Estimation of Primaries By Sparse Inversion - Parameterization Via the Focal Domain

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 in surface-related multiple elimination (SRME), it involves quite a different process. Instead of the traditional 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 way, multiples contribute to the estimation of the primaries. Therefore, the EPSI method is also able to simultaneously reconstruct missing near offsets, which is a great advantage in certain situations. In this paper an algorithm is proposed to prepare the EPSI process for the full 3D case, in which simultaneous data reconstruction is required to successfully predict the primary response. This algorithm will probe it's capacity to reconstruct large data gaps and provide confident primary responses. By defining primary reflections as spikes in the focal domain, data can be efficiently represented, allowing effective primary estimation and data reconstruction.