1. Tidal Corrections to Direction Observations
Catherine Le Cocq
SLAC - Metrology Department - Advanced Methods Group

2. Displacement-Strain RelationQ P´ Q´
Displacement vector u
u = PP’ = x’-x
Final state
Strain tensor e
Original state
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

3. Angular Formula r´ q´ Final state r q Original state
2 infinitesimal vectors q and r r q θ r´ q´ θ´
transform into q’ and r’
Final state
Introducing =-’
 and  the cosine directors of q and r
Original state
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

4. Surface Strain
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

5. Mathematical Cartography
Original state = sphere or ellipsoid as a model of earth
p (,)
Final state = plane or map
P(X,Y)
Fundamental quadratic form
Linear alteration =
Angular alteration =  = A- = V--
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

6. Tidal Displacement Vector
At point P (r,,), the tidal displacement vector u is given in spherical coordinates by
North-South horizontal component
East-West horizontal component
Vertical component
W is the tidal potential, g is the mean gravity at point P
h and l are the first and third Love numbers
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

7. Tidal Potential B φ P l d C r
Equator
North
South γ O α E δ B H
Zenith
Pole φ
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

8. Tidal Strain Tensor
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

9. Celestial Coordinates: ,
Computational Steps
Location
r,,
Love Numbers
l,h
Date&Time
d,ut
Local Sideral Time: s
Celestial Coordinates: ,
Hour Angle: H
Strain Tensor: e
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

10.  = 37°25’  = 122°12’30’’ h=0 on 11-7-2000 at 1AM
Azimuth Variations
 = 37°25’  = 122°12’30’’ h=0 on at 1AM
1.08e-8 degree
4.39e-7 degree
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq

11. Same location between 11-6-2000 and 11-9-2000 with  = -/2
Time Variations
Same location between and with  = -/2
Ground Motion Workshop, November 6-9, 2000, SLAC Catherine Le Cocq