The ERF sky density is such that the mean distance from any given quasar to the closest ERF VLBI position is 1.7°. On average, there are 10 ERF VLBI positions within a radius of 4.4° around any given quasar, the largest distance being on average 6.3°.

Under such conditions for each of the combinations of quasar list and stellar reference frame, hence for every quasar a correction for the local inhomogeneities towards the VLBI position can be obtained from the average of 10 ERF quasars.

Within the ERF quasars radius, objects are removed one by one if both their right ascension. and declination offsets are larger than 2σ. On average, 1.3 ERF quasars are removed, what shows the robustness of the local inhomegeneities corrections.

The autocorrelation between adjacent corrections fades into a characteristic value at a distance of 20◦. Figure 17 illustrates the weakness of the autocorrelations by taking each quasar in turn as a pole source, and plotting the standard deviation in the inhomogeinity correction within growing distance rings. For nearby sources, i.e., very small rings, the inhomogeneities are much the same, and the standard deviation is accordingly small. Rapidly, however, before reaching the distance of 20◦, the standard deviation already reaches the limit of scatter characteristic of each family of input catalog and stellar reference frame solutions.

By determining in this way the correction for the local inhomogeneities, it is seen in Figs. 15 and 16 (filled symbols) that the clumps are clearly minimized. After applying the corrections by harmonic functions, the optical minus radio offsets are typically null within 1.3σ, what is reduced further to within 0.7σ after applying the complementary local inhomogeneities corrections .