Time reversal acoustics

Multiple scattering can enlarge the angular diversity reaching a receiver array. Reversing the paths then makes the array act like a larger aperture, improving the focus in appropriate regimes of wave propagation in a random medium.

For a linear operator $H$ mapping transmitted signals to recorded signals, the positive operator $H^{\ast }H$ describes adjoint back-propagation after recording. In a reciprocal array, physical time reversal acoustics implements this operation up to a final complex conjugation and the chosen signal conventions.

The DORT method uses eigenvectors of a time reversal operator to focus on individual point scatterers. A separate nonzero eigenvalue corresponds to each scatterer in the ideal weak-scattering, well-resolved limit; coherent overlap and multiple scattering can change this correspondence.