Beating Level-Set Methods for 5-D Seismic Data Interpolation: A Primal-Dual Alternating Approach

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to “fill in” data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for these techniques. Residual-constrained formulations require less parameter tuning when the target noise floor is known. We propose a new approach to solve residual constrained formulations for interpolation. We represent the data volume in a compressed manner using low-rank matrix factors, and build a block-coordinate algorithm with constrained convex subproblems that are solved with a primal-dual splitting scheme. The develop optimization framework works on the whole seismic temporal frequency slices and does not require windowing or nontrivial sorting of seismic data. The new approach is competitive with state of the art level-set algorithms that interchange the role of objectives with constraints. We use the new algorithm to successfully interpolate a large scale 5-D seismic data volume (upto 10
¹⁰
data points), generated from the geologically complex synthetic 3-D Compass velocity model, where 80% of the data have been removed. We also develop a robust extension of the primal-dual approach to deal with the outliers (or noise) in the data.