Use must ask on CorsixTH forum, i think. It like offtopic here (outside of pinned topic dedicated to cotsixth). Anyway, more active users on corsixth forum - so better ask there.

Im sure it can be switched off somewhere: in config, in ingame settings, or maybe in dev\cheat mode. Lurk FAQs for cheats or config editing. Or google it earthquake site:corsixth.com/

UPD: forum not work for me right now, only site and github wiki
http://github.com/CorsixTH/CorsixTH/wiki

Any update on that one?

it cannot be disabled in Theme Hospital (DOS, Windows or GOG DOS+MAC).

It is possible for CorsixTH.
Here is more oldest discussion than this thread. They discuss that there is an option - and it didnt work properly
http://github.com/CorsixTH/CorsixTH/issues/559
So as i guess above - it should be in config, in level file config, and as i guess now - it should be properly worked. Disabling globaly disable random quakes (like for early-campaign stage. for CorsixTH it is differ things - random quakes), disabling in level - level-specific quaes

Maybe, current version of CorsixTH dont have so much quakes like it be previously with that randomnes quakes?