Defining the translational velocity of the reference frame of Earth

SUMMARY 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.

[1]  Hans-Peter Plag,et al.  A geophysical interpretation of the secular displacement and gravity rates observed at Ny-Ålesund, Svalbard in the Arctic—effects of post-glacial rebound and present-day ice melting , 2006 .

[2]  J. Wahr,et al.  Measurements of Time-Variable Gravity Show Mass Loss in Antarctica , 2006, Science.

[3]  Jean-Mathieu Nocquet,et al.  Geodetic constraints on glacial isostatic adjustment in Europe , 2005 .

[4]  Zuheir Altamimi,et al.  IGS reference frames: status and future improvements , 2004 .

[5]  W. Peltier.  GLOBAL GLACIAL ISOSTASY AND THE SURFACE OF THE ICE-AGE EARTH: The ICE-5G (VM2) Model and GRACE , 2004 .

[6]  Yehuda Bock,et al.  Error analysis of continuous GPS position time series , 2004 .

[7]  Pascal Willis,et al.  Terrestrial reference frame effects on global sea level rise determination from TOPEX/Poseidon altimetric data , 2004 .

[8]  Michael B. Heflin,et al.  Large‐scale global surface mass variations inferred from GPS measurements of load‐induced deformation , 2003 .

[9]  D. Wolf,et al.  Pleistocene and recent deglaciation in Svalbard: implications for tide-gauge, GPS and VLBI measurements , 2003 .

[10]  T. P. Yunck,et al.  Origin of the International Terrestrial Reference Frame , 2003 .

[11]  G. Blewitt.  Self‐consistency in reference frames, geocenter definition, and surface loading of the solid Earth , 2003 .

[12]  Jean-François Crétaux,et al.  Seasonal and interannual geocenter motion from SLR and DORIS measurements: Comparison with surface loading data , 2002 .

[13]  C. Scholz,et al.  Mapping secondary mineral formation in porous media using heavy metal tracers , 2002 .

[14]  Zuheir Altamimi,et al.  ITRF2000: A new release of the International Terrestrial Reference Frame for earth science applications , 2002 .

[15]  J. Johansson,et al.  Continuous GPS measurements of postglacial adjustment in Fennoscandia 1. Geodetic results , 2002 .

[16]  Timothy H. Dixon,et al.  REVEL: A model for Recent plate velocities from space geodesy , 2002 .

[17]  J. Gregory,et al.  Changes in sea‐level , 2002 .

[18]  G. Blewitt,et al.  A New Global Mode of Earth Deformation: Seasonal Cycle Detected , 2001, Science.

[19]  M. Greff-Lefftz.  Secular variation of the geocenter , 2000 .

[20]  Anny Cazenave,et al.  Geocentre motion from the DORIS space system and laser data to the Lageos satellites: comparison with surface loading data , 2000 .

[21]  M. Watkins,et al.  Glacial isostatic adjustment observed using very long baseline interferometry and satellite laser ranging geodesy , 1999 .

[22]  R. Nerem,et al.  Geophysical interpretation of observed geocenter variations , 1999 .

[23]  T. Dixon,et al.  Noise in GPS coordinate time series , 1999 .

[24]  M. Watkins,et al.  Observations of tidally coherent diurnal and semidiurnal variations in the geocenter , 1997 .

[25]  M. K. Cheng,et al.  Geocenter variations caused by atmosphere, ocean and surface ground water , 1997 .

[26]  John Langbein,et al.  Correlated errors in geodetic time series: Implications for time‐dependent deformation , 1997 .

[27]  W. Peltier.  Mantle Viscosity and Ice-Age Ice Sheet Topography , 1996, Science.

[28]  D. Argus,et al.  Tests of the rigid-plate hypothesis and bounds on intraplate deformation using geodetic data from very long baseline interferometry , 1996 .

[29]  D. Argus.  Postglacial rebound from VLBI geodesy: On establishing vertical reference , 1996 .

[30]  Kosuke Heki,et al.  Horizontal and vertical crustal movements from three‐dimensional very long baseline interferometry kinematic reference frame: Implication for the reversal timescale revision , 1996 .

[31]  L. V. Morrison,et al.  Long-term fluctuations in the Earth’s rotation: 700 BC to AD 1990 , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[32]  Richard G. Gordon,et al.  Effect of recent revisions to the geomagnetic reversal time scale on estimates of current plate motions , 1994 .

[33]  W. Peltier,et al.  Ice Age Paleotopography , 1994, Science.

[34]  M. Watkins,et al.  Long term changes in the Earth's shape, rotation, and geocenter , 1993 .

[35]  J. Wahr,et al.  Effect of melting glaciers on the Earth's rotation and gravitational field: 1965–1984 , 1992 .

[36]  Richard G. Gordon,et al.  No-net-rotation model of current plate velocities incorporating plate motion model NUVEL-1 , 1991 .

[37]  Richard H. Rapp,et al.  The development of an isostatic gravitational model to degree 360 and its use in global gravity modelling , 1990 .

[38]  Richard G. Gordon,et al.  Current plate motions , 1990 .

[39]  W. Peltier.  The impulse response of a Maxwell Earth , 1974 .

[40]  W. Farrell.  Deformation of the Earth by surface loads , 1972 .