Seismic Deconvolution Based on a Non-Convex L1-L2 Norm Constraint

Abstract

Summary Deconvolution with the L1 norm, based on a sparse reflectivity assumption, enjoys better stability and sparsity than those methods using the conventional L2 norm. Although such L1-regularized problem can be efficiently solved by alternating direction method of multipliers (ADMM), it may yield suboptimal solution due to the convex approximation of L1 norm to the L0 norm. To alleviate this issue, we introduce the nonconvex L1–L2 metric, which exhibits a better approximation to the L0 norm than L1 norm, to the deconvolution processing and present a L1–L2-regularized deconvolution for sparse reflectivity recovery. The proposed L1–L2-regularized deconvolution can be decomposed into two convex subproblems via difference of convex algorithm (DCA), which can be solved respectively by gradient method and ADMM. Compared with the L1-regularized deconvolution, the proposed L1–L2-regularized deconvolution has better accuracy and fidelity. The synthetic examples demonstrate the superior performance of the L1–L2-regularized deconvolution over the L1-regularized deconvolution. The field data experiment further verifies the practicability of the L1–L2-regularized deconvolution.