3D primary estimation by sparse inversion using the focal domain parameterization

Recently, a new approach to multiple removal has been introduced: estimation of primaries by sparse inversion (EPSI). Although based on the same relationship between primaries and multiples as surface-related multiple elimination (SRME), it involves quite a different process: instead of prediction and subtraction of multiples, in EPSI the unknown primaries are the parameters of a large-scale inversion process. Based on a sparseness constraint, primaries are estimated in such a way that together with their corresponding surface multiples they explain the input data. In this paper a new algorithm is proposed to extend the EPSI process to the full 3D case, in which data reconstruction and primary estimation are combined, based on parameterization of the primaries in the socalled focal domain. This algorithm will allow reconstruction of large data gaps and yields reliable primaries. Results of this algorithm for a simple 3D example are shown.