Non-linear regularization in seismic imaging

TitleNon-linear regularization in seismic imaging
Publication TypeConference
Year of Publication2005
AuthorsFelix J. Herrmann, Peyman P. Moghaddam
Conference NameCSEG Annual Conference Proceedings
KeywordsPresentation, SLIM

Two complementary solution strategies to the least-squares imaging problem with sparseness & continuity continuity constraints are proposed. The applied formalism explores the sparseness of curvelets coefficients of the reflectivity and their invariance under the demigration-migration operator. We achieve the solution by jointly minimizing a weighted l1-norm on the curvelet coefficients and an anisotropic difussion or total variation norm on the imaged reflectivity model. The l1-norm exploits the sparsenss of the reflectivity in the curvelet domain whereas the anisotropic norm enhances the continuity along the reflections while removing artifacts residing in between reflectors. While the two optimization methods (convex versus non-convex) share the same type of regularization, they differ in flexibility how to handle additional constraints on the coefficients of the imaged reflectivity and in computational expense. A brief sketch of the theory is provided along with a number of synthetic examples.

Citation Keyherrmann2005CSEGnlr