Scattering of elastic waves by randomly distributed and oriented scatterers

We analyze the two-dimensional problem of multiple scattering by randomly distributed and oriented scatterers, and compare the results with those for the aligned scatterers. Waterman’s T-matrix approach in conjunction with the statistical averaging for both position and orientation are employed to obtain the phase velocity and attenuation due to geometric dispersion for a wide range of frequencies. Analytical expressions for the dispersion relation are also derived at low frequencies for both randomly distributed and oriented inclusions and cracks.