In order to derive geologically meaningful anomalies, the effects of known non-geological
factors must be removed. As shown in Figure 1 in highly exaggerated form, the Earth is an
ellipsoid not a sphere (the actual flattening of the Earth is about 1 part in 300). Thus at
sea level, the gravitational attraction of the Earth is diminished at the equator because
this is the place where one is farthest from the center of mass of the Earth. Gravity at the
equator is further diminished because the rotation of the Earth creates a centrifugal
acceleration (C) that opposes gravity. This acceleration is greatest at the equator because
the distance to the rotational axis (R) is the greatest
(C = RW2, whereW
is the angular velocity of the Earth’s rotation). These effects are partly offset by the
fact that the equatorial bulge effectively produces extra mass at the equator. The International
Gravity Formula that takes these effects into account is of the form:
Gt = Ge (1 + f1sin
q2 + f2sin q4),
where
- Ge is the average value of gravity at the equator ~978 Gal
- qis the latitude
- f1, f2depend on the flattening of the Earth and its
gravity field, and the centrifugal force
The effects of elevation also have to be considered before a geologically meaningful
anomaly can be calculated. The “Free effect” is the decrease of gravity with elevation
due to the increased distance from the Earth’s center of mass. This effect is the vertical
gradient of the gravity field whose value is about 0.3 mGal/m and is negative. However,
any location above the datum has extra mass beneath it. The effect of this mass is
calculated via a volume integral, where an average density of the topography must be
estimated (the value used in regional studies is 2670 kg/m3). This effect
(the Bouguer correction) is opposite in sign to the Free Air effect and is about 1/3 of
its value. Thus, the total effect of elevation is to decrease gravity by ~ 0.2 mGal/m.
When these effects of elevation are considered, the results is a geological meaningful
value for the Bouguer anomaly. In order to fully account for the effects of topography,
a terrain correction must be calculated. If this is done, a complete Bouguer anomaly value
results.