Poincaré wavelet techniques in depth migration

A method based on space-time wavelets is developed for the migration problem in a smooth layered medium. The problem is to restore reflection boundaries inside the medium if signals emitted from the surface of the medium and reflected wavefield received on the same surface are known. Boundaries are determined as maxima of a function of sub-surface fields: a forward-propagated radiated field and a back-propagated received one. We represent the subsurface fields in terms of localized solutions running in the medium. Initial amplitudes of these localized solutions are calculated by means of the continuous space-time wavelet analysis for the boundary value (seismic) data. An example with seismograms calculated by the finite differences method is presented.