Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

Two effective medium models for two-dimensional scalar wave propagation in random inhomogeneous media are examined in a single theoretical framework.It is shown how the hypotheses and self-consistency conditions in these models are mathematically formulated.As a special case, a two-phase composite in which circular cylindrical inclusions are embedded in a continuous matrix is considered.Numerical calculations are performed for such composites with different combinations of constituent properties in the frequency range up to ka = 10, where geometric optic behavior starts appearing.The models mutually deviate when the motion of inclusions is relatively large, such as at the resonance scattering of the inclusions.Otherwise, deviations in the low-frequency regime (ka < 1) are negligible and those at high frequencies are also strikingly small.The same facts are observed for two composites having very different constituent properties and in the high-frequency limit.