1887
Volume 72, Issue 5
  • E-ISSN: 1365-2478

Abstract

Abstract

Geostatistical seismic inversion is an important method for establishing high‐resolution reservoir parameter models. There is no accurate representation method for reservoir structural features, and prior information about structural features cannot be incorporated into geostatistical inversion. Based on the assumption of the sparsity of stratigraphic sedimentary features, the same type of structural feature is used to represent the sedimentary pattern of reservoirs within the same facies. Different sparse representation patterns are used to represent the differences in sedimentary patterns between facies. Although changes in depositional environment might result in the multi‐scale characteristics of geological structures for varying sedimentary rhythms, this paper proposes a facies‐constrained geostatistical inversion method based on multi‐scale sparse representation to better accommodate such situation. Using the method of sparse representation combined with wavelet transform, the multi‐scale sedimentary structural features of reservoirs are learned from well‐logging data. Seismic facies and multi‐scale features are used as prior information for geostatistical inversion. Further, the likelihood function is constructed using seismic data to obtain the posterior probability distribution of reservoir parameters. Finally, the accurate inversion result is obtained by using multi‐scale sparse representation as a constraint in the posterior probability distribution of reservoir parameters. Compared with conventional geostatistical methods, this algorithm can better match the structural features of reservoir parameters with varying geological conditions. Field data tests have shown the effectiveness of this method in improving the accuracy and resolution of reservoir parameter structural features.

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

Article metrics loading...

/content/journals/10.1111/1365-2478.13476
2024-05-21
2026-01-17

  • From This Site

    /content/journals/10.1111/1365-2478.13476
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Abzalov, M. (2016) Introduction to geostatistics. In: Applied mining geology. Modern approaches in solid earth sciences, vol. 12. Cham: Springer. Available from: https://doi.org/10.1007/978‐3‐319‐39264‐6_17
     [Google Scholar]
  2. Aharon, M., Elad, M. & Bruckstein, A. (2006) K‐SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 54(11), 4311–4322. Available from: https://doi.org/10.1109/tsp.2006.881199
     [Google Scholar]
  3. Ahmed, J., Baloch, G.L. & Ozkaramanli, H. (2017) Coupled K‐SVD dictionary learning algorithm in wavelet domain for single image super‐resolution. In: 2017 IEEE International Conference on Imaging Systems and Techniques (IST), Beijing, IEEE. pp. 1–5. Available from: https://doi.org/10.1109/ist.2017.8261520
  4. Aleardi, M., Ciabarri, F. & Gukov, T. (2018) A two‐step inversion approach for seismic‐reservoir characterization and a comparison with a single‐loop Markov‐chain Monte Carlo algorithm TS and SL inversion algorithms. Geophysics, 83(3), R227–R244. Available from: https://doi.org/10.1190/geo2017‐0387.1
     [Google Scholar]
  5. Aleardi, M. & Salusti, A. (2020) Markov chain Monte Carlo algorithms for target‐oriented and interval‐oriented amplitude versus angle inversions with non‐parametric priors and non‐linear forward modellings. Geophysical Prospecting, 68(3), 735–760. Available from: https://doi.org/10.1111/1365‐2478.12876
     [Google Scholar]
  6. Azevedo, L., Nunes, R., Soares, A., Neto, G.S. & Martins, T.S. (2018) Geostatistical seismic amplitude‐versus‐angle inversion. Geophysical Prospecting, 66(S1), 116–131. Available from: https://doi.org/10.1111/1365‐2478.12589
     [Google Scholar]
  7. Azevedo, L. & Soares, A. (2017) Geostatistical methods for reservoir geophysics. Cham: Springer.
     [Google Scholar]
  8. Beckouche, S. & Ma, J. (2014) Simultaneous dictionary learning and denoising for seismic data. Geophysics, 79(3), A27–A31. Available from: https://doi.org/10.1190/geo2013‐0382.1
     [Google Scholar]
  9. Bosch, M., Carvajal, C., Rodrigues, J., Torres, A., Aldana, M. & Sierra, J. (2009) Petrophysical seismic inversion conditioned to well‐log data: methods and application to a gas reservoir. Geophysics, 74(2), O1–O15. Available from: https://doi.org/10.1190/1.3043796
     [Google Scholar]
  10. Bosch, M., Mukerji, T. & Gonzalez, E.F. (2010) Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review. Geophysics, 75(5), 75A165–75A176. Available from: https://doi.org/10.1190/1.3478209
     [Google Scholar]
  11. Chen, J., Chen, W., Wang, X., Zhou, Y., Shi, Z. & Zhang, G. (2018) DAS coupling noise suppression using wavelet and DCT dictionary based on sparse optimization. In: SEG Technical Program Expanded Abstracts 2018, Houston, Society of Exploration Geophysicists. pp. 4938–4942. Available from: https://doi.org/10.1190/segam2018‐2996038.1
  12. Chen, T., Wang, Y., Li, K., Cai, H., Yu, G. & Hu, G. (2023) A prestack seismic inversion method constrained by facies‐controlled sedimentary structural features. Geophysics, 88(2), R209–R223. Available from: https://doi.org/10.1190/geo2022‐0301.1
     [Google Scholar]
  13. Dash, S.S., Rahaman, A., Taid, D., Singh, M., Singh, S.K. & Singh, H.K. (2020) Play fairway analysis and depositional model of Panna formation using high frequency sequence stratigraphic framework and pre‐stack geostatistical inversion: screening tools for geological risk constrained exploration. In: 13th Biennial International Conference and Exhibition, Beijing, INOVA. 1–6.
  14. de Figueiredo, L.P., Grana, D., Roisenberg, M. & Rodrigues, B.B. (2019) Gaussian mixture Markov chain Monte Carlo method for linear seismic inversion. Geophysics, 84(3), R463–R476. Available from: https://doi.org/10.1190/geo2018‐0529.1
     [Google Scholar]
  15. Deutsch, C.V. & Journel, A.G. (1992) GSLIB geostatistical software library and user's guide. vol. 119, New York: Oxford University Press. Available from: https://doi.org/10.1080/00401706.1995.10485913
     [Google Scholar]
  16. Dhara, A., Sen, M.K. & Biswas, R. (2023) Facies‐constrained transdimensional amplitude versus angle inversion using machine learning assisted priors. Geophysical Prospecting, 71(4), 590–613. Available from: https://doi.org/10.1111/1365‐2478.13339
     [Google Scholar]
  17. Du, X., Wang, Q., Zhao, M. & Liu, X. (2020) Sedimentary characteristics and mechanism analysis of a large‐scale fan delta system in the Paleocene Kongdian Formation, southwestern Bohai Sea, China. Interpretation, 8(2), SF81–SF94. Available from: https://doi.org/10.1190/int‐2019‐0143.1
     [Google Scholar]
  18. Fatti, J.L., Smith, G.C., Vail, P.J., Strauss, P.J. & Levitt, P.R. (1994) Detection of gas in sandstone reservoirs using AVO analysis: a 3‐D seismic case history using the geostack technique. Geophysics, 59(9), 1362–1376. Available from: https://doi.org/10.1190/1.1443695
     [Google Scholar]
  19. Fjeldstad, T. & Grana, D. (2018) Joint probabilistic petrophysics‐seismic inversion based on Gaussian mixture and Markov chain prior models probabilistic petroelastic prediction. Geophysics, 83(1), R31–R42. Available from: https://doi.org/10.1190/geo2017‐0239.1
     [Google Scholar]
  20. Foreman‐Mackey, D., Hogg, D.W., Lang, D. & Goodman, J. (2013) Emcee: the MCMC hammer. Publications of the Astronomical Society of the Pacific, 125(925), 306–312. Available from: https://doi.org/10.1086/670067
     [Google Scholar]
  21. González, E.F., Mukerji, T. & Mavko, G. (2008) Seismic inversion combining rock physics and multiple‐point geostatistics. Geophysics, 73(1), R11–R21. Available from: https://doi.org/10.1190/1.2803748
     [Google Scholar]
  22. Grana, D., Paparozzi, E., Mancini, S. & Tarchiani, C. (2013) Seismic driven probabilistic classification of reservoir facies for static reservoir modelling: a case history in the Barents Sea. Geophysical Prospecting, 61(3), 613–629. Available from: https://doi.org/10.1111/j.1365‐2478.2012.01115.x
     [Google Scholar]
  23. Grijalba‐Cuenca, A., Torres‐Verdin, C. & van der Made, P. (2000) Geostatistical inversion of 3D seismic data to extrapolate wireline petrophysical variables laterally away from the well. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas, SPE. 1–4. Available from: https://doi.org/10.2118/63283‐MS
  24. Haas, A. & Dubrule, O. (1994) Geostatistical inversion‐a sequential method of stochastic reservoir modelling constrained by seismic data. First Break, 12(11), 561–569. Available from: https://doi.org/10.3997/1365‐2397.1994034
     [Google Scholar]
  25. Hansen, T.M., Journel, A.G., Tarantola, A. & Mosegaard, K. (2006) Linear inverse Gaussian theory and geostatistics. Geophysics, 71(6), R101–R111. Available from: https://doi.org/10.1190/1.2345195
     [Google Scholar]
  26. Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. Available from: https://doi.org/10.1093/biomet/57.1.97
     [Google Scholar]
  27. Hoijtink, H. (2000) Posterior inference in the random intercept model based on samples obtained with Markov chain Monte Carlo methods. Computational Statistics, 15, 315–336. Available from: https://doi.org/10.1007/s001800000037
     [Google Scholar]
  28. Hu, X., Hou, J., Yin, Y., Liu, Y., Wang, L., Kang, Q. et al. (2023) A multi‐scale blocking moving window algorithm for geostatistical seismic inversion. Computers and Geosciences, 173, 105313. Available from: https://doi.org/10.1016/j.cageo.2023.105313
     [Google Scholar]
  29. Kazemeini, S.H., Juhlin, C., Zinck‐Jørgensen, K. & Norden, B. (2009) Application of the continuous wavelet transform on seismic data for mapping of channel deposits and gas detection at the CO2SINK site. Ketzin, Germany. Geophysical Prospecting, 57(1), 111–123. Available from: https://doi.org/10.1111/j.1365‐2478.2008.00723.x
     [Google Scholar]
  30. Laloy, E., Hérault, R., Jacques, D. & Linde, N. (2018) Training‐image based geostatistical inversion using a spatial generative adversarial neural network. Water Resources Research, 54(1), 381–406. Available from: https://doi.org/10.1002/2017wr022148
     [Google Scholar]
  31. Lang, X. & Grana, D. (2017) Geostatistical inversion of prestack seismic data for the joint estimation of facies and impedances using stochastic sampling from Gaussian mixture posterior distributions. Geophysics, 82(4), M55–M65. Available from: https://doi.org/10.1190/geo2016‐0670.1
     [Google Scholar]
  32. Li, X., Chen, Q., Wu, C., Liu, H. & Fang, Y. (2016) Application of multi‐seismic attributes analysis in the study of distributary channels. Marine and Petroleum Geology, 75, 192–202. Available from: https://doi.org/10.1016/j.marpetgeo.2016.04.016
     [Google Scholar]
  33. MacBeth, C., Stephen, K.D. & McInally, A. (2005) The 4D seismic signature of oil–water contact movement due to natural production in a stacked turbidite reservoir. Geophysical Prospecting, 53(2), 183–203. Available from: https://doi.org/10.1111/j.1365‐2478.2004.00463.x
     [Google Scholar]
  34. Maggioni, M. & Gerber, S. (2013) Multiscale dictionaries, transforms, and learning in high‐dimensions. In: Wavelets and sparsity XV. vol. 8858. Bellingham: SPIE, pp. 482–504. Available from: https://doi.org/10.1117/12.2021984
     [Google Scholar]
  35. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., & Teller, E. (1953) Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092. Available from: https://doi.org/10.1063/1.1699114
     [Google Scholar]
  36. Murray, I., Ghahramani, Z. & MacKay, D. (2012) MCMC for doubly‐intractable distributions. Report number: UAI‐P‐2006‐PG‐359‐366. arXiv preprint arXiv:1206.6848. Available from: https://doi.org/10.48550/arXiv.1206.6848
  37. Nowak, W., De Barros, F.P.J. & Rubin, Y. (2010) Bayesian geostatistical design: task‐driven optimal site investigation when the geostatistical model is uncertain. Water Resources Research, 46(3), 1–17. Available from: https://doi.org/10.1029/2009wr008312
     [Google Scholar]
  38. Ògúnsàmì, A., Jackson, I., Borgomano, J.V., Fortin, J., Sidi, H., Gerhardt, A. et al. (2021) Elastic properties of a reservoir sandstone: a broadband inter‐laboratory benchmarking exercise. Geophysical Prospecting, 69(2), 404–418. Available from: https://doi.org/10.1111/1365‐2478.13048
     [Google Scholar]
  39. Oh, S.H. & Kwon, B.D. (2001) Geostatistical approach to Bayesian inversion of geophysical data: Markov chain Monte Carlo method. Earth, Planets and Space, 53, 777–791. Available from: https://doi.org/10.1186/bf03351676
     [Google Scholar]
  40. Pacheco, J.M.Ú., Bayón, P.V., Correia, U., Kneller, E. & Peiro, M. (2022) Unlocking the properties of a presalt carbonate reservoir offshore Brazil with facies‐constrained geostatistical inversion. The Leading Edge, 41(12), 832–839. Available from: https://doi.org/10.1190/tle41120832.1
     [Google Scholar]
  41. Roberts, G.O. (1995) Markov chain concepts related to sampling algorithms. In: Markov chain Monte Carlo in practice, 57, 45–58. Boca Raton: CRC Press.
     [Google Scholar]
  42. Rubinstein, R., Bruckstein, A.M. & Elad, M. (2010) Dictionaries for sparse representation modeling. Proceedings of the IEEE, 98(6), 1045–1057. Available from: https://doi.org/10.1109/jproc.2010.2040551
     [Google Scholar]
  43. Sabeti, H., Moradzadeh, A., Ardejani, F.D., Azevedo, L., Soares, A., Pereira, P. et al. (2017) Geostatistical seismic inversion for non‐stationary patterns using direct sequential simulation and co‐simulation. Geophysical Prospecting, 65(S1), 5–48. Available from: https://doi.org/10.1111/1365‐2478.12502
     [Google Scholar]
  44. Saussus, D. & Sams, M. (2012) Facies as the key to using seismic inversion for modelling reservoir properties. First Break, 30(7), 45–52. Available from: https://doi.org/10.3997/1365‐2397.2012009
     [Google Scholar]
  45. Shao, J., Wang, Y., Yao, Y., Wu, S., Xue, Q. & Chang, X. (2019) Simultaneous denoising of multicomponent microseismic data by joint sparse representation with dictionary learning. Geophysics, 84(5), KS155–KS172. Available from: https://doi.org/10.1190/geo2018‐0512.1
     [Google Scholar]
  46. She, B., Wang, Y., Liang, J., Liu, Z., Song, C. & Hu, G. (2018) A data‐driven amplitude variation with offset inversion method via learned dictionaries and sparse representation. Geophysics, 83(6), R725–R748. Available from: https://doi.org/10.1190/geo2017‐0615.1
     [Google Scholar]
  47. Sheets, B.A., Hickson, T.A. & Paola, C. (2002) Assembling the stratigraphic record: depositional patterns and time‐scales in an experimental alluvial basin. Basin Research, 14(3), 287–301. Available from: https://doi.org/10.1046/j.1365‐2117.2002.00185.x
     [Google Scholar]
  48. Stoker, M.S., Evans, D. & Ramp, A. (Eds.). (1998) Geological processes on continental margins: sedimentation, mass‐wasting and stability. London: Geological Society of London.
     [Google Scholar]
  49. Tarantola, A. (2005) Inverse problem theory and methods for model parameter estimation. Philadelphia: Society for Industrial and Applied Mathematics.
     [Google Scholar]
  50. Wang, Y., Zhang, G., Li, H., Yang, W. & Wang, W. (2022) The high‐resolution seismic deconvolution method based on joint sparse representation using logging–seismic data. Geophysical Prospecting, 70(8), 1313–1326. Available from: https://doi.org/10.1111/1365‐2478.13232
     [Google Scholar]
  51. Wei, L.I., Huaqi, Y.U. & Hongbin, D.E.N.G. (2012) Stratigraphic division and correlation and sedimentary characteristics of the Cambrian in central‐southern Sichuan Basin. Petroleum Exploration and Development, 39(6), 725–735. Available from: https://doi.org/10.1016/s1876‐3804(12)60097‐4
     [Google Scholar]
  52. Wolf, L.J., Anselin, L. & Arribas‐Bel, D. (2018) Stochastic efficiency of Bayesian Markov chain Monte Carlo in spatial econometric models: an empirical comparison of exact sampling methods. Geographical Analysis, 50(1), 97–119. Available from: https://doi.org/10.1111/gean.12135
     [Google Scholar]
  53. Wu, D., Liu, X., Du, Y., Jiang, L. & Cheng, Z. (2018) Predictive distribution of high‐quality tight reservoirs of coarse clastic rocks by linking diagenesis to sedimentary facies: evidence from the upper Sha 4 member in the northern Bonan Sag, Bohai Bay Basin, eastern China. Interpretation, 6(2), T413–T429. Available from: https://doi.org/10.1190/int‐2017‐0139.1
     [Google Scholar]
  54. Yenugu, M., Marfurt, K.J. & Matson, S. (2010) Seismic texture analysis for reservoir prediction and characterization. The Leading Edge, 29(9), 1116–1121. Available from: https://doi.org/10.1190/1.3485772
     [Google Scholar]
  55. Yu, B., Zhou, H., Wang, L. & Liu, W. (2020) Prestack Bayesian statistical inversion constrained by reflection features. Geophysics, 85(4), R349–R363. Available from: https://doi.org/10.1190/geo2019‐0810.1
     [Google Scholar]
  56. Zhang, D. (2019) Wavelet transform. In: Fundamentals of image data mining. Texts in computer science. Cham: Springer. 35–44. Available from: https://doi.org/10.1007/978‐3‐030‐17989‐2_3
     [Google Scholar]
  57. Zhang, Z., Xu, Y., Yang, J., Li, X. & Zhang, D. (2015) A survey of sparse representation: algorithms and applications. IEEE Access: Practical Innovations, Open Solutions, 3, 490–530. Available from: https://doi.org/10.1109/access.2015.2430359
     [Google Scholar]
/content/journals/10.1111/1365-2478.13476
Loading
A facies‐constrained geostatistical seismic inversion method based on multi‐scale sparse representation
Geophysical Prospecting 72, 1657 (2024); https://doi.org/10.1111/1365-2478.13476
/content/journals/10.1111/1365-2478.13476
/content/journals/10.1111/1365-2478.13476
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): geostatistical seismic inversion; inversion; multi‐scale sparse representation; Parameter estimation; Reservoir geophysics; seismic facies; sparse representation

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