'earthquake-proof' is a modern English compound combining 'earthquake' and the suffix 'proof' (as in 'waterproof'), formed in Modern English to mean 'proof against earthquakes.'

'earthquake' itself is from the compound of 'earth' (Old English 'eorþe') + 'quake' (Old English 'cwacian', 'to tremble'); the suffix 'proof' comes from Middle English 'proof' (from Old French 'prouve'/'preuve', ultimately from Latin 'probare' meaning 'to test/approve'). Compounds using '-proof' (e.g. 'waterproof') appeared earlier, and 'earthquake-proof' was formed by analogy.

Originally 'proof' carried the sense of 'tested' or 'proven'; in compounds it shifted to mean 'resistant to' or 'protective against,' yielding the current meaning 'resistant to earthquake damage.'