T env M t t t f a v b t e e s r

It is well known that the acoustic wave equation in a nondissipa-ive heterogeneous medium is invariant under a time-reversal opera-ion. Indeed, the equation contains only a second-order time-deriva-ive operator. Therefore, for every burst of sound r,t diverging rom a source — and possibly reflected, refracted, or scattered by ny heterogeneous media — there exists, in theory, a set of waves r,−t that precisely retraces all of these complex paths and con-that uses complex environments to appear wider than it is, resulting in a refocusing quality that does not depend on the TRM aperture. It must be noticed that the research on time-reversal acoustics was initially focused on two main applications, ultrasound therapy tu-mor or kidney stone destruction and acoustic communications in the ocean. In both applications, self-focusing on the source with a TRM is accomplished without any knowledge of the medium be-tween the source and the TRM. Time-removal acoustics does notime-reversal acoustics in comple