; that the fields of regional and local sources add LINEARLY (a direct consequence of potential-field superposition, always true for gravity/magnetics); and that the regional field varies SMOOTHLY across the survey area relative to the local target's own spatial scale, so that a low-order polynomial, wide moving-average window, or modest upward-continuation height can faithfully represent it without also removing part of the local signal of interest.
