Matrix and tensor completion for large-scale seismic interpolation: a comparative study

Owing to their high dimensionality, interpolating 3D seismic data volumes remains a computationally daunting task. In this work, we outline a comprehensive framework for sampling and interpolating such volumes based on the well-understood theory of Matrix and Tensor completion. This interpolation theory consists of three components major signal structure, structure-destroying sampling, and structure-restoring optimization. By viewing interpolation in the context of this theory, we are able to specify exactly when these approaches are expected to perform well. We also introduce structure-revealing transformations that promote the inherent low-rank structure in seismic data as well as a factorization approach that scales to large problem sizes. Our methods are able to handle large-scale data volumes more accurately and more quickly compared to other more ad-hoc approaches, as we will demonstrate. This is joint work with Curt Da Silva, Rajiv Kumar, Ben Recht, and Felix J. Herrmann.