Skip to main content
SpringerLink
Log in

Geometric Element Preserving Reconstruction of a Geological Surface

  • Research Article-Earth Sciences
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

A reconstruction of geological surfaces clearly displays the shape and three-dimensional (3D) spatial distribution of the geological surfaces, such as horizons and faults. It is the basis for understanding the geological structure and establishing reservoir models. Because of deficiencies in the acquisition, conversion, and interpretation, the obtained data inevitably contain a certain degree of noise and some outliers, which usually lead to the blurring or even the extinction of the original surface geometry elements (such as ridges, valleys, and fold hubs) that determine the shape of the geological surface; thus, the accuracy of geometric elements of the reconstructed geological surface is not high. Therefore, the extraction and preservation of geometric elements is one of the key factors in geological surface reconstruction, which is of great significance to reducing the risks associated with hydrocarbon exploration and development caused by structural uncertainty. In this paper, we propose a geometric element preserving reconstruction framework for the geological surfaces of two important elements: ridges and valleys. First, we use the classification algorithm to identify the candidate ridge and valley points within the seismic interpretation data, and then, we generate ridge and valley curves according to the support vector regression. Finally, we construct a geological surface reconstruction model using the geometric element curves as constraints. Our framework can be easily extended to various 3D surface reconstructions with other geometric elements. The experimental results obtained using a real data set show that the proposed framework effectively preserves the geomorphological features of the reconstructed surface.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Guo, J.; Lixin, W.; Zhou, W.; Jiang, J.; Li, C.: Towards automatic and topologically consistent 3d regional geological modeling from boundaries and attitudes. ISPRS Int. J. Geo-Inf. 5(2), 17 (2016)

    Article  Google Scholar 

  2. Hillier, M.J.; Schetselaar, E.M.; de Kemp, E.A.; Perron, G.: Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions. Math. Geosci. 46(8), 931–953 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wellmann, J.F.; Varga, M.D.L.; Murdie, R.E.; Gessner, K.; Jessell, M.: Uncertainty estimation for a geological model of the sandstone greenstone belt, western australia–insights from integrated geological and geophysical inversion in a Bayesian inference framework. Geological Society, London, Special Publications, 453(1):41–56 (2018)

  4. Matheron, G.: Principles of geostatistics. Econ. Geol. 58(8), 1246–1266 (1963)

    Article  Google Scholar 

  5. Eyers, J.: Interactive modelling of geological data with uniras. Terra Nova 2(2), 176–181 (1990)

    Article  Google Scholar 

  6. Lajaunie, C.; Courrioux, G.; Manuel, L.: Foliation fields and 3d cartography in geology: principles of a method based on potential interpolation. Math. Geol. 29(4), 571–584 (1997)

    Article  Google Scholar 

  7. Liu, Y.; Chen, Z.; BaoDan, H.; Jin, J.K.; Zhao, W.: A non-uniform spatiotemporal kriging interpolation algorithm for landslide displacement data. Bull. Eng. Geol. Environ. 78(6), 4153–4166 (2019)

    Article  Google Scholar 

  8. Jia, Q.; Li, W.; Che, D.: A triangulated irregular network constrained ordinary kriging method for three-dimensional modeling of faulted geological surfaces. IEEE Access 8, 85179–85189 (2020)

    Article  Google Scholar 

  9. Mallet, J.-L.: Discrete smooth interpolation in geometric modelling. Comput. Aided Des. 24(4), 178–191 (1992)

    Article  MATH  Google Scholar 

  10. Qing-niu, W.; Zu-qiang, X.; Hua-min, L.: Research on application of dsi in fitting geological curved surface. In: 2009 International Conference on Computational Intelligence and Software Engineering (2009)

  11. Mei, G.: Summary on several key techniques in 3d geological modeling. Sci. World J. 1–11, 2014 (2014)

    Google Scholar 

  12. Caumon, G.; Collon-Drouaillet, P.L.C.D.; De Veslud, C.L.; Viseur, S.; Sausse, J.: Surface-based 3d modeling of geological structures. Math. Geosci. 41(8), 927–945 (2009)

    Article  MATH  Google Scholar 

  13. Li, J.; Meng, X.; Li, Y.; Yang, Q.: A efficient and robust method for complexly faulted horizon reconstruction based on meshes cutting and interpolating. In: 2012 IEEE International Conference on Computer Science and Automation Engineering (CSAE), volume 3, pp. 396–400. IEEE (2012)

  14. Zehner, B.; Börner, J.H.; Görz, I.; Spitzer, K.: Workflows for generating tetrahedral meshes for finite element simulations on complex geological structures. Comput. Geosci. 79, 105–117 (2015)

    Article  Google Scholar 

  15. Li, B.; Liu, H.; Li, Y.-M.: 3-d seismic data discrete smooth interpolation using the conjugate gradient method. Chin. J. Geophys. 45(5), 730–739 (2002)

    Article  Google Scholar 

  16. Wellmann, F.; Caumon, G.: 3-d structural geological models: Concepts, methods, and uncertainties. In: Advances in Geophysics, volume 59, pp. 1–121. Elsevier (2018)

  17. de la Varga, M.; Schaaf, A.; Wellmann, F.: Gempy 1.0: open-source stochastic geological modeling and inversion. Geoscientific Model Development (2019)

  18. Renaudeau, J.; Malvesin, E.; Maerten, F.; Caumon, G.: Implicit structural modeling by minimization of the bending energy with moving least squares functions. Math. Geosci. 51(6), 693–724 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. Frank, T.; Tertois, A.-L.; Mallet, J.-L.: 3d-reconstruction of complex geological interfaces from irregularly distributed and noisy point data. Comput. Geosci. 33(7), 932–943 (2007)

    Article  Google Scholar 

  20. Collon, P.; Steckiewicz-Laurent, W.; Pellerin, J.; Laurent, G.; Caumon, G.; Reichart, G.; Vaute, L.: 3d geomodelling combining implicit surfaces and Voronoi-based remeshing: a case study in the Lorraine Coal Basin (France). Comput. Geosci. 77, 29–43 (2015)

    Article  Google Scholar 

  21. Laurent, G.; Ailleres, L.; Grose, L.; Caumon, G.; Jessell, M.; Armit, R.: Implicit modeling of folds and overprinting deformation. Earth Planet. Sci. Lett. 456, 26–38 (2016)

    Article  Google Scholar 

  22. Laurent, G.: Iterative thickness regularization of stratigraphic layers in discrete implicit modeling. Math. Geosci. 48(7), 811–833 (2016)

    Article  MathSciNet  Google Scholar 

  23. Carr, J.C.; Beatson, R.K.; Cherrie, J.B.; Mitchell, T.J.; Fright, W.R.; McCallum, B.C.; Evans, T.R.: Reconstruction and representation of 3d objects with radial basis functions. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, pp. 67–76 (2001)

  24. Morse, B.S.; Yoo, T.S.; Rheingans, P.; Chen, D.T.; Subramanian, K.R.: Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In: ACM SIGGRAPH 2005 Courses, pp. 78–87 (2005)

  25. Jia, Q.; Che, D.; Li, W.: Effective coal seam surface modeling with an improved anisotropy-based, multiscale interpolation method. Comput. Geosci. 124, 72–84 (2019)

    Article  Google Scholar 

  26. Zhong, D.; Wang, L.; Lin, B.I.; Jia, M.: Implicit modeling of complex orebody with constraints of geological rules. Trans. Nonferrous Met. Soc. China 29(11), 2392–2399 (2019)

    Article  Google Scholar 

  27. Martin, R.; Boisvert, J.B.: Iterative refinement of implicit boundary models for improved geological feature reproduction. Comput. Geosci. 109, 1–15 (2017)

    Article  Google Scholar 

  28. Qiang, W.; Hua, X.; Zou, X.: An effective method for 3d geological modeling with multi-source data integration. Comput. Geosci. 31(1), 35–43 (2005)

    Article  Google Scholar 

  29. Wellmann, J.F.; Horowitz, F.G.; Schill, E.; Regenauer-Lieb, K.: Towards incorporating uncertainty of structural data in 3d geological inversion. Tectonophysics 490(3–4), 141–151 (2010)

    Article  Google Scholar 

  30. Qiang, W.; Hua, X.; Zou, X.; Lei, H.: A 3d modeling approach to complex faults with multi-source data. Comput. Geosci. 77, 126–137 (2015)

    Article  Google Scholar 

  31. Liedtke Tesar, M.L.: A Comparison of Spatial Prediction Techniques Using Both Hard and Soft Data. PhD thesis, University of Nebraska (2011)

  32. Che, D.; Jia, Q.: Three-dimensional geological modeling of coal seams using weighted kriging method and multi-source data. IEEE Access 7, 118037–118045 (2019)

    Article  Google Scholar 

  33. Shi-Cheng, Yu; Cai, L.; Guang-Min, H.: Reconstruction of geological surfaces using chance-constrained programming. Appl. Geophys. 16(1), 125–136 (2019)

    Article  Google Scholar 

  34. Liu, Z., Cao, W., Gao, Z., Bian, J., Chen, H., Chang, Y., Liu, T.-Y.: Self-paced ensemble for highly imbalanced massive data classification. In: 2020 IEEE 36th International Conference on Data Engineering (ICDE), pp. 841–852. IEEE (2020)

  35. Drucker, H.; Burges, C.J.; Kaufman, L.; Smola, A.; Vapnik, V.: Support vector regression machines. Adv. Neural Inf. Process. Syst. 9, 155–161 (1996)

    Google Scholar 

  36. Gunn, S.R.; et al.: Support vector machines for classification and regression. ISIS Tech. Rep. 14(1), 5–16 (1998)

    Google Scholar 

  37. Smola, A.J.; Schölkopf, B.: A tutorial on support vector regression. Stat. Comput. 14(3), 199–222 (2004)

    Article  MathSciNet  Google Scholar 

  38. Liu, H.; Dai, N.; Zhong, B.; Li, T.; Wang, J.: Extract feature curves on noisy triangular meshes. Graph. Models 93, 1–13 (2017)

    Article  MathSciNet  Google Scholar 

  39. Wang, Y.; Zhang, H.; Ning, X.; Hao, W.; Shi, Z.; Zhao, M.; Zhou, H.; Sui, L.; Lv, K.: Ridge-valley-guided sketch-drawing from point clouds. IEEE Access 6, 13697–13705 (2018)

    Article  Google Scholar 

  40. Digne, J.; Cohen-Steiner, D.; Alliez, P.; De Goes, F.; Desbrun, M.: Feature-preserving surface reconstruction and simplification from defect-laden point sets. J. Math. Imaging Vis. 48(2), 369–382 (2014)

    Article  MathSciNet  Google Scholar 

  41. Harary, G.; Tal, A.; Grinspun, E.: Feature-preserving surface completion using four points. In: Computer Graphics Forum, volume 33, pp. 45–54. Wiley Online Library (2014)

  42. Behrens, T.; Zhu, A.-X.; Schmidt, K.; Scholten, T.: Multi-scale digital terrain analysis and feature selection for digital soil mapping. Geoderma 155(3–4), 175–185 (2010)

    Article  Google Scholar 

  43. Kane, W.F.; Peters, D.C.; Speirer, R.A.: Remote sensing in investigation of engineered underground structures. J. Geotech. Eng. 122(8), 674–681 (1996)

    Article  Google Scholar 

  44. Filippis, L.D.; Anzalone, E.; Billi, A.; Faccenna, C.; Poncia, P.P.; Sella, P.: The origin and growth of a recently-active fissure ridge travertine over a seismic fault, Tivoli, Italy. Geomorphology 195, 13–26 (2013)

    Article  Google Scholar 

  45. Kim, S.K.: Extraction of ridge and valley lines from unorganized points. Multimed. Tools Appl. 63(1), 265–279 (2013)

    Article  Google Scholar 

  46. Lindeberg, T.: Edge detection and ridge detection with automatic scale selection. In: Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 465–470. IEEE (1996)

  47. Koka, S.; Anada, K.; Nomaki, K.; Sugita, K.; Tsuchida, K.; Yaku, T.: Ridge detection with the steepest ascent method. Proc. Comput. Sci. 4, 216–221 (2011)

    Article  Google Scholar 

  48. Lin, Y.; Wang, C.; Cheng, J.; Chen, B.; Jia, F.; Chen, Z.; Li, J.: Line segment extraction for large scale unorganized point clouds. ISPRS J. Photogram. Remote Sens. 102, 172–183 (2015)

    Article  Google Scholar 

  49. Daniels, J. II; Ha, L.K.; Ochotta, T.; Silva, C.T.: Robust smooth feature extraction from point clouds. In: IEEE International Conference on Shape Modeling and Applications 2007 (SMI’07), pP. 123–136. IEEE (2007)

  50. Galil, Z.; Italiano, G.F.: Data structures and algorithms for disjoint set union problems. ACM Comput. Surv. CSUR 23(3), 319–344 (1991)

    Article  Google Scholar 

  51. Pan, D.-Z.; Liu, Z.-B.; Ding, X.-F.; Zheng, Q.: The application of union-find sets in Kruskal algorithm. In: 2009 International Conference on Artificial Intelligence and Computational Intelligence, volume 2, pp. 159–162. IEEE (2009)

  52. Qiang, W.; Hua, X.: An approach to computer modeling and visualization of geological faults in 3d. Comput. Geosci. 29(4), 503–509 (2003)

    Article  Google Scholar 

  53. Schuman, W.: Microstructures, deformation mechanisms and strain patterns in a vertical profile, inner Appalachian fold-thrust belt, Alabama. J. Struct. Geol. 15(2), 129–144 (1993)

    Article  Google Scholar 

  54. Mitra, S.: Fold-accommodation faults. AAPG Bull. 86(4), 671–693 (2002)

    Google Scholar 

  55. Ustaszewski, M.E.; Pfiffner, O.A.; et al.: Composite faults in the swiss alps formed by the interplay of tectonics, gravitation and postglacial rebound: an integrated field and modelling study. Swiss J. Geosci. 101(1), 223–235 (2008)

    Article  Google Scholar 

  56. Aki, K.: Seismic displacements near a fault. J. Geophys. Res. 73(16), 5359–5376 (1968)

    Article  Google Scholar 

  57. Zhu, L.-F.; Zheng, H.; Xin, P.; Wu, X.-C.: An approach to computer modeling of geological faults in 3d and an application. J. China Univ. Min. Technol. 16(4), 461–465 (2006)

    Article  Google Scholar 

  58. Yu, S.-C.; Chen, T.; Hu, G.-M.: Confidence-constrained support vector regression for geological surface uncertainty modeling. IEEE Access (2020)

Download references

Acknowledgements

The authors thank the anonymous reviewers for their helpful comments and Hanpeng Cai, Kunhong Li and Chengyun Song for their discussion with the authors and their inspiration for this study. We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript. This research is supported by grants from the National Natural Science Foundation of China (No. 41974147 & 41874155).

Author information

Authors and Affiliations

  1. School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    ShiCheng Yu, Cai Lu & GuangMin Hu

  2. The Engineering and Technical College of Chengdu University of Technology, Leshan, 614000, China

    ShiCheng Yu

  3. Center for Information Geoscience, University of Electronic Science and Technology of China, Chengdu, 611731, China

    ShiCheng Yu, Cai Lu & GuangMin Hu

Authors
  1. ShiCheng Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cai Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. GuangMin Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to GuangMin Hu.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, S., Lu, C. & Hu, G. Geometric Element Preserving Reconstruction of a Geological Surface. Arab J Sci Eng 47, 577–589 (2022). https://doi.org/10.1007/s13369-021-05536-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05536-4

Keywords

Search

Navigation