# Controlling linearization errors in $\ell_1$ regularized inversion by rerandomization

 Title Controlling linearization errors in $\ell_1$ regularized inversion by rerandomization Publication Type Conference Year of Publication 2013 Authors Ning Tu, Xiang Li, Felix J. Herrmann Conference Name SEG Technical Program Expanded Abstracts Volume 32 Page 4640-4644 Month 9 Keywords inversion, message passing, rerandomization, SEG, sparsity Abstract Linearized inversion is a data fitting procedure that tries to match the observed seismic data with data predicted by linearized modelling. In practice, the observed data is not necessarily in the column space of the linearized modelling operator. This can be caused by lack of an accurate background velocity model or by coherent noises not explained by linearized modelling. Through carefully designed experiments, we ob- serve that a moderate data mismatch does not pose an issue if we can use all the data in the inversion. However, artifacts do arise from the mismatch when randomized dimensionality reduction techniques are adopted to speed up the inversion. To stabilize the inversion for dimensionality reduction with randomized source aggregates, we propose to rerandomize by drawing independent simultaneous sources occasionally during the inversion. The effect of this rerandomization is remarkable because it results in virtually artifact-free images at a cost comparable to a single reverse-time migration. Implications of our method are profound because we are now able to resolve fine-scale steep subsalt features in a computationally feasible manner. URL https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle.pdf DOI 10.1190/segam2013-1302.1 Presentation https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013S... Citation Key tu2013SEGcle Full Text