Reduction of Gravity Data
Recall that, if the Earth were an homogeneous ellipsoid, the value of gravity at the surface would be given by:
g = g0 (1 + k1 sin2 ϕ – k2 sin2 2ϕ)
The objective of gravity surveys is to look for deviations from this reference value. In actual practice, gravity measurements are usually not made on the reference ellipsoid. Hence corrections are required to be made, in that measured gravity must be reduced to sea-level equivalent. This allows the recognition of an anomaly by subtracting the value for normal gravity from the actual measured value. Reductions made to observed gravity are done in a number of ways:
1. The free-air reduction, from which free-air anomalies are obtained;
2. The Bouguer reduction, which combined with the free-air reduction and terrain corrections, leading to Bouguer anomalies; and
3. The isostatic reduction, which leads to isostatic anomalies.
Some other corrections may also be made to observed gravity where needed. These include corrections for moving platforms, for terrain, for earth curvature, for earth tides, and for assumed geological structures.
Ideally, anything that is left over is the result of density inhomogenities due to local geology and perhaps of local exploration interest.
The diagram above is a conceptual flow chart for the gravity correction process.
The goal of data reduction is to remove the known effects caused by predictable features that are not part of the ‘target’. The remaining anomaly is then interpreted in terms of sub-surface variations in density. Each known effect is removed from observed data. First the various ‘corrections’ are described, and then the presentation options are listed.
Drift correction: Correction for instrumental drift is based on repeated readings at a base station periodically throughout the day. The meter reading is plotted against time (Fig. 1), and drift is assumed to be linear between consecutive base readings. The drift correction at time t is d, which is subtracted from the observed value.
Latitude correction: The earth's poles are closer to the centre of the equator than is the equator. However, there is more mass under the equator and there is an opposing centrifugal acceleration at the equator. The net effect is that gravity is greater at the poles than the equator.
For values relative to a base station, gravity increases as you move north, so subtract 0.811 sin(2a) mGal/km as you move north from the base station. (where a is latitude).
The maximum correction values will be 0.008 mGal / 10 cm, which occurs at a=45o.
Free-air correction: The free-air correction (FAC) corrects for the decrease in gravity with height in free air resulting from increased distance from the centre of the Earth, according to Newton’s Law. To reduce to datum an observation taken at height h (Fig. 1(a) is given by:
FAC = 0.3086 h mgal (h in metres ),
The FAC is positive for an observation point above datum to correct for the decrease in gravity with elevation. The free-air correction accounts solely for variation in the distance of the observation point from the centre of the Earth; no account is taken of the gravitational effect of the rock present between the observation point and datum.
Bouguer correction: This corrects the free-air value to account for material between the reference and measurement elevations. If you are further above the reference, there is more material (effect is greater), so subtract 0.04191 h× d mGal (h in metres, d in g/cc) from the reading. The derivation involves determining the effect of a point, then integrating for a line, then again for a sheet, and finally for a slab.
In the equation for the Bouguer correction, density, d, must be estimated; this can be done if the material is known, or by using a "crustal" value of 2.67 g/cc. Alternatively, trial and error can be used to find the density that causes the data to least reflect the patterns of topography.
Topography, or terrain correction: The terrain corrections take undulations of topography into account. Topographic variations results in the upwards attraction of hills above the plane of the gravity measuring station and valleys below, which decrease the observed value of gravity. Both these effects must therefore be added to readings to correct for topography. Manually correcting for the effects of topography involves the use of a ‘Hammer chart’ and tables. This approach, although very accurate, is too time consuming. More modern methods require software that makes use of digital terrain models (DTM) available from third party sources.
Earth-tides: Tidal variations are slow enough that, for most surveys, they are handled as part of the drft corection; i.e. by recording values at a base station every few hours.
Eötvös correction: This is the correction necessary if the instrument is on a moving platform, such as a ship or aircraft. It accounts for centrifugal acceleration due to motion on the rotating earth. The relation is:
EC = 7.503 x V x sin(α) cos(φ) + 0.04154 x V2
where V is
speed in knots, α is heading, and φ is latitude. At mid-latitudes,
it is about 7.5 mGal for 1 knot of E-W motion.
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