Structured tensor missing-trace interpolation in the Hierarchical Tucker format

TitleStructured tensor missing-trace interpolation in the Hierarchical Tucker format
Publication TypeConference
Year of Publication2013
AuthorsCurt Da Silva, Felix J. Herrmann
Conference NameSEG Technical Program Expanded Abstracts
Keywordsdifferential geometry, gauss newton, hierarchical tucker, riemannian optimization, SEG, structured tensor, tensor interpolation

Owing to the large scale and dimensionality of a 3D seismic experiment, acquiring fully-sampled data according to the Nyquist criterion is an exceedingly arduous and cost-prohibitive task. In this paper, we develop tools to interpolate 5D seismic volumes with randomly missing sources or receivers using a relatively novel tensor format known as the Hierarchical Tucker (HT) format. By exploiting the underlying smooth structure of HT tensors, specifically its smooth manifold structure, we develop solvers which are fast, immediately parallelizable, and SVD-free, making these solvers amenable to large-scale problems where SVD-based projection methods are far too costly. We also build on intuition of multidimensional sampling from the perspective of matrix-completion and demonstrate the ability of our algorithms to recover frequency slices even amidst very high levels of source subsampling on a synthetic large-scale 3D North Sea dataset.

Citation Keydasilva2013SEGhtuck