Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

Abstract

Abstract. In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneitiesthe so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position × wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.

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

“…The consideration of discrete random media is possible by considering the appropriate correlation structures, but will not be discussed here (see for instance [35,36,37,38]). Likewise, the anisotropic case is fully treated in Baydoun et al [39] but will be left aside here.…”

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

“…The medium is under vertically inhomogeneous initial stress, and stresses and wave velocities in the medium were analyzed. Multiple scattering of elastic waves in heterogeneous anisotropic media was modeled by Baydoun et al Relying on the kinetic approach, the waves are described in terms of their associated energy densities. The model has practical application meaning to metallic and mineral crystals.…”

Influence of local cubic anisotropy on the transition towards an equipartition regime in a 3D texture-less random elastic medium

“…In the case of anisotropic materials, Turner [8] derived the RTEs of elastic waves in a transversely isotropic heterogeneous medium. More recently, Baydoun et al [26] derived the RTEs of elastic waves in a general anisotropic case,…”

“…The objective of this paper is to challenge this conclusion for a particular texture-less anisotropic material, for which local behavior is cubic. The equipartition time for such a material is therefore derived analytically (Section 3.3), using a particular parameterization (Section 2) and theoretical results of Baydoun et al [26] for scattering cross-sections (Section 3 and Appendix A). The formula obtained is then compared to the results of numerical simulations of wave propagation in a set of random media with different statistical properties, and to results in the isotropic case (Section 4).…”