Optimal wave focusing in acoustic media

Focusing waves inside a medium has applications in various science and engineering fields, e.g., in medicine, nondestructive evaluation, ocean acoustics, and geophysics. The goal in focusing is to concentrate the wave energy at a specific time and location inside a medium. Various techniques have been devised and used to achieve this goal. Time-reversal is a method that is routinely used to focus acoustic and seismic waves. One important geophysical application of time-reversal focusing is in seismic source imaging. However, the method is not optimal for source imaging when acquisition is incomplete. Here, we propose a new technique wherein wave focusing is cast as an optimization problem. The new technique mitigates the adverse effects that incomplete acquisition has on time-reversal focusing and source imaging.