Inverse data-space multiple elimination with 3D curvelet sparsity promotion

This paper describes an effective implementation of the inverse data-space multiple elimination method via the three-dimensional (3D) curvelet domain. The method can separate the surface-related operator (A) and primaries (P₀) through seismic data matrix inversion. A 3D curvelet transform is introduced to sparsely represent the seismic data in the inverse data space. Hence, this approach is suitable for obtaining an accurate solution because of its multiscale and multidirectional analysis properties. The L1 norm is used to promote sparseness in the transform domain. Then, a high-fidelity separation of the operator (A) and the primaries (P₀) is realized. The proposed method is applied to synthetic data from a model containing a salt structure. We compare the results with that of the traditional inverse data-space multiple elimination method and also with that of two-dimensional surface-related multiple elimination. The findings fully demonstrate the superiority of the proposed method over the traditional inverse method; moreover, the proposed method protects the primary energy more effectively than the SRME method.