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Wikipedia indicates the approximate energy released by an earthquake relative to the destructive power of TNT With reasonably large quakes (> 4.0 on the Richter Scale), the energy dissipated is of the order of Giga-joules. If a seam (Uranium, Thorium, whatever) were caught in plate movement could seismic activity trigger a chain reaction?

What if such an earthquake were to hit a waste depot?

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You are confusing nuclear weapons, which require a mechanical trigger, with nuclear reactors, which are almost unaffected by pressure. Pressure waves have the ability to chance density temporary, which could cause a spike in power, but otherwise have basically nothing to do with "triggering a chain reaction". – Alan Rominger Aug 24 '12 at 12:04
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Natural occurrence of a nuclear fission chain reaction, similar to the ones occurring in nuclear weaponry, is extremely unlikely. It is actually very difficult to get fission material to explode, much more difficult than most schematics you can find on internet would suggest :)

Natural fission reactors do exist, though the power output (around 100kW as stated on the wiki) is pretty insignificant compared to even a small Earthquake. And the conditions under which these reactors will happen are pretty uncommon already (there's only one place in the world known to have had natural reactors).

Regarding an Earthquake hitting nuclear waste -- it's waste for a good reason: there is not much energy left in it. Certainly not compared to the vast amounts of energy associated with an Earthquake. What you need to worry about is not so much the energy release, but the breach of the containers, spilling and spread, etc. of the waste due to the Earthquake. Although not suited for energy production, it can be pretty unhealthy to touch, be near, inhale, etc. the bare unprotected stuff.

Here's a nice populist chart to put things in perspective. Not the most reliable source, so do your homework before basing life-or-death decisions on this chart :)

credit to XKCD

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