Multichannel Reflectivity Inversion With Sparse Group Regularization Based on HPPSG Algorithm

Abstract

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 $L_{1}$ 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.