Fluctuations of elastic waves due to random scattering from inclusions

Exact solutions for elastic compressional and shear waves scattered from a homogeneous sphere are used to obtain formulas for fluctuations of velocity and attenuation of plane waves propagating through a layer of randomly dis tributed inclusions over a broad range of frequencies. The size and contras t of the inclusions axe arbitrary, but interactions between scatterers are not considered and the concentration of scatterers is assumed to be small. The analytical solutions are also compared with numerical simulations and i t is demonstrated that they satisfactorily explain the effects of scatterin g on both the mean and variance of the phase and the mean and variance of t he attenuation. The need for spatial averaging of observational data and me thods of interpreting such averaged data in terms of the material propertie s of the scattering medium are discussed.