Table 2. Geopotential computed in different tide systems.
Tide System
a
Iff
W o
(m)
(m 2 /s 2 )
Tide - free
6,378,136.46 298.25766 62,636,856.898
Zero
6,378,136.49 298.25643 62,636,856.893
Mean
6,378,136.59 298.25231 62,636,856.881
Table 3. Geoidal geopotential and geopotential scale factor
Source
GEOSAT
(Bursa, Sima and Kostelecky, 1992)
GEOSAT
(Nesvomy and Sima, 1994)
TOPEXIPOSEIDON
(Ries, 1995)
Computed from adopted parameters
a=6 378 136.59±O.1O (Rapp, 1995)
62,636,856.5±3.0
62,636,857.5±1.0
62,636,856.5± 1.0
62,636,856.88±1.0
Ra ±rms
(m)
6,363,672.50±0.30
6363,672.40±0.10
6,363,672.50±0.10
6,363,672.46±0.10
The independence of W o from the tidal system can also be shown theoretically by
considering the radial distortion of the equipotential surface due to oviD) and the
distortion of liO). The radial distortion due to oviD) is given by:
oY(O)
op=(I+k)-2-.
g
The distortion of liD) is given by:
01'°) = k L (P..-J2 oY(O).
2
GM a o
2
(7)
(8)
In equations (7) and (8), k is the Love number related to how the Earth's surface
responds to tidal forces, g is gravity, and a o = 6378137 m is the scaling parameter
rendering liD) to be dimensionless.
Let us introduce the following expression for the distortion in Wo due to the tidal
potential given by equation (5):
OW o = oviD) - GAf op + GM (a o J2 oliO) .
(9)
P
p P
Substituting (7) and (8) into (9) we obtain (in the usual spherical Earth's tidal model):
OW o =0,
(10)
which is the expected result if W o is independent of the tidal system.
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