Seismic data interpolation using deep internal learning

Abstract

Seismic data interpolation is a meaningful research topic in the field of seismic data processing. In this paper, we propose deep internal learning for interpolating regularly sampled aliased seismic data, to improve the upsampling accuracy of regularly sampled aliased seismic data. The proposed algorithm, contrary to previous deep external learning-based seismic interpolation relying on prior training for vast external seismic data, exploits the characteristics of the field data itself, based on the feature similarity between the regularly missing and remaining samples. Internal learning generates training samples solely from the currently remaining regularly undersampled seismic data, and then trains a simple convolutional neural network using the training set. Finally, the trained model is used to upsample the current seismic traces regularly with high accuracy, and can adapt itself intelligently to different field data for the upsampling requirement. This enables seismic data antialiasing interpolation on regularly sampled seismic data with a small sample in the case of insufficient data. The performance of the proposed deep internal learning is assessed using synthetic and field data, respectively. Moreover, the comparison of the proposed deep internal learning with a classic prediction-based interpolation method and deep external learning-based seismic interpolation validates the effectiveness of the proposed algorithm.

KEYWORDS:

• Interpolation
• neural network
• algorithm
• prestack
• poststack

Acknowledgments

We are sincerely grateful to the editors and reviewers for their constructive comments and suggestions that have improved the quality of this research paper. This work was supported by the National Key R&D Program of China under Grants 2018YFC1503705 and 2017YFC0601504, Science and Technology Research Project of Hubei Provincial Department of Education under Grants B2017597, Hubei Subsurface Multi-scale Imaging Key Laboratory (China University of Geosciences) under Grants SMIL-2018-06 and the Fundamental Research Funds for the Central Universities under Grants CCNU19TS020.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The field data and synthetic data in Example 4.1, 4.3, 4.4 of Numerical experiments section support the findings of this study are openly available in SEG (Society of Exploration Geophysicists) open datasets at https://wiki.seg.org/wiki/Open_data. The poststack field data which supports the findings of this study is available at https://github.com/sevenysw/MathGeo2018.

Additional information

Funding

This work was supported by the National Key R&D Program of China [grants numbers 2018YFC1503705, 2017YFC0601504], Science and Technology Research Project of Hubei Provincial Department of Education [grant number B2017597], Hubei Subsurface Multi-scale Imaging Key Laboratory (China University of Geosciences) [grant number SMIL-2018-06] and the Fundamental Research Funds for the Central Universities [grants number CCNU19TS020].