Not sure if this method exists for data analysis... or even if I can word my question clearly:
If you took multiple transparancies with a map of the world on it, and then placed a 'very light' dot of color at places of interest (one dot on each transparency), when you stacked all of the transparancies on top of each other (in any order really), the 'very light' dots of color would combine to form 'darker' spots indicating increased interest in these locations. Likewise, the 'answer' would become readily apparant just by looking at overlayed maps with little to no calculations
Does this sound like any establised technique that you have heard of? And if so, what is its name?
Yes.
This technique is commonly known as heat map (Wikipedia), and a standard visualization technique.
This is popularly used with multivariate density estimation (Wikipedia).
Picture from Wikipedia, see File:Old Faithful Geyser KDE with plugin bandwidth.png (CC by-sa-3.0 licensed).
I would not call this "data mining". This is much much older. It's a visualization technique popular in statistics, though; but not so much an "analysis" technique.