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There's a small mathematical-geophysics research group at NASA/JPL led by Richard Gross. They are in the habit of putting out misleading press releases detailing how (any) large earthquake changes the rate of the Earth's rotation and slightly shifts its axis. Tragic earthquake happens... they issue a press release. It's a bit nasty, in my opinion. It gets them publicity, and NASA, as a publicly-funded bureaucratic organization, thrives on publicity. These are reasonable calculations, but the NASA/JPL press releases inevitably fail to emphasize strongly enough that these changes are far below our ability to observe, and they are masked by much larger variations from non-catastrophic geophysical phenomena. Thes folks have not "detected" changes in the Earth's rotation caused by an earthquake. They've merely calculated what those changes would be if we had omniscient observational data and the ability to exclude all other phenomena. 

One of the largest causes of variations in the Earth's rotation arises from the meandering of the jet streams. These "rivers" of air, though they are low density, travel at high speeds and cover enormous distances. They are a significant element of the Earth's angular momentum budget, and when they shift there are detectable changes in the location of the Earth's true axis (in other words, the poles move a few centimeters) and there are measurable changes in the rate of rotation.

So is it "true" that the Kobe earthquake, for example, changed the Earth's rate of rotation and shifted its axis? Well, yes -- from a theoretical perspective. If the laws of physics are consistent, then that must be true. And given measurements of changes in the gravity field and therefore the mass distribution, it is possible to calculate what those changes should be for any given earthquake. But it is "not true" that we have detected these changes in the observational data. Nor is it true that we will eventually detect them in the data in the years ahead. All of these earthquake-induced changes are well below the minimum "noise" level in the observational data. We can calculate them, just as we can calculate the changes in the Earth's rotation that would result from everyone in the world taking one step towards the equator, but they are insignificant.

For some ground truth on this, you can look at graphical representations of "delta-T" and also the actual LOD (length of day) data. Look for discontinuities in slope. Compare those with great earthquakes. You may even see a hint of correlation. "Hints" of correlation are easy to spot! But that, of course, is the trouble with eyeball analysis of statistical data. You will most probably not find any statistically interesting correlation between those rotation changes and earthquakes, let alone anything statistically "significant".

That quantity, delta-T, by the way, is where this enters into positional astronomy (and celestial navigation). It connects time based on the Earth's rotation with the pure time of the laws of physics (known by many names including "ephemeris time" and realized in practice as "atomic time"). Here's a Wikipedia article on the topic with a nice graphic of delta-T, too: https://en.wikipedia.org/wiki/ΔT. Be aware that the graphic in this article does not include error bars on the values. The implied accuracy in earlier centuries is wrong. And here's a Wikpedia article on leap seconds: https://en.wikipedia.org/wiki/Leap_second. Linked in that article is a very nice graphic of changes in "length of day". There's a wealth of science in that graphic. Notice the strong seasonal cycle, and the greatly reduced variability in the 365-day moving average. Can you see any earthquakes in there?? 

While we're here, there are also anthropogenic changes in the Earth's rotation. Like the earthquake-induced changes, they must exist, and they are calculable, but they are not "real" in the sense of being (even remotely) detectable in the observational data. For example, in the period from about 1920 to about 1970, mid-latitude countries created vast reservoirs. The USA and the USSR, especially, constructed colossal artificial lakes in this period. This transfered a huge amount of mass from a global average that is relatively equatorial into higher latitudes. And when mass is moved closer to the rotational axis in a system with nearly conserved angular momentum like the Earth, the rate of rotation necessarily increases (in the over-used textbook metaphor, it's the "figure skater pulling in her arms to increase her rate of spin"). That is a "true" statement of physics generally and geophysics specifically. But it is not true that we can see this in the data. This phenomenon, while intriguing, and really remarkably large relative to many other phenomena, is swamped by long-term trends. 

Frank Reed
ReedNavigation.com
Conanicut Island USA