Unsupervised deep learning with higher-order total-variation regularization for multidimensional seismic data reconstruction

Thomas André Larsen Greiner, Jan Erik Lie, Odd Kolbjørnsen, Andreas Kjelsrud Evensen, Espen Harris Nilsen, Hao Zhao, Vasily Demyanov, Leiv J. Gelius

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19 Citations (Scopus)
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In 3D marine seismic acquisition, the seismic wavefield is not sampled uniformly in the spatial directions. This leads to a seismic wavefield consisting of irregularly and sparsely populated traces with large gaps between consecutive sail-lines especially in the near-offsets. The problem of reconstructing the complete seismic wavefield from a subsampled and incomplete wavefield, is formulated as an underdetermined inverse problem. We investigate unsupervised deep learning based on a convolutional neural network (CNN) for multidimensional wavefield reconstruction of irregularly populated traces defined on a regular grid. The proposed network is based on an encoder-decoder architecture with an overcomplete latent representation, including appropriate regularization penalties to stabilize the solution. We proposed a combination of penalties, which consists of the L2-norm penalty on the network parameters, and a first- and second-order total-variation (TV) penalty on the model. We demonstrate the performance of the proposed method on broad-band synthetic data, and field data represented by constant-offset gathers from a source-over-cable data set from the Barents Sea. In the field data example we compare the results to a full production flow from a contractor company, which is based on a 5D Fourier interpolation approach. In this example, our approach displays improved reconstruction of the wavefield with less noise in the sparse near-offsets compared to the industry approach, which leads to improved structural definition of the near offsets in the migrated sections.

Original languageEnglish
Pages (from-to)V59-V73
Number of pages15
Issue number2
Early online date12 Nov 2021
Publication statusPublished - 1 Mar 2022


  • Geochemistry and Petrology
  • Geophysics

ASJC Scopus subject areas

  • Geochemistry and Petrology

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