Kevin B. answered 04/05/20
Geologist/Geophysicist
Acoustics as in seismology could be used to solve for the velocity of the materials, which could then help you deal with the identification. Because density is part of the wave equation, you could work back out the value. However you will have some difficulty depending on the arrangement of the layering as lower velocity layers will not reflect the signal (assuming a source receiver offset is on the surface). Due to the thin nature of the layers you would need to work out the frequency response. It is my guess that you would need some very high frequencies or you might be better served by switching to ground penetrating radar. You would need to work out the frequency and wavelength sizes first, to see if it fits within the individual layer and then see what your capabilities are.
Best of luck.