Off the Grid Tensor Completion for Seismic Data Interpolation

Abstract

The practical realities of acquiring seismic data in a realistic survey are often at odds with the stringent requirements of Shannon-Nyquist-based sampling theory. The unpredictable movement of the ocean's currents can be detrimental in acquiring exactly equally-spaced samples while sampling at Nyquist-rates are expensive, given the huge dimensionality and size of the data volume. Recent work in matrix and tensor completion for seismic data interpolation aim to alleviate such stringent Nyquist-based sampling requirements but are fundamentally posed on a regularly-spaced grid. In this work, we extend our previous results in using the so-called Hierarchical Tucker (HT) tensor format for recovering seismic data to the irregularly sampled case. We introduce an interpolation operator that resamples our tensor from a regular grid (in which we impose our low-rank constraints) to our irregular sampling grid. Our framework is very flexible and efficient, depending primarily on the computational costs of this operator. We demonstrate the superiority of this approach on a realistic BG data set compared to using low-rank tensor methods that merely use binning.

Iterative Deblending of off-the-Grid Simultaneous Source Data

“…Based on a linear event assumption, Lopezet et al [51] extended matrix completion to seismic data regularization on unstructured grids with discretized Fourier transform (DFT) and NDFT, then it can project the data on the regular grid to the irregular grid. For 3D off-the-grid data regularization, Da Silva and Herrmann [52] proposed a tensor completion, and it shows a good performance in stationary field data.…”