In general that shouldn't really be an issue, hard drives are pretty vibration resistant. If you're worried though, you might considering doing what they did, on a smaller scale.
If its a small earthquake, you might be able to simply isolate your home server by setting it on top of something that would dampen or resist vibrations, and of course secure your drives properly. Laptop drives and SSDs are probably better at this than desktops. If you consider that a hard drive turns are several thousand RPM, the 'vibrations' from a earthquake are minimal.
Vibration isn't really the thing that would worry you - earthquakes would be relatively low frequency - this suggests 0.1 to 70 hz is what engineers test against- its G-Forces. I'd need to find a proper citation for this, but 350G would void the warranty on seagate drives. I'll assume that that's a good average to work off of.
Now, its not entirely accurate to refer to acceleration due to the earth moving as "G" forces - the correct terminology is PGA, or peak ground acceleration. Dropping your laptop should cause 1G while dropping, or 1 ms^2, and stop based on whatever speed its dropping at right as it stops, up to terminal velocity. I'll leave it as an exercise to a VERY brave reader to work out what the terminal velocity of a given laptop is.
Lets then assume a worst case scenario. Lets assume an earthquake that will level your building, but somehow due to the magic of sheer dumb luck, nothing fell on your server, and its sitting there, untouched in the middle of all that carnage, like a cartoon character. Unfortunately there's nothing on the wikipedia page for what total damage would be like, but lets assume X+ on the mercali scale. Bad enough. Acceleration would be equivalent to 1.24g, which is significantly less than what drives are rated for! In short, unless a building falls on it, a earthquake that would cause a HDD to fail would be quite literally a end of world quake.
If this still worries you, there's a few options that might help.
Isolation mount the nas - maybe on a thick sheet of rubber. Isolation mount the drives - there's products meant to prevent vibration to quieten drives that may work. Practically though, it should be fine. I had trouble of finding reports of mass drive deaths due to earthquake related vibrations.
I see, but my initial concern was more with the earthquake occuring while the server was on use. Although you cover a general situation of earthquake, I'm more worried about in-use problems. Imagine the server trying to write information to the drives while the earthquake occurs. AFAIK, SDD are more tolerant to vibrations since there are no moving mechanical components but HDD have moving mechanical parts. – tomasyany – 2015-10-17T00:32:56.940
1In theory, it should be fine since the acceleration you face and vibrations would be less than what it would face in normal use. – Journeyman Geek – 2015-10-17T00:34:10.607
Ok, that reassures me. Still, the vibrations it faces in normal use are expected to be in a certain way (I guess that drives constructors thought of it). Vibrations during earthquake can be whatever the Earth wants them to be (in every direction, varying intensity, etc.). But yes, I guess after what you said, a NAS server should be able to resist such vibrations with no major issues. – tomasyany – 2015-10-17T00:37:53.763
One small clarification, you should state that modern hard drives are pretty vibration resistant. Yes the risk of running a NAS on 1998 vintage hard drives is non existent nowadays, but a lot of the myths surrounding the fragile nature of hard drives—and what can be done to fix them—comes from the olden days (pre-1995?) of computing when hard drives were definitely more fragile and error prone due to the way they were built and designed. – JakeGould – 2015-10-17T01:21:20.763
If the NAS supports it, set it to sleep the drives often. Unless the quakes happen exactly while you are read/writing, then you should be safer with the drives spun down. – Blackbeagle – 2015-10-17T03:20:07.067