Geoscience Reference
In-Depth Information
Referring to the results, the main output of this mission will be the following:
•
spherical-harmonic coe
cients for the gravitational potential, see, e.g.,
(2-80),
•
corresponding variance-covariance matrix.
Derived products from this main output are geoidal heights, gravity anoma-
lies, and also oceanographic data.
It is important to mention that the GPS orbit analysis of GOCE will
rather yield long-wavelength information of the gravity field, while the satel-
lite gravity gradiometry will yield the short-wavelength information.
GOCE is the first “drag-free” mission, which implies that the satellite
moves in free fall around the earth. Therefore, a drag compensation and
attitude control system is required to compensate for drag forces and torques.
This and more information may be found in Rebhahn et al. (2000),
Drinkwater et al. (2003), Pail (2003), www.esa.int/livingplanet/goce.
Measurements
The basic principle of gradiometry in GOCE is the measurement of accel-
eration differences for a very short baseline. Considering two accelerometers
separatedby50cmononeaxis,Muller (2001) and Pail (2003) write the two
observation equations as
a
1
=
M
+
˙
Ω
+
ΩΩ
∆
x
+
f
ng
,
(7-49)
−
M
+
˙
Ω
+
ΩΩ
∆
x
+
f
ng
,
a
2
=
where
a
1
and
a
2
are the measured accelerations of the two accelerometers
on the axis, and
M
is the Marussi tensor,
⎡
⎤
∂
2
V
∂x
2
∂
2
V
∂x ∂y
∂
2
V
∂x ∂z
⎣
⎦
∂
2
V
∂x ∂y
∂
2
V
∂y
2
∂
2
V
∂y ∂z
M
=
,
(7-50)
∂
2
V
∂x ∂z
∂
2
V
∂y ∂z
∂
2
V
∂z
2
which comprises the second derivatives of the gravitational potential (our
target quantity!). Furthermore, the skewsymmetric matrix
⎡
⎤
ω
3
−
ω
2
0
⎣
⎦
Ω
=
−
ω
3
0
ω
1
(7-51)
ω
2
−
ω
1
0
