Geology Reference
In-Depth Information
15.1.2 Ellipsoids
The Earth is, to a first approximation, spherical, but the equatorial radius
is about 22 km longer than the polar radius. An ellipsoid of revolution,
also known as a spheroid (in surveying, the terms are to all intents and
purposes synonymous) is commonly used as a second-order approximation.
Ellipsoids are characterised by the lengths of their major and minor axes,
or by the length of the major axis and a flattening factor (eccentricity),
and many different Earth ellipsoids have been used over the last 200 years.
This has not only been because of the steady advances in knowledge of the
true shape of the Earth over that period, but also because all ellipsoids are
approximations, and some fit given parts of the Earth's surface better than
others.
Latitudes and longitudes define points on an ellipsoid surface that ap-
proximates the Earth's surface. To use these coordinates accurately requires
knowledge of which ellipsoid is being used. The currently most widely used
system, the 1984 World Geodetic System (WGS84), with major and minor
axes of 6378.137 and 6356.752 314 km respectively, is a poor fit in some
parts of the world, where local and traditional systems continue to be used.
Choosing an ellipsoid does not, of itself, define a mapping system. It is
also necessary to define the location of its centre with respect to the true
centre of the Earth. This is now usually done in terms of its X, Y and Z
coordinates in a Cartesian system, so that transformations between different
systems using the same ellipsoid may be expressed (rather mysteriously to
the uninitiated) in terms of a
Z (in the direction of the Earth's spin axis),
a
Xanda
Y.
Deviations of the Earth's mean surface from the ellipsoid may affect basic
surveying. Conventional surveying techniques depend on gravity, since this
defines the orientation of a plumb bob or other levelling device. Surveys
relying on such methods are inherently referenced not to an ellipsoid but
to a surface over which the gravitational potential is constant. The most
important such surface is the one that, at sea, coincides with average sea
level. This
geoid
is in places as much as 100 m above or below the ellipsoid.
Topographic elevations are normally referred to the geoid, since most users
demand that their maps show local mean sea level as zero. GPS receivers,
however, may show heights relative either to the geoid or to an idealised
ellipsoid. It is not always easy to discover which!
With the increasing use of navigation satellites, these formerly rather
esoteric considerations have become very important in field surveys. GPS
receivers offer an enormous range of possible co-ordinate systems, and also
of possible ellipsoids. It is all too easy to input the correct projection and
co-ordinate system into the survey GPS and then relax, forgetting that the
