# The 2004 Indonesian and 2010 Chilean Earthquakes and Earth's Rotation

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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Since the great 2004 Indonesian earthquake I have gotten numerous inquiries about whether the earthquake affected the earth's axis.

What was affected was the so-called Chandler Wobble. Objects that are not perfectly spherical do not rotate around a single axis. That's just the laws of physics. I did the math in graduate school. Unless you know tensors, you don't want to go there. Anyway, the earth doesn't rotate smoothly around its axis, instead, the poles wander in rough circles about 10 meters in diameter. Another way to say it is your latitude changes a bit (0.7 seconds of arc) over a cycle of about a year. Anything that redistributes mass on the earth, even weather systems and the circulation of the oceans, can affect this wobble detectably. Think of a bunch of people on a merry-go-round all running over to one side. Since we can routinely locate ourselves nowadays to accuracies of meters, and precise surveys can locate points to millimeters, we can detect even these tiny changes. What happened here was a big chunk of the northern Indian Ocean lurched northward 10-20 meters relative to Asia. It also descended several meters into the mantle, and compressed and elevated northern Sumatra by several meters. It also likely triggered big submarine landslides that caused the tsunamis. So a fair amount of mass got redistributed. The U.S. Naval Observatory tracks this stuff and will tell you all you want to know about it, but I haven't see anything posted about the big quake yet. However, the US Geological Survey posted this:

Question: What effect did this earthquake have on the rotation of the earth? Answer: Richard Gross at JPL has modeled the coseismic effect on the Earth's rotation of the December 26 earthquake in Indonesia by using the PREM model for the elastic properties of the Earth and the Harvard centroid-moment tensor solution for the source properties of the earthquake. The result is:

• change in length of day: -2.676 microseconds
• polar motion excitation X : -0.670 milliarcseconds
• polar motion excitation Y: 0.475 milliarcseconds

Since the length of the day can be measured with an accuracy of about 20 microseconds, this model predicts that the change in the length-of-day caused by the earthquake is much too small to be observed. And, since the location of the earthquake was near the equator, this model predicts that the change in polar motion excitation is also rather small, being about 0.82 milliarcsecond in amplitude. Such a small change in polar motion excitation will also be difficult to detect.

Note this is a calculation, not an observation. What it means is the day became shorter by 0.0000027 seconds (Great - I don't have enough time as it is!). It will take about 1,000 years for that to throw the earth out of sync with clocks by one second, and other things like tidal friction will have much greater effects. The excitation is the motion of the actual pole, around which the earth is rotating at any given instant, compared to the "average" pole we use on maps and globes. One second of arc is 30 meters, or 3000 centimeters, so 0.8 milliseconds is 2.5 centimeters or about an inch.

How exactly did the earthquake change the earth's rotation speed? It seems to have done so because the earthquake involved plate convergence, and effectively reduced the earth's equatorial circumference by a few millimeters while pushing denser material into the earth, like an ice skater pulling in her arms. That would also reduce the earth's equatorial radius a fraction of a millimeter. The overall fault slip was 10-20 meters, but some of that was directed north-south, so the east-west compression was smaller.  The effect would be further reduced by the fact that the crust above the fault zone would have been uplifted, resulting in a bulge that would somewhat offset the reduction in circumference. Not all the local compression would affect the equator anyway, just like buttoning a shirt that's too tight pulls your waist in a little, but not as much as the gap between the last buttons.

The Earth's rotational properties are described by its moment of inertia, which is proportional to the square of its equatorial radius. The calculated change in rotation rate is about 3 x 10-11 of the length of the day, implying a similar change of 3 x 10-11 in the earth's equatorial radius (about 0.4 millimeters) or about 2.4 millimeters (1/10 inch) shortening of the equatorial circumference.

The Chilean earthquake of 2010 likewise produced calculated changes of a few microseconds in the length of the day and a few centimeters in the positions of the poles, and for the same reasons. A sudden shift of mass into the earth speeds up the rotation a tad, just like an ice skater drawing in her arms.

Long term, however, the earth is not going to suck into a black hole like the planet Vulcan in the Star Trek reboot. Matter is also rising out of the earth in the form of hot light mantle material at mid ocean ridges, as well as uplift of mountains. So overall we'd expect those motions to slow down the earth's rotation, but more gradually than the speedups due to earthquakes. Overall, the two effects should balance on a long time scale. If we could actually measure the effects, we'd likely see a saw-tooth graph with abrupt increases in rotation speed during big earthquakes and gradual increases in between, more or less erasing the speedups.

Created 12 January 2005, Last Update 03 March 2010

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