English Translation
Archeology is a science that studies the activities of human beings and their changes through the study of the traces left by them.
研究を「通じて」（つうじて）is the right word, meaning “through the study” or “by means of the study”.
研究を「通し」（とおし）means either 1) “throughout” (from the starting point to the end) or 2) “via”. 研究を通し in this particular sentence sounds like the speaker regards the area of study as a lens. 痕跡を通し makes sense but 痕跡の研究を通し doesn’t.
FYI: the author (translator) of the original Japanese sentence was posted on Tatoeba by non-Japanese native speaker.