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Can one earthquake trigger another? For instance, the quake in New Zealand, then the one in China and finally the big one in Japan.

This does not count aftershocks, but separate earthquakes in reasonably disparate geographical regions.

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This article on NPR written in April 2010 discusses perceived clusters of earthquakes; specifically the high profile ones from early 2010.

This section is particularly relevant:

On average, there are 17 magnitude 7 quakes around the world each year, and an additional 130 in the magnitude 6 range. That would be one quake every 2 1/2 days if they fell evenly spread on the calendar. So while this year's spate of seismic activity actually isn't out of the ordinary, the USGS researcher in California analyzed the data, running various models comparing this year's high-magnitude quakes with the previous 100 years.

"It's definitely more than most four-month periods, but things are not always exactly at the average," Michael says. "This is within what we expect variations to be from random models of earthquake occurrence."

It is very easy to perceive patterns in things like this, when really there is none. Earthquakes happen very frequently, and when a few high profile ones happen within a short timeframe, people tend to see a pattern, when really it's just random chance.

Also see this FAQ from the USGS, which provides good information and several credible explanations about the phenomenon.

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