Rank-constrained seismic data interpolation and denoising

Abstract

Rank-constrained seismic data interpolation methods have been used to cope with spatial sampling deficiencies, but some fundamental aspects are often neglected. Understanding their underlying features is the first step for developing new solutions to overcome existing limitations. We intend to provide an intuitive description regarding low-rank strategies using the similarities between irregular samplings and noise in terms of their eigenimage representation. The interpretation of data recovery as iterative denoising helps to clarify how the traces are retrieved and the role of the rank. To emphasize either signal recovery or denoising along with the iterations, we explore non-linear versions of the decreasing weighting factor that drives the reinsertion of original samples. This type of weighting factor shows superior denoising results when raised to an integer power. Simple synthetic numerical examples illustrate the mechanics of low-rank procedures and their responses to different parameters. We also show 3D field data examples from a land survey to demonstrate the robustness of reduced-rank approaches.