Study of the Earth rheological properties from polar motion

<pre>Since the beginning of the 20th century, the observation of the Earth rotation variations through astro-geodetic <br />techniques enables to investigate the global rheological properties of the Earth, in particular, the resonance <br />parameters of the free rotation modes reflect the solid Earth anelasticity, the ocean response to an external <br />forcing, and the properties of the fluid inner core, eventually of the solid inner core. Better constraints on <br />these resonance parameters can be obtained by confronting the observed terrestrial motion of the rotation pole <br />(the so-called polar motion) - including nutation as a retrograde diurnal polar motion - to the modeled excitation <br />producing it. The more precise the modeled excitation and the observed polar motion are, the better the<br />Earth rheological properties will be determined. For now, the best precision is reached in the<br />nutation band. So, the analysis has been first dedicated to a direct adjustment of the nutation components<br />from VLBI delays, then the adjustment of the resonance parameters in the transfer function between the observed <br />nutation terms and the corresponding rigid nutation terms that reflects the luni-solar forcing. The obtained <br />resonance parameters confirms in particular the shortening of the polar motion resonance period of about 40 - 50 day <br />in the retrograde diurnal band. Then, we show that the dynamical behavior of the oceans in the diurnal band is <br />mostly responsible for that. We also predicted a supplementary change of the resonance parameters in the vicinity<br />of the free core nutation resonance, as expected from the solid Earth response, and confirmed by the adjustment of <br />these parameters through the nutation terms. In addition to the nutation band, we revisit the estimation of the <br />polar motion resonance parameters in the seasonal band, dominated by the Chandler wobble, in light of the most <br />recent global circulation models of the hydro-atmospheric layers. Finally, we extend the investigation of polar motion resonance to the<br />prograde diurnal polar motion, where the excitations mostly result from the ocean tides. We obtain a resonance <br />period of about 393 days, and confirmed by our prediction based on the ocean tidal models. These results allow us to <br />impose constraints on the frequency dependence of the Love number k<sub>2</sub> and the Love number oceanic k<sub>o</sub>, characterizing <br />respectively the response of the solid Earth and the oceans to an external potential of degree 2. </pre>