A dilute random distribution of identical elastic spheres in a poroelastic isotropic matrix obeying Biot’s theory is considered. Using Luppe, Conoir and Norris (LCN) multiple scattering formula up to the corrective second order term in concentration, approximations are sought in the low frequency domain (Rayleigh limit) for the fast and slow effective wavenumbers. The contribution of the corrective second order term – which contains the coupling (i.e. mode conversions) between the fast, slow and shear waves and accounts for multiple scattering – is discussed. Considering the fast and slow wavenumbers, some effective quantities (bulk modulus, mass density and diffusion coefficient) are estimated.

考虑遵循Biot理论的多孔弹性各向同性矩阵中相同弹性球体的稀疏随机分布。使用Luppe，Conoir和Norris（LCN）多重散射公式，直到浓度的校正性二阶项，都在低频域（瑞利极限）中寻找快速和慢速有效波数的近似值。讨论了校正二阶项的贡献-包含快速波，慢波和切变波之间的耦合（即模式转换），并解释了多次散射。考虑到快波数和慢波数，估计了一些有效量（体模，质量密度和扩散系数）。