J. L. Akian, Space-time semiclassical measures for three-dimensional elastodynamics: boundary conditions for the hyperbolic set, Asymp. Anal, vol.78, issue.12, pp.37-83, 2012.

V. I. Alshits, On the Role of Anisotropy in Crystalloacoustics, Surface Waves in Anisotropic and Laminated Bodies and Defects Detection, pp.3-68, 2004.
DOI : 10.1007/1-4020-2387-1_1

V. I. Alshits and J. Lothe, Some basic properties of bulk elastic waves in anisotropic media, Wave Motion, vol.40, issue.4, pp.297-313, 2004.
DOI : 10.1016/j.wavemoti.2004.02.004

K. Atkinson, Numerical integration on the sphere, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol.120, issue.03, pp.332-347, 1982.
DOI : 10.1016/0041-5553(76)90100-2

G. Bal, Kinetics of scalar wave fields in random media, Wave Motion, vol.43, issue.2, pp.132-157, 2005.
DOI : 10.1016/j.wavemoti.2005.08.002

G. Bal, T. Komorowski, and L. Ryzhik, Kinetic limits for waves in a random medium, Kinetic and Related Models, vol.3, issue.4, pp.529-644, 2010.
DOI : 10.3934/krm.2010.3.529

. Ph, M. Boulanger, and . Hayes, Acoustic axes for elastic waves in crystals: theory and applications, Proc. R. Soc. Lond. A, pp.4542323-2346, 1977.

. Ph, M. Boulanger, and . Hayes, Bounds on elastic wave speeds in crystals: theory and applications, Proc. R. Soc. Lond. A, pp.4542289-2322, 1977.

M. Brassart, Semiclassical limit of Wigner transforms in periodic or random media, 2002.

M. Campillo and A. Paul, Long-Range Correlations in the Diffuse Seismic Coda, Science, vol.299, issue.5606, pp.547-549, 2003.
DOI : 10.1126/science.1078551
URL : https://hal.archives-ouvertes.fr/hal-00107924

M. Campillo, H. Sato, N. M. Shapiro, and R. D. , New developments on imaging and monitoring with seismic noise, Comptes Rendus Geoscience, vol.343, pp.8-9487, 2011.
URL : https://hal.archives-ouvertes.fr/insu-00679671

S. Chandrasekhar, Radiative Transfer, 1960.

T. L. Duvall-jr, S. M. Jefferies, J. W. Harvey, and M. A. Pomerantz, Time???distance helioseismology, Nature, vol.362, issue.6419, pp.430-432, 1993.
DOI : 10.1038/362430a0

L. Erdös and H. Yau, Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation, Comm. Pure Appl. Math., LIII, issue.6, pp.667-735, 2000.

C. Fermanian-kammerer and P. Gérard, Mesures semi-classiques et croisements de mode (semi-classical measures and mode crossing), Bull. SMF, vol.130, issue.1, pp.123-168, 2002.
DOI : 10.24033/bsmf.2416
URL : http://www.numdam.org/article/BSMF_2002__130_1_123_0.pdf

C. Fermanian-kammerer and P. Gérard, A Landau-Zener Formula for Non-Degenerated Involutive Codimension 3 Crossings, Annales Henri Poincar??, vol.4, issue.3, pp.513-552, 2003.
DOI : 10.1007/s00023-003-0138-4

U. Frisch, Wave propagation in random media, Probabilistic Methods in Applied Mathematics, pp.75-198, 1968.

P. Gérard, P. A. Markowich, N. J. Mauser, and F. Poupaud, Homogenization limits and Wigner transforms, Communications on Pure and Applied Mathematics, vol.50, issue.4, pp.323-379, 1997.
DOI : 10.1002/(SICI)1097-0312(199704)50:4<323::AID-CPA4>3.3.CO;2-Q

K. Goebbels, Materials Characterization for Process Control and Product Conformity, 1994.

J. Guilleminot and C. Soize, Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media, Multiscale Modeling & Simulation, vol.11, issue.3, pp.840-870, 2013.
DOI : 10.1137/120898346
URL : https://hal.archives-ouvertes.fr/hal-00854121

C. B. Guo, P. Höller, and K. Goebbels, Scattering of ultrasonic waves in anisotropic polycrystalline metals, Acustica, vol.59, issue.2, pp.112-120, 1985.

M. Guo and X. Wang, Transport equations for a general class of evolution equations with random perturbations, Journal of Mathematical Physics, vol.40, issue.10, pp.4828-4858, 1999.
DOI : 10.1063/1.533003

J. K. Hale, Ordinary Differential Equations, 1980.

S. Hirsekorn, The scattering of ultrasonic waves by polycrystals, The Journal of the Acoustical Society of America, vol.72, issue.3, pp.1021-1031, 1982.
DOI : 10.1121/1.388233

S. Hirsekorn, The scattering of ultrasonic waves in polycrystalline materials with texture, The Journal of the Acoustical Society of America, vol.77, issue.3, pp.832-843, 1985.
DOI : 10.1121/1.392052

A. Ishimaru, Wave Propagation and Scattering in Random Media, volume I & II, 1978.

Y. Itin and F. W. Hehl, The constitutive tensor of linear elasticity: Its decompositions, Cauchy relations, null Lagrangians, and wave propagation, Journal of Mathematical Physics, vol.54, issue.4, p.42903, 2013.
DOI : 10.1063/1.4801859

F. C. Karal and J. B. Keller, Elastic, Electromagnetic, and Other Waves in a Random Medium, Journal of Mathematical Physics, vol.5, issue.4, pp.537-547, 1964.
DOI : 10.1063/1.1704145

H. M. Ledbetter and R. P. Reed, Elastic Properties of Metals and Alloys, I. Iron, Nickel, and Iron???Nickel Alloys, Journal of Physical and Chemical Reference Data, vol.2, issue.3, pp.531-617, 1973.
DOI : 10.1063/1.3253127

P. Lions and T. Paul, Sur les mesures de Wigner (on Wigner measures), Rev. Mat. Iberoamericana, vol.9, issue.3, pp.553-618, 1993.
DOI : 10.4171/rmi/143

D. Liu and J. A. Turner, Influence of spatial correlation function on attenuation of ultrasonic waves in two-phase materials, The Journal of the Acoustical Society of America, vol.123, issue.5, pp.2570-2576, 2008.
DOI : 10.1121/1.2896757

J. Lukkarinen and H. Spohn, Kinetic Limit for Wave Propagation in a Random Medium, Archive for Rational Mechanics and Analysis, vol.19, issue.1, pp.93-162, 2007.
DOI : 10.1007/s00205-006-0005-9

L. Margerin, Attenuation, transport and diffusion of scalar waves in textured random media, Tectonophysics, vol.416, issue.1-4, pp.229-244, 2006.
DOI : 10.1016/j.tecto.2005.11.011
URL : https://hal.archives-ouvertes.fr/insu-00268212

A. Martinez, An Introduction to Semiclassical and Microlocal Analysis, 2002.
DOI : 10.1007/978-1-4757-4495-8

W. P. Mason and H. J. Mcskimin, Attenuation and Scattering of High Frequency Sound Waves in Metals and Glasses, The Journal of the Acoustical Society of America, vol.19, issue.3, pp.464-473, 1947.
DOI : 10.1121/1.1916504

J. R. Neighbours, F. W. Bratten, and C. S. Smith, The Elastic Constants of Nickel, Journal of Applied Physics, vol.23, issue.4, pp.389-393, 1952.
DOI : 10.1063/1.1702218

A. N. Norris, Acoustic axes in elasticity, Wave Motion, vol.40, issue.4, pp.315-328, 2006.
DOI : 10.1016/j.wavemoti.2004.02.005

L. V. Ryzhik, G. C. Papanicolaou, and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, vol.24, issue.4, pp.327-370, 1996.
DOI : 10.1016/S0165-2125(96)00021-2

H. Sato, M. C. Fehler, and T. Maeda, Seismic Wave Propagation and Scattering in the Heterogeneous Earth [42] ´ E. Savin. Transient vibrational power flows in slender random structures: theoretical modeling and numerical simulations, 43] ´ E. Savin. Kinetic modeling for transport of elastic waves in anisotropic heterogeneous media. Procedia IUTAM, pp.194-20597, 2012.

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, of Springer Series in Materials Science, 2006.

F. E. Stanke, Spatial autocorrelation functions for calculations of effective propagation constants in polycrystalline materials, The Journal of the Acoustical Society of America, vol.80, issue.5, pp.1479-1485, 1986.
DOI : 10.1121/1.394403

F. E. Stanke and G. S. Kino, A unified theory for elastic wave propagation in polycrystalline materials, The Journal of the Acoustical Society of America, vol.75, issue.3, pp.665-681, 1984.
DOI : 10.1121/1.390577

Q. Ta, D. Clouteau, and R. Cottereau, Modeling of random anisotropic elastic media and impact on wave propagation, Revue europ??enne de m??canique num??rique, vol.19, issue.1-3, pp.1-3241, 2010.
DOI : 10.3166/ejcm.19.241-253
URL : https://hal.archives-ouvertes.fr/hal-00709537

J. A. Turner, Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials, The Journal of the Acoustical Society of America, vol.106, issue.2, pp.541-552, 1999.
DOI : 10.1121/1.427024

J. A. Turner and P. Anugonda, Scattering of elastic waves in heterogeneous media with local isotropy, The Journal of the Acoustical Society of America, vol.109, issue.5, pp.1787-1795, 2001.
DOI : 10.1121/1.1367245

J. A. Turner and R. L. Weaver, Radiative transfer and multiple scattering of diffuse ultrasound in polycrystalline media, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3675-3683, 1994.
DOI : 10.1121/1.410587

J. A. Turner and R. L. Weaver, Radiative transfer of ultrasound, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3654-3674, 1994.
DOI : 10.1121/1.410586

M. C. Van-rossum and T. M. Nieuwenhuizen, Multiple scattering of classical waves: microscopy, mesoscopy and diffusion. Rev. Modern Phys, pp.313-371, 1999.

V. K. Varadan, Y. Ma, and V. V. Varadan, A multiple scattering theory for elastic wave propagation in discrete random media, The Journal of the Acoustical Society of America, vol.77, issue.2, pp.375-385, 1985.
DOI : 10.1121/1.391910

R. L. Weaver, Diffusivity of ultrasound in polycrystals, Journal of the Mechanics and Physics of Solids, vol.38, issue.1, pp.55-86, 1990.
DOI : 10.1016/0022-5096(90)90021-U

R. L. Weaver and O. I. Lobkis, Ultrasonics without a Source: Thermal Fluctuation Correlations at MHz Frequencies, Physical Review Letters, vol.87, issue.13, p.134301, 2001.
DOI : 10.1103/PhysRevLett.87.134301

(. I. Baydoun, M. Laboratoire, C. Paris, and E. France, ONERA?The French Aerospace Lab, France E-mail address: eric.savin@onera.fr (R. Cottereau) Laboratoire MSS-Mat