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

Study of the Earth rheological properties from polar motion

Christian Bizouard, Ibnu Nurul Huda, and Sébastien Lambert
Christian Bizouard et al.
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How to cite: Bizouard, C., Nurul Huda, I., and Lambert, S.: Study of the Earth rheological properties from polar motion, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-19240,, 2020

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Display material version 1 – uploaded on 06 May 2020
  • CC1: Comment on EGU2020-19240, Paul PUKITE, 07 May 2020

    (I posted this question before but for the wrong presentation) 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, Christian Bizouard, 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?  

      According to our present understanding, the 434 day wobble is a normal mode of the Earth rotation, produced by the Earth flattening (the Euler mode with a period of 304 days). The departure of the 434 period from the Euler period predicted for a rigid Earth results from the Earth deformation (the pole tide), produced by the tiny centrifugical variation accompagnying the polar motion. Effect of the Moon has never been proved, even if some authors invoke a possible synchronisation of the Chandler wobble with tidal cycles through non-linear processes, that has to be demonstrated. Dissipation accompaniying the pole tide results in a decay of the Chandler wobble: after 200 years its amplitude would be divided by 8-100 in abscence of excitation. So, its maintenance, at an amplitude of 50-200 mas, requires a forcing. According to my own studies, that one stems from atmospheric and oceanic mass transports.   

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

        Is the value of the Chandler wobble closer to 433 days rather than 434 days?

        The expected 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.  

        Any dissipation that occurs during the natural damping of a Chandler wobble with a window of resonance around Euler's 304 day prediction, will be reinforced by the recurring natural forcing of the lunar nodal cycle.  There is no question that the seasonal nodal cycle is responsible for the annual wobble, so I don't understand why the lunar contribution is so easily dismissed.



        • AC2: Reply to CC2, Christian Bizouard, 10 May 2020

          >Is the value of the Chandler wobble closer to 433 days rather than 434 days?

          432 +/- 1 day

          What do you mean by "recurring natural forcing of the lunar nodal cycle"?  There is another coincidence between lunar cycles and Chandler wobble period:

          432/27.5 = 6798/432. 

          Yours is 1/433 =  1/13.606 -26/365.242, but what is meaning of the frequency 26/365.242 cpd and 1/13.606?

          -1/365.242 + 1/13.66 = 1/14.2 = 26/365.242? 

          So 1/433 =  1/13.606 - 1/13.66 + 1/365.242.

          Nikolay Sidorenkov considers that ALL Earth rotation anf climatic cycles are synchronised with luni-solar tides. A kind a tidal lockdown. 


          • CC3: Reply to AC2, Paul PUKITE, 10 May 2020

            Sidorenkov is on the right track but I can't quite follow his math. The actual mechanism is a semi-annual impulse (i.e. delta function at each pole) due to the solar nodal cycle modulating the 13.606 day lunar nodal cycle. The formula shown determines the resultant cycle, with the value of 26 used to un-alias the result (there are ~26 lunar cycles in one year). But it is perhaps conceptally simpler  to show the result graphically.

            I added a low-pass inertial filter to smooth the pulse train but otherwise there is nothing magical to the phase alignment of this model  to the Chandler wobble frequency component.  It thus provides a long-term synchronzation pulse to maintain the 433 day CW period. It is a plausible and parsimonious mechanism that needs to be acknowledged.