The apparent position of jet base (core) in radio-loud active galactic nuclei changes with frequency because of synchrotron self-absorption. Studying this `core shift` effect enables us to reconstruct properties of the jet regions close to the central engine. We report here results from core shift measurements in AGNs observed with global VLBI at 2 and 8 GHz at epochs from 1994 to 2016. Our sample contains 40 objects observed at least 10 times during that period. The core shift is determined using a new automatic procedure introduced to minimize possible biases. The resulting multiple epoch measurements of the core position are employed for examining temporal variability of the core shift. We argue that the core shift variability is a common phenomenon, as established for 33 of 40 AGNs we study. Our analysis shows that the typical offsets between the core positions at 2 and 8 GHz are about 0.5 mas and they vary in time. Typical variability of the individual core positions is about 0.3 mas. The measurements show a strong dependence between the core position and its flux density, suggesting that changes in both are likely related to the nuclear flares injecting denser plasma into the flow. We determine that density of emitting relativistic particles significantly increases during these flares, while relative magnetic field changes less and in the opposite direction.
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