Geoscience Reference
In-Depth Information
we can use Cartesian, spherical, or other coordinate systems to describe the laws of
motion of a particle or a particle system. The origins of these coordinate systems are
all at the geocenter and they are mutually static. Hence, the laws of motion of the
particles described are completely identical and are independent of the choice of
coordinates. Therefore, one reference system includes many coordinate systems
that are essentially the same, such as geodetic Cartesian coordinates (X, Y, Z),
geodetic coordinates (L, B, H), and Gauss plane coordinates (x, y), which are called
equivalent or homogenous coordinate systems. Any arbitrary selection of these
coordinates will exert no effect on the description of objective laws.
In geodesy, if a coordinate system is chosen, it suggests that the reference system
is also selected. However, if a reference system is selected, any arbitrary coordinate
system under this reference system is readily accessible. It is helpful to distinguish
between the reference system and coordinate system at the conceptual level. When
the established system is applied in surveying and mapping engineering to allow the
geometric representation of the terrain, it is appropriate to call such a system the
coordinate system. When applied in a context such as deformation monitoring or
aerospace tests, with physical meaning involved, it will be more appropriate to call
it a reference system. In practice, the reference system and coordinate system are
often interchangeable with each other.
Ideal Terrestrial Reference System
The TRS is the reference system fixed to the Earth in some assured manner. If the
Earth were an ideal rigid body, then any triaxial coordinate system fixed to the Earth
could be well suited. The choice of the TRS merely depends on the user-
friendliness. However, the Earth is really a deformable body, and there is a relative
motion of parts of the crust with respect to each other. Hence, getting the coordinate
system fixed to the Earth in an ideal way has become a matter of vital importance.
The bodily movement (such as polar motion) and the partial movement (like
crustal deformation) of the Earth are superimposed upon each other in an observa-
tion. We can use an Earth-fixed reference system to separate them. The reference
system should be defined by the following theoretical conception: the crust only
deforms with respect to the reference system without rotation or translation as a
whole, while the inertia reference system only entails bodily movement of the Earth
such as revolution and self-rotation. This theoretical concept can be described by
the following Tisserand condition:
ð
0, and
ð
c
~
vdm
ﾼ
c
~
x
~
vdm
ﾼ
0,
where
v are the position and velocity of a mass unit of the Earth dm with
respect to the defined reference system. The domain of integration c is the entire
Earth. The first part of the condition indicates the zero linear momentum of the
Earth relative to the defined reference system and null translation of the Earth; the
~
x and
~
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