Analysis of Chandler wobble excitation, reconstructed from ...Analysis of Chandler wobble...

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

motion of the Earth

Leonid Zotov

Sternberg Astronomical InstituteLomonosov Moscow State University

Journees 2010, September 20 – 22, 2010, Paris Observatory

[email protected]

Earth’s pole motion from the bulletin IERS EOP C01

Since 1846 yr, step 0.05 yr

Journées 2010 "Systèmes de référence spatio-temporels", September 20-22, 2010, Paris, France

m(t)

1860 1880 1900 1920 1940 1960 1980 2000years

-0.4

-0.2

0

0.2

0.4

arc

sec

X-coordinate of the pole

X-coordinate


SSA method – “caterpillar”

[ ]KXXX ...1=Trajectorymatrix

[ ]KL×

Principal components grouping

Hankelization

http://www.gistatgroup.com/gus/books.html

Tddd

TT VUVUUSVX λλ ++== ...111

Singular value decomposition SVD��

0 200 400 600 800 1000

-5

0

5

10

15

SSA exampleinitial signaltrendoscillationoscillation with modulation

Jour

nées

201

0 "S

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Sep

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20-2

2, 2

010,

Par

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ranc

e

1860 1880 1900 1920 1940 1960 1980 2000years

-0.2

-0.1

0

0.1

0.2

arc

sec

SSA-decomposition of X-coordinate of the poleChandler componentannual componenttrend

Result of SSA of the 2-D pole coordinate time serieson the example of X-coordinate


Amplitude spectrum of initial signaland SSA-components

0

0.02

0.04

0.06

0.08

0.1

arcs

ec

0 0.2 0.4 0.6 0.8 1 1.2 1.4cycles per year

PM spectrumSSA ChandlerSSA annualEOP CO1

Jour

nées

201

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Sep

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Dynamical system of the rotating Earth

433

1=cf 175=QParameters used days-1

)(ˆ)()(ˆ ffLfm χ⋅=

To find - inverse problem)(tχ


Frequency response

0.6 0.7 0.8 0.9 1 1.1 1.2cycles per year

0

100

200

300 amplitude responseQ=175, fc=1/433Q=100, fc=1/425

0.6 0.7 0.8 0.9 1 1.1 1.2cycles per year

-200

-160

-120

-80

-40

0

deg

rees

e

frequency responseQ=175 fc=1/433Q=100, fc=1/425

Jour

nées

201

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Amplitude frequency response of inverse operators

0 0.2 0.4 0.6 0.8 1 1.2 1.4cycles per year

0

0.01

0.02

0.03

0.04

0.05Inversion amplitude response

corrective smoothingregularizationinverse operator

�

�

Jour

nées

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Wilson-Jeffreys filter

Jeffreys H. (1940) The variation of latitude, Mon Not Roy Astr. Soc., Vol. 100, 139-155Wilson C. (1985), Discrete polar motion equations, Geophys J. Roy. Astr. Soc., Vol. 80, 551-554


Tikhonov regularization

500=αparameter chosen

LSA-model of the annual oscillation


Panteleev corrective smoothing

Parameter used

04.00 =fJournées 2010 "Systèmes de référence spatio-temporels", September 20-22, 2010, Paris, France

Comparison with different processes

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010years

-0.004

-0.002

0

0.002

0.004

arc

sec

X-component of reconstructed Chandler excitationSSA + Wilson filterregularizationcorrective smoothing

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010years

-0.08

-0.04

0

0.04

0.08

arcs

ec

OAMAAM

-40

-20

0

20

40

Southern Oscillation Index


Chandler excitation and Tidal model for the Length of day LOD

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010years

-0.004

-0.002

0

0.002

0.004

arc

sec

X-component of reconstructed Chandler excitationSSA + Wilson filterregularizationcorrective smoothing

-0.8

-0.4

0

0.4

0.8

msIERS tidal variations in the length of the day (LOD) model


Spectrum of reconstructed excitation,amplitude modulation


0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0

0.5

1

1.5

2

2.5

SSA + Wilson filterRegularizationCorrective smoothing

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

0

0.5

1

1.5

2

2.5

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, 2002.


Gabor window-transform

ωt


Panteleev filters impulse response


Phase changes

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010year

-270

-180

-90

0

90

180

270

degr

eese

phaseinitial Chandler PMSSA + Wilson filterregularizationpanteleev filtering


Conclusions1) 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 grantМК-4234.2009.5 and RFBI grant 10-05-00215-а.


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Analysis of Chandler wobble excitation, reconstructed from ...Analysis of Chandler wobble...

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