Dating of volcanic ash
There is a number of different techniques available.
We can date volcanic rocks using a method called argon-argon dating for instance.
Hot, newly erupted lava and ash contain a form of the chemical element potassium (called potassium-40) that is radioactive.
The age of volcanic rock and ash can be "pinpointed" to within roughly twenty thousand years -- a mere moment in Earth's 4-billion-year history.
The results were very consistent and showed the shroud dated between AD.
Samples of rock are not able to be dated using radiocarbon, because rocks contain no organic carbon from living organisms that are of recent enough age.
Most rocks formed hundreds of thousands if not millions of years ago.