Estimation of the Earth's tensor of inertia from recent global gravity field solutions

Marchenko, A. N.; Schwintzer, P.

doi:10.1007/s00190-002-0280-7

Cited by 37 publications

(50 citation statements)

References 17 publications

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“…By solving an eigenvalue-eigenvector problem as discussed by Marchenko and Abrikosov (2001), Marchenko and Schwintzer (2003) and Chen and Shen (2010), we find A 20 , A 22 can be derived from C 2m , S 2m (m = 0, 1, 2):…”

Section: Dynamic Figure Factor Of the Earthmentioning

confidence: 99%

Consistent estimates of the dynamic figure parameters of the earth

Chen

Ray

et al. 2014

J Geod

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The Earth's dynamic figure parameters, namely the principal moments of inertia and dynamic ellipticities of the whole Earth, the fluid outer core and the solid inner core, are fundamental parameters for geodetic, geophysical and astronomical studies. This study aims to re-estimate the mass and the dynamic figure parameters of the Earth on the basis of some global gravity models (EGM2008, EIGEN-6C and EIGEN-6C2) recently released with unprecedented accuracies, as well as an improved value of the gravitational constant G recommended by the Committee on Data for Science and Technology (CODATA). With the potential coefficients of EGM2008, EIGEN-6C and EIGEN-6C2 rescaled to be consistent with the IAU (International Astronomical Union) and IAG (International Association of Geodesy) numerical standards, and other values of relevant parameters also being consistent with those numerical standards, we have obtained consistent estimates of the dynamic figure parameters of the stratified Earth using the theory described in Chen and Shen (J Geophys Res 115:B12419 2010). Our preferred principal moments of inertia for the whole Earth are A = (80,085.1 ± 9.6) × 10 33 kg m 2 , B = (80,086.8 ± 9.6) × 10 33 kg m 2 , and C = (80,349.0 ± 9.6) × 10 33 kg m 2 , respectively, the accu-

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Section: Dynamic Figure Factor Of the Earthmentioning

confidence: 99%

Consistent estimates of the dynamic figure parameters of the earth

Chen

Ray

et al. 2014

J Geod

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“…However, the axes of the principal moments of inertia differ from the axes of the above described terrestrial reference frame. This divergence is taken into account by means of a rotation [Marchenko and Schwintzer, 2003]. Consequently, I 0 does not have a diagonal structure with respect to the axes of the terrestrial reference frame.…”

Section: Liouville Differential Equationmentioning

confidence: 99%

Atmospheric and oceanic contributions to Chandler wobble excitation determined by wavelet filtering

Seitz¹,

Schmidt²

2005

J. Geophys. Res.

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[1] Fluctuations of Earth rotation are associated with the redistribution and motion of mass elements in the Earth system. On seasonal to interannual timescales, the largest effects are due to mass redistributions within atmosphere and oceans. In order to study the Earth's reaction on geophysical excitations, the dynamic Earth system model DyMEG has been developed. It is based on the balance of angular momentum in the Earth system. The model is forced by consistent atmospheric and oceanic angular momenta from reanalysis data and a global ocean circulation model. As rotational deformations of the Earth are regarded, forced variations of Earth rotation due to atmospheric and oceanic excitations influence the free polar motion (Chandler wobble) of DyMEG. The comparison of the numerical model results with geodetic observations reveals a good agreement in both the annual and the Chandler frequency band. In order to support the presumption that the excitation energy of atmospheric and oceanic angular momenta within a spectral band around the Chandler frequency is sufficient to reproduce the observed Chandler wobble, the excitation series are band-pass filtered. For consistent filtering and signal analysis, wavelet techniques based on the Morlet function are applied. When DyMEG is forced with the filtered excitations, the resulting polar motion resembles the actually observed Chandler oscillation, which is determined from geodetic observations applying the same filtering method. Between 1980 and 2002 the correlation coefficient between the unconstrained model result and the observed Chandler wobble amounts to 0.99 and the root-mean-square difference is 16 milliarc seconds.Citation: Seitz, F., and M. Schmidt (2005), Atmospheric and oceanic contributions to Chandler wobble excitation determined by wavelet filtering,

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“…(3). Thus, to avoid uncertainty in the deviatoric part of inertia tensor in the case of different sequences of finite rotations we will use in contrast to (Marchenko and Schwintzer, 2003) a commutative rotation about the nodes line of XYZ and X Y Z systems with the following transformation of the coordinate vector r = Q · r from XYZ to X Y Z frame, where according to Madelund (1957) …”

Section: Introductionmentioning

confidence: 99%

“…The preceding solution for the Earth's principal axes (A, B, C), principal moments of inertia (A, B, C), and other fundamental constants was created in (Marchenko and Schwintzer, 2003) from the A.N. Marchenko National University "Lviv Polytechnic", Institute of Geodesy, Bandera St. 12, 79013 Lviv, Ukraine adjustment at the epoch 1997 of four sets of 2nd degree gravitational harmonic coefficients C 2m , S 2m of the Earth's gravity models and six values of dynamical ellipticity H D .…”

Section: Introductionmentioning

confidence: 99%

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Current Estimation of the Earth’s Mechanical and Geometrical Parameters

Marchenko

2009

International Association of Geodesy Symposia

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The Earth's mechanical and geometrical parameters were estimated from the simultaneous adjustment of the 2nd-degree harmonic coefficients of six gravity field models and seven values of the dynamical ellipticity H D all reduced to the common MHB2000 precession constant at epoch J2000. The transformation of 2nd-degree harmonic coefficients in the case of a finite commutative rotation was developed to avoid uncertainty in the deviatoric part of inertia tensor. This transformation and the exact solution of eigenvalueeigenvector problem are applied to determine (a) the static components and accuracy of the Earth's tensor of inertia at epoch 2000 and (b) the time-dependent constituents of the inertia tensor. Special attention was given to the computation of temporally varying components of the Earth's inertia tensor, which are based on the time series of 2nd-degree coefficients through GRACE observations. A remarkable stability in time of the position of the axis A of inertia as the parameter of the Earth's triaxiality is discussed.

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Estimation of the Earth's tensor of inertia from recent global gravity field solutions

Cited by 37 publications

References 17 publications

Consistent estimates of the dynamic figure parameters of the earth

Consistent estimates of the dynamic figure parameters of the earth

Atmospheric and oceanic contributions to Chandler wobble excitation determined by wavelet filtering

Current Estimation of the Earth’s Mechanical and Geometrical Parameters

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