Multichannel Reflectivity Inversion with Sparse Group Regularization Based on HPPSG Algorithm

We proposed a multichannel deconvolution method. The method uses a mixed norm to promote structured forms of sparsity. To solve this deconvolution problem, we develop a new algorithm called the Hadamard product parametrization (HPP) sparse-group (HPPSG) algorithm. We define each layer of seismic profile as a group, and perform L_p-norm for all elements within each group to preserve the lateral continuity. Based on the assumption that the reflectivity is sparse, L_q-norm is applied among groups along the time direction. Then, we construct an L_p,q optimization problem. After that, we solve this problem using the proposed HPPSG algorithm. The HPPSG algorithm is formed by converting the L_p,q optimization function into the L₁ optimization function which is solved with the help of the HPP algorithm. The proposed algorithm is simple and applicable for an arbitrary L_p,q-norm inverse problem. Synthetic and real data examples demonstrate the effectiveness of the proposed method in improving the lateral continuity of seismic profiles.