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Efficient 3D seismic acquisition design using compressive sensing principles

MENGLI ZHANG
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Department of Geophysics, Colorado School of Mines, Golden, CO 80401, U.S.A.,
JSE 2023, 32(5), 427–454;
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/ )
Abstract

Zhang, M., 2023. Efficient 3D seismic acquisition design using compressive sensing principles. Journal of Seismic Exploration, 32: 427-454. The ability to acquire 3D seismic data efficiently and cost-effectively is a major consideration in many applications. One way to achieve this goal is through the theory of compressive sensing. Compressive sensing uses sparse acquisition designs combined with the post-acquisition reconstruction to reduce the number of sensors. Sensor deployment or sampling pattern is a critical component in compressive sensing. Therefore, we analyze sampling patterns based on a Spectral Resolution Function (SRF) to improve the quality of acquired data. We have investigated two types of sparse seismic acquisition designs that use fewer receivers deployed irregularly, and also have compared three proposed reconstruction methods for each acquisition design. We predict the reconstruction accuracies of these six strategies, and then we verify our prediction using SEAM seismic dataset. SEAM seismic data examples demonstrate three major results: First, irregular line and irregular point patterns have different properties of SRF, and these properties can be applied to improve the accuracy of compressive sensing results. Second, a good combination of acquisition design and post-acquisition reconstruction selected based on the properties of SRF is able to obtain better reconstructed shot gathers and imaging results. Third, numerical simulations show that we can reconstruct single shot gather using only 25% of receivers and then produce seismic migration images comparable to those obtained from the full shot gathers. The overall results indicate that, the combination of a sparse acquisition design and corresponding compressive sensing reconstruction method could help facilitate a new generation of cost-effective seismic acquisitions.

Keywords
acquisition design
compressive sensing
seismic acquisition
reconstruction
3D
References
  1. Abma, R., Howe, D., Foster, M., Ahmed, I., Tanis, M., Zhang, Q., Arogunmati, A. and
  2. Alexander, G., 2015. Independent simultaneous source acquisition and
  3. processing. Geophysics, 80(6): WD37-WD44.
  4. Baraniuk, R. and Kelly, K., 2007. Compressive sensing. Signal Process., 4: 12-21.
  5. Brown, L., Mosher, C.C., Li, C., Olson, R., Doherty, J., Carey, T.C., Williams, L., Chang,
  6. J. and Staples, E., 2017. Application of compressive seismic imaging at lookout
  7. field, Alaska: The Leading Edge, 36: 670-676.
  8. Candès, E. and Romberg, J., 2005. l1-magic: Recovery of sparse signals via convex
  9. programming: 1-19.
  10. Candès, E.J., Romberg, J. and Tao, T., 2006. Robust uncertainty principles: exact signal
  11. reconstruction from highly incomplete frequency information. IEEE Transact.
  12. Informat. Theory, 52: 489-509.
  13. Candès, E.J. and Tao, T., 2006. Near-optimal signal recovery from random projections:
  14. Universal encoding strategies?: IEEE Transact. Informat. Theory, 52: 5406-5425.
  15. Candès, E.J. and Wakin, M.B.. 2008. An introduction to compressive sampling. IEEE
  16. Signal Process. Magaz., 25: 21-30.
  17. Candès, M.W. and Boyd, S., 2008. Enhancing sparsity by reweighted l1 minimization. J
  18. Fourier Anal. Appl., 14: 877-905.
  19. Donoho, D.L., 2001. Uncertainty principles and ideal atomic decomposition. IEEE
  20. Transact. Informat. Theory, 47: 2845-2862.
  21. Donoho, D.L., 2006. Compressed sensing. IEEE Transact. Informat. Theory, 52. 1289-
  22. Donoho, D.L. and Tanner, J., 2010. Exponential bounds implying construction of
  23. compressed sensing matrices, error-correcting codes, and neighborly polytopes by
  24. random sampling. IEEE Transact. Informat. Theory, 56: 2002-2016.
  25. Donoho, D.L. and Tsaig, Y ., 2008. Fast solution of`1-norm minimization problems when
  26. the solution may be sparse. IEEE Transact. Informat. Theory, 54: 4789-4812.
  27. Donoho, D.L., Tsaig, Y ., Drori, I. and Starck, J., 2012. Sparse solution of underdeter-
  28. mined systems of linear equations by stagewise orthogonal matching pursuit:
  29. IEEE Transact. Informat. Theory, 58: 1094-1121.
  30. Hansen, P.C., 1992. Analysis of discrete ill-posed problems by means of the L-curve:
  31. SIAM Review, 34: 561-580. doi: 10.1137/1034115.
  32. Herrmann, F.J., 2009. Compressive imaging by wavefield inversion with group sparsity.
  33. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston: 2337-2341.
  34. Herrmann, F.J., Erlangga, Y .A. and Lin, T.T., 2009. Compressive simultaneous full-
  35. waveform simulation. Geophysics, 74(4): A35-A40.
  36. Janiszewski, F., Mosher, C., Li, C. and Malloy, J., 2017. Applying compressive sensing
  37. techniques in production o ffshore seismic surveys. Expanded Abstr., 87th Ann.
  38. Internat. SEG Mtg., New Orleans: 47-51.
  39. Li, C., Mosher, C., Keys, R., Janiszewski, F. and Zhang, Y ., 2017. Improving streamer
  40. data sampling and resolution via nonuniform optimal design and reconstruction,
  41. Expanded Abstr., 87th Ann. Internat. SEG Mtg., New Orleans: 4241-4245.
  42. Li, Y . and Oldenburg, D.W., 2003. Fast inversion of large-scale magnetic data using
  43. wavelet transforms and a logarithmic barrier method. Geophys. J. Internat., 152:
  44. 251-265.
  45. Lustig, M., Donoho, D. and Pauly, J.M., 2007. Sparse MRI: The application of
  46. compressed sensing for rapid MRI imaging: Magnetic Resonance in Medicine,
  47. 58, 1182-1195.
  48. Lustig, M., Donoho, D.L., Santos, J.M. and Pauly, J., 2008. Compressed sensing MRI.
  49. IEEE Signal Process. Magaz., 25: 72-82.
  50. Milton, A., Trickett, S. and Burroughs, L., 2011. Reducing acquisition costs with random
  51. sampling and multidimensional interpolation. Expanded Abstr., 81st Ann.
  52. Internat. SEG Mtg., San Antonio: 52-56.
  53. Moldoveanu, N., 2010. Random sampling: A new strategy for marine acquisition.
  54. Expanded Abstr., 80th Ann. Internat. SEG Mtg., Denver: 51-55.
  55. Moldoveanu, N., Bilsby, P., Quigley, J., Kumar, R. and Herrmann, F., 2018.
  56. Compressive sensing based design for land and obs surveys: The noise issue.
  57. Expanded Abstr., 88th Ann. Internat. SEG Mtg., Anaheim: 102–106.
  58. Mosher, C.C., Keskula, E., Kaplan, S.T., Keys, R.G., Li, C., Ata, E.Z., Morley, L.C.,
  59. Brewer, J.D., Janiszewski, F.D., Eick, P.M. and Olson, R.A., 2012. Compressive
  60. seismic imaging. Expanded Abstr., 82nd Ann. Internat. SEG Mtg., Las Vegas: 1-5.
  61. Mosher, C.C., Li, C., Janiszewski, F.D., Williams, L.S., Carey, T.C. and Ji, Y ., 2017.
  62. Operational deployment of compressive sensing systems for seismic data
  63. acquisition. The Leading Edge, 36: 661-669.
  64. Naghizadeh, M. and Sacchi, M.D., 2010. On sampling functions and Fourier
  65. reconstruction methods. Geophysics, 75(Issue No.????), WB137-WB151.
  66. Nocedal, J. and Wright, S.J., 1999. Numerical Optimization. Springer-Verlag, New York.
  67. Oppert, S., Stefani, J., Eakin, D., Halpert, A., Herwanger, J.V ., Bottrill, A., Popov, P.,
  68. Tan, L., Artus, V . and Oristaglio, M., 2017. Virtual time-lapse seismic monitoring
  69. using fully coupled flow and geomechanical simulations. The Leading Edge, 36;
  70. 750-768.
  71. Pawelec, I., Wakin, M. and Sava, P., 2021. Missing trace reconstruction for 2d land
  72. seismic data with randomized sparse sampling. Geophysics, 86(6): P25-P36.
  73. Rudin, S. and Osher, C. and Fatami, E., 1992. Nonlinear total variation noise removal
  74. algorithm. Phys. D, 60: 259-268.
  75. Tsaig, Y . and Donoho, D.L., 2006. Extensions of compressed sensing. Signal Process.,
  76. 86: 549-571. (Sparse Approximations in Signal and Image Processing).
  77. Wakin, M., Becker, S., Nakamura, E., Grant, M., Sovero, E., Ching, D., Yoo, J.,
  78. Romberg, J., Emami-Neyestanak, A. and Candès, E., 2012. A nonuniform
  79. sampler for wideband spectrally - sparse environments. IEEE J. Emerg. Select.
  80. Topics Circuits Syst., 2: 516-529.
  81. Wakin, M.B., Laska, J.N., Duarte, M.F., Baron, D., Sarvotham, S., Takhar, D., Kelly, K.F.
  82. and Baraniuk, R.G., 2006. An architecture for compressive imaging. Internat.
  83. Conf. Image Process.: 1273-1276.
  84. Wason, H. and Herrmann, F.J., 2013. Time-jittered ocean bottom seismic acquisition.
  85. Expanded Abstr., 83rd Ann. Internat. SEG Mtg., Houston: 1-6.
  86. Wright, S., 1997, Primal-Dual Interior-Point Methods. SIAM, Philaelphia.
  87. Zhang, M., 2020. Marchenko Green’s functions from compressive sensing acquisition.
  88. Expanded Abstr., 90th Ann. Internat. SEG Mtg., Huston: 2794-2798.
  89. Zhang, M., 2021. Time-lapse seismic data reconstruction using compressive sensing:
  90. Geophysics, 86(3): P37-P48.
  91. Zhang, M., 2022, Compressive sensing acquisition with application to Marchenko
  92. imaging. Pure Appl. Geophys., 179: 2383-2404.
  93. Zhang, M. and Li, Y ., 2021. Efficient ground EM acquisition using irregular sparse
  94. stations: A compressive sensing approach. Expanded Abstr., Internat. Mtg. Appl.
  95. Geosci. Energy: 1241-1245.
  96. Zhang, M. and Li, Y ., 2022. Irregular acquisition design to maximize information: From
  97. cross-lines to ergodic sampling. Expanded Abstr., Internat. Mtg. Appl. Geosci.
  98. Energy, Denver: 1150-1154.
  99. Zhang, M. and Lumley, D., 2019. Reconstruction of 3D seismic data from sparse random
  100. OBN acquisition by compressive sensing. Expanded Abstr., 89th Ann. Internat.
  101. SEG Mtg., New Orleans: 127-130.
  102. Zwartjes, P. and Gisolf, A., 2007. Fourier reconstruction with sparse inversion. Geophys.
  103. Prosp., 55: 199-221.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing