Question 4 of 10: The Zero-Length-Spring Gravimeter — Principle, Reading, Drift and Calibration

Question 4: The Zero-Length-Spring Gravimeter — Principle, Reading, Drift and Calibration (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.

Principle of the zero-length spring

An ordinary spring has finite unstretched length: to support a mass at angle θ on a hinged beam, the restoring torque is a nonlinear function of θ, so the instrument's sensitivity (period of oscillation, or displacement per unit change in g) varies strongly with the operating point — a design that is impractical to make sensitive over a useful range. A zero-length spring is manufactured (by pre-stressing the coil during winding) so that its tension is proportional to its total length rather than its extension beyond a natural length — i.e. its effective unstretched length is zero. When such a spring supports a mass on a hinged beam, geometry makes the restoring torque exactly proportional to the beam angle θ itself (not to sinθ or a more complex function), which is the condition for the beam's natural period to become very long (formally infinite for an idealized zero-length spring) at the balance point. This gives the LaCoste–Romberg-type gravimeter an extremely high sensitivity to small changes in gravity (of order 0.01 mGal) in a small, portable, temperature-compensated package.

Taking a reading

The gravimeter is levelled over the station using its bubble levels, then the operator turns a calibrated micrometer screw that adjusts the spring's tension until the beam returns to a fixed reference (null) position, viewed through an eyepiece against cross-hairs; this is a null (nulling) method, not a direct deflection reading, because operating always at the same null position avoids the nonlinearity that would otherwise exist away from that point. The micrometer dial reading is converted to milligals via the instrument's calibration constant/table. Several repeat readings are taken and averaged, and the operator also gently taps the instrument before each reading to overcome any static friction ("beam sticking") in the mechanism.

Monitoring instrument drift

All spring gravimeters exhibit slow instrumental drift (creep in the spring material) superimposed on the much larger, predictable Earth-tide variation. Drift is monitored the same way diurnal variation is monitored in magnetics: the survey is run as a series of loops that start and close at a base station (or at previously occupied stations) at known time intervals, typically within an hour or two; because the tidal component is calculable, the residual difference between the first and second reading at the closure station, after removing the calculated tide, is attributed to linear instrument drift and apportioned across the intervening stations in proportion to elapsed time.

Calibration to absolute gravity

A gravimeter measures only relative gravity differences (differences between stations, or between a station and a fixed reference), because the physical constant that would be needed to interpret the beam angle in absolute mGal is not independently known to the required precision. Absolute gravity is introduced into the network by tying the survey, through at least one loop, to a station with an independently known absolute value — historically the IGSN71 international gravity standardization network, or today a national base station whose value was established directly with an absolute (free-fall or rise-and-fall) gravimeter such as an FG5. Every other station's absolute gravity then follows by summing the calibrated relative differences read along the survey loops back to that known base. The manufacturer's calibration table/constant (established by reading the instrument across a precisely known gravity range, e.g. a calibration line with independently known gravity values at each end) converts dial units to mGal and corrects for the spring's slight departure from perfect linearity over large ranges.