4.9.2011To describe the figure of the earth and its
gravity field is the aim of geodesy.
There exist various typs of mathematical,
physical und topographical earth models to describe the figure,
shape and size of the earth.
Three definitions of "
figure of the
earth" [
Moritz
1990, p. 1]:A) The solid and
liquid earth bounded by the physical earth's surface, or
topographic surface, which is the surface which we see, on
which we stand, walk, drive, and, occasionally, swim. It is highly
irregular, even after some obvious smoothing which is always
necessary to make it a smooth surface amenable to mathematical
treatment, and also after some averaging with respect to time since
this surface undergoes temporal variations (on the order of
decimeter or more) because of tidal effects,
etc.
B) The (part of the
earth bounded by the) geoid, which is a level surface
coinciding (somewhat loosely speaking) with the free surface of the
oceans together with its continuation under the continents. It is
the geoid above which "heights above sea level" are measured. A
level surface is everywhere horizontal, that is, perpendicular to
the direction of the plumb line. Level surfaces are surfaces of
constant gravity potential W. , W = const. and the
geoid is one of them, W = W0,
denoting the constant geoid potential by
W0.
Again we are disregarding temporal (tidal) variations. Whereas the
physical earth's surface, in its picturesque variety and beauty, is
very irregular, the geoid is smoother and subject to a mathematical
equation, W = W0; however, even the gravity potential W is
far from being a simple mathematical function. Therefor, the geoid
is referred to a much regular, "normal", surface which approximates
the geoid while being more regular in an mathematical or physical
sense. Thus we arrive at the concept of a
C) Normal
earth, or reference earth, or earth model.
Mathematically the simplest model is an ellipsoid of
revolution, which therefor is practically almost exclusively used.
Physically the best reference for describing the small, more or
less elastic, temporal variations (free and forced oscillations
such as earth tides), is a hydrostatic equilibrium figure.
Figures of hydrostatic equilibrium for the earth are very close to
ellipsoids, but do not exactly coincide with an ellipsoid as we
shall have ample opportunity to see in this book. By the way, we
are frequently not distinguishing between a figure and the surface
bounding it; this is costumary and should not cause any
confusion.
