


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
= g_{0} (1 +
k_{1} sin^{2} ϕ – k_{2} sin^{2} 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 sealevel 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 freeair reduction, from which freeair
anomalies are obtained; 2.
The Bouguer
reduction, which combined with the freeair 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 subsurface variations in density. Each known
effect is removed from observed data. First the various ‘corrections’ are
described, and then the presentation options are listed. Corrections Applied 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=45^{o}. Freeair correction: The
freeair 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 freeair 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 freeair
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.
Earthtides: 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 V^{2} where V is
speed in knots, α is heading, and φ is latitude. At midlatitudes,
it is about 7.5 mGal for 1 knot of EW motion. 
This website is hosted by
S. Farooq
Department of Geology
Aligarh Muslim University, Aligarh  202 002 (India)
Phone: 915712721150
email: farooq.amu@gmail.com