  The variation of the kinematical properties of the Galactic thick disk with
Galactic height Z are studied by means of 412 red giants observed in the
direction of the south Galactic pole up to 4.5 kpc from the plane. We confirm
the non-null mean radial motion toward the Galactic anticenter found by other
authors, but we find that it changes sign at |Z|=3 kpc, and the proposed inward
motion of the LSR alone cannot explain these observations. The rotational
velocity decreases with |Z| by -30 km/s/kpc, but the data are better
represented by a power-law with index 1.25, similar to that proposed from the
analysis of SDSS data. All the velocity dispersions increase with |Z|, but the
vertical gradients are small. The dispersions grow proportionally, with no
significant variation of the anisotropy. The ratio sigma_U/sigma_W=2 suggests
that the thick disk could have formed from a low-latitude merging event. The
vertex deviation increases with Galactic height, reaching ~20 degrees at
|Z|=3.5 kpc. The tilt angle also increases, and the orientation of the
ellipsoid in the radial-vertical plane is constantly intermediate between the
alignment with the cylindrical and the spherical coordinate systems. The tilt
angle at |Z|=2 kpc coincides with the expectations of MOND, but an extension of
the calculations to higher |Z| is required to perform a conclusive test.
Finally, between 2.5 and 3.5 kpc we detect deviations from the linear trend of
many kinematical quantities, suggesting that some kinematical substructure
could be present.
