ARTICLE

Separation of blended data by sparse inversion based on the reciprocity theorem

CHENQING TAN1 LIGUO HAN1 QINGTIAN LV1,2 YAHONG ZHANG3 YUN LONG1 XIANGBO GONG1
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1 College of Geo Exploration Science and Technology, Jilin University, Changchun 130026, P.R. China.,
2 Chinese Academy of Geological Sciences, Beijing 100000, P.R. China.,
3 Sinopec Petroleum Geophysical Research Institute, Nanjing 210014, P.R. China.,
JSE 2013, 22(3), 209–222;
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

Recently a great change of mindset in seismic acquisition has occurred and much attention has been drawn to blended acquisition. Different sources at several locations are shot in an overlapping fashion and blended records are acquired, so that acquisition efficiency and potentially image quality can be significantly improved. The key factor of blended acquisition is source separation, which is the procedure of recovering data as if they were acquired in the conventional survey. From the mathematics point of view, it can be formulated as solving an underdetermined equation such as Ax = b, yet a simple least-square inversion is only able to get pseudodeblend data where the blending noises are not able to be removed. In this paper we find that in the 2D regularization acquisition system, the blended data in common receiver domain can be simply connected with that in common source domain according to the reciprocity theorem, so that the above equation would be more determined to be solved. While in the implementation procedure, spgL1 norm basic pursuit sparse inversion algorithm is utilized calculating the reflection coefficients of the single source data, and then the deblended data are acquired via convolution. Ideal results could be produced in field data tests.

Keywords
blended data
source separation
underdetermined equation
reciprocity theorem
L1 norm basic pursuit
References
  1. Abma, R. and Yan, J., 2009. Separating simultaneous sources by inversion. Extended Abstr., 71st
  2. EAGE Conf. Amsterdam: V002.
  3. Abma, R., Manning, T., Tanis, M., Yu, J. and Foster, M., 2010. High quality separation of
  4. simultaneous sources by sparse inversion. Extended Abstr., 72nd EAGE Conf., Amsterdam:
  5. B003.
  6. Bagaini, C., 2006. Overview of simultaneous vibroseis acquisition methods. Expanded Abstr., 76th
  7. Ann. Internat. SEG Mtg., New Orleans: 70-74.
  8. Beasley, C.J., Chambers, R.E. and Jiang, Z., 1998. A new look at simultaneous sources. Expanded
  9. Abstr., 68th Ann. Internat. SEG Mtg., New Orleans: 133-135.
  10. Beasley, C.J., 2008a. A new look at marine simultaneous sources. The Leading Edge, 27: 914-917.
  11. Beasley, C.J., 2008b. Simultaneous sources: A technology whose time has come. Expanded Abstr.,
  12. 78th Ann. Internat. SEG Mtg., Las Vegas, 27: 2796-2800.
  13. van den Berg, E. and Friedlander, M.P., 2008. Probing the pareto frontier for basis pursuit solutions
  14. SLAMJ. SCI Comput., 31: 890-912.
  15. Berkhout, A.J., 1982. Seismic Migration, Imaging of Acoustic Energy by Wave Field Extrapolation,
  16. A: Theoretical Aspects. Elsevier Science Publishers, Amsterdam.
  17. Berkhout, A.J., 2008. Changing the mindset in seismic data acquisition. The Leading Edge, 27:
  18. 924-938.
  19. Berkhout, A.J., Blacquiére, G. and Verschuur, D.J., 2009. The concept of double blending:
  20. Combining incoherent shooting with incoherent sensing. Geophysics, 74 (4): A59-A62,
  21. doi:10.1190/1.3141895.
  22. Doulgeris, P., Mahdad, A. and Blacquiére, G., 2011. Iterative separation of blended marine data:
  23. discussion on the coherence-pass filter. Expanded Abstr., 81th Ann. Internat. SEG Mtg.,
  24. San Antonio: 26-31.
  25. Ikelle, L.T., 2007. Coding and decoding: Seismic data modeling, acquisition and processing.
  26. Expanded Abstr., 77th Ann. Internat. SEG Mtg., San Antonio: 51-55.
  27. Ikelle, L.T., 2009. Reducing the pressure on data acquisition and processing: I. Multishooting
  28. processing of single-shot data. J. Seismic Explor., 18: 93-102.
  29. Ikelle, L.T. and Sturzu, I., 2009. Reducing the pressure on data acquisition and processing: II.
  30. Data-driven compression using conic coding. J. Seismic Explor., 18: 119-133.
  31. Ikelle, L.T., 2010. Coding and Decoding: Seismic Data. Elsevier Science Publishers, Amsterdam.
  32. Krohn, C.E. and Johnson, M.L., 2003. High fidelity vibratory seismic (HF VS) II: Superior source
  33. separation. Expanded Abstr., 73rd Ann. Internat. SEG Mtg., Dallas.
  34. Lin, T.T.Y. and Herrmann, F.J., 2009. Designing simultaneous acquisitions with compressive
  35. sensing. Extended Abstr., 71sth EAGE Conf., Amsterdam: S006.
  36. Mahdad, A., Doulgeris, P. and Blacquiére, G., 2011. Separation of blended data by iterative
  37. estimation and subtraction of blending interference noise. Geophysics, 76(3): Q9-Q17.
  38. Moore, I., 2010. Simultaneous sources - processing and applications. Extended Abstr., 72nd EAGE
  39. Conf., Barcelona: B001.
  40. Sallas, J., Corrigan, D. and Allen, K.P., 1998. High-fidelity vibratory source method with source
  41. separation. U.S. Patent 5 721, 710.
  42. Sallas, J., Gibson, J., Lin, F., Winter, O., Montgomery, B. and Nagarajappa, P., 2008. Broadband
  43. vibroseis using simultaneous pseudorandom sweeps. Expanded Abstr., 78th Ann. Internat.
  44. SEG Mtg., Las Vegas: 100-104.
  45. Silverman, D., 1979. Method of three dimensional seismic prospecting. U.S. Patent 4, 159, 463.
  46. Tan, C. Han, L. Zhang, Y. and Deng, W., 2012. Separation of blended data by iterative denoising.
  47. Extended Abstr., 74th EAGE Conf., Copenhagen: A045.
  48. Wapenaar, C.P.A., van der Neut, J. and Thorbecke, J., 2012. Deblending by direct inversion.
  49. Geophysics, 77(3): A9-A12.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing