Accurate measurement of the frequency-dependent shift of the self-absorbed radio core is required for multi-frequency analysis of VLBI data since absolute positional information is lost as a result of phase self-calibration .
We use the cross-correlation technique of Croke & Gabuzda ( 2008 ) on the optically thin jet emission to align our VLBA images .
Our results are consistent with those obtained from the phase-referencing method , as well as alignment by model-fitted optically thin jet components .
Physical parameters of the compact jet regions , such as the magnetic field strength ( B ) and the distance of the radio core to the jet origin ( r ) , can be calculated from these measurements .
For the source Mrk 501 , we find a magnetic field strength of 0.15 \pm 0.04 G in the 8.4-GHz core at a distance of 0.8 \pm 0.2 pc from the base of the jet .
By extrapolating our 4.6 to 15.4 GHz results for BL Lac ( 2200+420 ) , we estimate magnetic field strengths of the order of 1 G in the millimetre VLBI core .
Using our core-shift measurement between 1.6 and 4.8 GHz for 1803+784 , we find B _ { core } ( 4.8 GHz ) = 0.11 \pm 0.02 G and r _ { core } ( 4.8 GHz ) = 20 \pm 5 pc .
The phase-referencing observations of this source at 8.4 and 43 GHz by Jiménez-Monferrer et al .
( 2008 ) imply B _ { core } ( 43 GHz ) = 1.0 \pm 0.4 G and r _ { core } ( 43 GHz ) = 2.0 \pm 0.9 pc .