Geoscience Reference
In-Depth Information
These two hypotheses of Pratt and Airy are very different; but determining
whether one, the other or a combination of them operates in a particular part of
the Earth is not a simple matter - compensation can be and is achieved by both
methods. Determining whether or not a surface feature is in isostatic equilibrium
(compensated) is often easier (Section 5.5.4).
5.5.3 Calculation of gravity anomalies
Before any gravity measurements can be used, certain corrections have to be
made. First, allowance must be made for the fact that the Earth is not a perfect
sphere but is flattened at the poles and is rotating. The reference gravity formula
of 1967 (Eq. (5.19)) includes these effects and expresses gravity
g
as a function
of latitude
. This enables a correction for the latitude of the measurement point
to be made by subtracting the reference value
g
(
λ
λ
) (Eq. (5.19)) from the actual
gravity measurement.
The second correction which must be made to any gravity measurement allows
for the fact that the point at which the measurement was made was at an elevation
h
rather than at sea level on the spheroid. This correction, known as the
free-air
correction
, makes no allowance for any material between the measurement point
and sea level: it is assumed to be air. Therefore, using the inverse-square law
and assuming that the Earth is a perfect sphere, we find that gravity at elevation
h
is
g
(
h
)
=
g
0
2
R
R
+
h
(5.31)
where
R
is the radius of the Earth and
g
0
is gravity at sea level. Since
h
R
,
Eq. (5.31) can be written as
g
(
h
)
g
0
1
−
2
h
R
(5.32)
The measured value of gravity at height
h
is therefore less than the value of gravity
at sea level. The free-air correction,
g
F
,isthe amount that has to be added to the
measured value to correct it to a sea-level value:
g
F
=
g
0
−
g
(
h
)
2
h
R
=
g
0
(5.33)
Since gravity decreases with height above the surface, points above sea level are
therefore corrected to sea level by adding (2
h
/
R
)
g
0
. This correction amounts to
10
−
6
ms
−
2
per metre of elevation. A more accurate value for this correction
can be obtained by using McCullagh's formula for the gravitational attraction of
a rotating spheroid (e.g., Cook 1973, pp. 280-2).
3.1
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