Plate Motions on a Sphere
(Minster, J-B, T.H. Jordan, Present-day plate motions, J. Geophys. Res., 85, p. 5331-5354, 1978. DeMets et al., Current plate motions, Geophys. J. R. Astr. Soc., 101, p. 425- 478, 1990. DeMets, C., R. G. Gordon, and D. F. Argus, Geologically current plate motions, Geophys. J. Int., 181, 1-80, 2010)
ω − angular velocity vector ⎜⎛ rad⎞⎟ ⎝ s⎠
r − position on earth (m)
v − velocity vector at position r
m s ⎛ ⎝ ⎜ ⎞ ⎠ ⎟
Of course, the velocity of the plate must be tangent to the surface of the earth so the velocity is the cross product of the position vector and the angular velocity vector.
v = ˆ i ω y z − ω z y ( ) − ˆ j ω x z − ω z x ( ) + ˆ k ω x y − ω y x (
where i, j, and k are unit vectors. The magnitude of the velocity is given by
v = ω r sin(Δ)
where Δ is the angle between the position vector and the angular velocity vector. It is given by the following formula.