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?