  The apparent position of the "core" in a parsec-scale radio jet (a compact,
bright emitting region at the narrow end of the jet) depends on the observing
frequency, owing to synchrotron self-absorption and external absorption. While
providing a tool probing physical conditions in the vicinity of the core, this
dependency poses problems for astrometric studies using compact radio sources.
We investigated the frequency-dependent shift in the positions of the cores
(core shift) observed with very long baseline interferometry (VLBI) in
parsec-scale jets. We discuss related physics, as well as its effect on radio
astrometry and the connection between radio and optical positions of
astrometric reference objects. We searched for the core shift in a sample of
277 radio sources imaged at 2.3 GHz (13 cm) and 8.6 GHz (4 cm) frequency bands
using VLBI observations made in 2002 and 2003. The core shift was measured by
referencing the core position to optically thin jet features whose positions
are not expected to change with frequency. We present here results for 29
selected active galactic nuclei (AGN) with bright distinct VLBI jet features
that can be used in differential measurements and that allow robust
measurements of the shift to be made. In these AGN, the magnitude of the
measured core shift between 2.3 and 8.6 GHz reaches 1.4 mas, with a median
value for the sample of 0.44 mas. Nuclear flares result in temporal variability
of the shift. An average shift between the radio (4 cm) and optical (6000
Angstrom) bands is estimated to be approximately 0.1 mas, and it should be
taken into account in order to provide the required accuracy of the
radio-optical reference frame connection. This can be accomplished with
multi-frequency VLBI measurements... (abridged)
