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 International Geomagnetic Reference Field (IGRF) is a mathematical model of the Earth's main (core-generated) field, expressed as a truncated spherical-harmonic (Gauss coefficient) series, produced and updated every five years by the International Association of Geomagnetism and Aeronomy (IAGA). It is estimated by collecting candidate coefficient sets from many research groups worldwide, each derived from a global network of magnetic observatories together with satellite magnetic-survey data (e.g. Swarm, and historically Ørsted/CHAMP), and combining these candidates into a single consensus model for the current epoch plus a predictive secular-variation (SV) term describing how the coefficients are expected to change over the following five years. The field at any point and time within an epoch is then calculated by evaluating the spherical-harmonic series (truncated at degree/order 13 for the main-field part) with the coefficients linearly extrapolated forward from the epoch value using the SV term.
Every IGRF epoch is, at the time of its release, provisional for the years at and beyond the current release, because it relies on a predicted secular-variation term for years that have not yet happened. Once enough real, retrospective observatory/satellite data become available for a past epoch, IAGA re-derives and locks in a final, no-longer-revised set of coefficients for that epoch, which is then re-designated the Definitive Geomagnetic Reference Field (DGRF) for that period. In short: IGRF is the forward-looking, SV-predicted (and therefore slightly uncertain) version of the model; DGRF is the finalized, retrospectively-fitted (and therefore more accurate) version of the same epoch once its true secular variation is known.
The IGRF/DGRF main-field value at the survey location and date is subtracted from every raw total-field magnetic reading to isolate the crustal/anomalous field that is actually of geological interest — the main field's amplitude (tens of thousands of nT) is orders of magnitude larger than typical crustal anomalies (tens to a few thousand nT), so an inaccurate or wrong-epoch reference model can introduce an error comparable to, or larger than, the anomaly itself. Getting this right matters most (1) when comparing or merging surveys flown at different times, since the main field has secularly drifted between them and each must be corrected with the model appropriate to its own date; and (2) when reprocessing an older survey for which a DGRF has since been finalized, since using the (less accurate, SV-predicted) original IGRF instead of the now-available DGRF for that epoch introduces an avoidable systematic error into the anomaly map.
