Gravity - The Solid Earth - page 205

The free-air anomaly g F is then the measured gravity value g obs with these
two corrections applied:

g F = g obs − g ( λ ) + g F
= g obs − g ( λ ) 1 −

2 h
R

(5.34)

Two other corrections are frequently applied to gravity measurements.

1. The first is the Bouguer correction ,which allows for the gravitational attraction of the
rocks between the measurement point and sea level, assuming that these rocks are of
infinite horizontal extent. The Bouguer correction is given by

g B = 2 π G ρ h (5.35)

where G is the constant of gravitation, ρ the density of the material between the mea-
surement point and sea level, and h the height of the measurement point above sea level.
Taking G to be 6.67 × 10 − 11 m 3 kg − 1 s − 2 and assuming an average crustal density of
2.7 × 10 3 kg m − 3 ,weobtain a Bouguer correction of 1.1 × 10 − 6 ms − 2 per metre of
elevation. Alternatively, the Bouguer correction for a layer 1 km thick with density
10 3 kg m − 3 is 42 mgal.
2. The final correction is a terrain correction , g T ,which allows for deviations of the

surface from an infinite horizontal plane. This correction can be calculated graphically
by using a set of templates and a topographic map. The terrain correction is small and,
except for areas of mountainous terrain, can often be ignored in crustal studies.

The Bouguer anomaly g B is the free-air anomaly with these two extra correc-
tions applied:

g B = g F − g B + g T
= g obs − g ( λ ) + g F − g B + g T (5.36)

The Bouguer anomaly is therefore the observed value of gravity minus the theo-
retical value at the latitude and elevation of the observation point. Since we have
allowed for the attraction of all the rock above sea level, the Bouguer anomaly
represents the gravitational attraction of the material below sea level. The mantle
Bouguer anomaly is the Bouguer anomaly as calculated above but with an addi-
tional correction made for the gravitational attraction of the crust. It thus repre-
sents the anomalous attraction of material in the mantle (e.g., Fig. 9.16).
The free-air anomaly is usually used for gravity measurements at sea. It is
comparable to the Bouguer anomaly over continents since the measurements are
then all corrected to the sea-level datum. If a Bouguer anomaly is required for
oceanic gravity measurements, it must be calculated by 'replacing' the sea water
with rocks of average crustal density. A terrain correction must then also be
applied to account for the seabed topography.