Acoustic attenuation in self-affine porous structures

As acoustic waves propagate through fluid-filled porous materials possessing heterogeneity in the elastic compressibility at scales less than wavelengths, the local wave-induced fluid-pressure response will also possess spatial heterogeneity that correlates with the compressibility structure. Such induced fluid-pressure gradients equilibrate via fluid-pressure diffusion causing wave energy to attenuate. This process is numerically simulated using finite-difference modeling. It is shown here, both numerically and analytically, that in the special case where the compressibility structure is a self-affine fractal characterized by a Hurst exponent H, the wave's quality factor Q (where Q(-1) is a measure of acoustic attenuation) is a power law in the wave's frequency omega given by Q proportional to omega(H) when /H/<1, and given by Q proportional to omega(tanhH) in general.