Acoustic Rayleigh scattering in water-saturated granular medium with quasicrystalline approximation

A closed-form solution for the effective wavenumber in a water-saturated medium as a function of the Rayleigh parameter is derived up to the second leading terms in the real part and first leading term in the imaginary part. This is based on the Waterman multiple scattering formulation with the quasicrystalline approximation (QCA) and the Percus-Yevick pair-correlation function. The formula's resultant sound speed and attenuation are compared to the regression relation matching the measurements in the Rayleigh scattering region [Kimura, J. Acoust. Soc. Am. 129(6), 3544-3561 (2011)]. The sound speeds are comparable. However, for the attenuation, it is shown that the QCA result underestimates the measured attenuation while its behavior exhibits similar frequency dependency of f(4).