Jets of compact radio sources are highly relativistic and Doppler boosted, making studies of their intrinsic properties difficult. Observed brightness temperatures can be used to study the intrinsic physical properties of the relativistic jets, and constrain models of jet formation in the inner jet region. We aim to observationally test such inner jet models. The very long baseline interferometry (VLBI) cores of compact radio sources are optically thick at a given frequency. The distance of the

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... core from the central engine is inversely proportional to the frequency. Under the equipartition condition between the magnetic field energy and particle energy densities, the absolute distance of the VLBI core can be predicted. We compiled the brightness temperatures of VLBI cores at various radio frequencies of 2, 8, 15, and 86~GHz. We derive the brightness temperature on sub-parsec scales in the rest frame of the compact radio sources. We find that the brightness temperature increases with increasing distance from the central engine, indicating that the intrinsic jet speed (the Lorentz-factor) increases along the jet. This implies that the jets are accelerated in the (sub-)parsec regions from the central engine.