On effective attenuation in multiscale composite media

Experiments show that waves propagating through the earth’s crust experience frequency-dependent attenuation. Three regimes have been identified with specific attenuation properties: the low-, mid-, and high-frequency regimes with attenuation in general increasing with frequency. This paper shows how the observed behavior can be explained via theory for waves in random media. It considers multiple scattering of waves propagating in non-lossy one-dimensional random media with shortand/or long-range correlations. Using stochastic homogenization theory it is possible to show that pulse propagation is described by effective fractional damping exponents. The damping exponents are related to the Hurst parameters of the random media which are characteristic parameters of the correlation properties of the fluctuations of the random media. This description is the link in between the random medium properties and the observed damping behavior. In particular a simple binary medium is shown to reproduce well the experimental attenuation properties in the low-, mid-, and high-frequency regimes.