Robust estimation of primaries by sparse inversion via one-norm minimization

Even though contemporary methods for the removal of multiple events in seismic data due to a free-surface are built upon reciprocity relationships between wavefields, they are often still implemented as prediction-subtraction processes. The subtraction process does not always compensate for imperfect prediction of multiple events, and itself often leads to distortion of primary events. A recently proposed method called Estimation of Primaries by Sparse Inversion avoids the subtraction process altogether by directly prediction the primary impulse response as a collection of band-limited spikes under sparsity-regulated wavefield inversion approach. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the Estimation of Primaries by Sparse Inversion algorithm was not designed to seek such a solution, instead depending on a predetermined degree of sparsity as an inversion parameter. This leads to imperfect multiple rejection when the sparsity is overestimated, and problems with recovering late primary events when it is underestimated. In this paper, we propose a new algorithm where we make obtaining the sparsest solution our explicit goal. Our approach remains a gradient-based approach like the original algorithm, but is in turn derived from a new optimization framework based on an extended basis pursuit denoising formulation. We show that the sparsityminimizing objective of our formulation enables it to operate successfully on a wide variety of synthetic and field marine dataset without excessive tweaking of inversion parameters. We also demonstrate that Robust EPSI produces a more artifact-free impulse response compared to the original algorithm, which has interesting implications for broadband seismic applications. Finally we demonstrate through field data that recovering the primary impulse response under transform domains can significantly improve the recovery of weak primary late arrivals, without appreciable change to the underlying algorithm.