The use of modern broadband seismometers allows the observation of dynamic and static near-field effects. In the fortunate case of the great 1994 Bolivia earthquake a 6 mm coseismic permanent offset was observed at distances of about 600 km. On the other hand no surface static displacement from moderate events has been observed yet. This is mainly due to the intrinsic difficulties in the instrument removal. In the present paper we analyze broadband waveforms from a couple of events in southern Italy, recorded at distance of 50 km, by applying the technique for instrument removal recently introduced by Zhu <2003>. We derive stable and reliable measures of very small coseismic static offset produced by moderate magnitude earthquakes. Our results, successfully tested against synthetic prediction, give permanent displacement of a few tenths of millimeters, one order of magnitude smaller than usual geodetic resolution.