Studia Geophysica et Geodaetica

, Volume 63, Issue 4, pp 569–583 | Cite as

Simultaneous interpolation and denoising based on a modified thresholding method

  • Jingjie CaoEmail author
  • Shangxu Wang
  • Wenquan Liang


Seismic interpolation can provide complete data for some multichannel processing techniques such as time lapse imaging and wave equation migration. However, field seismic data often contains random noise and noisy data interpolation is a challenging task. A traditional method applies interpolation and denoising separately, but this needs two workflows. Simultaneous interpolation and denoising combines interpolation and denoising in one workflow and can also get acceptable results. Most existing interpolation methods can only recover missing traces but fail to attenuate noise in sampled traces. In this study, a novel thresholding strategy is proposed to remove the noise in the sampled traces and meanwhile recover missing traces during interpolation. For each iteration, the residual is multiplied by a weighting factor and then added to the iterative solution, after which the sum in the transformed domain is calculated using the thresholding operation to update the iterative solution. To ensure that the interpolation and denoising results are robust, the exponential method was chosen to reduce the threshold values in small quantities. The curvelet transform was used as sparse representation and three interpolation methods were chosen as benchmarks. Three numerical tests results proved the effectiveness of the proposed method on removing noise in the sampled traces when the minimum threshold values are correctly chosen.


interpolation sparsity seismic inversion noise thresholding method 


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The authors wish to thank F. Mahmoudian and three anonymous reviewers for greatly improving this manuscript. We thank the authors of CurveLab for providing access to their curvelet transform codes. This work was funded by National Natural Science Foundation of China (41674114, 41974116 and 41704120), Postdoctoral Research Foundation of China (2016M600171 and 2017T100137), Hundreds of Outstanding Innovative Talent Support Program for Colleges in Hebei Province (III) under grant number SLRC2017024, and Natural Science Foundation of Hebei Province under grant number D2017403027.


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Copyright information

© Inst. Geophys. CAS, Prague 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Petroleum Resources and ProspectingChina University of Petroleum (Beijing)BeijingChina
  2. 2.Hebei GEO UniversityShijiazhuang, HebeiChina
  3. 3.Longyan UniversityLongyan, FujianChina

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