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During the past three years, Wapenaar, Snieder, Broggini and others have developed an algorithm to compute the Green’s function for any point inside a medium to points on the surface from measurements on that surface only. Their algorithm is based on focusing an incoming wavefield to a single point in order to create a virtual source at the focus. The procedure has been justified only by heuristic arguments. In this review I am using simple physical arguments to prove an integral equation for single-sided, higher-dimensional inverse scattering. This integral equation is equivalent to the Wapenaar iteration algorithm. The equation will be exact, including all internal multiple reflections. The derivation makes use of time-invariance but does not use the explicit form of the wave equation. It is therefore not only applicable to the acoustic wave equation, but also to other time-reversal invariant systems.

Exact single-sided inverse scattering in three dimensions