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Seismic data interpolation using nonlinear shaping regularization

YANGKANG CHEN1 ,  LELE ZHANG2 ,  L.-WEI MO3
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1 Bureau of Economic Geology, John A. and Katherine G. Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X, Austin, TX 78713-8924, U.S.A.,
2 Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 102200, P.R. China.,
3 Research and Development Technology Group, Fairfield Nodal, 1111 Gillingham Lane, Sugar Land, TX 77478, U.S.A.,
JSE 2015, 24(4), 327–342;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Chen, Y., Zhang, L. and Mo, L.-W., 2015. Seismic data interpolation using nonlinear shaping regularization. Journal of Seismic Exploration, 24: 327-342. Seismic data interpolation plays an indispensable role in common seismic data processing workflows. Iterative shrinkage thresholding (IST) and projection onto convex sets (POCS) can both be considered as a specific form of nonlinear shaping regularization. Compared with linear form of shaping regularization, the nonlinear version can be more adaptive because the shaping operator is not limited to be linear. With a linear combination operator, we introduce a faster version of nonlinear shaping regularization. The new shaping operator utilizes the information of previous model to better constrain the current model. Both synthetic and field data examples demonstrate that the nonlinear shaping regularization can be effectively used to interpolate irregular seismic data and the proposed faster version of shaping regularization can indeed get obvious faster convergence.

Keywords
seismic data interpolation
nonlinear shaping regularization
faster shaping regularization
iterative shrinkage thresholding
projection onto convex sets
References
  1. Abma, R. and Kabir, N., 2006. 3D interpolation of irregular data with a POCS algorithm. Geophysics.
  2. 71: E91-E97.
  3. Candés, E.J., Demanet, L., Donoho, D.L. and Ying. L., 2006. Fast discrete curvelet transforms, SIAM,
  4. Multisc. Model. Simulat., 5: 861-899.
  5. Candés, E.J., Romberg, J. and Tao, T., 2006. Robust uncertainty principles: Exact signal reconstruction
  6. from highly incomplete frequency information. IEEE Transact. Informat. Theory, 52: 489-509.
  7. Canning, A. and Gardner, G.H.F., 1996. Reducing 3D acquisition footprint for 3D DMO and 3D prestack
  8. migration. Geophysics, 63: 1177-1183.
  9. Chen. Y., 2015. Deblending using a space-varying median filter. Explor. Geophys.. in press.
  10. doi:http://dx.doi.org/10.1071/EG14051.
  11. Chen, Y., Chen, K. Shi, P. and Wang, Y., 2014. Irregular seismic data reconstruction using a
  12. percentile-half-thresholding algorithm. J. Geophys. Engin., 11: 065001.
  13. Journal_SEISMIC_No24-4:JOURNAL SEISMIC 11-06 24/086 14:23 Page342
  14. 342 CHEN, ZHANG & MO
  15. Chen, Y., Fomel, S. and Hu, J., 2014. Iterative deblending of simultaneous-source seismic data using
  16. seislet-domain shaping regularization. Geophysics, 79: V179-V189.
  17. Chen, Y.. Gan, S., Liu, T., Yuan, J.. Zhang, Y. and Jin, Z., 2015. Random noise attenuation by a
  18. selective hybrid approach using f-x empirical mode decomposition. J. Geophys. Engin., 12: 12-25.
  19. Chen, Y., Yuan, J., Jin, Z., Chen, K. and Zhang, L., 2014. Deblending using normal moveout and
  20. median filtering in common-midpoint gathers. J. Geophys. Engin.. 11: 045012.
  21. Chen, Z. Wang, Y. and Chen, X., 2012. Gabor deconvolution using regularized smoothing. Expanded
  22. Abstr., 82nd Ann. Internat. SEG Mtg., Las Vegas: 1-4.
  23. Collatz. L., 1966. Functional Analysis and Numerical Mathematics. Academic Press, New York.
  24. Donoho, D.L.. 2006. Compressed sensing. IEEE Transact. Informat. Theory, 52: 1289-1306.
  25. Du. J., Lin, S., Sun, W. and Liu, G., 2010. Seismic attenuation estimation using S transform with
  26. regularized inversion. Expanded Abstr., 80th Ann. Internat. SEG Mtg., Denver: 2901-2904
  27. Fomel. S.. 2002. Application of plane-wave destruction filters. Geophysics, 67: 1946-1960.
  28. Fomel, S.. 2003. Seismic reflection data interpolation with differential offset and shot continuation.
  29. Geophysics, 68: 733-744.
  30. Fomel, S., 2007a. Local seismic attributes. Geophysics, 72: A29-A33.
  31. Fomel, S., 2007b. Shaping regularization in geophysical-estimation problems. Geophysics, 72: R29-R36.
  32. Fomel, S., 2008. Nonlinear shaping regularization in geophysical inverse problems. Expanded Abstr.. 78th
  33. Ann. Internat. SEG Mtg., Las Vegas: 2046-2051.
  34. Fomel, S., Sava, P., Vlad, 1.. Liu. Y. and Bashkardin, V. 2013. Madagascar open-source software
  35. project. J. Open Res. Softw.. 1: e8.
  36. Hennenfemt, G. and Herrmann, F.J.. 2008. Simply denoise: Wavefield reconstruction via jittered
  37. undersampling. Geophysics. 73: V19-V28.
  38. Herrmann, F.J., 2010. Randomized sampling and sparsity: Getting more information from fewer samples.
  39. Geophysics, 75: WB173-WB187.
  40. Landweber, L., 1951. An iteration formula for Fredholm integral equations of the first kind. Am. J.
  41. Mathemat., 73: 615-624.
  42. Li, C.. Mosher, C.C., Morley, L.C., Ji, Y. and Brewer, J.D., 2013. Joint source deblending and
  43. reconstruction for seismic data. Expanded Abstr., 83rd Ann. Internat. SEG Mtg., Houston: 82-87
  44. Liu, B. and Sacchi, M.D., 2004. Minimum weighted norm interpolation of seismic records. Geophysics.
  45. 69: 1560-1568.
  46. Liu. G., Chen, X.. Du, J. and Wu, K., 2012. Random noise attenuation using f-x regularized
  47. nonstationary autoregression. Geophysics. 77: V61-V69.
  48. Liu, G., Fomel. S. and Chen, X., 201 1a. Stacking angle-domain common-image gathers for normalization
  49. of illumination. Geophys. Prosp., 59: 244-255.
  50. Liu, G., Fomel, S. and Chen, X., 2011b. Time-frequency analysis of seismic data using local attributes.
  51. Geophysics, 76: P23-P34.
  52. Liu, G., Fomel, S., Jin, L. and Chen, X., 2009. Stacking seismic data using local correlation. Geophysics.
  53. 74: V43-V48.
  54. Liu, Y. and Fomel, S., 2012. Seismic data analysis using local time-frequency decomposition. Geophys.
  55. Prosp., 60: 1-10.
  56. Naghizadeh, M. and Sacchi, M.D.. 2007. Multistep autoregressive reconstruction of seismic records
  57. Geophysics, 72: VI11-V118.
  58. Naghizadeh, M. and Sacchi, M.D., 2010. Beyond alias hierarchical scale curvelet interpolation of regularly
  59. and irregularly sampled seismic data. Geophysics, 75: WB189-WB202.
  60. Oropeza, V. and Sacchi, M.D., 2011. Simultaneous seismic data denoising and reconstruction via
  61. multichannel singular spectrum analysis. Geophysics, 76: V25-V32.
  62. Porsani, M.J., 1999. Seismic trace interpolation using half-step prediction filters. Geophysics, 64: 1461-
  64. Sacchi, M.D,, Ulrych. T. and Walker, C., 1998. Interpolation and extrapolation using a high- resolution
  65. discrete fourier transform. IEEE Transact. Signal Process., 46: 31-38.
  66. Spitz. S., 1991. Seismic trace interpolation in the fx domain. Geophysics, 56: 785-794.
  67. Tikhonov, A.N., 1963. Solution of incorrectly formulated problems and the regularization method. Sovj
  68. Mathemat. Doklady, 5: 1035-1038.
  69. Wang, Y., 2002. Seismic trace interpolation in the fxy domain. Geophysics, 67: 1232-1239.
  70. Wang, Y., 2003. Sparseness-constrained least-squares inversion: application to seismic wave propagation
  71. Geophysics, 68: 1633-1638.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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