EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Constraints on the Rheology of the Earth's Deep Mantle from Decadal Observations of the Earth's Figure Axis and Rotation Pole

Alexandre Couhert1, Christian Bizouard2, Flavien Mercier3, Kristel Chanard4, Marianne Greff5, and Pierre Exertier6
Alexandre Couhert et al.
  • 1Centre National d'Etudes Spatiales, Toulouse, France (
  • 2Observatoire de Paris, SYRTE, Paris, France (
  • 3Centre National d'Etudes Spatiales, Toulouse, France (
  • 4Institut National de l'Information Géographique et Forestière, LAREG, Paris, France (
  • 5Institut de Physique du Globe de Paris-Sorbonne Paris Cité, UMR CNRS 7154, Paris, France (
  • 6Observatoire Midi-Pyrénées, GET, Toulouse, France (

The over four decades long record of Satellite Laser Ranging (SLR) observations to a variety of historical geodetic spherical satellites makes it possible to directly observe the long-term (seasonal to decadal time scales) displacement of the Earth’s mean axis of maximum inertia, namely its principal figure axis, with respect to the crust, through the determination of the degree-2 order-1 geopotential coefficients over the 34-year period 1984—2017.

On the other hand, the pole coordinate time series (mainly from GPS and VLBI data), yield the motion of the rotation pole with even a greater accuracy.

The time-dependent nature of the response of the Earth’s mantle to external forces, where it behaves either elastically on short time scales (seconds) or like a viscous fluid over geological time scales (millions of years), is poorly constrained at decadal periods. Here we propose to relate oscillations of the figure axis to those of the Earth’s rotation pole (through the Euler-Liouville equations) to study the mass-related excitation of polar motion and provide global constraints on the rheological properties of the deep Earth.

How to cite: Couhert, A., Bizouard, C., Mercier, F., Chanard, K., Greff, M., and Exertier, P.: Constraints on the Rheology of the Earth's Deep Mantle from Decadal Observations of the Earth's Figure Axis and Rotation Pole, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18545,, 2020

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Display material version 1 – uploaded on 10 Apr 2020
  • CC1: Comment on EGU2020-18545, Paul PUKITE, 07 May 2020

    Why isn't the 434 day wobble a result of the lunar nodal torqueing cycle (13.606 day) acting on a non-spheroidal earth?  

    • AC1: Reply to CC1, Alexandre Couhert, 07 May 2020

      Thank you for your comment. The variability of the Chandler wobble had been quite well reconstructed from the mass transports in the oceans and the atmosphere, see the article from Bizouard et al. (2011) ("The Earth’s variable Chandler wobble").

      • CC2: Reply to AC1, Paul PUKITE, 07 May 2020

        The value is 365.242/(365.242/13.606-26) = 433 days, which matches the established value of the Chandler wobble cycle.  This is easily validated by any experiment with a North-South polarized gyro in proximity to an orbiting charged source with a nodal cycle.  This is fundamental mathematical physics that can be reapplied to the case of an equivalent gravitational field and orbital configuration. 

        I realize that this is a difficult experiment to do in a controlled laboratory environment, but the electromagnetic analogy is a mathematically equivalent controlled validation.

        • AC2: Reply to CC2, Alexandre Couhert, 07 May 2020

          Your hypothesis indeed sounds reasonable in theory. However, in practice, on the plots of my slide 4 you can see a very good match between the C21/S21 series I derived (in blue), removing all the known tidal effects, and the Chandler polar motion evolution (in red). This shows that tidal effects cannot be the source of this ~430-day oscillation.

          • CC3: Reply to AC2, Paul PUKITE, 08 May 2020

            A semiannual impulse (due to the sun nodal crossing) modulating the lunar nodal cycle (precisely the well-known draconic 27.2122 day cycle) will produce this waveform, with the phase trained over the interval shown.  The implausibility of this alignment happening by chance is remote.

            The recent paper by Na, Sung-Ho, et al. "Chandler Wobble and Free Core Nutation: Theory and Features." Journal of Astronomy and Space Sciences  (2019) agrees with this assertion even though they don''t show the equivalence via a periodic impulse as shown above.


            • AC3: Reply to CC3, Christian Bizouard, 10 May 2020

              Dear Paul,

              Can you send me the paper "Na, Sung-Ho, et al. Chandler Wobble and Free Core Nutation: Theory and Features. Journal of Astronomy and Space Sciences  (2019)"


              • CC4: Reply to AC3, Paul PUKITE, 10 May 2020

                Dear Christian,

                The paper by Sung-Ho Na is open-access and found here

                There are two passages in the article that make the claim:

                "Due mainly to the tidal torque exerted by the moon and the sun on the Earth’s equatorial bulge, the
                Earth undergoes precession and nutation. "

                and in the appendix

                "Semiannual nutation is roughly six times larger than fortnightly one (lunar tidal force is about twice larger). Due to symmetric nature of tidal force, semi-annual nutation is of larger amplitude than annual nutation (particularly for Δε), and fortnightly nutation amplitude is larger than monthly. If the lunar/solar orbits were completely circular, then the monthly and annual nutation will no longer exist. "

                Based on this information with the fortnightly tidal force at 13.606 days, it is straightforward to resolve the 433 day cycle. I don't understand why Na et al did not make this calculation explicit in their paper.