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Possibly a dumb question, but are tsunamis in the Mediterranean as big a threat as they are in the world's major oceans? 
In my head at least as the Mediterranean isn't nearly as deep and the volume of water isn't as great so the capacity for destruction might be lessened.
Does alert mean there is a tsunami or just one is possible? >

Possible. Tsunamis are tricky, it's best to assume they're happening and then rule them out afterwards.