Mean field renormalization techniques determine the phase distortion (time delay) and effective attenuation as functions of frequency for a plane acoustic wave, normally incident on a layered medium, when the medium also contains a distribution of scattering centers at random sites. The power spectra of impedance fluctuations of both the bedding layers and the random centers contribute to the time delay and mean field effective attenuation.
At low frequencies (long wavelengths), the power spectrum of the bedding planes dominates the mean wave response, producing most of the time delay and the effective attenuation. At high frequencies (short wavelengths), the random scattering centers dominate the mean wave behavior. The wave no longer propagates exactly perpendicularly to bedding planes since the random scattering centers cast energy into directions transverse to the normal to the bedding planes.
The precise frequency dependence of both the time delay and the effective attenuation of the mean wave are sensitive to the power spectrum of impedance fluctuations of the bedding planes relative to the power spectrum of the random scattering centers.