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 distributed inclusions over a broad range of frequencies. The size and contrast of the inclusions are 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 it is demonstrated that they satisfactorily explain the effects of scattering on both the mean and variance of the phase and the mean and variance of the attenuation. The need for spatial averaging of observational data and methods of interpreting such averaged data in terms of the material properties of the scattering medium are discussed.