Statistical Stability in Time Reversal

Authors:
  • GPGeorge Papanicolaou
    George Papanicolaou
  • KSKnut Solna
    Knut Solna
  • LRLeonid Ryzhik
    Leonid Ryzhik
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Abstract
When a signal is emitted from a source, recorded by an array of transducers, time-reversed, and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency remote-sensing regime and show that, because of multiple scattering in an inhomogeneous or random medium, it can improve beyond the diffraction limit. We also show that the back-propagated signal from a spatially localized narrow-band source is self-averaging, or statistically stable, and relate this to the self-averaging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is self-averaging only for broad-band signals. The array of transducers operates in a remote-sensing regime, so we analyze time reversal with the parabolic or paraxial wave equation.

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