Earth's centre is fundamental to geodesy and geoscience because motions of sites on the surface are estimated relative to it. International Terrestrial Reference Frames ITRF2000 and ITRF2005 are defined by the centre of mass of Earth's system (CM), consisting of solid Earth, the ice sheets, the oceans, and the atmosphere. Satellite LAGEOS rotates about CM; satellite laser ranging (SLR) is used to estimate the velocity of CM relative to sites on the surface. However, ITRF2000 and ITRF2005 differ by 1.8 mm yr−1, suggesting that the velocity of CM is constrained poorly by SLR.
In this study, we define Earth's reference frame with the centre of mass of solid Earth (CE). Site velocities estimated using SLR, VLBI, GPS and DORIS are corrected for a postglacial rebound model and inverted for the rotational velocities of the plates and the rotational and translational velocities of the four space techniques. Because the postglacial rebound predictions are relative to CE, the velocity of CE relative to sites on the surface is estimated. Because the input SLR site velocities are relative to CM, the output SLR translational velocity is the velocity of CM relative to CE.
The estimated velocity of CE does not depend strongly on the postglacial rebound model corrected for. Equal within uncertainties and having a root mean square of 0.5 mm yr−1 are estimates of the velocity of CE determined assuming that plate interiors are deforming radially as predicted by three postglacial rebound models and an estimate of the velocity of CE determined assuming that parts of plate interiors neither beneath nor along the margins of the late Pleistocene ice sheets are not deforming laterally.
The velocity of CE equals within uncertainties (probability greater than 5 per cent) the velocity of CM in ITRF2000. The velocity of CE differs significantly (0.05 per cent probability) from the velocity of CM in ITRF2005. Earth's reference frame (and, we believe, ITRF's) should be defined with the tightly constrained velocity of CE, not with the poorly constrained velocity of CM. Because CE is believed to be moving relative to CM no faster than 0.5 mm yr−1, the velocity of CE estimated in this study is likely to be nearer the true velocity of CM than is the velocity of CM estimated using SLR.