Scaling properties of attenuation and grain size

The fractal characteristics of attenuation are evaluated, and an attempt is made to establish an alternative theoretical model for ultrasonic scattering at grain boundaries. The theoretical development starts with attenuation scaled by wavelength and an inverse power law expression for the grain size distribution function. The wavelength dependence of the attenuation is found to be also an inverse power law with the same exponent as the grain size distribution function. Theoretical justifications for such a size distribution are given, as well as the representation of a 3-D self-similar size distribution in a 2-D image.<
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