Joseph Kohlbeck, Resident Scientist at the Hercules Aerospace Center in Utah, and Richard Levi-Setti of the Enrico Fermi Institute at the University of Chicago, studied embedded dirt particles taken from the Shrouds surface. The dirt turned out to be travertine aragonite limestone.
Using a high-resolution microprobe, Levi-Setti and Kolbeck compared the spectra of samples taken from the Shroud with samples of limestone from ancient Jerusalem tombs.
The chemical signatures of the Shroud samples and the tomb limestone were identical except for some minute fragments of organic cellulous linen fiber that could not be separated from the Shroud samples.
Kolbeck acknowledges that this is not absolute proof that the Shroud was in Jerusalem and that there might be other places in the world -- though none are known and it is statistically unlikely any will be found -- where travertine aragonite has the identical trace chemical composition. It is also slightly possible though highly implausible that this dirt was applied by a forger.