Cheng-Li Huang

The scalar boundary conditions for the motion of the elastic earth to second order in ellipticity

The scalar equations of infinitesimal elastic gravitational motion for a rotating, slightly elliptical Earth are always used to study the Earths nutation and tides theoretically, while the determination of the integration of the equations depends, to a certain extent, on the choice of a set of appropriate boundary conditions. In this paper, a continuity quantity related to the displacement is first transformed from the elliptical reference boundary to the corresponding effective spherical domain, and then converted from a vector (or tensor) form to a scalar form by generalized surface spherical harmonics expansion. All the related components, including the displacement vector field (or the stress tensor field), are then decomposed into the poloidal and toroidal field using the symmetry restrictions on the normal mode eigenfunctions. After truncation, the boundary conditions are finally derived, in a scalar ordinary differential form. The process of the derivation is second order in ellipticity and in full detail. Moreover, the other boundary conditions are also presented as second order in ellipticity at the end of this paper.

On the coupling between magnetic field and nutation in a numerical integration approach

Nutation amplitudes are computed in a displacement field approach that incorporates the influence of a prescribed magnetic field inside the Earths core. The existence of relative nutational motions between the liquid core and its surrounding solid parts induces a shearing of the magnetic field. An incremental magnetic field is then created, which in return perturbs the nutations themselves. This problem has already been addressed within a nutation model computed from an angular momentum budget approach. Here we incorporate the magnetic field influence directly in the motion equation and in the boundary conditions used in precise nutation theory, and a new strategy to compute nutations is established. As in previous studies, we assume that the root-mean-square of the radial magnetic field amplitude at the core-mantle boundary is 6.9 Gauss, that the magnetic diffusivity at the bottom of the mantle and in the fluid outer core side is 1.6 m(2)/s, and that the thickness of the conductive layer at the bottom of the mantle is 200 m. The Coriolis force is included in this work. The results show that the free core nutation period decreases by 0.38 days, and that the out-of-phase (in-phase) amplitudes of the retrograde 18.6 year and the retrograde annual nutations increase (decrease) by 20 and 39 mu as, respectively. Comparisons of these results with previous studies are made, and discussions are also presented on the contribution of Coriolis force and the prescribed magnetic field on the coupling constants.

A generalized theory of the figure of the Earth: formulae

Traditionally a laterally homogeneous and spherical base Earth model (e.g., the PREM model) is considered as input when computing the Earth’s equipotential surfaces, which are then resulted to be in symmetric shape. However, the Earth, known with a complex distribution of interior material and density, especially in the upper mantle and the crust, cannot be treated as a symmetric sphere. Recently, a CRUST1.0 model of crust layer is published and well accepted. But the effect caused by the asymmetric crust (and mantle) on equilibrium figures of the Earth cannot be analyzed by the traditional theories. A generalized theory of the figure of the Earth to third-order precision is firstly proposed in this paper, as well as the iterative calculation strategy to solve the complex equation system. In order to validate this generalized theory, the degeneration of this generalized theory with the PREM model is made and is compared with traditional theories, and it is shown that the result of this generalized theory, after degeneration, is consistent very well with traditional theory. Meanwhile, the effect (including both the direct and indirect effects) of the crust layer, from the CRUST1.0 model, on the figures of equipotential surfaces of the Earth’s interior, as well as their effects on the global dynamics flattening, will be presented as an application of this theory in accompanying paper.

A generalized theory of the figure of the Earth: on the global dynamical flattening

A generalized theory of the figures of the Earth’s interior to a third-order precision of ellipticity is proposed in accompanying paper in which all the odd degree and nonzero order spherical harmonic terms are included. As both the direct and indirect contributions of the asymmetric crust are included, this theory makes a significant improvement for calculating the asymmetric equilibrium figures of the real Earth comparing with the traditional theories which can only deal with the ideal symmetric Earth. The principal moments of inertia (PMOI: A, B, C) and global dynamical flattening (H) are important quantities in studying the rotating Earth. Precession and gravity observations give observation value of H (

Preliminary result of the earth's free oscillations by galerkin method

H_{\mathrm{obs}} \approx 1/305.4559

Commission 19: Rotation of the Earth: (Rotation De La Terre)

Hobs≈1/305.4559) with very high precision, while its theoretical calculated value (

A new nutation model of a non-rigid earth with ocean and atmosphere

H_{\mathrm{theory}} \approx 1/308.5