Measurement of diurnal and semidiurnal rotational variations and tidal parameters of Earth


  • Thomas A. Herring,

  • Danan Dong


We discuss the determination of diurnal and semidiurnal variations in the rotation rate and the direction of rotation axis of Earth from the analysis of 8 years of very long baseline interferometry (VLBI) data. This analysis clearly show that these variations are largely periodic and tidally driven; that is, the periods of the variations correspond to the periods of the largest lunar and solar tides. For rotation rate variations, expressed in terms of changes in universal time (UT), the tidal lines with the largest observed signals are O1 (amplitude 23.5 microseconds in time (μs), period 25.82 solar hours); K1 (18.9 μs, 23.93 hours); M2 (17.9 μs, 12.54 hours); and S2 (8.6 μs, 12.00 hours). For variations in the direction of the rotation axis (polar motion), significant signals exist in the retrograde semidiurnal band at the M2 and S2 tides (amplitudes 265 and 119 microarc seconds (μas), respectively); the prograde diurnal band at the O1, K1, and P1 tides (amplitudes 199,152, and 60 μas, respectively); and the prograde semidiurnal band at the M2 and K2 tides (amplitudes 58 and 39 μas, respectively). Variations in the retrograde diurnal band are represented by corrections to the nutations of Earth's body axes, and our estimates here are consistent with previous estimates except that a previously noted discrepancy in the 13.66-day nutation (corresponding to the O1 tide) is largely removed in this new analysis. We estimate that the standard deviations of these estimates are 1.0 μs for the UTl variations and 14–16 μas for the polar motion terms. These uncertainties correspond to surface displacements of ∼0.5 mm. From the analysis of atmospheric angular momentum data we conclude that variations in UTl excited by the atmosphere with subdaily periods are small (∼1 μs). We find that the average radial tidal displacements of the VLBI sites in the diurnal band are largely consistent with known deficiencies in current tidal models, i.e., deficiencies of up to 0.9 mm in the treatment of the free core nutation resonance. In the semidiurnal band, our analysis yields estimates of the second-degree harmonic radial Love number h2 at the M2 tide of 0.604+i0.005±0.002. The most likely explanation for the rotational variations are the effects of ocean tides, but there may also be some contributions from atmospheric tides, the effects of triaxiality of Earth, and the equatorial second-degree-harmonic components of the core-mantle boundary.