The Earth's rotation is perturbed by mass redistributions and relative motions within the Earth system, as well as by the torques from both the internal Earth and celestial bodies. The present study aims to establish a theory to incorporate all these factors perturbing the rotation state of the triaxial Earth, just like the traditional rotation theory of the axial-symmetric Earth. First of all, we reestimate the Earth's inertia tensor on the basis of two new gravity models, EIGEN-GLO5C and EGM2008. Then we formulate the dynamic equations and obtain their normal modes for an Earth model with a triaxial anelastic mantle, a triaxial fluid core, and dissipative oceans. The periods of the Chandler wobble and the free core nutation are successfully recovered, being —433 and —430 mean solar days, respectively. Further, the Liouville equations and their general solutions for that triaxial nonrigid Earth are deduced. The Liouville equations are characterized by the complex frequency-dependent transfer functions, which incorporate the effects of triaxialities and deformations of both the mantle and the core, as well as the effects of the mantle anelasticity, the equilibrium, and dissipative ocean tides. Complex transfer functions just reflect the fact that decays and phase lags exist in the Earth's response to the periodic forcing. Our theory reduces to the traditional rotation theory of the axial-symmetric Earth when assuming rotational symmetry of the inertia tensor. Finally, the present theory is applied to the case of atmospheric-oceanic excitation. The effective atmospheric-oceanic angular momentum function (AMF) x_(eff) = X_(eff) + iX_(eff2) for the present theory is compared with the AMF x_(eff) = X_(eff) + ix__(eff) for the traditional theory and the observed AMF X~(obs)=X ~(obx)+iX_2; we find that the difference between x_(eff)and x_(eff) is of a few milliseconds of arc (mas) and can sometimes exceed 10 mas. In addition, spectrum analyses indicate that x_(eff) is in good agreement with x_(eff) and, further, show an increase of coherency with x~(obs) especially in the low-frequency band. The obvious advantage of x_(eff) in the low-frequency band with respect to x_(eff) is the critical support of the present theory. However, still better performance of our theory can be expected if the models of the mantle anelasticity and oceanic dynamics were improved. Thus we conclude that the traditional Earth rotation theory should be revised and upgraded to include the effects of the Earth's triaxiality, the mantle anelasticity, and oceanic dynamics. The theory presented in this study might be more appropriate to describe the rotation of the triaxial Earth (or other triaxial celestial bodies such as Mars), though further studies are needed to incorporate the effects of the solid inner core and other possible influences.
展开▼
