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

• Published in: GEOPHYSICS
• Main Authors: Greiner, Thomas Larsen, Lie, Jan-Erik, Kolbjørnsen, Odd, Kjelsrud Evensen, Andreas, Harris Nilsen, Espen, Zhao, Hao, Demyanov, Vasily, Gelius, Leiv Jacob
• Format: Article in Journal/Newspaper
• Language: English
• Published: Society of Exploration Geophysicists Foundation 2021
• Subjects: Barents Sea
• Online Access: http://hdl.handle.net/10852/89335; http://urn.nb.no/URN:NBN:no-91945; https://doi.org/10.1190/geo2021-0099.1

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.