Question 2 of 10: The Gravity Method — Physical Laws, Instrumentation and Corrections

Question 2: The Gravity Method — Physical Laws, Instrumentation and Corrections (16.66% of paper)

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.

Physical laws. The gravity method rests directly on Newton's law of universal gravitation, $F=Gm_1m_2/r^2$, which for a test mass at the Earth's surface gives the familiar gravitational acceleration $g=GM_{\oplus}/R_{\oplus}^2\approx9.8\text{ m/s}^2$. Because the exploration signal of interest is a tiny perturbation on this large background value, the practical unit is the milliGal, $1\text{ mGal}=10^{-5}\text{ m/s}^2$, roughly one part in a hundred million of $g$. A buried body of anomalous density $\Delta\rho$ produces an excess (or deficit) gravitational attraction that superposition adds linearly to the regional field, so the gravity method is fundamentally a superposition problem: every observed reading is the sum of the Earth's normal field, a slowly varying regional trend, and the local anomaly of interest.

Instrument and measurement. The workhorse relative instrument is a spring (LaCoste–Romberg-type, zero-length-spring) gravimeter: a small mass is suspended on a precisely engineered spring inside a temperature-stabilized housing, and the operator uses a micrometer screw to null the beam back to a reference position, reading the applied restoring torque as a dial reading that converts, via a calibration constant, to a gravity DIFFERENCE relative to a base station. The instrument is levelled and read at each station for several tens of seconds to average out microseismic noise, and every survey loop returns periodically to the base station to allow drift and tide removal (below).

Relative vs. absolute measurement. A relative gravimeter measures only the DIFFERENCE in $g$ between two points; it must be tied to at least one station of known absolute value and requires periodic recalibration because its spring's elastic properties creep over time. An absolute gravimeter instead measures true $g$ directly, most commonly by timing the free fall of a retroreflecting corner cube in a vacuum chamber with a laser interferometer and an atomic clock — distance and time are both directly traceable to physical standards, so the result needs no calibration constant and suffers no drift, at the cost of a much larger, slower and more expensive instrument.

Earth tides. Yes — at a target accuracy of 0.01 mGal, solid-earth (and ocean-loading) tides absolutely must be corrected. The Sun and Moon's gravitational attraction, modulated by the Earth's own elastic yielding, produces a periodic variation in observed $g$ with a semi-diurnal (roughly 12-hour) period and an amplitude on the order of 0.2–0.3 mGal — twenty to thirty times larger than the requested 0.01 mGal accuracy — so an uncorrected tidal signal would completely swamp any genuine exploration anomaly of comparable or smaller amplitude. The correction is computed from a well-established astronomical tidal model (station latitude/longitude and time of observation are the only inputs needed) and subtracted from every reading; modern gravimeters commonly apply this correction automatically in real time.

Drift correction procedure. Instrument drift (slow creep of the spring's zero point, distinct from the periodic tidal signal) is removed by returning to a fixed base station at intervals through the survey day (e.g. every 1–2 hours) and re-reading it. Because the base station's true value never changes, any change recorded between successive base-station visits (after tide correction) is attributed entirely to drift, and is assumed to accumulate LINEARLY with elapsed time between the two visits. Each intervening field station's reading is then corrected by subtracting the linearly interpolated drift value appropriate to the time it was occupied, which removes the instrument's own slow creep and leaves only the tide-corrected, drift-free relative gravity value at each station, ready for the further latitude, free-air, Bouguer and terrain corrections needed to isolate the anomaly of interest.