'organically-induced' is a compound of the adverb 'organically' and the past-participle adjective 'induced'. 'organically' derives from the adjective 'organic' + adverbial suffix '-ally'; 'organic' ultimately comes from Greek 'organon' meaning 'tool, instrument' via Latin/Old French. 'induced' derives from Latin 'inducere' (in- 'into' + ducere 'to lead').

'organic' came into English via Latin 'organicus' and Old French, itself from Greek 'organon'; 'induce' entered English from Latin 'inducere' through Old French 'induire' and Middle English, where it developed the sense 'bring about' or 'lead to', producing the past participle 'induced' used adjectivally. The modern compound follows productive English compounding (adverb + past participle) to form descriptive adjectives.

Individually, 'organic' shifted from 'related to an organ or instrument' to 'of living things' and then broadly 'natural'; 'induce' originally meant 'lead into' and evolved to 'cause or bring about'. Combined, 'organically-induced' now means 'caused by natural/biological processes.'