Analysis of Chandler wobble excitation, reconstructed from observations of the polar motion of the Earth

Transcription

1 Analysis of Chandler wobble excitation, reconstructed from observations of the polar motion of the Earth Leonid Zotov Sternberg Astronomical Institute Lomonosov Moscow State University Journees 21, September 2 22, 21, Paris Observatory

2 Earth s pole motion from the bulletin IERS EOP C1 Since 1846 yr, step.5 yr m(t)

3 X-coordinate.4 X-coordinate of the pole.2 arc sec years

4 SSA method caterpillar Trajectory matrix X SSA example initial signal trend oscillation oscillation X with = modulation... [ X ] 1 [ L K] Singular value decomposition SVD T T = USV = λ 1U1V Principal components grouping Hankelization X K λ U d d V T d

5 Result of SSA of the 2-D pole coordinate time series on the example of X-coordinate.2 SSA-decomposition of X-coordinate of the pole Chandler component annual component trend.1 arc sec years

6 .1.8 Amplitude spectrum of initial signal and SSA-components PM spectrum SSA Chandler SSA annual EOP CO cycles per year arcsec

7 Dynamical system of the rotating Earth To find χ(t) - inverse problem mˆ ( f ) = L( f ) ˆ( χ f ) 1 fc = Q = Parameters used days -1

8 Frequency response degreese 3 amplitude response Q=175, fc=1/ Q=1, fc=1/ cycles per year frequency response Q=175 fc=1/433 Q=1, fc=1/ cycles per year

9 Amplitude frequency response of inverse operators Inversion amplitude response corrective smoothing regularization inverse operator cycles per year

10 Wilson-Jeffreys filter Jeffreys H. (194) The variation of latitude, Mon Not Roy Astr. Soc., Vol. 1, Wilson C. (1985), Discrete polar motion equations, Geophys J. Roy. Astr. Soc., Vol. 8,

11 Tikhonov regularization parameter chosen α = 5 LSA-model of the annual oscillation

12 Panteleev corrective smoothing Parameter used f =.4

13 Comparison with different processes.4 X-component of reconstructed Chandler excitation SSA + Wilson filter regularization corrective smoothing.2 arc sec years Southern Oscillation Index OAM AAM.8.4 arcsec years

14 Chandler excitation and Tidal model for the Length of day LOD.4 X-component of reconstructed Chandler excitation SSA + Wilson filter regularization corrective smoothing.2 arc sec years.8 IERS tidal variations in the length of the day (LOD) model.4 ms

15 Spectrum of reconstructed excitation, amplitude modulation SSA + Wilson filter Regularization Corrective smoothing

16 Full moon in perigee repetition cycle and ocean days Avsyuk Yu. N. Tidal forces and natural processes, 1996, Moscow, Schmidt Institute of Physics of the Earth, Russian Academy of Sciences. Anisimova E P., Pokazeev K.V. Introduction to physics of hydrosphere. Moscow, MSU, 22.

17 Gabor window-transform t ω

18 Panteleev filters impulse response

19 Phase changes degreese phase initial Chandler PM SSA + Wilson filter regularization panteleev filtering year

20 Conclusions 1) Chandler excitation was reconstructed by three methods for inverse problems solving: Panteleev corrective smoothing, Wilson-Jeffreys filter after SSA, Tikhonov regularization with annual component subtraction The results are similar. It gives hope they are reliable. 2) 18,6-year modulation of Chandler excitation, synchronous with the saros tidal cycle and related LOD changes has been found. It could prove that tidal energy is transferred to chandler excitation, probably, through the ocean and atmosphere. The mechanism is still to be found. This work is performed with support of the President of Russia grant МК and RFBI grant а.

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