The frequency dependent position shift of VLBI cores can be used for studying the  most compact regions of extragalactic jets, and obtaining quantitative estimates for physical conditions in the immediate vicinity of central engine. In the absence of high--precision position measurements, a more simplistic approach can be employed, assuming that positions of optically thin features in the jet remain the same at all frequencies. Then, the position offsets of optically thin features can be interpreted as a frequency dependent shift of the self--absorbed core of the jet. In some sources (1038+528A, 3C345, Cygnus A), insufficient resolution and blending at lower frequencies may undermine the offset measurements. A way to detect and, to a certain degree, to correct the errors due to the blending can be found in introduction of an offset measure, which is supposed to remain constant for the case of ideal measurements and unchanged opacity of the jet. Listed below are the main results from deriving the offset measures in 6 sources with reported position offsets of VLBI core:

1. The jet luminosity, the maximum brightness temperature, the core magnetic field and location with respect to the jet origin can be determined, from offset measures. For the well studied sources (Cygnus A, 3C345), the derived values are shown to agree well with values determined by other methods. In Cygnus A, the jet-to-counter-jet ratio determined from the estimated location of the central engine results in a self-consistent source geometry. In 3C345, the derived maximum brightness temperature indicates that the ultracompact jet is strongly particle--dominated, and must release its energy through inverse Compton scattering. The obtained magnetic field distribution in the ultracompact jet of 3C345 is in a good agreement with the values derived from inhomogeneous synchrotron models applied to the extended jet components. Based on the derived characteristic magnetic field, it appears more likely that the jet is produced by a thin, magnetized accretion disk, rather than by a single supermassive black hole with a strong dipole magnetic field.

2. External pressure and density gradients typical for the broad line region may change the optical depth along the jet via both synchrotron self--absorption and free--free absorption in an ambient medium.  The offset measures derived for different frequency pairs and different objects can be used for studying the opacity effects in ultracompact jets. Changes of jet opacity in 3C309.1 deduced from the variations of $k_{\rm r}$ appear to be consistent with a self--absorbed jet propagating through a region with strong density gradients. Similar conclusion can be drawn from the variations of $k_{\rm r}$ determined for all studied objects, although the agreement with the model may in this case be coincidental (one argument for making such a reservation is that the initial pressure gradients required to fit the data for all sources simultaneously are very high: $N(r) \propto r^{-6}$, at $r\sim r_{\rm c}$).
 

3.~The distance at which the observed VLBI core is located at a given frequency is scaled with jet luminosity, so that $r_{\rm core}\propto L_{\rm syn}^{2/3}$. At the same time the magnetic field in the core appears to be almost unchanged, from one source to another. This can be taken as another evidence for the synchrotron self--absorption to be a primary factor influencing the observed properties of the jet core.