Optimal Seismic Reflectivity Inversion: Data-driven ℓ p -loss-ℓ q -regularization Sparse Regression.

Abstract

Seismic reflectivity inversion is widely applied to improve the seismic resolution to obtain detailed underground understandings. Based on the convolution model, seismic inversion removes the wavelet effect by solving an optimization problem. Taking advantage of the sparsity property, the ℓ 1 norm is commonly adopted in the regularization terms to overcome the noise/interference vulnerability observed in the ℓ p -losses minimization. However, no one has provided a deterministic conclusion that ℓ1 norm regularization is the best choice for seismic reflectivity inversion. Instead of using an unproved fixed regularization norm, we propose an optimal seismic reflectivity inversion approach. Our method adaptively adopts a ℓ p -loss-ℓ q -regularization (i.e. ℓ p,q regularization) for p = 2, 0 < q < 1 to estimate a more accurate and detailed reflectivity profile. In addition, we employ a K fold cross-validation based approach to obtain the optimal damping factor λ to further improve the seismic inversion results. The letter starts with the introduction of non-convex constraint for seismic inversion, and the necessity of the ℓ q norm regularization. Then the majorization-minimization and cross validation algorithms are briefly described. The performance of the proposed seismic inversion approach is evaluated through synthetic examples and a field example from the Bohai Bay Basin, China.