Flattening of the Earth: further from hydrostaticity than previously estimated

Abstract

International audienceThe knowledge of the gravitational potential coefficients J2 and J4 of a hydrostatic Earth model is necessary to deal with non-hydrostatic properties of our planet. They are indeed fundamental parameters when modelling the 3-D density structure or the rotational behaviour of our planet. The most widely used values computed by Nakiboglu need to be updated for two reasons. First, we have noted a mistake in one of his formulae. Secondly, the value of the inertia ratio I/MR2 chosen at the time of PREM is not any more the best estimate. Both corrections slightly but significantly reduce the hydrostatic J2 value: the dynamical flattening of the Earth is even further from hydrostaticity than previously thought. The difference between the polar and equatorial radii appears to be 113 +/- 1 m (instead of 98 m) larger than the hydrostatic value. Moreover, uncertainties upon the hydrostatic parameters are estimated

Dynamic topography, gravity and the role of lateral viscosity variations from inversion of global mantle flow

“…Geruo et al (2013) load a compressible, viscoelastic earth with the ICE-5G global ice loading history and then infers the glacial isostatic adjustment and the present-day gravitational signals due to the incomplete postglacial rebound. Compared to the Nakiboglu (1982) hydrostatic Earth model, the Chambat et al (2010) model yields a more oblate non-hydrostatic geoid, with the geoid at the equator higher than that using the Nakiboglu correction. However, the inverted mantle structure is not significantly affected by changes in the hydrostatic model.…”

“…It has also recently been suggested that the gravity gradients (for example, from the GOCE, Gravity field and steady-state Ocean Circulation Explorer, mission) provide additional constraints on mantle structure and dynamics (Panet et al, 2014). The zonal coefficients of the hydrostatic (Chambat et al, 2010) and coefficients of incomplete postglacial rebound (Geruo et al, 2013) have been subtracted from the GOCE (Reguzzoni and Tselfes, 2009) geopotential models to reveal a gravitational signal putatively related to mantle flow. Geruo et al (2013) load a compressible, viscoelastic earth with the ICE-5G global ice loading history and then infers the glacial isostatic adjustment and the present-day gravitational signals due to the incomplete postglacial rebound.…”

Efficient early global relaxation of asteroid Vesta

“…However, no such feature is observed at degree-2 (Ermakov et al, submitted). The correponding global disequilibrium factor (f −f eq ) of 0.07 is more than three orders of magnitude greater than the value for the Earth (Chambat et al, 2010). The impact basins and the non-hydrostatic bulge may have formed in the same giant impact events, which may contribute to topographic disequilibrium via direct redistribution of mass and change to the rotation period or axis.…”

Third-order development of shape, gravity, and moment of inertia for highly flattened celestial bodies. Application to Ceres

“…Computing the hydrostatic shape for a multi-layered solid body is not straightforward and involves theoretical and numerical techniques to reach high-order accuracy. Here, we follow the currently best technique for Earth studies, which is based on Kopal (1960), Lanzano (1974), and Chambat et al (2010).…”

“…2), we introduce the shape-modeling framework inherited from Earth geodetic studies by Chambat et al (2010) and extended to third order by using the formalism of Lanzano (1974). Then we introduce the density profiles we used to apply our modeling to Ceres.…”