  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.
