Did ancient miners have ways of predicting ore/stone deposits?

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In short, no. With no knowledge of sedimentary processes, chemistry of ores, or continental-shelf subduction, the ancients were completely dependent on surface geology for location of ore bodies. However, this was not usually a limiting factor - given that the world population only hit 200 million during the Roman Republic, and 500 million in the 15th century, the readily available surface ore deposits for most elements was usually sufficient. Regional differences actually stimulated trade and exploration, such as for British tin or Cypric copper (the origin of the name).

This is not to say that underground mining didn't exist - it certainly did from at least Roman times. But the mines were dug into cliffs and escarpments to follow seams down from the surface. The ancients being as smart, if not as knowledgeable, as we are today, there were certainly some who may have deduced the likely extensions of already known seams, and taken some shortcuts.

Here is a link on some ancient Greek and Roman mining methods, and here is one on ancient Egyptian gold-mining techniques. Note the similarities of the latter to panning during the California gold rush 2000 years later.

Details of historic prospecting can be found here.

Googling "ancient mining" and "ancient prospecting" yield additional references.

Update
The Map that Changed the World by Simon Winchester outlines the quest by William (Strata) Smith, from 1793 to 1815, to prepare the first map of geological strata, for the United Kingdom, and lay the foundations of modern geology. William Smith is believed to be the first person to recognize, and study, the geological significance of sedimentary deposition of rocks. On Page 75 of the book, Winchester quotes from Smith's diary in regards to the belief of the colliers that the evident and well known patterns of the coal mines did not exist in general:

I was told there was "nothing regular above the Red Ground", which in their sinkings varied much in thickness. This did not deter me from pursuing my own thoughts upon this subject.

The "Red Ground" was the sedimentary deposition above the Carboniferous Uncomformity in Somerset (where Smith worked at the time) and indeed much if not all of Britain and Western Europe.

Although the nascent science of geology existed prior to Smith's work, and the stratification of sedimentary deposits had been observed by others, the conclusions reached by earlier geologists were often bizarrely incorrect, by modern terms, and thus of no particular use in predicting the behaviour, existence, and location of buried strata.

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Believe it or not, ancient prospect was not too much different than modern prospecting.

The main improvement modern prospectors have is aerial photography and the ability to bore test holes quickly.

Geologic knowledge in the past was more primitive, but still effective. For example, if you were looking for lead (galena) and had a competition between a modern geologist and ancient Roman prospector to find lead just based on geology alone the ancient prospector would probably have just as good a chance against the modern prospector.

In truth, geology is actually not too important in prospecting compared to surface indications, which you have already mentioned. Nearly all mineral deposits such as gold or iron are found by prospecting the surface and working backwards.

When you find the mineral you want on the surface, you trace it back. For example, for gold you will find it in a stream. You then follow the stream back to find where it is getting the gold from. Typically this will lead you to a hill or mountain. Then by digging into the hill you will find the seam containing the gold.

Last summer I was out in the pueblos and I heard of a prospector who had made some good money from a deposit of turquoise. The way he found it was wandering around he saw an anthill (which are abundant there) with blue specks in it. He dug down and found the turquoise. The ants had helped him. Methods like these haven't changed since the beginning of civilization.

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