My calculations don't match yours.

Here http://www.bluebulbprojects.com/MeasureOfThings/results.php?...

That says there are 148 trillion square meters of land area on earth. So the technosphere (at 30 trillion tons) is about 1/5ton per square meter, or about 200 kg. If you use the all of the Earth's surface, it's 510 trillion square meters, so about 1/17th of a ton per square meter, or about 58 kg per square meter.

Assuming the dirt weighs about 2 tons per cubic meter, this corresponds to 58 kg/m^2 / 2000 kg/m^3 =~ 0.03 m, so it seems like the gp just used the incorrect unit.

You are correct. I had 1000000000 as a trillion. Scientific notation is a much better way to calculate things. At 30mm that is a big enough layer that a geologist could see it in the rock record, if it looked different enough.

I believe that we've spewed enough radiation that no visual distinction would necessary for detection, at least for the next several tens of thousands of years.

It's true that atmospheric nuclear testing has produced trace elements that were basically never on Earth before 1945, like Strontium-90 [https://en.wikipedia.org/wiki/Strontium-90]. Strontium-90 has a half life of about 29 years, so it will be detectable for a few thousand years or so. Some others last longer.

But the amount of dirt we have to turn over to find the 'good stuff' is maybe orders of magnitude bigger?