1887
Volume 73, Issue 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We compare classical and adjoint‐state first‐arrival tomography approaches in subsurface model reconstruction, focusing on pre‐salt updates with a circular‐shot ocean bottom node geometry. The investigation demonstrates that, whereas conventional tomography has faster convergence and better alignment with observed data, it produces significant noise artefacts and fails to adequately represent the reservoir section. In contrast, adjoint‐state tomography provides superior model reconstruction by taking into account the complete travel time volume, significantly lowering noise and boosting reservoir imaging despite its higher computational cost. A quantitative investigation of root mean squared errors for ultra‐long offsets confirms the efficacy of adjoint‐state tomography in minimizing data misfit and improving model fidelity. The findings emphasize the potential of adjoint‐state tomography in enhancing subsurface imaging and underscore the limits of conventional tomography in handling complex subsurface details with sparse acquisition geometry.

© 2025 European Association of Geoscientists & Engineers. © 2024 European Association of Geoscientists & Engineers.
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13657
2025-04-17
2026-02-15

  • From This Site

    /content/journals/10.1111/1365-2478.13657
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Afnimar & Koketsu, K. (2000) Finite difference traveltime calculation for head waves travelling along an irregular interface. Geophysical Journal International, 143(3), 729–734. https://doi.org/10.1046/j.1365‐246X.2000.00269.x
     [Google Scholar]
  2. Alkhalifah, T. & Choi, Y. (2014) From tomography to full‐waveform inversion with a single objective function. Geophysics, 79(2), R55–R61. https://doi.org/10.1190/geo2013‐0291.1
     [Google Scholar]
  3. Alves, P.H.B., Cetale, M., Moreira, R.M., Silva, S.L.E.F. & Lopez, J. (2024) Seismic first arrival tomography for top salt velocity update: a case study in the Santos Basin, Brazil. In the Fourth International Meeting for Applied Geoscience & Energy Expanded Abstracts. Tulsa, OK: AAPG, pp. 1393–1397. https://doi.org/10.1190/image2024-4101257.1
  4. Alves, P.H.B., Santos, L.A., Capuzzo, F.V. & Cetale, M. (2023) 3D refraction travel time accuracy study in high contrasted media. Brazilian Journal of Geophysics, 41(1), 1–20. https://doi.org/10.22564/brjg.v41i1.2295
     [Google Scholar]
  5. Azevedo Filho, E.T., Palma, M.A.M., Perestrelo, M., da Hora, H.R.M. & Lira, R.A. (2019) The pre‐salt layer and challenges to competitiveness in Brazil: critical reflections on the local content policy in the oil and gas sector. The Extractive Industries and Society, 6(4), 1168–1173. https://doi.org/10.1016/j.exis.2019.09.009
     [Google Scholar]
  6. Benaichouche, A., Noble, M. & Gesret, A. (2015) First arrival traveltime tomography using the fast marching method and the adjoint state technique. 2015(1), 1–5. https://doi.org/10.3997/2214‐4609.201412568
  7. Capozzoli, A., Curcio, C., Liseno, A. & Savarese, S. (2013) A comparison of fast marching, fast sweeping and fast iterative methods for the solution of the eikonal equation. In the 2013 21st Telecommunications Forum Telfor (TELFOR). Piscataway, NJ: IEEE, pp. 685–688. https://doi.org/10.1109/TELFOR.2013.6716321
  8. Cerveny, V. (2001) Seismic ray theory. Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/CBO9780511529399
     [Google Scholar]
  9. Chen, J., Wu, S., Xu, M., Nagaso, M., Yao, J., Wang, K., Li, T., Bai, Y. & Tong, P. (2023) Adjoint‐state teleseismic traveltime tomography: method and application to Thailand in Indochina Peninsula. Journal of Geophysical Research: Solid Earth, 128(12), e2023JB027348. e2023JB027348 2023JB027348. https://doi.org/10.1029/2023JB027348
     [Google Scholar]
  10. Costa, F., Capuzzo, F., de Souza, A., Jr., Moreira, R., Lopez, J. & Cetale, M. (2020) Understanding refracted wave paths for Brazilian pre‐salt target‐oriented imaging. In SEG technical program expanded abstracts 2020. Houston, TX: Society of Exploration Geophysicists, pp. 2375–2380. https://doi.org/10.1190/segam20203426868.1
  11. Costa, F., da Silva, S.L.E.F., Karsou, A.A., Capuzzo, F., Moreira, R.M., Lopez, J. & Cetale, M. (2023) Data selection for velocity model estimation using a circular shot OBN survey. In the Third international meeting for applied geoscience & energy expanded abstracts. Houston, TX: Society of Exploration Geophysicists, pp. 581–585. https://doi.org/10.1190/image2023‐3910079.1
  12. Cypriano, L., Yu, Z., Ferreira, D., Huard, B., Pereira, R., Jouno, F., Khalil, A., Urasaki, E.N.A., da Cruz, N.M.S.M., Yin, A., Clarke, D. & Jesus, C.C. (2019) OBN for pre‐salt imaging and reservoir monitoring ‐ potential and road ahead. In the 16th International Congress of the Brazilian Geophysical Society & Expogef Abstracts. Rio de Janeiro: Brazilian Geophysical Society, pp. 318. https://doi.org/10.22564/16cisbgf2019.318
  13. da Silva, S.L., Costa, F., Karsou, A., Capuzzo, F., Moreira, R., Lopez, J. & Cetale, M. (2024) Research note: Application of refraction full‐waveform inversion of ocean bottom node data using a squared‐slowness model parameterization. Geophysical Prospecting, 72(3), 1189–1195. https://doi.org/10.1111/1365‐2478.13454
     [Google Scholar]
  14. da Silva, S.L., Karsou, A., Moreira, R., Lopez, J. & Cetale, M. (2022) Klein‐Gordon equation and variable density effects on acoustic wave propagation in Brazilian pre‐salt fields. In the 83rd EAGE Annual Conference & Exhibition, June 2022, Volume 2022. Houten, the Netherlands: European Association of Geoscientists & Engineers, pp. 1–5. https://doi.org/10.3997/22144609.202210385
  15. da Silva, S.L., Lopez, J., de Araújo, J.M. & Corso, G. (2021) Multiscale q‐FWI applied to circular shot OBN acquisition for accurate presalt velocity estimates. In the First International Meeting for Applied Geoscience & Energy expanded abstracts. Houston, TX: Society of Exploration Geophysicists, pp. 712–716. https://doi.org/10.1190/segam2021‐3581021.1
  16. da Silva, S.L.E., Costa, F.T., Karsou, A., de Souza, A., Capuzzo, F., Moreira, R.M., Lopez, J. & Cetale, M. (2024) Refraction FWI of a circular shot OBN acquisition in the Brazilian presalt region. IEEE Transactions on Geoscience and Remote Sensing, 62, 5920518. https://doi.org/10.1109/TGRS.2024.3426956
     [Google Scholar]
  17. Detrixhe, M., Gibou, F. & Min, C. (2013) A parallel fast sweeping method for the eikonal equation. Journal of Computational Physics, 237, 46–55. https://doi.org/10.1016/j.jcp.2012.11.042
     [Google Scholar]
  18. Duarte, E.F., da Silva, D., Carvalho, P.T., de Araújo, J.M. & Lopez, J.L. (2023) Full‐waveform inversion of a Brazilian presalt ocean‐bottom node data set using a concentric circle source geometry. Geophysics, 88(1), B33–B46. https://doi.org/10.1190/geo2021‐0727.1
     [Google Scholar]
  19. Fokkema, J.T. & van den Berg, P.M. (2013) Seismic applications of acoustic reciprocity. Amsterdam: Elsevier. https://doi.org/10.1016/C2009‐0‐10209‐X
     [Google Scholar]
  20. García‐Yeguas, A., Koulakov, I., Ibáñez, J.M. & Rietbrock, A. (2012) High resolution 3D P wave velocity structure beneath Tenerife Island (Canary Islands, Spain) based on tomographic inversion of active‐source data. Journal of Geophysical Research: Solid Earth, 117(B9), B09309. https://doi.org/10.1029/2011JB008970
     [Google Scholar]
  21. Gómez, J.V., Álvarez, D., Garrido, S. & Moreno, L. (2019) Fast methods for eikonal equations: an experimental survey. IEEE Access, 7, 39005–39029. https://doi.org/10.1109/ACCESS.2019.2906782
     [Google Scholar]
  22. Huang, X., Guo, Z., Zhou, H. & Yue, Y. (2020) First arrival Q tomography based on an adjoint‐state method. Journal of Geophysics and Engineering, 17(4), 577–591. https://doi.org/10.1093/jge/gxaa008
     [Google Scholar]
  23. Jiang, W. & Zhang, J. (2018) 3D first‐arrival traveltime tomography with modified total variation regularization. Journal of Geophysics and Engineering, 15(1), 207–223. https://doi.org/10.1088/1742‐2140/aa84d1
     [Google Scholar]
  24. Kalachand, S. & Damodara, N. (2022) Inverse problem, In Active seismic tomography . Hoboken, NJ: John Wiley & Sons, pp. 23–27. https://doi.org/10.1002/9781119594925.ch4
     [Google Scholar]
  25. Leung, S. & Qian, J. (2006) An adjoint state method for three‐dimensional transmission traveltime tomography using first‐arrivals. Communications in Mathematical Sciences, 4(1), 249–266. https://doi.org/10.4310/CMS.2006.v4.n1.a10
     [Google Scholar]
  26. Li, Y., Zhang, G., Hu, G., Li, K., Luo, Y., Liang, C. & Duan, J. (2023) High‐precision and high‐efficiency first‐arrival slope tomography via eikonal solvers and the adjoint‐state method. Journal of Geophysics and Engineering, 20(4), 774–787. https://doi.org/10.1093/jge/gxad051
     [Google Scholar]
  27. Liu, Q. & Gu, Y. (2012) Seismic imaging: from classical to adjoint tomography. Tectonophysics, 566‐567, 31–66. https://doi.org/10.1016/j.tecto.2012.07.006
     [Google Scholar]
  28. Lopez, J., Cox, B., Hatchell, P. & Wang, K. (2017) Technology options for low‐cost on‐demand seismic monitoring in deepwater Brazil. In the 15th International Congress of the Brazilian Geophysical Society & Expogef Abstracts. Rio de Janeiro: Brazilian Geophysical Society, pp. 1730–1735. https://doi.org/10.1190/sbgf2017‐341
  29. Lopez, J., Neto, F., Cabrera, M., Cooke, S., Grandi, S. & Roehl, D. (2020) Refraction seismic for pre‐salt reservoir characterization and monitoring. In SEG technical program expanded abstracts 2020. Houston, TX: Society of Exploration Geophysicists, pp. 2365–2369. https://doi.org/10.1190/segam2020‐3426667.1
  30. Loris, I., Douma, H., Nolet, G., Daubechies, I. & Regone, C. (2010) Nonlinear regularization techniques for seismic tomography. Journal of Computational Physics, 229(3), 890–905. https://doi.org/10.1016/j.jcp.2009.10.020
     [Google Scholar]
  31. Menke, W. (2012) Chapter 9 ‐ nonlinear inverse problems. In W.Menke (Ed.), Geophysical data analysis: Discrete Inverse theory, 3rd ed.Boston, MA: Academic Press, pp. 163–188. https://doi.org/10.1016/B978‐0‐12‐397160‐9.00009‐6
     [Google Scholar]
  32. Michelena, R.J., Muir, F. & Harris, J.M. (1993) Anisotropic traveltime tomography. Geophysical Prospecting, 41(4), 381–412. https://doi.org/10.1111/j.1365‐2478.1993.tb00576.x
     [Google Scholar]
  33. Noble, M., Gesret, A. & Belayouni, N. (2014) Accurate 3‐D finite difference computation of traveltimes in strongly heterogeneous media. Geophysical Journal International, 199(3), 1572–1585. https://doi.org/10.1093/gji/ggu358
     [Google Scholar]
  34. Noble, M., Thierry, P., Taillandier, C. & Calandra, H. (2010) High‐performance 3D first‐arrival traveltime tomography. The Leading Edge, 29(1), 86–93.
     [Google Scholar]
  35. Nolet, G. (2012) Seismic tomography: With applications in global seismology and exploration geophysics. Modern Approaches in Geophysics, volume 5. Berlin: Springer Science & Business Media. https://doi.org/10.1007/978-94-009-3899-1
     [Google Scholar]
  36. Pegah, E. & Liu, H. (2016) Application of near‐surface seismic refraction tomography and multichannel analysis of surface waves for geotechnical site characterizations: a case study. Engineering Geology, 208, 100–113. https://doi.org/10.1016/j.enggeo.2016.04.021
     [Google Scholar]
  37. Plessix, R.‐E. (2006) A review of the adjoint‐state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167(2), 495–503. https://doi.org/10.1111/j.1365‐246X.2006.02978.x
     [Google Scholar]
  38. Podvin, P. & Lecomte, I. (1991) Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. Geophysical Journal International, 105(1), 271–284. https://doi.org/10.1111/j.1365‐246X.1991.tb03461.x
     [Google Scholar]
  39. Prieux, V., Lambaré, G., Operto, S. & Virieux, J. (2012) Building starting models for full waveform inversion from wide‐aperture data by stereotomography. Geophysical Prospecting, 109–137. https://doi.org/10.1111/j.1365‐2478.2012.01099.x
     [Google Scholar]
  40. Rawlinson, N., Pozgay, S. & Fishwick, S. (2010) Seismic tomography: A window into deep earth. Physics of the Earth and Planetary Interiors, 178(3), 101–135. https://doi.org/10.1016/j.pepi.2009.10.002
     [Google Scholar]
  41. Reta‐Tang, C., Sheng, J., Liu, F., Cantú, A.V. & Vargas, A.C. (2023) Application of full‐waveform inversion to land data: case studies in onshore Mexico. The Leading Edge, 42(3), 190–195. https://doi.org/10.1190/tle42030190.1
     [Google Scholar]
  42. Ristow, J., Lanznaster, D. & Jouno, F. (2024) Advances in OBN imaging for pre‐salt fields. In the 85th EAGE Annual Conference & Exhibition. Houten, the Netherlands: European Association of Geoscientists and Engineers (EAGE), pp. 1–5. https://doi.org/10.3997/2214‐4609.2024101421
  43. Rodrigues Cezário, W., Maria de Souza Antunes, A., Fernando Leite, L. & Pio Borges de Menezes, R. (2015) The energy revolution in the USA and the pre‐salt reserves in Brazil: risks and opportunities for the Brazilian petrochemical industry. Futures, 73, 1–11. https://doi.org/10.1016/j.futures.2015.07.013
     [Google Scholar]
  44. Saad, Y. (2003) Iterative methods for sparse linear systems. Philadelphia, PA: Society for Industrial and Applied Mathematics.
     [Google Scholar]
  45. Scales, J.A., Gersztenkorn, A. & Treitel, S. (1988) Fast IP solution of large, sparse, linear systems: Application to seismic travel time tomography. Journal of Computational Physics, 75(2), 314–333. https://doi.org/10.1016/0021‐9991(88)90115‐5
     [Google Scholar]
  46. Sei, A. & Symes, W.W. (1994) Gradient calculation of the traveltime cost function without ray tracing. In SEG technical program expanded abstracts 1994. Tulsa, OK: Society of Exploration Geophysicists, pp. 1351–1354. https://doi.org/10.1190/1.1822780
  47. Taillandier, C., Noble, M., Chauris, H. & Calandra, H. (2009) First‐arrival traveltime tomography based on the adjoint‐state method. Geophysics, 74(6), 1–10. https://doi.org/10.1190/1.3250266
     [Google Scholar]
  48. Tape, C., Liu, Q., Maggi, A. & Tromp, J. (2010) Seismic tomography of the southern California crust based on spectral‐element and adjoint methods. Geophysical Journal International, 180(1), 433–462. https://doi.org/10.1111/j.1365‐246X.2009.04429.x
     [Google Scholar]
  49. Tong, P. (2021) Adjoint‐state traveltime tomography: eikonal equation‐based methods and application to the Anza area in Southern California. Journal of Geophysical Research: Solid Earth, 126(5), e2021JB021818. https://doi.org/10.1029/2021JB021818
     [Google Scholar]
  50. Tong, P., Li, T., Chen, J. & Nagaso, M. (2023) Adjoint‐state differential arrival time tomography. Geophysical Journal International, 236(1), 139–160. https://doi.org/10.1093/gji/ggad416
     [Google Scholar]
  51. van Trier, J. & Symes, W.W. (1991) Upwind finite‐difference calculation of traveltimes. Geophysics, 56(6), 812–821. https://doi.org/10.1190/1.1443099
     [Google Scholar]
  52. Vidale, J. (1988) Finite‐difference calculation of travel times. Bulletin of the Seismological Society of America, 78(6), 2062–2076. https://doi.org/10.1785/BSSA0780062062
     [Google Scholar]
  53. Vidale, J. (1990) Finite‐difference calculation of traveltimes in three dimensions. Geophysics, 55(5), 521–526. https://doi.org/10.1190/1.1442863
     [Google Scholar]
  54. Waheed, U.b., Flagg, G. & Yarman, C.E. (2016) First‐arrival traveltime tomography for anisotropic media using the adjoint‐state method. Geophysics, 81(4), R147–R155. https://doi.org/10.1190/geo2015‐0463.1
     [Google Scholar]
  55. Wang, Y. (2016) Seismic tomography based on ray theory. In Y.Wang (Ed.) Seismic inversion: Theory and applications. Hoboken, NJ: John Wiley & Sons, chapter 11, pp. 139–155. https://doi.org/10.1002/9781119258032.ch11
     [Google Scholar]
  56. Yao, Z.S. & Roberts, R.G. (1999) A practical regularization for seismic tomography. Geophysical Journal International, 138(2), 293–299. https://doi.org/10.1046/j.1365‐246X.1999.00849.x
     [Google Scholar]
  57. Zhang, J. (2015) Explicit statics optimization in the first‐arrival traveltime tomography. In the 77th EAGE Conference and Exhibition 2015. Houten, the Netherlands: European Association of Geoscientists & Engineers, pp. 1–5. https://doi.org/10.3997/2214‐4609.201412991
  58. Zhang, J., Dong, L., Wang, J. & Wang, Y. (2023) Illumination compensation for the adjoint‐state first‐arrival traveltime tomography in VTI media. Journal of Applied Geophysics, 211, 104964. https://doi.org/10.1016/j.jappgeo.2023.104964
     [Google Scholar]
  59. Zhao, H. (2005) A fast sweeping method for eikonal equations. Mathematics of Computation, 74(250), 603–627. https://doi.org/10.1090/S00255718‐04‐01678‐3
     [Google Scholar]
  60. Zhao, H. (2007) Parallel implementations of the fast sweeping method. Journal of Computational Mathematics, 25(4), 421–429. http://www.jstor.org/stable/43693378
     [Google Scholar]
/content/journals/10.1111/1365-2478.13657
Loading
Comparative analysis of eikonal‐based first‐arrival tomography: A case study from the Santos Basin, Brazil
Geophysical Prospecting 73, 1060 (2025); https://doi.org/10.1111/1365-2478.13657
/content/journals/10.1111/1365-2478.13657
/content/journals/10.1111/1365-2478.13657
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): acoustics; acquisition; computing aspects; inverse problem; numerical study; tomography

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error