Fast and slow effective waves across dilute random distributions of elastic spheres in a poroelastic medium

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 concentration, approximations are sought low frequency domain (Rayleigh limit) for fast slow effective wavenumbers. The contribution – which contains coupling (i.e. mode conversions) between fast, shear waves accounts discussed. Considering wavenumbers, some quantities (bulk modulus, mass density diffusion coefficient) estimated.