1887
Volume 71 Number 9
  • E-ISSN: 1365-2478

Abstract

Abstract

The high‐resolution model of elastic properties is of great significance for fine reservoir characterization and precise oil and gas exploration. However, it is difficult to obtain a satisfactory high‐resolution reservoir model with the existing technologies. In this paper, a novel high‐resolution stochastic modelling strategy based on the fast Fourier transform moving average is proposed. In this strategy, several structural parameters are optimized to improve the rationality of the stochastic model, including vertical autocorrelation length, horizontal autocorrelation length, roughness factor and angle parameter. Among them, the optimization of the vertical autocorrelation length is crucial for vertical high‐resolution modelling. To this end, a nonlinear optimal inversion strategy of the vertical autocorrelation length is designed based on the idea of minimizing the spectral Jensen–Shannon divergence between the modelling result and the logging curve. However, nonlinear inversion is usually unstable, so it is necessary to introduce a regularization operator in the inversion to improve the stability. Considering that the heterogeneity of the subsurface medium is consistent or gradual within the stratums, but discontinuous and abrupt at the interfaces, edge‐preserving regularization is applied to obtain a blocky estimation of the vertical autocorrelation length. The optimal estimation experiment of the vertical autocorrelation length based on the measured logging data shows that the edge‐preserving regularization significantly improves the stability of the nonlinear optimal inversion, and blocky estimation results with sharp edges are obtained. Then, the optimized vertical autocorrelation length and the other structural parameters are applied to fast Fourier transform moving average modelling on an actual reservoir profile. The result shows that the resolution of the model is significantly improved, which realizes the fine reservoir characterization. In addition, the optimized structural parameters effectively constrain the small‐scale heterogeneity and ensure the rationality of the stochastic model.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13408
2023-11-10
2025-03-21
Loading full text...

Full text loading...

References

  1. AlBinHassan, N.M., Luo, Y. & Al‐Faraj, M.N. (2006) 3D edge‐preserving smoothing and applications. Geophysics, 71(4), P5–P11.
    [Google Scholar]
  2. Ali, A., Alves, M.T., Saad, A.F., Ullah, M., Toqeer, M. & Hussain, M. (2018) Resource potential of gas reservoirs in south Pakistan and adjacent Indian subcontinent revealed by post‐stack inversion techniques. Journal of Natural Gas Science and Engineering, 49, 41–55.
    [Google Scholar]
  3. Armstrong, M. & Matheron, G. (1986) Disjunctive Kriging revisited: Part I. Mathematical Geology, 18(8), 711–728. https://doi.org/10.1007/BF00899739
    [Google Scholar]
  4. Chunduru, R., Sen, M. & Stoffa, P. (1997) Hybrid optimization methods for geophysical inversion. Geophysics, 62, 1196–1207. https://doi.org/10.1190/1.1444220
    [Google Scholar]
  5. Cordua, K.S., Hansen, T.M., Gulbrandsen, M.L., Barnes, C. & Mosegaard, K. (2016) Mixed‐point geostatistical simulation: a combination of two‐ and multiple‐point geostatistics. Geophysical Research Letters, 43(17), 9030–9037. https://doi.org/10.1002/2016GL070348
    [Google Scholar]
  6. Davy, R.G., Frahm, L., Bell, R., Arai, R., Barker, D.H.N., Henrys, S. et al. (2021) Generating high‐fidelity reflection images directly from full‐waveform inversion: Hikurangi Subduction Zone case study. Geophysical Research Letters, 48(19), e2021GL094981.
    [Google Scholar]
  7. Emery, X. & Peláez, M. (2011) Assessing the accuracy of sequential Gaussian simulation and cosimulation. Computational Geosciences, 15(4), 673–689. https://doi.org/10.1007/s10596‐011‐9235‐5
    [Google Scholar]
  8. Goff, J.A. & Jennings, J.W. (1999) Improvement of Fourier‐based unconditional and conditional simulations for band limited fractal (von Kármán) statistical models. Mathematical Geology, 31(6), 627–649.
    [Google Scholar]
  9. Greenhalgh, S.A., Bing, Z. & Green, A. (2006) Solutions, algorithms and inter‐relations for local minimization search geophysical inversion. Journal of Geophysics and Engineering, 3(2), 101–113. https://doi.org/10.1088/1742‐2132/3/2/001
    [Google Scholar]
  10. Gu, Y., Zhu, P., Li, H. & Li, X. (2014) Estimation of 2D stationary random medium parameters from post‐stack seismic data. Chinese Journal of Geophysics, 57(7), 2291–2301.
    [Google Scholar]
  11. Guardiano, F.B. & Srivastava, R.M. (1993) Multivariate geostatistics: beyond bivariate moments. In: Geostatistics Tróia '92, vol. 5. Dordrecht: Springer, pp. 133–144. https://doi.org/10.1007/978‐94‐011‐1739‐5_12
    [Google Scholar]
  12. Haldorsen, H.H. & Lake, L.W. (1984) A new approach to shale management in field‐scale models. Society of Petroleum Engineers Journal, 24(04), 447–457. https://doi.org/10.2118/10976‐PA
    [Google Scholar]
  13. Han, F., Zhang, H., Guo, Q., Shang, Z. & Li, T. (2019) A matching method for integrating multiscale components to model elastic parameters. Exploration Geophysics, 50(5), 532–540.
    [Google Scholar]
  14. Huiyuan, B., Wang, F., Zhang, C., Gao, X. & Li, D. (2019) A new model between dynamic and static elastic parameters of shale based on experimental studies. Arabian Journal of Geosciences, 12(19), 609.
    [Google Scholar]
  15. Ikelle, L.T., Yung, S.K. & Daube, F. (1993) 2‐D random media with ellipsoidal autocorrelation functions. Geophysics, 58(9), 1359–1372.
    [Google Scholar]
  16. Irving, J., Knight, R. & Holliger, K. (2009) Estimation of the lateral correlation structure of subsurface water content from surface‐based ground‐penetrating radar reflection images. Water Resources Research, 45(12), 193–204.
    [Google Scholar]
  17. Kyriakidis, P.C., Deutsch, C.V. & Grant, M.L. (1999) Calculation of the normal scores variogram used for truncated Gaussian lithofacies simulation: theory and FORTRAN code. Computers & Geosciences, 25(2), 161–169. https://doi.org/10.1016/S0098‐3004(98)00124‐1
    [Google Scholar]
  18. Masoomi, Z., Mesgari, M.S. & Menhaj, M.B. (2011) Modeling uncertainties in sodium spatial dispersion using a computational intelligence‐based Kriging method. Computers & Geosciences, 37(10), 1545–1554. https://doi.org/10.1016/j.cageo.2011.02.002
    [Google Scholar]
  19. Misra, S. & Sacchi, M.D. (2008) Global optimization with model‐space preconditioning: application to AVO inversion. Geophysics, 73(5), R71–R82.
    [Google Scholar]
  20. Okoye, P.N., Zhao, P. & Uren, N.F. (1996) Inversion technique for recovering the elastic constants of transversely isotropic materials. Geophysics, 61(5), 1247–1257.
    [Google Scholar]
  21. Oliver, M.A. & Webster, R. (2014) A tutorial guide to geostatistics: computing and modelling variograms and Kriging. CATENA, 113, 56–69. https://doi.org/10.1016/j.catena.2013.09.006
    [Google Scholar]
  22. Pang, X.‐Q., Jia, C.‐Z. & Wang, W.‐Y. (2015) Petroleum geology features and research developments of hydrocarbon accumulation in deep petroliferous basins. Petroleum Science, 12(1), 1–53. https://doi.org/10.1007/s12182‐015‐0014‐0
    [Google Scholar]
  23. Peredo, O.F., Baeza, D., Ortiz, J.M. & Herrero, J.R. (2018) A path‐level exact parallelization strategy for sequential simulation. Computers & Geosciences, 110, 10–22.
    [Google Scholar]
  24. Pyrcz, M.J., Boisvert, J.B. & Deutsch, C.V. (2008) A library of training images for fluvial and deepwater reservoirs and associated code. Computers & Geosciences, 34(5), 542–560. https://doi.org/10.1016/j.cageo.2007.05.015
    [Google Scholar]
  25. Ravalec, M.L., Noetinger, B. & Hu, L.Y. (2000) The FFT moving average (FFT‐MA) generator: an efficient numerical method for generating and conditioning Gaussian simulations. Mathematical Geology, 32(6), 701–723.
    [Google Scholar]
  26. Robertson, R.K., Mueller, U.A. & Bloom, L.M. (2006) Direct sequential simulation with histogram reproduction: a comparison of algorithms. Computers & Geosciences, 32(3), 382–395. https://doi.org/10.1016/j.cageo.2005.07.002
    [Google Scholar]
  27. Scholer, M., Irving, J. & Holliger, K. (2010) Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data. Geophysical Journal International, 183(3), 1408–1428.
    [Google Scholar]
  28. Soares, A. (2001) Direct sequential simulation and cosimulation. Mathematical Geology, 33(8), 911–926. https://doi.org/10.1023/A:1012246006212
    [Google Scholar]
  29. Tikhonov, A.N. & Arsenin, V.Y. (1977) Solutions of ill‐posed problems. Mathematics of Computation, 32(144), 491–491.
    [Google Scholar]
  30. Tsvankin, I., Gaiser, J., Grechka, V., Mirko, V. & Thomsen, L. (2010) Seismic anisotropy in exploration and reservoir characterization: an overview. Geophysics, 75(5), 75A15–75A29.
    [Google Scholar]
  31. Virieux, J. & Operto, S. (2009) An overview of full‐waveform inversion in exploration geophysics. Geophysics, 74(6), WCC1–WCC26.
    [Google Scholar]
  32. Williamson, P.R. & Worthington, M.H. (1993) Resolution limits in ray tomography due to wave behavior: numerical experiments. Geophysics, 58(5), 727–735.
    [Google Scholar]
  33. Xi, X. & Yao, Y. (2004) Wavefield characteristics in two‐dimensional elastic random media. Progress in Geophysics, 39(6), 147–154.
    [Google Scholar]
  34. Yang, X., Zhu, P., Mao, N., Xu, Z. & Xiao, D. (2018) Random medium modeling based on FFT‐MA. Chinese Journal of Geophysics, 61(12), 5007–5018.
    [Google Scholar]
  35. Yang, X., Mao, N., Zhu, P. (2022) Hybrid inversion of reservoir parameters based on cosimulation and the gradual deformation method. IEEE Transactions on Geoscience and Remote Sensing, 60, 5913211.
    [Google Scholar]
  36. Yamamoto, J.K. (2008) Estimation or simulation? That is the question. Computational Geosciences, 12(4), 573–591. https://doi.org/10.1007/s10596‐008‐9096‐8
    [Google Scholar]
  37. Yin, X., Sun, R., Wang, B. & Zhang, G. (2014) Simultaneous inversion of petrophysical parameters based on geostatistical a priori information. Applied Geophysics, 11(3), 311–320.
    [Google Scholar]
  38. Zhang, H., Guo, Q., Liang, L., Cao, C. & Shang, Z. (2017) A nonlinear method for multiparameter inversion of pre‐stack seismic data based on anisotropic Markov random field. Geophysical Prospecting, 66(3), 461–477.
    [Google Scholar]
  39. Zhang, H., Shang, Z. & Yang, C. (2007) A non‐linear regularized constrained impedance inversion. Geophysical Prospecting, 55(6), 819–833.
    [Google Scholar]
  40. Zou, C., Yang, Z., Zhu, R., Zhang, G., Hou, L., Wu, S. et al. (2015) Progress in China's unconventional oil & gas exploration and development and theoretical technologies. Acta Geologica Sinica – English Edition, 89(3), 938–971.
    [Google Scholar]
/content/journals/10.1111/1365-2478.13408
Loading
/content/journals/10.1111/1365-2478.13408
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): elastics; inverse problem; modeling; parameter estimation

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