Decomposition of the time reversal operator: Application to dispersion curve measurements

Abstract

This paper presents an application of the DORT (Decomposition of the Time Reversal Operator) method to the ultrasonic characterization of extended scatterers with large arrays of transducers. The DORT method takes advantage of the invariance of wave propagation under time reversal. A time reversal operator is defined and measured from the inter-element impulse responses of each pair of transducers in the array. This operator is diagonalized and the analysis of its eigenvectors provides significant information on the scattering medium. The 2-dimensional problem of a hollow cylinder immersed in water is considered. Circumferential waves contributing to the scattered field are detected and characterized. It is shown that each of these waves is associated to an eigenvector of the time reversal operator. The points from which these waves radiate in the observation direction are determined. The analysis performed at each frequency provides the phase velocity dispersion curves V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</sub> (w) and the resonance spectrum of the shell