Seismic data interpolation via low-rank matrix factorization in the hierarchical semi-separable representation

TitleSeismic data interpolation via low-rank matrix factorization in the hierarchical semi-separable representation
Publication TypeSINBAD Presentation
AuthorsRajiv Kumar, Hassan Mansour, Aleksandr Y. Aravkin, Felix J. Herrmann
PublisherSINBAD
Year of Publication2013
Abstract

Recent developments in matrix rank optimization have allowed for new computational approaches in the field of seismic data interpolation. One of the main requirements of exploiting rank-minimization approaches is that the target data set should exhibit a low-rank structure. Seismic frequency slices exhibit low-rank structure at the low-frequencies, but not at the high frequencies. This behavior is due to the increase in oscillations as we move from low to high-frequency slices, even though the energy remains focused around the diagonal. Therefore, interpolation via rank minimization in the high-frequency range requires extended formulations that incorporate low-rank structure. We propose an approach for seismic data interpolation which incorporates the Hierarchical Semi-Separable Structure (HSS) inside rank-regularized least-squares formulations for the missing-trace interpolation problem. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the advantages of the new HSS approach by interpolating a seismic line from the Gulf of Suez and compare the reconstruction with conventional rank minimization.

KeywordsPresentation, private, SINBAD, SINBADSPRING2013, SLIM
URLhttps://www.slim.eos.ubc.ca/Publications/Private/Conferences/SINBAD/2013/Spring/kumar2013SINBADhss/kumar2013SINBADhss.pdf
Citation Keykumar2013SINBADhss