Ultrasonic characterization of fractal models

Ultrasonic scattering in inhomogeneous fluid media is examined. Of particular interest are those media having a compressibility that varies on a continuum of spatial scales. It is shown that the internal features of such media can be extracted by an analysis of the forward scattered field. The angular distribution of scattered pressure intensity is found to vary with frequency and compressibility contrast. The scattered field data can be rendered stationary to such variations by an application of a similarity transformation. Examples are given for cases where the spatial variation in the compressibility of the media obeys either a power law or exponential correlation function. When these similarity transformations are applied, an estimate of the characteristic radius of the scatterers and the fractal dimension of the medium can be directly obtained.<
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