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Influence of the earthquakes on polar motion with emphasis on the Sumatra event

Influence of the earthquakes on polar motion with emphasis on the Sumatra event. Christian Bizouard Observatoire de Paris International Earth Rotation Service 61 av. de l'Observatoire 75014 Paris, France. Les Journées Systèmes de Référence 2005 CBK Warsaw. N. (Stein, Okal ,2005).

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Influence of the earthquakes on polar motion with emphasis on the Sumatra event

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  1. Influence of the earthquakes on polar motion with emphasis on the Sumatra event Christian BizouardObservatoire de ParisInternational Earth Rotation Service61 av. de l'Observatoire 75014 Paris, France Les Journées Systèmes de Référence 2005 CBK Warsaw

  2. N (Stein, Okal ,2005)

  3. 2004 Dec. 26 00h 58min 51s UT Western COAST OF NORTHERN SUMATRA Epicenter latitude : 3.298° longitude : 95.778° Magnitude = 9.2 4th biggest Earthquake since 1900 or second one ever recorded ? N (Stein, Okal Nature,2005)

  4. N -31° Strike (direction of the fault) Burma microplate 11 m Indian Plate Slip=110° Dip 8° S 1200 km 200 km Seismic parameters for Sumatra

  5. z W (1+m3) w <1” Wm1 Wm2 x Theory(I) • Angular momentum conservation of the solid Earth : dHEarth/dt = 0 • In cartesian terrestrial frame Oxyz (Oxy : equatorial plane, Oz : geographic axis), Earth angular momentum : [HEarth] =I [w] + [h]: • [w]= instantaneous rotation vector [wx , wy , wy] = W[m1,m2,1+m3] • [h] = relative angular momentum with respect to the crust • I : inertia matrix y

  6. Theory (II) Earthquake : relative angular momentum h is negligible. After some algebra, it can be shown that inertia increment cij and rotation vector are related by : Terre rigide Terre élastique where : • m=m1 + i m2 • se is the Euler frequency : se = (C-A)/A W (305 days) • sCW is the Chandler frequency : sCW = 1.4 se (432 days) • A is the Earth’s equatorial inertia moment, C the axial inertia moment • c(t) = c12 + i c23 is the off-diagonal increment of inertia tensor

  7. Theory (III) The mass redistribution is achieved after a few minutes. The inertia increment can be modeled as step function c,c33 beginning at instant t0 , as soon as the Earthquake is over. It follows that effect on polar motion is given by : constant offset change in free wooble

  8. Inertia moment increments : Dahlen’s model (1973) Elastic dislocation theory  expression of equatorial inertia moment increment in function of seismic parameters : seismic moment M0, strike a, dip d, slip angle l, colatitude q, longitude f G1(h),G2(h),G3(h)function of the depth

  9. Seismic parameters from USGS/CMT catalogs : 1962-2005 • Seismic parameters from USGS/ CMT catalog +0.2 mas/yr yy yx -0.2 mas/yr 1994 y polar shift : 1980 -1994 : -3.3± 0.2 mas/yr 1994-2005 : -1.2 ± 0.2 mas/yr x polar shift : 1980 -1994 : -1.0 ± 0.1 mas/yr 1994-2005 : -1.9 ± 0.1 mas/yr

  10. Effect on polar motion 1962-2005 Sumatra Changes of the Chandler wobble amplitude of a few mas, much smaller than the observed one (60 mas) 145°E

  11. Results for the big Sumatra Earthquake According to Gross & Chao (2005) : 2.5 cm towards 145° E. The same Earthquake located in mid-latitudes regions would have shifted the rotation pole by 7 - 21 cm !

  12. 90°E Toward Greenwich Geographic pole Path of rotation pole January 1 2004 December 26 2004 Daily atmospheric/oceanic induced shift : 2 - 6 mas/day April 7 2005 Accuracy : 0.1 mas  0.3 cm 1 m

  13. DEC 25 12 h DEC 26 12 h DEC 27 12 h 0.7 mas ? JAN 1 12 h JAN 5 12 h ? 1 mas = 0,001” ↔ 3 cm at Earth surface

  14. DEC 25 12 h DEC 26 12 h DEC 27 12 h ~1.5 mas 1 mas = 0,001” ↔ 3 cm at Earth surface

  15. Dec 26 2004 0hUT Dec 27 2004 0hUT Jan 5 2005 Dec 10 2004

  16. Dec 26 2004 0hUT Jan 5 2005 Dec 10 2004

  17. Conclusion • Sumatra Earthquake may have shifted the rotation axis at observable level (2-3 cm at the Earth surface in a few min) • Hardly distinguishable from common polar motion caused by the atmospheric/oceanic process (6-15 cm / day). • Atmospheric angular momentum (NCEP) quite well explain polar path of December 26-27 2004 . • Expected shift for x, actually observed for y (1.5 mas).  Sumatra effect has not been observed ! • 1962-1994 : excitation function stable. Since 1994, drift towards 145° E. • Earthquake impact still to be proved !

  18. Effect on the rotation rate ? • Chao & Gross (NASA) modeled the axial inertia change. • The Earth rotation velocity increased, corresponding to a 2 microseconds increase of the length of day • Far below the accuracy of the GPS / Satellite Laser Ranging observations.

  19. Polarization towards 140° E in the seismic polar shift

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