Optimal wave focusing for imaging and microseismic event location

Focusing waves inside a medium has applications in geophysics in areas such as imaging and microseismic event location. 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. Timereversal (TR) is a well-researched method that has been used routinely to focus waves. The ability of TR methods to focus wave fields inside heterogeneous media is bounded by limitations caused by imperfect acquisition, attenuation, and the diffraction limit. To go beyond these limitations, we present a solution by formulating wave focusing as an optimization problem. Solving this optimization problem gives the needed signals for transmission to the medium to get the best focus. These signals are optimized for the configuration of the injection points, velocity of the medium, and the focusing target.