Page 334 - Physical Principles of Sedimentary Basin Analysis

10

Gravity and gravity anomalies

The gravitational acceleration is often taken to be the constant g = 9.8m s −2 , although
this is not quite accurate. The value of g depends on where on the planet it is measured,
because the Earth is not a perfect sphere and also because the Earth is rotating. There are
also small regional and local variations in g due to density variations in the subsurface.
These small variations in g can be measured with a great deal of precision, and they are an
important source of information about the distribution of mass (or density) in the subsur-
face. Figure 10.1 shows an example of a gravity anomaly measured along the sea surface
(free-air gravity). The sea bed is smooth and cannot explain the observed gravity. The
increased gravity turns out to be caused by a ridge of crustal rocks with a density larger
than the surrounding sedimentary rocks.
Differences in g over mountains are closely linked to the concept of isostasy. Measure-
ments show that g is less in high mountain areas than close to sea level. One might easily
have guessed the opposite – that gravity would be higher in the mountains since they are
large masses of rock. We have seen that isostatic equilibrium means that there is the same
mass in all columns down to the same depth in the ductile mantle. Each column is simply
floating on the ductile mantle, and a column in the mountains therefore needs deep crustal
roots of “low” density to float high compared to areas close to sea level. The mass of the
mountains is compensated by a mass deficiency in the crust below. These deep crustal roots
are precisely what is measured by the lowered values for g in the mountains compared with
areas close to sea level.
We have seen that mountains or peaks with a small lateral extent are only partly sup-
ported by buoyancy of the ductile mantle, because they are also supported by the elastic
strength of the lithosphere. In this chapter will see how the degree of isostatic equilibrium
is reflected by variations in g.

10.1 Newton’s law of gravity
The gravitational attraction between two masses is given by Newton’s law. It says that the
attractive force between the masses m and M a distance r apart is
mM
F = G (10.1)
r 2

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