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There are articles that state that silver has been found on the moon.

moons treasure chest includes silver
Moon's Silver Hints at Lunar Water Origins
Silver found on Moon – and you thought it was made of cheese

How could such resources be estimated?

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    $\begingroup$ Your question assumes that the amount could be estimated with current data. It should be rephrased to ask if it could be estimated and then how it could be if it were possible. But it is an interesting topic, so +1 $\endgroup$
    – called2voyage
    Jan 7, 2014 at 14:30

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This Wikipedia page shows the abundance of silver on earth as $50$ parts per billion by mass. One could assume that the moon is not too far off that. Multiply by the mass of the moon $7.3477 \cdot 10^{22} \text { kg } \cdot 5 \cdot 10^{-8}\approx 4\cdot 10^{15}$kg

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Earlier missions put silver at a concentration of 100 parts per billion (ppb). The LCROSS mission found a possibly higher concentration, but the original publication (subscription only) does not contain an estimate of the concentration. In fact, the article only says this:

This (spectral lines found in images of the crater) suggests a concentration of volatile Na (and perhaps Ag) near but not on the surface.

It appears that the popular-science press has been hyping this up beyond what's supported by actual data.

Even if LCROSS found a higher concentration of silver, that measurement is only valid for the impact site. It'd be very difficult to extrapolate this to the entire Moon. On Earth, the concentration of silver and other materials varies wildly, and it's only high enough to economically mine the silver in a few places. To give an idea, one silver mine has a silver concentration of 0.3 %.

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