Geoscience Reference
In-Depth Information
The geoid is an irregular curved surface. The magnitude and direction of the
gravitational force differ from point to point due to the terrain undulations and
inhomogeneous distribution of mass inside the Earth, which will also cause irreg-
ular direction changes of the plumb line at different points. Hence, this geoid,
everywhere perpendicular to the direction of the plumb line, is correspondingly an
irregular curved surface with slight undulations. Therefore, the geoid is a physical
rather than a mathematical surface.
With the in-depth studies of oceanography, people have realized that the MSL
and the geoid are different concepts. The MSL is not the level (equipotential)
surface, for many factors can exert influence on the oceans such as temperature
and pressure variations, salinity, winds, currents, rotation of the Earth, etc. Mean-
while, the MSL measured using tide gauges in different countries or areas also
varies. If a certain equipotential surface is chosen as the standard sea level, then
separation between MSL and the standard sea level is referred to as the sea surface
topography or sea surface slope. The rise and fall is about 1-2 m on a global scale.
For the eastern sea area of China, the sea surface slope has high elevation in the
south and low elevation in the north. The height difference is approximately 60 cm.
It is imprecise to define the MSL as the geoid, for the MSL is not an equipotential
surface. Therefore it is recommended that the geoid be defined as an equipotential
surface passing through the point to which heights are referred (zero level).
Based on the properties of potential function, we can conclude that the derivative
of gravity potential W with respect to an arbitrary direction s is equal to the
component g of gravity g s in the same direction, namely:
dW
ds ¼
g s ¼
g cos g
ðÞ
;
s
ð
4
:
20
Þ
In the case that the direction s is perpendicular to that of gravity, cos(g, s)
¼
0,
then:
dW
ds ¼
0
:
The integration yields:
W x;y;z
Þ ¼
constant
:
ð
4
:
21
Þ
ð
Assigning a fixed value to the constant on the right-hand side of the equation will
yield an equation of the curved surface. It is referred to as the equipotential surface
given that the gravity potential value is equal everywhere on this surface. In the
meantime, the direction of gravity at any point intersects the surface. The surface is
in an equilibrium state, i.e., the level surface (also the equipotential surface or
constant geopotential surface) of gravity. The geoid is the level surface passing
through the reference point for heights.
Some properties of the level surface can be further studied by applying the
concept of gravity potential.
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