Time-Reversal Movie (14 Megs!)

NB: You've got to wait until it stops rotating

Here are some explanations on the Time Reversal experiment.

Initial condition at time t=0:

Acoustic signal at time t=T-0 after propagation through a random medium:

Acoustic signal at time t=T+0 after truncation and time-reversion (where pressure is kept constant and the velocity field (or equivalently the time derivative of the pressure field) is reversed):

Acoustic pulse at time 2T after propagation through the same random medium. Notice the peak in the center at the location of the initial pulse:

Zooms of the same pulse at time 2T near the origin:

Rotation of the pulse in the vicinity of the origin:

Unlike the initial pulse (a peaked Gaussian which is positive everywhere), the repropagated signal has essentially mean zero. The time-reversal procedure is a filter that kills low frequencies.

You can get more information on time reversal from the following papers and their references:

  • Time Reversal and Refocusing in Random Media (with L.Ryzhik), SIAM J. Appl. Math, 63(5), pp. 1475-1498, 2003.
  • Time Reversal for Classical Waves in Random Media (with L.Ryzhik), C. R. Acad. Sci. Paris, Serie I, 333, pp. 1041--1046, 2001.