Wavefield Finite Time Focusing with Reduced Spatial Exposure

Wavefield focusing is often achieved by Time-Reversal Mirrors, where wavefields emitted by a source located at the focal point are evaluated at a closed boundary and sent back, after Time-Reversal, into the medium from that boundary. Mathematically, Time-Reversal Mirrors are derived from closed-boundary integral representations of reciprocity theorems. In heterogeneous media, Time-Reversal Focusing theoretically involves in- and output signals that are infinite in time and the resulting waves propagate through the entire medium. Recently, integral representations have been derived for single-sided wavefield focusing. Although the required input signals for this approach are finite in time, the output signals are not and, similar to Time-Reversal Mirroring, the resulting waves propagate through the entire medium. Here, an alternative solution for double-sided wavefield focusing is derived. This solution is based on an integral representation where in- and output signals are finite in time, and where the energy of the waves propagating in the layer embedding the focal point is smaller than with Time-Reversal Focusing. We explore the potential of the proposed method with numerical experiments involving a head model consisting of a skull enclosing a brain.