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Abstract. The qualification and the maintenance of the International Celestial Reference Frame (ICRF) source directions are currently based on global statistics regarding the complete data set of VLBI observations of extragalactic radio sources. The founding hypothesis in the selection of extragalactic objects to access a quasi-inertial reference system is that their directions are fixed in space. Therefore the study of the time variability of the sources is an important step in the process of checking and improving the reliability of the ICRF, in view of high precision applications such as Earth rotation studies or the unification with future space astrometry results. In this paper we investigate the systematic and random behaviours in time series of individual determinations of coordinates for several hundred sources over 1987-1999. New criteria for the qualification of sources in a future revision of the ICRF are proposed.

The residual signal in VLBI, SLR, DORIS and GPS station motion, after a linear trend and seasonal components have been removed, is analysed to investigate site-specific and technique-specific error spectra. The study concentrates on 60 sites with dense observation history by two or more space geodetic techniques. Statistical methods include the Allan variance analysis and the three-cornered hat algorithm. The stability of time-series is defined by two parameters, namely the Allan deviation for a one-year sampling time (noise level) and the slope of the Allan variance graph with its spectral interpretation (noise type). The site-specific noise level is found to be in the range 0.5-3.5 mm in either horizontal direction and 1-4.5 mm in height for most sites. The distribution of site-specific noise type includes both white noise and flicker noise. White noise is predominant in the East direction. Both types of noise are found in the North direction, with no particular geographical clustering. In the Up direction, the Northern hemisphere sites seem to be split in two large geographical sectors characterised either by white noise or by flicker noise signatures. Technique-specific noise characteristics are estimated in several ways, leading to a white noise diagnostic for VLBI and SLR in all three local directions. DORIS has also white noise in the horizontal directions, whereas GPS has a flicker noise spectrum. The vertical noise spectrum is indecisive for both DORIS and GPS. The three-dimensional noise levels for the one-year sampling time are 1.7 mm for VLBI, 2.5 mm for SLR, 5.2 mm for DORIS, and 4.1 mm for GPS. For GPS, the long-term analysis homogeneity has a strong influence. In the case of a test solution reanalysed in a fully consistent way, the noise level drops to the VLBI level in horizontal and to the SLR level in vertical. The three-dimensional noise level for a one-year sampling time decreases to 1.8 mm. In addition, the percentage of stations with flicker noise drops to only about 20% of the network.