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TL;DR - given a sample of bone which has been encased in asphalt for tens of thousands of years and has become saturated with the asphalt, how can you get an accurate age for the specimen through carbon dating?

This past weekend I took my kids to the Page Museum at the La Brea Tar Pits in Los Angeles. While there we saw an astonishing number of fossilized Pleistocene animals. The interesting thing is that all of these fossils have a lovely (to my eyes, at least) brown color which is staining from the asphalt in which these bones have lain for thousands of years.

While there, we saw a presentation which explained that the asphalt seeps into the porous bones and it was explained that we know how old the specimens are through carbon dating. Which got me thinking - if the specimens are all highly contaminated with asphalt, how can they know that the sample they're testing contains carbon from the bone and not from the asphalt (which is presumably much older than the bone)? I did try asking one of the docents, but they're really not equipped to handle such a technical question.

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Various articles in the scientific literature confirm your assumption that the removal of asphalt from bone samples poses a significant challenge for accurate radiocarbon dating.

Several methods and results are summarized in O’Keefe, F. R.; Fet, E. V.; Harris, J. M.; Compilation, Calibration, and Synthesis of Faunal and Floral Radiocarbon Dates, Rancho La Brea, California Contrib Sci 2009, 518, 1–16. All techniques involve a combination of solvent washes (e.g. Soxhlet treatment) followed by the isolation of the bone collagen (since bone collagen does not exchange carbon with the environment) under different hydrolysis conditions (time, temperature, acid strength, etc.)

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According to Radiocarbon dating of petroleum-impregnated bone from tar pits at Rancho La Brea, California. Science 30 May 1969: Vol. 164, Issue 3883, pp. 1051-1052 :

Extensive bone dating was not possible before a method was devised for the removal of the impregnating petroleum...Bone is now routinely dated from its collagen

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