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.
Station spacing and line spacing are set by the expected depth/size of the target, following the same aliasing logic as Question 1. Because gravity reduction is elevation- and position-sensitive (unlike magnetics), planning must also secure a method of precise station levelling/positioning (differential GNSS or spirit-levelling to the accuracy needed for the free-air correction, ~0.3086 mGal per metre of elevation error) and, where terrain is rugged or structures are nearby, a digital elevation model or field terrain survey for the terrain correction. A base station is selected in a stable, accessible, magnetically/vibrationally quiet location and tied, through at least one loop, into a regional absolute-gravity network so the survey's relative readings can be converted to absolute gravity. Loops are planned so that each closes back to a tie point within roughly one to two hours, short enough that instrument drift over the loop stays close to linear.
The instrument is read at each station following the loop plan, with station coordinates, elevation and reading time logged at every point (time is essential for the drift/tide correction below). The gravimeter is protected from shock in transport (a "tare," or sudden offset in the reading, can occur from a jolt and must be caught by loop closure) and levelled carefully at every station since even a small tilt error corrupts the reading. Vehicles and personnel are kept clear of stations during reading to avoid local mass effects.
Two distinct effects change a gravimeter's reading with time even at a perfectly fixed station: the solid-earth (and ocean-loading) tide, a real, calculable semi-diurnal/diurnal variation of amplitude up to about 0.3 mGal caused by the Sun's and Moon's gravitational attraction on the Earth itself, and instrumental drift, a slow, essentially linear creep of the spring material with time. Because the tide is calculable in closed form (e.g. by Longman's formula) from the station's latitude/longitude and the reading time, it is computed and subtracted first, exactly as for any other station and instant. What remains at a repeated (loop-closing) station is attributed to instrument drift: the residual difference between the first and second, tide-corrected reading at the same point, divided by the elapsed time, gives a drift rate that is then apportioned linearly across the intervening stations in proportion to their own elapsed time since the loop start — the same loop-closure logic used for magnetic diurnal correction in Question 2, but with the (separately calculable) tide removed first.
