Four close radio sources in the International Celestial Reference Frame (ICRF) catalog were observed using phase referencing with the VLBA at 43, 23 and 8.6 GHz, and with VERA at 23 GHz over a one year period. The goal was to determine the stability of the radio cores, and to assess structure effects associated with positions in the ICRF. Although the four sources were compact at 8.6 GHz, the VLBA images at 43 GHz with 0.3-mas resolution showed that all were composed of several components. A component in each source was identified as the radio core using some or all of the following emission properties: compactness, spectral index, location at the end of the extended emission region, and stationary in the sky. Over the observing period, the relative positions between the four radio cores were constant to 0.02 mas, the phase referencing positional accuracy obtained at 23 and 43 GHz among the sources, suggesting that once a radio core is identified, it remains stationary in the sky to this accuracy. Other radio components in two of the four sources had detectable motion in the radio jet direction. Comparison of the 23 and 43 GHz VLBA images with the VLBA 8.6 GHz images and the ICRF positions suggests that some ICRF positions are dominated by a moving jet component; hence, they can be displaced up to 0.5 mas from the radio core, and may also reflect the motion of the jet component. Future astrometric efforts to determine a more accurate quasar reference frame at 23 and 43 GHz and from the VLBI2010 project are discussed, and supporting VLBA or EVN observations of ICRF sources at 43 GHz are recommended in order to determine the internal structure of the sources. A future collaboration between the radio (ICRF) and the optical frame of Gaia is discussed.
