Computing focusing functions for model-based redatuming: an inverse filter approach

Standard model-based redatuming techniques consist in applying time shifts to the surface data, to simulate an acquisition made at depth. The time shifts are computed using prior knowledge of the overburden, such as a macro velocity model. These techniques allow focusing of the direct waves at the new datum, but the focus can be degraded because of surface multiples and internal multiples in the overburden. We show that if the medium above the redatuming level is known, these multiples can be removed. We compute exact focusing functions, free of multiples, using an inverse filter approach. These focusing functions create downgoing and upgoing virtual sources at the new datum. The surface responses to these virtual sources are then used to compute the objective redatumed dataset through multi-dimensional deconvolution. The redatumed dataset corresponds to a virtual acquisition made at the new datum and for which the effect of the overburden is completely canceled. We demonstrate the technique on a 2D acoustic synthetic example.