Did the 26 December 2004 Sumatra, Indonesia,

Earthquake Disrupt the Earths Rotation as the

Mass Media Have Said?

Eos, Vol. 86, No. 1, 4 January 2005




B. F. Chao, Space Geodesy Brancy, NASA Goddard

Space Flight Center, Greenbelt, Md.; R.S. Gross,

Space Geodetic Science and Applications Group, Jet

Propulsion Laboratory, California Institute of

Technology, Pasadena.


The answer to this question is a definite yes.

But then again, the same is true of any earthquake,

large or small, or for that matter of any

worldly event that involves mass transport,

from atmospheric and ocean seasonality, to

melting of glaciers and tropical storms, to a

bus driving around town. All one needs to

convince oneself of this is to invoke the

conservation of angular momentum and apply it

to the Earth system.


The real question should be, Did this

particular earthquake disrupt the Earth's rotation to

a level large enough to be noticeable, or,

technically, observable? The answer is a sobering

hardly, but at the same time very exciting in

scientific implications.


Following Chao and Gross [1987; see also

Chao and Gross,2000], we have been routinely

calculating earthquakes' coseismic effects in

changing the Earth's rotation (in both length

of day (LOD) and polar motion) as well as

the low-degree gravitational field. The algorithm

uses the normal-mode summation scheme by

inputting the Harvard centroid-moment tensor

solution (courtesy of http://www.seismology.

harvard.edu/CMTsearch.html), which represents

the magnitude and focal mechanism of a given

earthquake. The results are reported and

updated on the Web site of the Special Bureau

for Mantle of the International Earth Rotation

and Reference Systems Service's (IERS) Global

Geophysical Fluids Center (http://bowie.gsfc.

nasa.gov/ggfc/mantle.htm/). Currently included

are 21,600 major earthquakes worldwide

with magnitude greater than 5 since 1977.


Their cumulative, coseismic geodynamic

effects show intriguing long-term trends for

geophysicists to ponder. For instance, the

earthquakes collectively have an extremely

strong tendency to make the whole Earth

rounder and more compact in all directions,

shortening LOD. They have also been nudging

the mean North Pole position toward the

direction of ~140E.However,they did these

so very slightly that the resultant signals have

so far eluded detection, even with today's

space geodetic technique capabilities. Worse

still, these signals were buried in other signals

that are orders of magnitude larger resulting

from various other geophysical and climatic

causes occurring all the time.


This was the case at least up until recently.

Previously, however, there had been two gigantic

earthquakes in the 1960s that had also been

geophysically modeled, namely, the 1960

Chilean event and the 1964 Alaskan event.

They should have caused geodynamic changes

that were large enough to be detected under

today's observational capability, which was of

course lacking at the time. For example, the

Chilean earthquake should have shifted the

North Pole toward ~115E by about 23 mas,

corresponding to ~70 cm, compared with

today's subcentimeter measurement precision.

The corresponding change in LOD, on the other

hand, was only about -8 microseconds (s), a

few times below today's detection level. The

Alaskan earthquake should have changed the

Earth's oblateness J2 by +5.3 10**-11,which would

take the postglacial rebound 2 years to "iron

out, "compared with today's detectability level

of ~10**-11 by the satellite-laser ranging (SLR)



What about the magnitude Mw = 9 earthquake

that happened off the west coast of Sumatra,

Indonesia, on 26 December 2004? Estimating

the seismic moment at 39.5 10**2 1 newton-m,

this earthquake is the fourth largest in the

century-long modern record, about half the

size of the Alaskan event.


Our calculation results in the following for

the coseismic changes: (1) LOD decreased by

2.68 s. Physically this is analogous to a

spinning skater drawing arms closer to the body,

resulting in a faster spin. (2) Mean North Pole

was shifted by about 2.5 cm in the direction

of ~145E.The latter is remarkably continuing

the aforementioned coseismic cumulative trend.

(3) Earth's oblateness J2 decreased by 0.90

10**-11,continuing the trend in making the Earth

less oblate.(4) Earth's pear-shapedness J3

decreased by 0.19 10**-11. Note that this

earthquake being near the equator maximizes its

effects on J2 and J4 (antinode at equator) and

minimizes its effects on J3 and polar motion

(node at equator),although these effects are

really integrations over the entire body of the

Earth. To put these quantities in a human

perspective, the great Three Gorges reservoir of

China, when filled, will impound 40 km3 of

water. This net mass redistribution on Earth

will lengthen LOD by only 0.06 s, increase J2

by only 0.03 10**-11, and shift the pole position

by as much as 0.64 mas, or about 2 cm. Incidentally,

the physical reason why the pole is in

general relatively easy to shift is that its excitation

needs only to overcome the Earth's oblateness

in the form of C-A (C and A being the

axial and equatorial moments of inertia,

respectively),which is about 1/300 of C itself

which is to be overcome in exciting LOD



Compared with today's detectability level

quoted above, we conclude that the Sumatra

earthquake has caused a LOD change too

small to detect, an oblateness change barely

detectable, and a pole shift large enough to

be possibly identified in the observation series.

An outstanding quest for several decades

[e.g.,Chao and Gross, 2000], the latter is potentially

very interesting but in the least will require

careful scrutiny in sifting through various other

signals that are present. Another prospect is

the current space gravity mission GRACE

which observes up to much higher harmonic

degrees than SLR, potentially useful for studying

large earthquakes [e.g.,Gross and Chao,

2001; Sun and Okubo,2004]. Finally, we should

stress that the above only refers to the coseismic

effects, independent of any anelastic preseismic

or postseismic movements or aseismic

deformations, which normally augment the

coseismic effects with an amount that varies

from case to case.




The work described in this article is supported

by the NASA Solid Earth and Natural Hazards

(SENH) Program. The research of R.S.G. was

carried out at the Jet Propulsion Laboratory,

California Institute of Technology, under a

contract with NASA/SENH.




Chao, B. F., and R. S. Gross(1987), Changes in the

Earths rotation and low-degree gravitational field

Induced by earthquakes, Geophys. J. R. Astron. Soc.,

91, 569-596.


Chao, B. F., and R. S. Gross (2000), Coseismic excita-

tion of the Earth's polar motion, in Polar Motion:

Historical and Scientific Problems, edited by S. Dick

et al., IAU Coll. 178, Astron. Soc. of the Pac., San

Francisco, Calif.


Gross, R. S.,and B. F. Chao (2001),The gravitational

signature of earthquakes, in Gravity, Geoid, and

Geodynamics 2000, IAG Symposia vol. 123, edited

by M. G. Sideris, pp. 205210, Springer, New York.


Sun, W.,and S.Okubo (2004), Coseismic deformations

detectable by satellite gravity missions: A case

study of Alaska (1964, 2002) and Hokkaido (2003)

earthquakes in the spectral domain, J. Geophys.

Res., 109,B04405, doi:10.1029/2003JB002554.