We have investigated a frequency-dependent shift in the absolute position of the optically thick apparent origin of parsec-scale jets ("core shift" effect) to probe physical conditions in ultra-compact relativistic outflows in active galactic nuclei. We used multi-frequency Very Long Baseline Array (VLBA) observations of 191 sources carried out in 12 epochs in 2006 within the Monitoring Of Jets in Active galactic nuclei with VLBA Experiments (MOJAVE) program. The observations were performed at 8.1, 8.4, 12.1, and 15.4GHz. We implemented a method of determining the core shift vector based on (i) image registration by two-dimensional normalized cross-correlation and (ii) model-fitting the source brightness distribution to take into account a non-zero core component offset from the phase center.