Time–frequency analysis of acoustic scattering from elastic objects

Some characteristics of an insonified object are generally present in the signal carried by the returning scattering wave. As an echo is the result of the wave interaction with a material structure, such a response is distinctive for a body of given shape and composition. Traditionally, to express the information content in the echo signature, either the frequency response (transfer/form function) or the time signature (impulse response) is employed; however, for a detailed study of the scatterer’s structure, a joint time and frequency analysis is performed. The aim of this analysis is to develop a simple processing algorithm for extracting the prominent features, which can then be used to determine the physical parameters of the object. The approach is based on the modified version of the Wigner distribution function (WDF) and utilizes an image-processing technique to depict the outstanding highlights of the scatterer’s response in a two-dimensional time and frequency display. The physical parameters of the scatterer are then extracted from this diagram with the proper interpretation and understanding of the scattering phenomena. Several examples, based on data obtained from numerically simulated models and laboratory measurements for elastic spheres and shells, are used to illustrate the capability and proficiency of the algorithm. Separable traces in time-frequency space are related to the specular reflection, creeping waves, and various reradiated elastic modes. From these, the general physical size, the corresponding wave speeds (elastic properties), and the density of the insonified object can be estimated.