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

Fixed axis

Moving axis

Antenna Reference Point (ARP)

OTelescope Invariant Point

Reference point: electronic definition

i. frequency dependentii. 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 circlej-th horizontal plane

j-th “horizontal” sphere

i-th vertical circlei-th vertical plane

i-th “vertical” sphere

Medicina: visione globaledella rete locale

20m

N

Medicina:posizione degli

strumenti geodetici spaziali

GPS

VLBI

Medicina:dettaglio deisegnalirilevatisul radiotelescopio

   P1

(mm)P3

(mm)G7

(mm)

GPS ARP(mm)

VLBI IP

(mm)

2002-2001

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

2003-2001

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

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

O

eOD f cose

Df

Receiver

Focal length

Vertex

Clark and Thomsen 1988

VRFL VRF

F

Elevation 90 deg

Elevation 75 deg

Elevation 60 deg

Elevation 45 deg

Elevation 30 deg

Elevation 15 deg

g

g

g

0 10 20 30 40 50 60 70 80 90

-10

0

10

20

30

40

Focal length variation (Laser)

(m

m)

Elevation (deg)

VRFL VRF

R

Displacement of the receiver

g

Displacement of the receiver

g

Displacement of the receiver

g

Displacement of the receiver

g

0 20 40 60 80 100-3

0

3

6

9

12

15

18

Dis

pla

cem

en

t (m

m)

Elevation (deg)

Topography FEM

R2

0 20 40 60 80 100-3

0

3

6

9

12

15

18

Dis

pla

cem

en

t (m

m)

Elevation (deg)

Topography FEM

R1

0 20 40 60 80 100-3

0

3

6

9

12

15

18

Dis

pla

cem

en

t (m

m)

Elevation (deg)

Topography FEM

R3

0 10 20 30 40 50 60 70 80 90

-10

0

10

20

30

40

Focal length variation (Laser)

Receiver displacement (Topography)

(m

m)

Elevation (deg)

FVRL FVR

V

g

Displacement of the vertex

g

0 10 20 30 40 50 60 70 80 90

-10

0

10

20

30

40

Focal length variation (Laser)

Receiver displacement (Topography)

Vertex displacement (FEM)

(m

m)

Elevation (deg)

0 10 20 30 40 50 60 70 80 90

-10

0

10

20

30

40

Focal length variation (Laser)

Receiver displacement (Topography)

Vertex displacement (FEM)

(m

m)

Elevation (deg)

FVRL FVR

56.11

44.01

56.014

1ln8

2

20

20

2

RV

RF

R f

r

r

f

0 10 20 30 40 50 60 70 80 90

-10

0

10

20

30

40

Receiver displacement (Topography)

Vertex displacement (FEM)

Focal length variation (Laser)

Path length variation

(m

m)

Elevation (deg)

0 10 20 30 40 50 60 70 80 900

5

10

15

20

25

R

ece

ive

r d

isp

lace

me

nt (

mm

)

Elevation (deg)

Astronomical measurements