Well, a Mine has <iDiscoverRand>10000</iDiscoverRand>, and an Earth Mana provides <iDiscoverRandModifier>20</iDiscoverRandModifier>.
If you use the World Builder mouseovers, you see a 1 in 38% Chance of Discovering... on a normal mine, and you cannot get such a tip on a mine that reflects the changes from Earth mana. (Using the Civlopedia by the way gives you a junk number)
My guess would be that it is probably a roll on a 0 to 10000 random, and if it gets under 100 then you discover a resource normally. Now, without any earth mana you don't seem to discover all that much, but with 5 earth mana you make a discovery almost every turn. Thus I would think that the modifier of 20 divides your result. So essentially with 1 earth mana you are now doing a random 0 to 500, need a value under 100. With 2 it is now 0 to 250, then 0 to 167, 0 to 125, 0 to 100....
But this does seem a little TOO likely too fast.
The other way it could work is that the 20 modifier adds. So you always random from 0 to 10000, but without earth mana you need a 100, with 1 mana you need a 120, 2 mana for a 140....
But this seems a little too UNLIKELY.
End result... here's some numbers! Earth Mana does something!