How can I repair leaks in an underground home's roof?
Uncovering it is the only way that will work. Given the expense and hassle involved, budget for a whole new waterproof membrane (EDPM rubber is one typical product - the expansion of "green roofs" in the past 30+ years means you'll find a bit more applicable knowledge and material than was around in the 1980's...) rather than trying to locate a leak. Root barriers are sometimes added as a separate layer to protect the actual membrane.

But...

This place claims to have a leak detection/mapping system (electrical- based) that MIGHT let you actually find the leak (without digging first) and dig a smaller hole - I have no direct knowledge of it and remind you to treat all words from sales-people with due caution. But the principle seems legit.