Time reversal through a solid-liquid interface and super-resolution

We present numerical computations that reproduce the time-reversal experiments of Draeger et al (Draeger C, Cassereau D and Fink M 1998 Appl. Phys. Lett. 72 1567-9), where ultrasound elastic waves are time-reversed back to their source with a time-reversal mirror in a fluid adjacent to the solid. We also show numerically that multipathing caused by random inhomogeneities improves the focusing of the back-propagated elastic waves beyond the diffraction limit seen previously in acoustic wave propagation (Dowling D R and Jackson D R 1990 J. Acoust. Soc. Am. 89 171-81, Dowling D R and Jackson D R 1992 J Acoust. Soc. Am. 91 3257-77, Fink M 1999 Sci. Am. 91-7, Kuperman W A, Hodgkiss W S, Song H C, Akal T, Ferla C and Jackson D R 1997 J. Acoust. Soc. Am. 103 25-40, Derode A, Roux P and Fink M 1995 Phys. Rev. Lett. 75 4206-9), which is called super-resolution. A theoretical explanation of the robustness of super-resolution is given, along with several numerical computations that support this explanation (Blomgren P, Papanicolaou G and Zhao H 2002 J. Acoust. Soc. Am. 111 238-48). Time reversal with super-resolution can be used in non-destructive testing and, in a different way, in imaging with active arrays (Borcea L, Papanicolaou G, Tsogka C and Berryman J 2002 Inverse Problem's 18 1247-79).