We explore the tensor completion problem in a dataset obtained over a heavy oil field in the Western Canadian Sedimentary Basin. The fully sampled prestack volume in the frequency-space domain is a low-rank fourth order tensor. In this context, the reconstruction problem becomes a tensor completion problem that we choose to solve via a nuclear norm minimization approach. The nuclear norm of a tensor is the closest convex approximation to the rank of a tensor. The reconstruction problem entails minimizing the nuclear norm of the tensor subject to data constraints and is implemented with the alternating direction method of multipliers. Our land data example clearly exhibits the performance of this reconstruction method.
We describe the use of a higher-order singular value decomposition (HOSVD) in the regularization of pre-stack seismic volumes. Pre-stack seismic data in the