The effective medium for a cylinder with cylindrical inclusions

In this paper, the scattering from a fluid-filled (infinite length) cylinder is considered. This cylinder, C, has a different interior sound speed and density than the surrounding water. Within the cylinder's interior, there are a number of smaller cylinders, inclusions, with yet other sound speeds and densities. The mean coherent field scattered from C is computed using Monte Carlo simulations with respect to the random realizations of the inclusion positions and compared to the results computed using an effective sound speed for C. An original formula for the effective sound speed is derived by equating the reflection coefficient for C (without inclusions) to the expected coherent scattered field from C with inclusions, assuming a single-scattering approximation. A single realization of inclusions is also considered with the backscattered spectra averaged azimuthally over the angle of the source/receiver pair. This result is then compared to the coherent fields predicted by the effective medium theory. This is performed for both spectra and the computed time series.