Earthquake of Sumatra: did the axis of the Earth tremble?


The recent earthquake of magnitude 9.3 which took place on December 26, 2004 close to Sumatra is the second stronger in the world since 1900 and is even stronger than the one which occurred in Alaska in 1964 (mag 9.2). Could it have a perceptible effect in the rotation of the Earth?
The expert researchers in Paris Observatory, pertaining to IERS (International Earth Rotation Service) show that the effect is not discernible.

Theoretical bases: Relations between seismicity and variations in the rotation of the Earth

A seismic event, apart from the effect of jolt related to the earthquake involves a redistribution of mass in the earth. That modifies the earth tensor of inertia which theoretically can affect the movement of the axis of rotation of the earth compared to the crust called the "movement of the pole" or "polhodie". There can also be a weak effect in the earth rotation speed according to the conservation of angular momentum. Theoretical calculations show that the greatest earthquakes can involve co-seismic variations of a few microseconds of time in the duration of the day and of 0.1 mas to 1 mas (a few millimetres to a few centimetres) in the movement of the pole (Smylie and Manshina, 1971; Chao and Gross, 1987; Varga, 1987). However these amplitudes are completely masked by those associated with transport of atmospheric and oceanic masses, which are one or two orders of magnitude higher. According to recent studies on the diffusion of post-seismic constraints (Soldati and Spada 1999), in spite of the weak signal due to seisms, it can however exist a phenomenon of amplification due to the viscosity of the asthenosphere, which could involve visible effects in Earth rotation.

Polhodie 2003-2005
Figure 1 : The axis of rotation of the earth is not fixed compared to the earth's crust. Projected on a plane tangent to the pole, it describes "the movement of the pole" or "Polhodie" (here represented by the red dotted curve) contained in a square of 20 meters size. The principal components of the motion are a term of period 432 days, the term of Chandler ( see here a schematic representation of the Chandler oscillation) attributed to a free mode of the earth as well as a term of 1 year period due to transport of atmospheric masses. A possible jump due to the earthquake of last 26 December (instant inside of the pink circle) is currently not separable from atmospheric signals.
Click on the image to enlarge it

Observations: What can be seen in the observations of IERS?

There exist several data bases concerning the major earthquakes in particular the catalogue of U.S. Geological Survey. From several parameters (magnitude, localization, seismic moment..) characterizing the event one can from a model make an estimate of the effect of an event in the variations of the rotation of the earth. According to various calculations made independently from these parameters by R. Gross (JPL), B Chao (NASA) and by C Bizouard (Paris Observatory), the effect in the movement of the pole should be of a few centimetres in the polhodie and of a few microseconds of time in the duration of the day, which is not very likely to be detected seen the current precision of the observations. The Earth rotation Center of the International Earth Rotation Service (IERS) at the Observatory of Paris has in particular the role of follow-up in quasi-real time of the variations of the earth motion by using the observations resulting from various space techniques like the GPS, interferometry on extragalactic radio sources as well as laser telemetry on satellites and the Moon. The fine analyses of the variations observed in the "polhodie" (see figure 1) did not show a discernible effect.

References
Chao B.F.and Gross R.S., 1987: Changes in the Earth.s rotation and low degree gravitational field induced by earthquakes. Geophys J. Roy.Astron. Soc., 91, 569-596.
Smylie D.E. and Manshina L., 1971: The elasticity theory of dislocation in real Earth models and changes in the rotation of the Earth, Geophys. J. Roy. Astron. Soc., 23, 329-354.
Soldati G. and Spada G., 1999: Large earthquakes and Earth rotation: the role of mantle relaxation. Geophys. Res. Lett., 26 , 911-914.
Varga P., 1987: Influence of the elastic stress accumulation on the Earth.s polar position. Proc. of the int. Symp. .Figure and dynamics of the Earth, Moon and Planets., Prague, 257-269.

Contact
Daniel Gambis (Observatoire de Paris, SYRTE)