Tecniche terrestri di rilievo applicate
alle antenne VLBI per lo studio delle
deformazioni gravitazionali
P. Sarti, C. Abbondanza,
S. Montaguti, M. Negusini, L. Vittuari
Summary
• Space geodetic instrument reference point:
– Definition (conventional, stochastic, electronic)
– Stability
• Local ties and eccentricity vectors
• Investigation on gravitational deformations affecting
Medicina’s VLBI telescope:
– Terrestrial measurements:
• Topography
• Laser scanning
– Finite Element Model
• An elevation-dependent signal path correction model:
– Combination of deformations
– Signal path variation
Reference point: conventional definition
Telescope
Invariant Point
O
Moving axis
Antenna Reference Point (ARP)
Fixed axis
Reference point: electronic definition
i. frequency dependent
ii. elevation dependent
Reference point: stochastic definition
a. RP is realized using observations
performed by space techniques
b. RP is realized with terrestrial surveying
−
−
−
Direct method
Indirect method
Hybrid method
GPS survey approach
j-th horizontal circle
j-th horizontal plane
j-th “horizontal” sphere
i-th vertical circle
i-th vertical plane
i-th “vertical” sphere
Medicina: visione globale
della rete locale
N
20m
VLBI
GPS
Medicina:
posizione degli
strumenti geodetici spaziali
Medicina:
dettaglio dei
segnali
rilevati
sul
radiotelescopio
P1
(mm)
P3
(mm)
G7
(mm)
GPS
ARP
(mm)
VLBI
IP
(mm)
X
-1.87
-1.87
3.17
-1.51
2.08
Y
1.57
-2.85
0.01
-0.81
2.09
Z
0.57
-2.38
-0.53
2.48
-0.13
mod
2.51
4.16
3.22
3.01
2.95
X
-6.32
-6.32
6.45
-3.51
9.69
Y
4.73
-0.32
0.68
-4.32
-0.77
Z
0.89
-3.14
0.84
1.83
-0.42
mod
7.94
7.06
6.54
5.86
9.73
2002-2001
2003-2001
U IPF=17.6933±0.0007 (m)
U IP0=17.7003±0.0008 (m)
U IPE=17.7030±0.0003 (m)
(U IPE -U IPF)  1 cm
Focal length
Receiver
Vertex
Df
O
e
  D f  O cos e
Clark and Thomsen 1988
L   F F   R R  V V
F
Elevation 90 deg
Elevation 75 deg
Elevation 60 deg
Elevation 45 deg
Elevation 30 deg
Elevation 15 deg
g
g
g
40
30
20
(mm)
Focal length variation (Laser)
10
0
-10
0
10
20
30
40
50
Elevation (deg)
60
70
80
90
L   F F   R R  V V
R
Displacement of the receiver
g
Displacement of the receiver
g
Displacement of the receiver
g
Displacement of the receiver
g
18
R2
15
Topography
FEM
Displacement (mm)
12
9
6
3
0
-3
0
20
40
60
Elevation (deg)
80
100
18
R1
15
Topography
FEM
Displacement (mm)
12
9
6
3
0
-3
0
20
40
60
Elevation (deg)
80
100
18
R3
15
Topography
FEM
Displacement (mm)
12
9
6
3
0
-3
0
20
40
60
Elevation (deg)
80
100
40
30
20
(mm)
Focal length variation (Laser)
Receiver displacement (Topography)
10
0
-10
0
10
20
30
40
50
Elevation (deg)
60
70
80
90
L   R R  V V   F F
V
g
Displacement of the vertex
g
40
30
20
(mm)
Focal length variation (Laser)
Receiver displacement (Topography)
Vertex displacement (FEM)
10
0
-10
0
10
20
30
40
50
Elevation (deg)
60
70
80
90
40
30
20
(mm)
Focal length variation (Laser)
Receiver displacement (Topography)
Vertex displacement (FEM)
10
0
-10
0
10
20
30
40
50
Elevation (deg)
60
70
80
90
L   R R  V V   F F
2

r0 
8f
 R  2 ln 1  2   1  0.56
r0
 4f 
 F  1   R  0.44
2
V  1   R  1.56
Receiver displacement (Topography)
Vertex displacement (FEM)
40
Focal length variation (Laser)
Path length variation
30
(mm)
20
10
0
-10
0
10
20
30
40
50
Elevation (deg)
60
70
80
90
Receiver displacement (mm)
25
20
15
10
5
Astronomical measurements
0
0
10
20
30
40
50
Elevation (deg)
60
70
80
90