Theoretical Topics in Wave Propagation in a Random Medium
ARIZONA UNIV TUCSON DEPT OF MATHEMATICS
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Three aspects of wave propagation in a random medium are considered. The first is the scattering of a plane compressional wave by a spherical inhomogeneity of specified radius. This result is then averaged over a Rayleigh distribution of sphere radii. As a second topic, the scattering by a medium in which an elastic parameter varies randomly is considered. When the randomness is assumed to be described by a Gaussian correlation function, it is found that the frequency and angular dependence of the scattering is the same as that obtained in the previous calculation with the Rayleigh distribution when the average diameter of the spheres is set equal to the correlation distance appearing in the random medium. The third topic considered is the effect of the randomness on the focusing of the wave. The total incident sound field may be viewed as being composed of a sum of coherent field reflected from an object of interest and an incoherent field resulting from the scattering due to inhomogeneities in the surrounding medium. The fluctuations in the imaging of the incoherent field can be decreased by increasing the size of the receiving system and this dependence on receiver size will have been achieved when the receiver has been increased to a size equal to about twice the correlation length of the fluctuations in the incident field.