If your talking about geological layering, then you could use seismic refraction, seismic reflection, Multi-Channel Analysis of Surface Waves. Also, there is surface to borehole, borehole to borehole and vertical Seismic Profiling. Seismic is an acoustic and therefore there will be an equivalent test method for testing smaller structures just that the frequency used will be much higher.

Are you referring to the acoustic transmission in multi-layer composite structures？If so, then this paper may be helpful to you.

See the book and papers of Brokohvskikh (may be incorrect spelling) -- in particular Waves in Layered Media...he received the RayleighMedal for his work in this area.

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