# A generalized theory of the figure of the Earth: on the global dynamical flattening

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## Abstract

A generalized theory of the figures of the Earth’s interior to a third-order precision of ellipticity is proposed in accompanying paper in which all the odd degree and nonzero order spherical harmonic terms are included. As both the direct and indirect contributions of the asymmetric crust are included, this theory makes a significant improvement for calculating the asymmetric equilibrium figures of the real Earth comparing with the traditional theories which can only deal with the ideal symmetric Earth. The principal moments of inertia (PMOI: *A*, *B*, *C*) and global dynamical flattening (*H*) are important quantities in studying the rotating Earth. Precession and gravity observations give observation value of *H* (\(H_{\mathrm{obs}} \approx 1/305.4559\)) with very high precision, while its theoretical calculated value (\(H_{\mathrm{theory}} \approx 1/308.5\)) from traditional theories and a starting symmetric Earth model (like PREM model) is about \(1\%\) less than \(H_{\mathrm{obs}}\). Using the new theory in accompanying paper and replacing the homogeneous outermost crust and oceanic layers in PREM with CRUST1.0 model, we recalculate the equilibrium figures of the Earth’s interior and finally get new values of PMOI and \(H_{\mathrm{theory}}\) (\({\approx } \,1/304.7167\)) whose consistency with \(H_{\mathrm{obs}}\) are significantly improved to 0.24%. Furthermore, the asymmetric figures of some interesting boundaries, like inner core boundary, core-mantle boundary, are also given as by-products of this work as these boundaries’ figures are key input for studies of their topographic effect on global rotation and geodynamics, like nutation, normal modes, especially like free core nutation.

## Keywords

Figure of the Earth Global dynamical flattening Principal moments of inertia Inner core boundary Core-mantle boundary CRUST1.0## Notes

### Acknowledgements

This work is supported by NSFC (11773058/113 73058). Three anonymous reviewers are appreciated for their constructive comments and suggestions.

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