Wavefield finite time focusing with reduced spatial exposure
Giovanni Angelo Meles (TU Delft - Applied Geophysics and Petrophysics)
J.R. Van der Neut (ImPhys/Acoustical Wavefield Imaging )
K. W.A. van Dongen (ImPhys/Acoustical Wavefield Imaging )
C.P.A. Wapenaar (TU Delft - Applied Geophysics and Petrophysics, ImPhys/Acoustical Wavefield Imaging )
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Abstract
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. The potential of the proposed method is explored with numerical experiments involving a head model consisting of a skull enclosing a brain.