Multiple reflections on Huygens' principle

According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the waves emitted by the secondary sources are represented by Green's functions. In many present-day applications of Huygens' principle, these Green's functions are replaced by their time-reversed versions, thus forming a basis for backpropagation, imaging, inversion, seismic interferometry, etc. However, when the input wave field is available only on a single open boundary, this approach has its limitations. In particular, it does not properly account for multiply reflected waves. This is remedied by a modified form of Huygens' principle, in which the Green's functions are replaced by focusing functions. The modified Huygens' principle forms a basis for imaging, inverse scattering, monitoring of induced sources, etc., thereby properly taking multiply reflected waves into account.