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

Chandrasekhar, 1960 Weaver, 1990, Diffusivity of ultrasound in polycrystals, J. Mech. Phys. Solids, 38, 55, 10.1016/0022-5096(90)90021-U Zeng, 1993, Theory of scattered P-wave and S-wave energy in a random isotropic scattering medium, Bull. Seismol. Soc. Am., 83, 1264, 10.1785/BSSA0830041264 Sato, 1994, Multiple isotropic scattering model including P-S conversions for the seismogram envelope formation, Geophys. J. Int., 117, 487, 10.1111/j.1365-246X.1994.tb03946.x Turner, 1994, Radiative transfer and multiple scattering of diffuse ultrasound in polycrystalline media, J. Acoust. Soc. Am., 96, 3675, 10.1121/1.410587 Ryzhik, 1996, Transport equations for elastic and other waves in random media, Wave Motion, 24, 327, 10.1016/S0165-2125(96)00021-2 Margerin, 2000, Monte Carlo simulation of multiple scattering of elastic waves, J. Geophys. Res., 105, 7873, 10.1029/1999JB900359 Turner, 1999, Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials, J. Acoust. Soc. Am., 106, 541, 10.1121/1.427024 Przybilla, 2008, Monte Carlo simulation of radiative energy transfer in continuous elastic random media – three-component envelopes and numerical validation, Geophys. J. Int., 173, 566, 10.1111/j.1365-246X.2008.03747.x Gaebler, 2015, Seismic scattering and absorption parameters in the W-Bohemia/Vogtland region from elastic and acoustic radiative transfer theory, Geophys. J. Int., 201, 1471, 10.1093/gji/ggv393 Sanborn, 2017, Combined effects of deterministic and statistical structure on high-frequency regional seismograms, Geophys. J. Int., 210, 1143, 10.1093/gji/ggx219 Shapiro, 2000, The energy partitioning and the diffusive character of the seismic coda, Bull. Seismol. Soc. Am., 90, 655, 10.1785/0119990021 Hennino, 2001, Observation of equipartition of seismic waves, Phys. Rev. Lett., 86, 3447, 10.1103/PhysRevLett.86.3447 Weaver, 2001, Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies, Phys. Rev. Lett., 87, 10.1103/PhysRevLett.87.134301 Campillo, 2003, Long-range correlations in the diffuse seismic coda, Science, 299, 547, 10.1126/science.1078551 Saito, 2003, Simulating the envelope of scalar waves in 2D random media having power-law spectra of velocity fluctuation, Bull. Seismol. Soc. Am., 93, 240, 10.1785/0120020105 Borcea, 2006, Coherent interferometric imaging in clutter, Geophysics, 71, SI165, 10.1190/1.2209541 Kawase, 2011, The optimal use of horizontal-to-vertical spectral ratios of earthquake motions for velocity inversions based on diffuse-field theory for plane waves, Bull. Seismol. Soc. Am., 101, 2001, 10.1785/0120100263 Sánchez-Sesma, 2011, Energy partitions among elastic waves for dynamic surface loads in a semi-infinite solid, Bull. Seismol. Soc. Am., 101, 1704, 10.1785/0120100196 Sato, 2012, Seismic Wave Propagation and Scattering in the Heterogeneous Earth Grigorev, 1980, Propagation of ultrasonic waves in polycrystals of cubic symmetry with allowance for multiple scattering, J. Appl. Math. Mech., 44, 217, 10.1016/0021-8928(80)90150-1 Hirsekorn, 1982, The scattering of ultrasonic waves by polycrystals, J. Acoust. Soc. Am., 72, 1021, 10.1121/1.388233 Stanke, 1984, A unified theory for elastic wave propagation in polycrystalline materials, J. Acoust. Soc. Am., 75, 665, 10.1121/1.390577 Guo, 1985, Scattering of ultrasonic waves in anisotropic polycrystalline metals, Acustica, 59, 112 Engler, 2009 Baydoun, 2014, Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media, Wave Motion, 51, 1325, 10.1016/j.wavemoti.2014.08.001 Ta, 2010, Modeling of random anisotropic elastic media and impact on wave propagation, Eur. J. Comput. Mech., 19, 241, 10.3166/ejcm.19.241-253 Shiomi, 1997, Broad-band power-law spectra of well-log data in Japan, Geophys. J. Int., 130, 57, 10.1111/j.1365-246X.1997.tb00987.x Voigt, 1928 Chadwick, 2001, A new proof that the number of linear elastic symmetries is eight, J. Mech. Phys. Solids, 49, 2471, 10.1016/S0022-5096(01)00064-3 Guilleminot, 2013, On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties, J. Elasticity, 111, 109, 10.1007/s10659-012-9396-z Klimeš, 2002, Correlation functions of random media, Pure Appl. Geophys., 159, 1811 Khazaie, 2016, Influence of the spatial correlation structure of an elastic random medium on its scattering properties, J. Sound Vib., 370, 132, 10.1016/j.jsv.2016.01.012 Bal, 2006, Accuracy of transport models for waves in random media, Wave Motion, 43, 561, 10.1016/j.wavemoti.2006.05.005 Weaver, 1982, On diffuse waves in solid media, J. Acoust. Soc. Am., 71, 1608, 10.1121/1.387816 Papanicolaou, 1996, Stability of the P to S energy ratio in the diffusive regime, Bull. Seismol. Soc. Am., 86, 1107, 10.1785/BSSA0860041107 Turner, 1998, Scattering and diffusion of seismic waves, Bull. Seismol. Soc. Am., 88, 276, 10.1785/BSSA0880010276 Margerin, 2013, Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media, Geophys. J. Int., 192, 326, 10.1093/gji/ggs022 Trégourès, 2002, Generalized diffusion equation for multiple scattered elastic waves, Waves Random Media, 12, 21, 10.1088/0959-7174/12/1/302 Margerin, 2001, Effect of absorption on energy partition of elastic waves in the seismic coda, Bull. Seismol. Soc. Am., 91, 624, 10.1785/0120000228 Nakahara, 2011, Radiative transfer of elastic waves in two-dimensional isotropic scattering media: Semi-analytical approach for isotropic source radiation, Earth Planets Space, 63, 459, 10.5047/eps.2011.03.006 Cupillard, 2012, RegSEM: a versatile code based on the spectral element method to compute seismic wave propagation at the regional scale, Geophys. J. Int., 188, 1203, 10.1111/j.1365-246X.2011.05311.x R. Cottereau, D. Clouteau, J.-P. Vilotte, R. Madariaga, Validation of software for 3D propagation of waves in heterogeneous and random media, in: 9th US National Congress on Computational Mechanics, USNCCM, San Francisco, USA, 2007. Khazaie, 2017, Numerical observation of the equipartition regime in a 3D random elastic medium, and discussion of the limiting parameters, Comput. Geosci., 102, 56, 10.1016/j.cageo.2017.02.007 Panunzio, 2018, Large scale random fields generation using localized Karhunen-Loève expansion, Adv. Model. Simul. Eng. Sci., 5, 1 Shinozuka, 1991, Simulation of stochastic processes by spectral representation, Appl. Mech. Rev., 44, 191, 10.1115/1.3119501 de Carvalho Paludo, 2019, Scalable parallel scheme for sampling of Gaussian random fields over large domains, Internat. J. Numer. Methods Engrg., 117, 845, 10.1002/nme.5981 Bal, 2003, Self-averaging of Wigner transforms in random media, Comm. Math. Phys., 242, 81, 10.1007/s00220-003-0937-y Graff, 2012 Aki, 2002 Margerin, 2006, Attenuation, transport and diffusion of scalar waves in textured random media, Tectonophysics, 416, 229, 10.1016/j.tecto.2005.11.011