The Boltzmann constitutive representation is shown to provide a consistent means of incorporating dispersion effects into the mathematical modeling of wave behavior in layered elastic media. Attention is restricted to long wavelength conditions, with the waves propagating normal to the planes of layering. Special forms of a general Boltzmann law are derived for the special cases of periodic layering and one dimensionally random layering. Although there is no attenuation of harmonic waves in the periodic media case, an analytical representation is obtained for the attenuation measure in random media.

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