Hamiltonian theory for the non-rigid Earth: 
Semidiurnal terms

Getino, Juan; Ferrándiz, José M.; Escapa, Alberto

doi:10.1051/0004-6361:20010186

Cited by 12 publications

(10 citation statements)

References 16 publications

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“…However, as will be seen from the theoretical development to be presented in later sections, the use of that transfer function, which was constructed for the low frequency nutations, is inappropriate in principle for high frequency nutations. Semidiurnal nutations of the nonrigid Earth have been computed by Getino et al (2001). Their results are consistent with the transfer function being essentially constant across the semidiurnal band.…”

Section: The New Nutation Series Thus Constructed Includesupporting

confidence: 56%

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

Mathews¹,

Bretagnon

2003

A&A

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Abstract. The coefficients of polar motions of the rigid/nonrigid Earth in frequency bands other than the retrograde diurnal one are systematically computed using general expressions, derived here for the first time, for the prograde and retrograde torques exerted on the Earth by lunisolar potentials of arbitrary spherical harmonic type. Taken together with the already known coefficients of low frequency nutations and UT1 variations, they provide a complete characterization, with high precision, of the motions of the pole of the terrestrial reference frame in space; this is needed for high precision studies in astronomy and space geodesy. The inputs used for our computations are a table of tidal amplitudes, and values of the geopotential coefficients of degrees up to 4 and of other relevant basic Earth parameters. General relations which connect the coefficients of high frequency nutations to those of the equivalent polar motions are established and used for deducing the former. The Chandler resonance plays a significant role in low frequency polar motions. In this context, the role of mantle anelasticity and the nature of the Earth's deformational response to zero frequency forcing are given special consideration. The free core nutation (FCN) resonance of low frequency nutations is shown to affect the prograde semidiurnal nutations through the coupling produced between the nutations in the two frequency bands by triaxiality terms in the angular momenta of the whole Earth and of its fluid core. It is shown in a transparent fashion that the effect of the core triaxiality arises almost exclusively from the huge FCN-related resonance in the wobble of the core. The magnitude of the effect is found to be a few times smaller than reported in a recent paper; it is also found, unlike in that paper, that the changes in the eigenfrequencies due to trixiality are only of the second order in the triaxiality parameter. Numerical results for the polar motions of the nonrigid Earth in different frequency bands, as well as for the elliptical nutations of the rigid Earth, are tabulated and compared with available numbers from earlier works.

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Section: The New Nutation Series Thus Constructed Includesupporting

confidence: 56%

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

Mathews¹,

Bretagnon

2003

A&A

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“…Finally, let us point out that the internal structure of the Earth could amplify these effects due to the resonance caused by the fluid core, that could reach even a few microarcseconds. So, this discussion should be extended to non-rigid Earth models, in the same way as Getino et al (2001), who studied the effect of the C 22 and S 22 coefficients on the nutations of a two layer Earth model. This work is in progress and will be presented in a forthcoming paper.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The first effect has already been calculated by Kinoshita & Souchay (1990), Souchay & Kinoshita (1997), Souchay et al (1999) and Folgueira et al (1998aFolgueira et al ( , 1998b and it will not be treated in this work. On the other hand, Getino et al (2001) computed the "direct effect" of the C 22 and S 22 harmonics for a two-layer, non-rigid Earth model.…”

Section: Introductionmentioning

confidence: 99%

Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations

Escapa

Getino

Ferrándiz

2002

A&A

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“…Since the tidal observation at minor tides are The Earth is a triaxial body. The principal inertia moments of the Earth A, B, and C are not equal, and it is customary to assume A < B < C. Because of the triaxiality of the Earth [Liu and Chao, 1991;Wang, 1994;Dehant et al, 1999;Marchenko and Schwintzer, 2003;Chen and Shen, 2010], external torque will contribute to the prograde diurnal polar motion [Getino et al, 2000[Getino et al, , 2001Escapa et al, 2002aEscapa et al, , 2002bEscapa et al, , 2003Mathews and Bretagnon, 2003]. The largest component of this contribution is at K 1 frequency, at which the influence has an amplitude of 16 μas [Mathews and Bretagnon, 2003].…”

Section: Introductionmentioning

confidence: 99%

“…Contribution from the triaxaility of the whole Earth to the prograde diurnal polar motion that is induced by external torque is also provided in IERS Conventions (2010) based on Mathews and Bretagnon [2003]. The core could also be a triaxial body, which will also contribute to the prograde polar motion [Getino et al, 2001;Escapa et al, 2003;Mathews and Bretagnon, 2003]. However, IERS Conventions (2010) neglects the contribution of a triaxial core because of the large uncertainty of the triaxiality of the core [Petit and Luzum, 2010].…”

Section: Introductionmentioning

confidence: 99%

Influence of dynamical equatorial flattening and orientation of a triaxial core on prograde diurnal polar motion of the Earth

Sun

Shen

2016

JGR Solid Earth

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The noise floor of empirical models of the prograde diurnal Earth rotation could reach as low as 1 µas as shown by several recent studies. In another aspect, the differences between these empirical models with the theoretical model predictions given by International Earth Rotation and Reference Systems Service (IERS) Conventions (2010) for certain diurnal frequencies are more than 10 µas (e.g., K1). The triaxiality of the core is ignored in the theoretical model given by IERS Conventions (2010) because it is highly uncertain. To explain the differences between the empirical models and the theoretical model, we consider the possible influence of a triaxial core. We use the differences between the empirical models and the theoretical model predictions given by IERS Conventions (2010) as inputs to invert the triaxiality parameter of the core. In the inversion, we assume the ocean tide response is subjected to the admittance theory. So extra six admittance parameters are introduced to model the differences between the smooth responses inferred from the empirical models and that given by theoretical model predictions from IERS Conventions (2010). The results show that adding core triaxiality into the theoretical model could narrow the differences between the empirical models and the theoretical model at the prograde diurnal band. As for the dynamical equatorial flattening of the core, the estimates inverted based on the different empirical models are consistent within standard deviation. The results also suggest that the principal axes of the triaxial core do not coincide with the principal axes of the whole Earth.

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Hamiltonian theory for the non-rigid Earth: Semidiurnal terms

Cited by 12 publications

References 16 publications

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations

Influence of dynamical equatorial flattening and orientation of a triaxial core on prograde diurnal polar motion of the Earth

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