Pre-stack Seismic Inversion with L1-2-norm Regularization Via a Proximal DC Algorithm and Adaptive Strategy

Abstract Seismic inversion in geophysics is an effective way to obtain underground rock properties from seismic survey data on the Earth’s surface. Especially, we can obtain much more information to characterize subsurface geological structure and lithology via pre-stack seismic inversion due to offset information added to the inversion than by post-stack seismic inversion. However, pre-stack seismic inversion is usually a nonlinear and complicated process. In this article, we adopt a \({L_{1 - 2}}\)-norm as a constraint on pre-stack seismic inversion, promoting the generation of a sparse solution. We also propose a novel pre-stack seismic inversion method that reduces the complexity of the solving method by utilizing an objective function decomposition scheme. Comparison of calculation time, accuracy and sparsity of the inversion solutions indicates that the proposed algorithm has better accuracy and robustness. Moreover, considering the difficulty of regularization parameter selection, we develop an adaptive parameter selection strategy based on Generalized Stein unbiased risk estimation (G-SURE) and incorporate it into the solving algorithm. The adaptive approach finds an appropriate regularization parameter in each iteration, and obtains the optimal solution directly, which is beneficial for improving computational efficiency. A synthetic data test verifies that the adaptive method can converge to the optimal solution iteratively in the case of arbitrary initial regularization parameters. Finally, in application to real field data, we explain why the adaptive method is the better choice even though adaptive and non-adaptive methods can obtain solutions with similar accuracy.