Scattering in an Infinitely Extended Inhomogeneous Medium

Abstract

Scattering in a medium containing patches of inhomogeneities consists of a splitting up of the incident sound into incoherent waves as well as of a focusing and defocusing action of the inhomogeneities. The first phenomenon causes rapidly varying interferences leading to an amplitude distribution between Gaussian and Rayleigh; the second causes a slow spreading of this amplitude distribution toward lower and higher values of sound pressure. The interference component can be derived from a simple model consisting of infinite slabs having properties similar to those of the patches of inhomogeneity along the line connecting source and receiver; the focusing component follows from a consideration of the divergence of a beam caused by refraction. The pressure scattered in the forward direction is out of phase by 90 degrees with respect to the unscattered sound and causes only a change of phase when the patches are large; but when the patches are small, the scattered pressure is found to be Rayleigh distributed and to affect the amplitude as well as the phase of the transmitted sound. With the aid of results derived by Potter and Murphy (Applied Physics Laboratory, University of Washington, APL/UW/TE/55-12), the total pressure and its fluctuation can be computed for any frequency and any size of the scattering patches. The maximum radius “a” of a patch sensibly contributing to the intensity at a distance r is found to be given by a + (r/k)12, where k is the wave number. With increasing frequency, scattering turns from a first-order to a second-order phenomenon, so that finally we are left with focusing effects as given by ray theory. The usual practice connecting the correlation function with the intensity proves to be applicable only when the frequency is low or the patches are small and leads to completely wrong results for higher frequencies or for larger patches.