Context : The effect of a frequency dependent shift of the VLBI core position ( known as the “ core shift ” ) was predicted more than three decades ago and has since been observed in a few sources , but often within a narrow frequency range . This effect has important astrophysical and astrometric applications . Aims : To achieve a broader understanding of the core shift effect and the physics behind it , we conducted a dedicated survey with NRAO ’ s Very Long Baseline Array ( VLBA ) . Methods : We used the VLBA to image 20 pre-selected sources simultaneously at nine frequencies in the 1.4 – 15.4 GHz range . The core position at each frequency was measured by referencing it to a bright , optically thin feature in the jet . Results : A significant core shift has been successfully measured in each of the twenty sources observed . The median value of the core shift is found to be 1.21 mas if measured between 1.4 and 15.4 GHz , and 0.24 mas between 5.0 and 15.4 GHz . The core position , r _ { c } , as a function of frequency , \nu , is found to be consistent with an r _ { c } \propto \nu ^ { -1 } law . This behavior is predicted by the Blandford & Königl model of a purely synchrotron self-absorbed conical jet in equipartition . No systematic deviation from unity of the power law index in the r _ { c } ( \nu ) relation has been convincingly detected . Conclusions : We conclude that neither free-free absorption nor gradients in pressure and/or density in the jet itself and in the ambient medium surrounding the jet play a significant role in the sources observed within the 1.4 – 15.4 GHz frequency range . These results support the interpretation of the parsec-scale core as a continuous Blandford-Königl type jet with smooth gradients of physical properties along it .