Hybrid Norm Adaptive Subtraction for Multiple Removal

The adaptive subtraction of the predicted multiples from the input data plays an important role in the overall multiple removal task. Adaptive filters are routinely computed by minimizing the difference (or misfit) between the input data and the filtered multiples in a least-squares sense. However, this approach does have some limitations, one of which is that the L2-norm approach rarely provides the statistically optimal solution because of the super-Gaussian nature of the seismic data due to the interfering fields (i.e., primaries). An alternative approach based on a hybrid-norm solver is proposed to combine the advantages in terms of stability and speed of convergence of the L2-norm with those of L1-norm that better takes into account the properties of the data. Moreover, the proposed formulation allows to take advantage of any required regularization or a-priori knowledge of the model, as further improvements can be obtained by properly choosing differentiated norms for data and model misfits in order to better match the statistics of both spaces. The results on synthetic dataset validates the robustness of the proposed subtraction scheme.