# Elliptic polarisation of the polar motion excitation

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## Abstract

Because of its geophysical interpretation, Earth’s polar motion excitation is generally decomposed into prograde (counter-clockwise) and retrograde (clockwise) circular terms at fixed frequency. Yet, these later are commonly considered as specific to the frequency and to the underlying geophysical process, and no study has raised the possibility that they could share features independent from frequency. Complex Fourier Transform permits to determine retrograde and prograde circular terms of the observed excitation and of its atmospheric, oceanic and hydrological counterparts. The total prograde and retrograde parts of these excitations are reconstructed in time domain. Then, complex linear correlation between retrograde and conjugate prograde parts is observed for both the geodetic excitation and the matter term of the hydro-atmospheric excitation. In frequency domain, the ratio of the retrograde circular terms with their corresponding conjugate prograde terms favours specific values: the amplitude ratio follows a probabilistic gamma distribution centred around 1.5 (maximum for 1), and the argument ratio obeys a distribution close to a normal law centred around \(2 \alpha = 160^{\circ }\). These frequency and time domain characteristics mean an elliptical polarisation towards \(\alpha ={\sim } 80^{\circ }\) East with an ellipticity of 0.8, mostly resulting from the matter term of the hydro-atmospheric excitation. Whatsoever the frequency band above 0.4 cpd, the hydro-atmospheric matter term tends to be maximal in the geographic areas surrounding the great meridian circle of longitude \({\sim }80^{\circ }\) or \({\sim } 260^{\circ }\) East. The favoured retrograde/prograde amplitude ratio around 1.5 or equivalently the ellipticity of 0.8 can result from the amplification of pressure waves propagating towards the west by the normal atmospheric mode \(\Psi _3^1\) around 10 days.

## Keywords

Earth’s rotation Polar motion Hydro-atmospheric excitation Elliptical polarisation## Notes

### Acknowledgments

We are grateful to our three reviewers for their careful analysis, which permitted to improve the quality of this study. We are especially indebted to Leonid Zotov for having carried out some computational check.

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