Effective wave operator for a medium with random isolated inclusions

In this chapter, we consider a homogeneous medium containing a random set of isolated inclusions. The effective field method is applied to the solution of the homogenization problem for wave propagation. The dispersion equation for the mean wave field in the composite is derived using the long-wave solutions of the one-particle problem. We show that this dispersion equation corresponds to a homogeneous medium (effective medium) with attenuation and dispersion. The Green function of the wave operator for the effective medium is constructed and analyzed. The velocities and attenuation coefficients of the long waves propagating in the composites with inclusions of various forms are calculated in the framework of the EFM.