


Derivation of FreeAir
and Bouguer Gravity Anomaly Maps Gravity anomalies are differences between the observed
acceleration of the earth’s (or any planet's) reaction to gravity and a value
predicted from a model. A location with a positive anomaly exhibits more
gravity than predicted, while a negative anomaly exhibits a lower value than
predicted. The anomaly is the body or effect that causes the deviation from
the "ideal" gravity model. Many data corrections must be made to
the measured gravity value in order to extract the response of the local
anomaly, or local geology, which is invariably the purpose of the survey. Lateral variations in gravity anomalies are related to anomalous
density distributions within the Earth. Gravity measurements help us to
understand the internal structure of the planet. Calculations show that the
gravity anomaly signature of a thickened crust (for example, in orogenic belts) is negative and larger in absolute value,
relative to a case where thickening affects the entire lithosphere. In geodesy and geophysics, the usual theoretical model is the
gravity on the surface of a reference ellipsoid such as WGS84.To understand the nature of the gravity anomaly due to the
subsurface, a number of corrections must be made to the measured gravity
value: The theoretical gravity (smoothed normal gravity) should be removed in
order to leave only local effects. The elevation of the point where each gravity measurement was
taken must be reduced to a reference datum to compare the whole profile. This
is called the Freeair Correction, and when combined with the removal of
theoretical gravity leaves the freeair anomaly. Correction for the differing elevations of gravity stations is
made in three parts. 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. To reduce to datum an
observation taken at height h. 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. Thus, apart from the free
air correction, we need to correct for the effects of any material between
the gravity station and the geoid. To do this we model the material in
between as being made up of an infinite number of slabs of thickness t. These
slabs have no lateral variation in density, but each slab may have a
different density than the one above or below it. This is called the Bouguer correction. The Bouguer correction (BC) removes
this effect by approximating the rock layer beneath the observation point to
an infinite horizontal slab with a thickness equal to the elevation of the
observation above datum. If ρ is the density of the rock, then: BC =
2πGρh = 0.4191 ρh
gu
(h in metres ρ in Mg m^{3})
On land the Bouguer correction must be
subtracted, as the gravitational attraction of the rock between observation
point and datum must be removed from the observed gravity value. The Bouguer correction of sea surface observations is
positive to account for the lack of rock between surface and sea bed. The
correction is equivalent to the replacement of the water layer by material of
a specified rock density ρw. In this case: BC = 2πG (ρ1
 ρw) z where z is the water depth
and ρw the density of water. The freeair and Bouguer corrections
are often applied together as the combined elevation correction. The Bouguer correction makes the
assumption that the topography around the gravity station is flat. This is
rarely the case and a further correction, the terrain correction (TC), must
be made to account for topographic relief in the vicinity of the gravity
station. This correction is always positive as may be appreciated from the
figure above. The regions designated A form part of the Bouguer
correction slab although they do not consist of rock. Consequently, the Bouguer correction has overcorrected for these areas and
their effect must be restored by a positive terrain correction. Region B
consists of rock material that has been excluded from the Bouguer
correction. It exerts an upward attraction at the observation point causing
gravity to decrease. Its attraction must thus be corrected by a positive
terrain correction. Terrain effects are low in areas of subdued topography, rarely
exceeding 10 gu in flatlying areas. In areas of
rugged topography terrain effects are considerably greater, being at a
maximum in steepsided valleys, at the base or top of cliffs and at the
summits of mountains. Where terrain effects are considerably less than the desired
accuracy of a survey, the terrain correction may be ignored. Sprenke (1989) provides a means of assessing the distance
to which terrain corrections are necessary. However, the usual necessity for
this correction accounts for the bulk of time spent on gravity reduction and
is thus a major contributor to the cost of a gravity survey. FreeAir and Bouguer Gravity Anomaly Maps: The Bouguer anomaly forms the basis
for the interpretation of gravity data on land. In marine surveys Bouguer anomalies are conventionally computed for inshore
and shallow water areas as the Bouguer correction
removes the local gravitational effects associated with local changes in
water depth. Moreover, the computation of the Bouguer
anomaly in such areas allows direct comparison of gravity anomalies offshore
and onshore and permits the combination of land and marine data into gravity
contour maps. These may be used, for example, in tracing geological features
across coastlines. The Bouguer anomaly is not
appropriate for deeper water surveys, however, as in such areas the
application of a Bouguer correction is an
artificial device that leads to very large positive Bouguer
anomaly values without significantly enhancing local gravity features of
geological origin. Consequently, the freeair anomaly is frequently used for
interpretation in such areas. Moreover, the FAA provides a broad assessment
of the degree of isostatic compensation of an area. Gravity anomalies are conventionally displayed on profiles or as
contoured (isogal) maps. Interpretation of the
latter may be facilitated by utilizing digital image processing techniques
similar to those used in the display of remotely sensed data. In particular, colour and shaded relief images may reveal structural
features that may not be readily discernible on unprocessed maps. The Bouguer anomalies are usually negative in mountains because of isostasy: the rock density of their roots is lower, compared with the surrounding earth's mantle. Typical anomalies in the Central Alps are −150 milligals (−1.5 mm/s²). Rather local anomalies are used in applied geophysics: if they are positive, this may indicate metallic ores. At scales between entire mountain ranges and ore bodies, Bouguer anomalies may indicate rock types. Salt domes are typically expressed in gravity maps as lows, because salt has a low density compared to the rocks the dome intrudes. Anomalies can help to distinguish sedimentary basins whose fill differs in density from that of the surrounding region. 
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