Consistent estimates of the dynamic figure parameters of the earth

Abstract

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-

Contributions of the Elasticity to the Precession of a Two-Layer Earth Model

“…Although there is a high degree of agreement among different determinations of it, we found no recent, reliable, explicit evaluation of its uncertainty and had to resort to indirect estimations. For instance, we could consider the recent determinations of the moments of inertia of Earth's layers appearing in Table 9 of Chen et al (2015), which assimilate information from the most accurate geopotential models. The r cm uncertainty estimated from those data is ±0.00005 and contributes with ±0.006 mas/ cy to the dp uncertainty, whose final value has been set to ±0.01 mas/cy in Table 4.…”

Formulation of a Triaxial Three‐Layered Earth Rotation: Theory and Rotational Normal Mode Solutions

“…The dynamical figure parameters are the principal moments of inertia and dynamical ellipticities of the whole Earth, the fluid outer core, and the elastic inner core, respectively. In Model 1, we use the triaxial three‐layered dynamical figure parameters of Case III of Table 8 from Chen et al (), who estimated these parameters based on new gravity field models EGM2008 (Pavlis et al, ), EIGEN‐6C (Förste et al, ), and EIGEN‐6C2 (Förste et al, ). In Model 2, the rotational symmetric equatorial principal moments of inertia , , and are obtained by averaging Model 1's equatorial principal moments of inertia, and the polar principal moments of inertia are obtained by , , , with the dynamical ellipticities deploying Model 1's values.…”

“…In Chen et al (), only the uncertainties of principal moments of inertia for whole Earth are estimated simply, and in Mathews et al (), the uncertainties for dynamical ellipticities of the whole Earth and fluid outer are, respectively, 0.0000000012 and 0.0000020, while the dynamical ellipticity of the elastic inner core is a theoretical value based on PREM Earth model, and the corresponding uncertainty is not provided.…”

“…Hence, by treating m, m , m s , n s , c s i , c i , and c i as first-order small quantities and neglecting higher-order terms, the new triaxial three-layered Earth rotation theory with properly inner core elastic deformations modeling can be formulated as Chen et al (2015), only the uncertainties of principal moments of inertia for whole Earth are estimated simply, and in Mathews et al (2002), the uncertainties for dynamical ellipticities of the whole Earth and fluid outer are, respectively, 0.0000000012 and 0.0000020, while the dynamical ellipticity of the elastic inner core is a theoretical value based on PREM Earth model, and the corresponding uncertainty is not provided.…”

Geodynamics

“…It should be noted that the accuracy of satellite observations became more precise after the launch of the Italian LARES mission designed to test General Relativity in the weak gravity field of the Earth, including geodetic data. In the last decades these satellites together with astronomical data allow to determine with higher accuracy the Earth's fundamental constants by means of different approaches [Marchenko & Schwintzer, 2003;Groten, 2004;Petit & Luzum, 2010;Chen & Shen 2010;Chen et al, 2015;Cheng et al, 2011;Cheng, et al, 2013;etc]. Generally speaking due to unstable determination of the precession constant (before 2002) [Marchenko & Schwintzer, 2003].…”