Earthquakes behave exactly like stocks, wind bursts, solar flares, whatever. In fact, wherever, there are fundamental laws working at the smallest to largest scale, we have what is called a power law. For stocks, there is a pattern that the number of daily price-swings of 1%, is, perhaps, 8 times the number of days when the swing is 2%, which is eight times the number of days at 4%. Once in a while, there is a major 'stock-quake' with a big swing!
Earthquakes generally follow a power law, as well. They are rated in size by a logarithmic scale: Magnitude (calculated in different ways). An M3 earthquake has about 30 times more energy than an M2. Also, M2 earthquakes occur 10 times more often than M3's, which are 10 times more frequent than M4's, etc.
Most of Nature follows power laws because it is fractal, self-similar over all scales. As a result of this ubiquity, people generally see 'patterns' or 'things' in any fractal distribution. Thus, the background of stars has its constellations, but do the stars care? You may see a duck in a fluffy cloud, but does this help you predict the shape of the next one?
Like stocks, the pattern of earthquakes is quite capable of being correlated with anything -- once! People have 'associated' the onset of an earthquake with such things as animal behavior, the weather, motion in the level of water wells, etc. Unfortunately, much like clouds, all these patterns tend to break down with the next earthquake.
To be socially useful, earthquake predictions have to be quite precise in magnitude, time and place. Useless predictions tend to be overly general, 'predicting' such things as a small earthquake in California 'any day now'. This is somewhat like saying a horse will win the Kentucky Derby!
As scientists study earthquakes they will become more precise in their estimates of seismic hazard, using such advanced tools as real-time GPS. Whether this ever evolves into useful earthquake prediction, is a question for the future.
The USGS view on earthquake prediction http://www.geophys.washington.edu/SEIS/PNSN/INFO_GENERAL/eq_prediction
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