The Theory Of Rotation Of Non-rotational-symmetric Earth:Proper Modes, Forced Nutation And Diurnal Polar Motion

Development of gravity field techniques makes the determination of inertia moments of triaxial Earth more and more accurate. Development of space geodetic survey enables people observe and model the rotation of the Earth at an unprecedented accuracy level. The development of seismic tomography makes the setting up a mantle model with lateral inhomogeneity a possible option. In this dissertation, based on relevant models and formulas, Euler-Liouville equation appropriate for elastic, tri-axial and inhomogeneous Earth is set up and the influence of lateral inhomogeneity on Earth's nutation is discussed. Second-degree coefficients of static and time-varying gravity fields together with dynamical ellipticity are used to estimate the principal inertia moments as well as their variations and determine the orientation of principal axes and their variations. Based on density model of the Earth's surface CRUST2.0, contribution of each layer in the crust on the difference of equatorial principal inertia moments of the whole Earth is estimated. After considering the magnitude of dynamical equatorial flattening, Euler-Liouville equations appropriate for the considering the triaxiality of the whole Earth is given with discussion of relevant parameters in those equations. Analytical formula of FCN (Free Core Nutation) for a tri-axial Earth with two layers (mantle and the core) is also provided. Based on the theory of linear ordinary differential equations, equations appropriate for determining the proper modes of Euler-Liouville equations are also given. Based on the perturbation method proposed by Molodenskiy and lateral inhomogeneous mantle model GyPSuM, the influence of lateral inhomogeneity on the deformation parameters is studied. The influence of lateral inhomogeneity on the forced nutation is also studied. By using the Euler-Liouville's equation corresponding to a triaxial two layered Earth model, the response of the Earth's diurnal polar motion to excitation function is expressed as the sum of its responses to excitation of the same frequency and opposite frequency. Main conclusions are as follows:(1) Inertia moments estimated by using different static gravity field models are different, since different static gravity filed could belong to different reference epoch. For an Earth in postglacial rebound, different epoch means different second degree zonal coefficients.(2) Variation of orientation parameters of principal axes of tri-axial Earth is related with variation of certain second-degree spherical harmonic coefficient of Earth's gravity field. The longitude variation of equatorial principal axe is mainly related to the variations of C22and S22of second-degree spherical harmonic coefficient.(3) Dominant annual variations exist in the variations of longitude of equatorial principal axes. This dominant change can be proved to be real by using land surface water storage model.(4) The contribution of lateral inhomogeneity on the difference of equatorial principal inertia moments of the crust is of the same order to that of the difference of equatorial principal inertia moments of the rest of the Earth, but with opposite signs, which means that the difference of equatorial principal inertia moments of the whole Earth is also resulted from the layers bellow the crust while crust is actually a compensating mechanism to the difference of equatorial principal inertia moments of the whole Earth.(5) Analytical formula of FCN (Free Core Nutation) corresponding to tri-axial, elastic, two layered (the mantle and the core) is given. After truncating this formula, one can find that the contribution of equatorial flattenning of the core to the FCN is of second order of Earth's dynamical ellipticity.(6) Based on the theory of solution of linear ordinary differential equation, proper mode solutions of tri-axial Euler-Liouville equation containing complex deformation parameters are provided. It is also pointed out that four eigenvalues of that equation actually correspond to two normal modes:CW and FCN. If these two proper mode movements are elliptical movements, then each elliptical movement can be decomposed into the sum of two circular movements of opposite frequencies.(7) The increment of deformation parameters resulted from lateral inhomogeneity of the mantle is one order of ellipticity smaller than the zeroth order deformation parameters. Due to the lateral inhomogeneity, the compliances will be complex values. But as the lateral inhomogeneity of the mantle is small, the imaginary parts of the compliances can be ignored.(8) The influence of lateral heterogeneity on the forced nutation is of the order of1?as.(9) The response of the polar motion of the Earth includes same frequency response as well as opposite frequencies.(10) The influence of Earth's triaxiality on the ocean tide induced prograde/retrograde polar motion could reach1?as.