  The measurement of the Sun's surface motions with a high spatial and temporal
resolution is still a challenge. We wish to validate horizontal velocity
measurements all over the visible disk of the Sun from Solar Dynamics
Observatory/ Helioseismic and Magnetic Imager (SDO/HMI) data. Horizontal
velocity fields are measured by following the proper motions of solar granules
using a newly developed version of the Coherent Structure Tracking (CST) code.
The comparison of the surface flows measured at high spatial resolution
(Hinode, 0.1 arcsec) and low resolution (SDO/HMI, 0.5 arcsec) allows us to
determine corrections to be applied to the horizontal velocity measured from
HMI white light data. We derive horizontal velocity maps with spatial and
temporal resolutions of respectively 2.5 Mm and 30 min. From the two components
of the horizontal velocity Vx and Vy measured in the sky plane and the
simultaneous line of sight component from SDO/HMI dopplergrams v_D, we derive
the spherical velocity components (Vr, Vtheta, Vphi). The azimuthal component
Vphi gives the solar differential rotation with a high precision (+-0.037km/s)
from a temporal sequence of only three hours. By following the proper motions
of the solar granules, we can revisit the dynamics of the solar surface at high
spatial and temporal resolutions from hours to months and years with the SDO
data.
