Influence of the spatial correlation structure of an elastic random medium on its scattering properties

Shahram Khazaie (1, 2) , Régis Cottereau (2) , Didier Clouteau (2)

1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres
2 MSSMat - Laboratoire de mécanique des sols, structures et matériaux

In the weakly heterogeneous regime of elastic wave propagation through a random medium, transport and diffusion models for the energy densities can be set up. In the isotropic case, the scattering cross sections are explicitly known as a function of the wave number and the correlations of the Lamé parameters and density. In this paper, we discuss the precise influence of the correlation structure on the scattering cross sections, mean free paths and diffusion parameter, and separate that influence from that of the correlation length and variance. We also analyze the convergence rates towards the low-and high-frequency ranges. For all analyses, we consider five different correlation structures, that allow us to explore a wide range of behaviors. We identify that the controlling factors for the low-frequency behavior are the value of the Power Spectral Density Function (PSDF) and its first non-vanishing derivative at the origin. In the high frequency range, the controlling factor is the third moment of the PSDF (which may be unbounded).

Keywords: Elastic wave propagation; Radiative transfer equation; Waves in random media; Correlation; Scattering cross-section

Domains: Vibrations [physics.class-ph]; Geophysics [physics.geo-ph]; Solid mechanics [physics.class-ph]

Shahram Khazaie, Régis Cottereau, Didier Clouteau. Influence of the spatial correlation structure of an elastic random medium on its scattering properties. Journal of Sound and Vibration, 2016, 370, pp.132-148. ⟨10.1016/j.jsv.2016.01.012⟩. ⟨hal-01281405⟩