Geology Reference
In-Depth Information
14
Gravity Field of the Earth
Abstract
This conclusive chapter introduces the Earth's gravity field and the concept
of geopotential. The approach follows the potential field techniques
along with the methods for processing gravity data. The chapter concludes
with the important topic of dynamic topography, which links the geoid to
mantle dynamics.
relativistic equations of the Earth's gravity field
g
D
g
(
r
):
14.1 Gravity Field
and Geopotential
r
g
D
4 G¡.r/
r
g
D
0
(14.1)
In this chapter, we shall review some fundamental
properties of the Earth's gravity field, which have
a strong impact on plate tectonics research. Often,
researchers involved in plate kinematics studies
have a limited “contact area” with the these top-
ics, which essentially consists into the inspection
of gravity anomaly maps with the purpose of
better identifying fracture zone tracks, detect the
presence of seamounts, or analyze the structural
features of sedimentary basins. Conversely, a
more in-depth understanding the Earth's gravity
field is essential in many geodynamic studies,
because the pressure gradients that are associ-
ated with asthenospheric flows and the upper
mantle heterogeneities have a strong impact on
the gravity anomalies at the Earth's surface and
the shape of the Earth. In the following, we
will apply the same potential field techniques
discussed in Chap.
4
in the context of geomag-
netism. Therefore, our starting point are the non-
where
¡
D
¡
(
r
) is the mass density and
G
is the
gravitational constant:
G
D
6:67259
10
-
11
m
3
kg
-
1
s
-
2
(14.2)
The field equations (
14.1
) imply that
g
is a po-
tential field, thereby there exists a scalar function
V
D
V
(
r
) such that:
g
Dr
V
(14.3)
The potential
V
D
V
(
r
) is called the
gravita-
tional geopotential
and represents the fundamen-
tal quantity for the analysis of the field properties
through spherical harmonic expansions. In fact,
by (
14.1
) it satisfies Poisson's equation:
2
V
D
4 G¡.r/
r
(14.4)
