Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media
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 inhomogeneities-the 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 (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.
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- Applied Mathematics
- 5103 Classical physics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0203 Classical Physics
- 0102 Applied Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Applied Mathematics
- 5103 Classical physics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0203 Classical Physics
- 0102 Applied Mathematics