Question 5 of 10: Gravity Meter Principles and Gravity Gradiometry

Question 5: Gravity Meter Principles and Gravity Gradiometry (Choose 6 of 10 – equal value)

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.

Part (i) — the zero-length-spring relative gravimeter

The most common exploration gravity meter is a relative (not absolute) instrument built around a zero-length spring: a coil pre-stressed during manufacture so its tension is proportional to its total length rather than its extension beyond a natural length — i.e. its effective unstretched length is zero. Supporting a small mass on a hinged beam with such a spring makes the restoring torque exactly proportional to the beam angle θ itself, which is the condition for the beam's natural period to become very long at the balance point, giving extreme sensitivity (of order 0.01 mGal) in a compact, portable, temperature-compensated package (the LaCoste–Romberg design and its descendants). The operator levels the instrument, then turns a calibrated micrometer screw until the beam returns to a fixed null position viewed through cross-hairs (a null, not a deflection, reading), and the dial value is converted to milligals via the instrument's calibration table. Because this measurement senses only the CHANGE in spring tension needed to re-null the beam between stations, it reads only relative gravity differences, not the absolute field; converting to absolute gravity at every station requires tying the survey, through a loop, to a station of independently known absolute gravity, itself established with a genuinely absolute instrument — a free-fall (or rise-and-fall) laser-interferometer gravimeter such as an FG5, which measures the ENTIRE field directly from a falling object's measured acceleration and needs no external reference.

Part (ii) — the gravity gradiometer

A gravity gradiometer measures not the gravitational field itself but its spatial derivatives — the components of the gravity gradient tensor (e.g. G_zz = ∂g_z/∂z), typically using pairs of differential accelerometers on a rotating disk (full-tensor gradiometry, FTG) that cancel common-mode platform accelerations while retaining the differential gravitational signal, historically developed for airborne/marine naval applications and now widely used in airborne mineral and petroleum exploration.

Advantages: because the gradient of a compact source's field falls off one power of distance faster than the field itself (1/r³ versus 1/r² for a point mass), gradiometry sharpens and better localizes shallow, compact targets and improves discrimination between closely spaced sources; it is also inherently less sensitive to distant/deep regional gravity (which varies slowly, so its gradient is small), reducing the regional-residual separation burden (Question 9); and because gradiometry is a differential measurement referenced to the platform itself rather than to a fixed base station, it does not suffer the same drift-versus-base-station problem as conventional gravimetry, making it well suited to fast airborne surveying.

Disadvantages: the instrumentation is complex, expensive and historically specialized/limited in availability; processing and interpreting a full tensor of gradient data requires more sophisticated software than a scalar field; the steeper 1/r³ decay that sharpens shallow targets also means the instrument is comparatively insensitive to larger, deeper sources, giving reduced depth of investigation for a given noise floor; and gradiometers, being differential accelerometer systems, are especially sensitive to platform vibration and angular acceleration noise, demanding careful stabilization and post-processing.