2002/01/08 by Guillaume Bal, Bal, Guillaume, Leonid Ryzhik +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Geophysical Methods and Applications #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #cond-mat.dis-nn #math.AP #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0201011
Better quality figures are available at http://www.math.uchicago.edu/~ryzhik
arxiv created 2002/01/08 · arxiv updated 2009/11/30
In time reversal acoustics experiments, a signal is emitted from a localized source, recorded at an array of receivers-transducers, time reversed, and finally re-emitted into the medium. A celebrated feature of time reversal experiments is that the refocusing of the re-emitted signals at the location of the initial source is improved when the medium is heterogeneous. Contrary to intuition, multiple scattering enhances the spatial resolution of the refocused signal and allows one to beat the diffraction limit obtained in homogeneous media. This paper presents a quantitative explanation of time reversal and other more general refocusing phenomena for general classical waves in heterogeneous media. The theory is based on the asymptotic analysis of the Wigner transform of wave fields in the high frequency limit. Numerical experiments complement the theory.