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Accurate correction models for tidal gravity in Chinese continent are developed by using the recent theoretical and experimental models for the Earth's tidal gravity, in which the loading effects of the global and local ocean tides are combined. The relative difference of tidal gravity variations induced from different Earth's tidal gravity models is less than 0.06%. The ocean tide loading effects are about 4% of the total tidal gravity in coastal area while they are about 1% in inland. The difference between the ocean tide loading effects estimated from global ocean tide models and modified global models with local tides is about 10% of the total ocean tide loading effects. And the interpolated and extrapolated ocean tide loading effects are about 3% of the total ones. Comparing the observed tidal gravity variations by superconducting gravimeter with the ones calculated through the correction models, it is confirmed that the models developed in this study can accurately predict the tidal gravity signatures with a precision much better than 0.5 × 10−8 m·s−2. Consequently, it is expected that the models should provide an effective reference and accurate correction models for gravity measurements.

The retrograde rotational eigenmodes are produced by the interaction between solid mantle and liquid core in a rotating elliptical Earth, usually called free core nutation (FCN). The FCN quality factor (Q value), which depends on viscosity at the core-mantle boundary (CMB), can eectively reflect the characteristics of energy dissipation at the CMB. The viscosity of the CMB is estimated for the first time based on the FCN quality factor Q values determined from stacking 27 high-rate sampling and high-precision tidal gravity observations at 23 stations in the Global Geodynamics Project (GGP) network around the world. The numerical results show that the dynamic viscosity can reach the order of 10 3 Pa·s. It is in good agreement with the most recent values deduced from VLBI observations by Smylie and Palmer. This result indicates that gravity is one of ecient techniques for the investigation of the Earth deep internal structure.

Using observations of the superconducting gravimeter GWR-C032 at station Wuhan, the tidal gravity parameters reflecting the characteristics of the Earth's interior medium are obtained based on the harmonic analysis after variable preprocessing to the raw data. Meanwhile the gravity loading are calculated using the loading theory and a numerical integral convolution technique based on various global ocean tide models developed by methods of the altimetry technology and finite element with consideration of tidal gauge data as constraints. The loading corrections are carried out for tidal gravity parameters in diurnal and semidiurnal wave bands, respectively in order to investigate the adaptability of global ocean tide models. The numerical results show that the efficiencies of loading correction reach to 91% (O1, NAO99) and 92% (M2, ORI96) for instance. The average efficiencies of the loading corrections obtained with 11 oceanic models for four main constituents (O1, K1, M2 and S2) are 86%, 70%, 73% and 84%, respectively. And the discrepancies between amplitude factors and theoretical values decrease from (2.12%, 1.55%, 1.16% and 0.80%) to (0.31%, 0.39%, 0.34% and 0.08%), respectively. The comparison among various ocean models also shows that the loading correction efficiencies when using NAO99 and ORI96 models are higher than those when using other models. Additionally, other observations obtained with superconducting gravimeters at 7 stations in a network of the Global Geodynamic Project are also adopted to investigate the adaptability of the global ocean models. The results show that there exist obvious local tidal characteristics for different constituents in different ocean models and the earlier constructed SCW80 ocean model can still be used as an important reference in geodesy research.

Possibility of detection of the long-period core modes has been discussed in this paper by using the long-term gravity observations recorded with 13 superconducting gravimeters (SGs) in a worldwide network of the Global Geodynamics Projects. Identical techniques are used to remove the luni-solar gravity tides, the long-term trends of instrument drift, and the effects of atmospheric pressure from all 13 SG data sets. The power spectral density of each data set, as well as the product spectral density of all the data sets, is evaluated. The background noise levels in various non-tidal bands are estimated and analyzed. The results indicate that the background noise level of the global SG observations is 0.0649nm/s2 in inter-tidal band from 0.047 to 0.075cph, 0.0350nm/s2 in another inter-tidal band from 0.089 to 0.117cph, and 0.0138nm/s2 in the sub-tidal band from 0.172 to 0.333cph. The magnitude thresholds of any global harmonic signals, which may be detected by the global SGs, in these three non-tidal bands are 0.0416, 0.0231 and 0.0098nm/s2, respectively. It implies that the signals, related to the long-period core modes, may be identified in the global SG observations, if they exist. The spectral peaks of the global harmonic signals with periods of 16.55, 15.79, 11.00 and 10.09h are detected in the two inter-tidal bands of the global SG records, and they may come from the long-period oscillations in the fluid outer core of the Earth. In the sub-tidal band, there are no obvious peaks relating to the Slichter triplet claimed by Smylie in 1992. Instead, 8 spectral peaks of global harmonic signatures significantly emerge from the background noise. Comparing their periods with those of the Slichter triplet predicted theoretically, it may be concluded that the Slichter triplet is the possible sources of three peaks of them. Of course, a more certain conclusion cannot be drawn now until further knowledge of the deep interior of the Earth is obtained and more acceptable theoretical technique for the dynamic study of the fluid outer core is developed.

This study is based on the elasto-gravitational motion equations for a hydrostatic equilibrium Earth. The relative rotation among the solid elastic mantle, the fluid outer core and the solid elastic inner core is governed by the angular momentum equation. The deformation response of the mantle and inner core to the core dynamics, generated by the perturbations on the boundaries of the fluid outer core, is considered on the assumption of spherical symmetry and employed to constrain the movement on the boundaries of the fluid outer core. Based on the general symmetrical characteristics of the Earth's eigenmodes, the variational principle of free oscillations in a rotating, inviscid and elliptically stratified fluid outer core is developed and the corresponding functional is deduced.