Inhomogeneity size and shape determination from scattering of low-frequency sound waves

The scattering of sound waves by isolated inhomogeneities in a solid is examined using the Born approximation. A procedure is developed to extract information about the effective volume and shape of the scatterer. The procedure uses data from the long-wavelength region where this approximation is valid. The volume and shape information is in the form of special moments of the volume of the scatterer which depend on the orientation of the scatterer relative to the direction of the difference in the incoming and outgoing wave vectors. A scheme is described which permits the characterization of the scatterer in terms of an equivalent ellipsoid. The scheme provides a second-moment solution of the inverse scattering problem.