Abstract At long lapse times in randomly fluctuating media with macroscopic isotropy (texture-less media), the energy of elastic waves is equipartitioned between compressional (P) and shear (S) waves. This property is independent of the local isotropy or anisotropy of the heterogeneous constitutive tensor and of the type of source. However the local symmetry of the constitutive tensor does influence the rate of convergence to equipartition and this paper discusses the precise influence of local anisotropy on the time required to reach equipartition. More particularly, a randomly-fluctuating medium is considered, whose behavior is statistically isotropic, and locally cubic. After calculating all the differential and total scattering cross-sections in that case, an analytical formula is derived for the rate of convergence to the equipartition regime, function of the second-order statistics of the mechanical parameter fields (bulk and shear moduli and anisotropy parameter). The local anisotropy is shown to influence strongly that transition rate, with a faster transition when the fluctuations of the anisotropy parameter are positively correlated to those of the shear modulus. A numerical model is constructed to illustrate numerically these results. Since the asymptotic regime of equipartition cannot be simulated directly because it would require too large a computational domain, boundaries are introduced and mechanical properties are chosen so as to minimize their influence on equipartition.

中文翻译：

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局部三次各向异性对在 3D 无纹理随机弹性介质中向均分状态转变的影响

摘要 在具有宏观各向同性的随机波动介质（无纹理介质）中，在较长的时间间隔内，弹性波的能量在压缩（P）波和剪切（S）波之间均分。该性质与异质本构张量的局部各向同性或各向异性以及源类型无关。然而，本构张量的局部对称性确实会影响收敛到均分的速度，本文讨论了局部各向异性对达到均分所需时间的精确影响。更具体地说，考虑了一种随机波动的介质，其行为在统计上是各向同性的，并且是局部立方的。在这种情况下计算所有微分和总散射截面后，推导出均分机制收敛速率的解析公式，力学参数场（体积和剪切模量以及各向异性参数）的二阶统计函数。局部各向异性显示出强烈影响转变速率，当各向异性参数的波动与剪切模量的波动呈正相关时，转变速度更快。构建一个数值模型以数值说明这些结果。由于均分的渐近状态不能直接模拟，因为它需要太大的计算域，因此引入了边界并选择了机械特性，以尽量减少它们对均分的影响。当各向异性参数的波动与剪切模量的波动呈正相关时，转变速度更快。构建一个数值模型以数值说明这些结果。由于均分的渐近状态不能直接模拟，因为它需要太大的计算域，因此引入了边界并选择了机械特性，以尽量减少它们对均分的影响。当各向异性参数的波动与剪切模量的波动呈正相关时，转变速度更快。构建一个数值模型以数值说明这些结果。由于均分的渐近状态不能直接模拟，因为它需要太大的计算域，因此引入了边界并选择了机械特性，以尽量减少它们对均分的影响。