Time Reversed Absorbing Conditions (TRAC) in the Time and Frequency Domains

introduce the time reversed absorbing conditions (TRAC) in time reversal methods. These new boundary conditions enable one to"recreate the past"without knowing the source that has emitted the signals that are back-propagated. This new method does not rely on any a priori knowledge of the physical properties of the inclusion. We prove an energy es- timate for the resulting non-standard boundary value prob- lem. Numerical tests are presented in two dimensions for the wave and the Helmholtz equation. In particular the TRAC method is applied to the differentiation between a single in- clusion and a two close inclusion case. This technique is fairly insensitive with respect to noise in the data.