Wave scattering from cylindrical fluid inclusions in an elastic medium and determination of effective medium properties

Abstract

The goal of this thesis is to be able to predict acoustic wave speeds in sea ice with known concentrations of inhomogeneities. To accomplish this, ice is modeled as a solid in which cylindrical fluid brine channels are embedded. The solution is formulated by deriving the scattering from a single cylindrical fluid-filled inclusion in an attenuating elastic medium. The scattering vs. angle results are shown for a laboratory experiment in which a single water-filled cylindrical inclusion is embedded in polypropylene. Four different radius-towavelength ratios of 1.9, 2.4, 8.8 and 11.0 were measured and proved qualitatively consistent with theory. An extension of the single scattering approximation is used to derive effective moduli for multiple fluid-filled cylinders in an elastic medium. The theory assumes the acoustic wavelength in the medium is long compared to the radius of the cylindrical inclusion so that fluctuations in material properties are effectively averaged over. A separate laboratory experiment was conducted using polypropylene to measure compressional wave speeds for different concentrations of inclusions. The experimental results were within 1% of the wave speeds predicted by effective medium theory. The effective compressional wave speeds predicted by this theory were then compared with wave speeds calculated using empirical relations derived from Arctic ice field data. The maximum error between the two is less than 4%. This effective medium theory is extremely useful for acoustic tomography applications and can be expanded to include other inhomogeneity geometries besides cylinders.