On the effect of the mantle elasticity on the earth's rotation

Abstract

Starting from the Hamiltonian model for a solid Earth with an elastic mantle previously developped by the authors, analytical expressions are derived which give the nutation series corresponding to the plane perpendicular to the angular momentum vector, to the plane perpendicular to the rotational axis and to the equator of figure, as well as the series that give the polar motion. The effects of the different perturbations -solid Earth, centrifugal and tidal potentials -are calculated separately. The corrections due to the elasticity of the mantle, which mostly correspond to the Oppolzer terms, are calculated with an accuracy of 10 -6 arc sec., given that the intrinsic observational accuracy has reached 0.0l mas.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

“…As A m \A, frequency r 1 is larger for a Poincaré Earth than for a rigid Earth, so that the period of the polar oscillation is shortened by the fluid core. The lengthening of the period is mainly due to the elastic yielding of the earth, as already explained by NEWCOMBE (1892)-see also GETINO and FERRÁ NDIZ (1995) who performed more detailed calculations.…”

“…Accurate solutions for a Poincaré model were computed much later by GETINO (1995) and GETINO and FERRÁ NDIZ (1997), but using their Hamiltonian method. Let the tensors of inertia be P m for the mantle, P c for the core and P ¼ P m þ P c for the whole Earth, which are assumed constant in a frame attached to the (rigid) mantle.…”

“…Þmeans that an appropriate definition of the core rotation (MORITZ 1982) has been made, so that it is referred to a Tisserand frame (MORITZ 1982), as detailed in GETINO (1995). The kinetic energy is thus…”

Dynamical adjustments in IAU 2000A nutation series arising from IAU 2006 precession

“…On the other one, the Hamiltonian formalism can be extended to consider other non-rigid Earth models (e.g., Getino & Ferrándiz 1995;Escapa et al 2001, Escapa 2011. Hence, the developments made here can be directly incorporated to those theories, providing an integrated framework to study the Earth's rotational motion.…”

Canonical treatment of dissipative forces between Earth mantle and core

“…The study of the Earth rotation is not an exception, and the theory of Kinoshita (1977) is the most complete and accurate among those for a rigid Earth model. Recently, the Hamiltonian approach has been followed by the authors in order to extend Kinoshita's theory to general models of deformable Earth through a series of papers, first considering an elastic mantle (Getino and Ferrândiz, 1995), then a liquid core (Getino, 1995a(Getino, , 1995b. We only point out here that the results obtained are completely analytical, and depend on parameters that are provided by the different Earth models available.…”