Numerical Solution of the Problem of the Computational Time Reversal in the Quadrant

Abstract

Abstract : The problem of the computational time reversal is posed as the inverse problem of the determination of an unknown initial condition with a finite support in a hyperbolic equation, given the Cauchy data at the lateral surface. A stability estimate for this ill-posed problem implies refocusing of the time reversed wave field. Two such two-dimensional inverse problems are solved numerically in the case when the domain is quadrant and the Cauchy data are given at finite parts of coordinate axis. The previously obtained Lipschitz stability estimate (if proven) rigorously explains and numerical results confirm the experimentally observed phenomenon of refocusing of time reversed wave fields.