Multiple Elimination Based on Mode Decomposition in the Elastic Half Norm Constrained Radon Domain

Multiple reflection is a common interference wave in offshore petroleum and gas exploration, and the Radon-based filtering method is a frequently used approach for multiple removal. However, the filtering parameter setting is crucial in multiple suppression and relies heavily on the experience of processors. To reduce the dependence on human intervention, we introduce the geometric mode decomposition (GMD) and develop a novel processing flow that can automatically separate primaries and multiples, and then accomplish the suppression of multiples. GMD leverages the principle of the Wiener filtering to iteratively decompose the data into modes with varying curvature and intercept. By exploiting the differences in curvature, GMD can separate primary modes and multiple modes. Then, we propose a novel sparse Radon transform (RT) constrained with the elastic half (EH) norm. The EH norm contains a l1/2 norm and a scaled l2 norm, which is added to overcome the numerical oscillation problem of the l1/2 norm. With the help of the EH norm, the estimated Radon model can reach a remarkable level of sparsity. To solve the optimization problem of the proposed sparse RT, an efficient alternating multiplier iteration algorithm is employed. Leveraging the high sparsity of the Radon model obtained from the proposed transform, we improve the GMD-based multiple removal framework. The high-sparsity Radon model obtained from the proposed Radon transform can not only simplify the separation of primary and multiple modes but also accelerate the convergence of GMD, thus improving the processing efficiency of the GMD method. The performance of the proposed GMD-based framework in multiple elimination is validated through synthetic and field data tests.