  While analyzing decades of very long baseline interferometry (VLBI) data, we
detected the secular aberration drift of the extragalatic radio source proper
motions caused by the rotation of the Solar System barycenter around the
Galactic center. Our results agree with the predicted estimate to be 4-6 micro
arcseconds per year ({\mu}as/yr) towards {\alpha} = 266\circ and {\delta} =
-29\circ. In addition, we tried to detect the quadrupole systematics of the
velocity field. The analysis method consisted of three steps. First, we
analyzed geodetic and astrometric VLBI data to produce radio source coordinate
time series. Second, we fitted proper motions of 555 sources with long
observational histories over the period 1990-2010 to their respective
coordinate time series. Finally, we fitted vector spherical harmonic components
of degrees 1 and 2 to the proper motion field. Within the error bars, the
magnitude and the direction of the dipole component agree with predictions. The
dipole vector has an amplitude of 6.4 \pm 1.5 {\mu}as/yr and is directed
towards equatorial coordinates {\alpha} = 263\circ and {\delta} = -20\circ. The
quadrupole component has not been detected. The primordial gravitational wave
density, integrated over a range of frequencies less than 10-9 Hz, has a limit
of 0.0042 h-2 where h is the normalized Hubble constant is H0/(100 km s-1).
