'non-earthquake-related' originates from English as a compound: the prefix 'non-' (from Latin 'non') meaning 'not', combined with 'earthquake' (English compound of 'earth' from Old English 'eor(th)e' meaning 'ground' and 'quake' from Old English 'cwacian' meaning 'to shake/tremble') and 'related' (from Latin 'relatus', past participle of 'referre', meaning 'brought back/connected').

'non-' came into English via Latin use; 'earth' is from Old English 'eor(th)e'; 'quake' developed from Old English 'cwacian' to Middle English 'queken' and then 'quake'; 'related' comes from Latin 'relatus' via past participle forms in Middle English, and the phrase evolved as modern English compounds combining these elements into phrases like 'non-earthquake-related'.

Initially the components meant 'not' + 'ground' + 'to tremble' + 'connected', and when combined the modern compound has come to specifically mean 'not connected with earthquakes' — the basic negative/compositional meaning has remained consistent.