The estimation of the source signature is often one of the necessary first steps in the processing of seismic reflection data, especially if the processing chain includes prestack multiple removal. However, most methods for source estimation are based on poststack data or assume that the earth is 1-D. In this work, a new source estimation method for prestack data is presented. It consists of finding the source signature that permits the removal of events attributable to the first-order free-surface reflections (i.e., first-order multiples). The method exploits the formulation of the relationship between the free-surface reflections and the source signature as a scattering Born series. In this formulation, the order of the scattering series coincides with that of the free-surface reflections, and the series is constructed exclusively with seismic data and the source signature without any knowledge of the subsurface other than the velocity of sea water.
By restricting the problem to first-order free-surface reflections, we have rendered the relationship between free-surface reflections and the source signature linear, which also corresponds to a truncation of the scattering Born series to its first two terms. Thus, the source signature estimation can be formulated as a linear inverse problem. Assuming that the removal of first-order free-surface events produces a significant reduction in the energy of the data, we posed the inverse problem as finding the source signature that minimizes this energy. The optimization leads to an iterative solution. The iterations are needed to correct for the truncation effects. Synthetic and real data examples show the applicability and stability of the source estimation method as well as its use for attenuating free-surface multiples.