Skip to main content

Advertisement

SpringerLink
Log in

Generalized Mathematical Morphological Method for 3D Shape Analysis of Geological Boundaries: Application in Identifying Mineralization-Associated Shape Features

  • Published:
Natural Resources Research Aims and scope Submit manuscript

Abstract

The shapes of geological boundaries such as contacts and faults play a crucial role in the transportation, deposition and preservation of metals in magmatic and hydrothermal systems. Analyzing the shapes of geological boundaries, in particular those associated with mineralization, is an important step in 3D mineral prospectivity modeling. However, existing methods of shape analysis are limited in the adaptation of various shapes, scales and topologies of geological boundaries. This paper presents a general method of shape analysis based on mathematical morphology (MM), which is a generalization of the original MM method for shape analysis. The generalization extends the applicability of the original MM method from closed surfaces to general surfaces, while inheriting the real 3D and multi-scale analysis capabilities of the original method. This is achieved by regarding MM operations on 3D sphere structural elements as their equivalent operations, and redefining the operations to general surfaces. The generalized MM method enables us to handle complex 3D shapes such as overturned and/or recumbent geological boundaries as well as incomplete shapes due to weathering processes and data unavailability. The proposed method was applied to analyze the shape of an intrusive contact in the Fenghuangshan Cu ore field, Eastern China, whose shape was in the form of a non-closed surface. This analysis revealed a stronger spatial association between the large concave parts of the contact zone and the mineralization. Due to its enhanced adaptability to different shapes, the generalized MM method, compared with the original MM method, allows us to capture shape features that are more plausible for the geological setting.

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19

Similar content being viewed by others

References

  • Arya, S., & Mount, D. M. (1998). ANN: library for approximate nearest neighbor searching. In Proceedings of IEEE CGC Workshop on Computational Geometry, Providence, RI.

  • Bonham-Carter, G. F. (1994). Geographic information systems for geoscientists: Modelling with GIS (No. 13). Elsevier.

  • Bonham-Carter, G. F., Agterberg, F. P., & Wright D.F. (1989). Weights of evidence modeling: A new approach to mapping mineral potential. Statistical applications in the earth sciences, pp. 171–183.

  • Bonham-Carter, G. F., Agterberg, F. P., & Wright, D. F. (1988). Integration of geological datasets for gold exploration in Nova Scotia. Photogrammetric Engineering and Remote Sensing, 54(11), 1585–1592.

    Google Scholar 

  • Cao, W., Liu, L., Liu, H., & Lai, F. (2020). Investigating the Irregular Localization of Skarn Orebodies by Computational Modeling in the Fenghuangshan Ore field, Tongling District, Anhui Province, China. Natural Resources Research, pp. 1–22.

  • Carranza, E. J. M. (2004). Weights of evidence modeling of mineral potential: A case study using small number of prospects, Abra, Philippines. Natural Resources Research, 13(3), 173–187.

    Article  Google Scholar 

  • Carranza, E. J. M. (2011). Geocomputation of mineral exploration targets. Computers and Geosciences, 37(12), 1907–1916.

    Article  Google Scholar 

  • Carranza, E. J. M., & Hale, M. (2002). Spatial association of mineral occurrences and curvilinear geological features. Mathematical Geology, 34(2), 203–221.

    Article  Google Scholar 

  • Chi, G., & Savard, M. M. (1998). Basinal fluid flow models related to Zn-Pb mineralization in the southern margin of the Maritimes Basin, eastern Canada. Economic Geology, 93(6), 896–910.

    Article  Google Scholar 

  • Dunham, R. E., & Crider, J. G. (2012). Geometric curvature analysis of intersecting kink bands: A new perspective on the 3D geometry of kink folds. Journal of Structural Geology, 37, 236–247.

    Article  Google Scholar 

  • Fallara, F., Legault, M., & Rabeau, O. (2006). 3-D integrated geological modeling in the Abitibi Subprovince (Québec, Canada): Techniques and applications. Exploration and Mining Geology, 15(1–2), 27–43.

    Article  Google Scholar 

  • Grohmann, C. H. (2005). Trend-surface analysis of morphometric parameters: A case study in southeastern Brazil. Computers & Geosciences, 31(8), 1007–1014.

    Article  Google Scholar 

  • Groves, D. I., Santosh, M., Goldfarb, R. J., & Zhang, L. (2018). Structural geometry of orogenic gold deposits: Implications for exploration of world-class and giant deposits. Geoscience Frontiers, 9(4), 1163–1177.

    Article  Google Scholar 

  • Hagemann, S. G., Groves, D. I., Ridley, J. R., & Vearncombe, J. R. (1992). The Archean lode gold deposits at Wiluna, Western Australia; high-level brittle-style mineralization in a strike-slip regime. Economic Geology, 87(4), 1022–1053.

    Article  Google Scholar 

  • Harris, J. F., Taylor, G. L., & Walper, J. L. (1960). Relation of deformational fractures in sedimentary rocks to regional and local structure. AAPG Bulletin, 44(12), 1853–1873.

    Google Scholar 

  • Hengl, T., & Reuter, H. I. (Eds.). (2008). Geomorphometry: concepts, software, applications. Newnes.

  • Hobbs, B. E., Zhang, Y., Ord, A., & Zhao, C. (2000). Application of coupled deformation, fluid flow, thermal and chemical modelling to predictive mineral exploration. Journal of Geochemical Exploration, 69, 505–509.

    Article  Google Scholar 

  • Hronsky, J. M. (2020). Deposit-scale structural controls on orogenic gold deposits: An integrated, physical process–based hypothesis and practical targeting implications. Mineralium Deposita, 55(2), 197–216.

    Article  Google Scholar 

  • Hu, X., Yuan, F., Li, X., Jowitt, S. M., Jia, C., Zhang, M., & Zhou, T. (2018). 3D characteristic analysis-based targeting of concealed Kiruna-type Fe oxide-apatite mineralization within the Yangzhuang deposit of the Zhonggu orefield, southern Ningwu volcanic basin, middle-lower Yangtze River metallogenic Belt, China. Ore Geology Reviews, 92, 240–256.

    Article  Google Scholar 

  • Hu, X., Li, X., Yuan, F., Jowitt, S. M., Ord, A., Ye, R., Li, Y., Dai, W., & Li, X. (2020). 3D Numerical Simulation-Based Targeting of Skarn Type Mineralization within the Xuancheng-Magushan Orefield, Middle-Lower Yangtze Metallogenic Belt, China. Lithosphere, 2020(1), 8351536.

    Article  Google Scholar 

  • Jacques, D., Vieira, R., Muchez, P., & Sintubin, M. (2018). Transpressional folding and associated cross-fold jointing controlling the geometry of post-orogenic vein-type W-Sn mineralization: Examples from Minas da Panasqueira, Portugal. Mineralium Deposita, 53(2), 171–194.

    Article  Google Scholar 

  • Kitt, S., Kisters, A., Vennemann, T., & Steven, N. (2018). Orebody geometry, fluid and metal sources of the Omitiomire Cu deposit in the Ekuja Dome of the Damara Belt in Namibia. Mineralium Deposita, 53(2), 261–276.

    Article  Google Scholar 

  • Lai, J., Chi, G., Peng, S., Shao, Y., & Yang, B. (2007). Fluid evolution in the formation of the fenghuangshan Cu-Fe-Au deposit, Tongling, Anhui, China. Economic Geology, 102(5), 949–970.

    Article  Google Scholar 

  • Leader, L. D., Wilson, C. J., & Robinson, J. A. (2013). Structural constraints and numerical simulation of strain localization in the Bendigo Goldfield, Victoria, Australia. Economic Geology, 108(2), 279–307.

    Article  Google Scholar 

  • Li, X., Yuan, F., Zhang, M., Jia, C., Jowitt, S. M., Ord, A., Zheng, T., Hu, X., & Li, Y. (2015). Three-dimensional mineral prospectivity modeling for targeting of concealed mineralization within the Zhonggu iron orefield, Ningwu Basin, China. Ore Geology Reviews, 71, 633–654.

    Article  Google Scholar 

  • Li, X., Yuan, F., Zhang, M., Jowitt, S. M., Ord, A., Zhou, T., & Dai, W. (2019). 3D computational simulation-based mineral prospectivity modeling for exploration for concealed Fe–Cu skarn-type mineralization within the Yueshan orefield, Anqing district, Anhui Province, China. Ore Geology Reviews, 105, 1–17.

    Article  Google Scholar 

  • Lisle, R. J. (1994). Detection of zones of abnormal strains in structures using Gaussian curvature analysis. AAPG Bulletin, 78(12), 1811–1819.

    Google Scholar 

  • Liu, L., Li, J., Zhou, R., & Sun, T. (2016). 3D modeling of the porphyry-related Dawangding gold deposit in south China: Implications for ore genesis and resources evaluation. Journal of Geochemical Exploration, 164, 164–185.

    Article  Google Scholar 

  • Liu, L., & Peng, S. L. (2003). Prediction of hidden ore bodies by synthesis of geological, geophysical and geochemical information based on dynamic model in Fenghuangshan ore field, Tongling district, China. Journal of Geochemical Exploration, 81(1–3), 81–98.

    Google Scholar 

  • Liu, L., Wan, C., Zhao, C., & Zhao, Y. (2011). Geodynamic constraints on orebody localization in the Anqing orefield, China: Computational modeling and facilitating predictive exploration of deep deposits. Ore Geology Reviews, 43(1), 249–263.

    Article  Google Scholar 

  • Liu, L., Zhao, Y., & Sun, T. (2012). 3D computational shape-and cooling process-modeling of magmatic intrusion and its implication for genesis and exploration of intrusion-related ore deposits: An example from the Yueshan intrusion in Anqing, China. Tectonophysics, 526, 110–123.

    Article  Google Scholar 

  • Liu, L., Zhao, Y., & Zhao, C. (2010). Coupled geodynamics in the formation of Cu skarn deposits in the Tongling-Anqing district, China: Computational modeling and implications for exploration. Journal of Geochemical Exploration, 106(1–3), 146–155.

    Article  Google Scholar 

  • Lu, Y., Liu, L., & Xu, G. (2016). Constraints of deep crustal structures on large deposits in the Cloncurry district, Australia: Evidence from spatial analysis. Ore Geology Reviews, 79, 316–331.

    Article  Google Scholar 

  • Mallet, J. L. (1989). Discrete smooth interpolation. ACM Transactions on Graphics (TOG), 8(2), 121–144.

    Article  Google Scholar 

  • Mallet, J. L. (1992). GOCAD: A computer aided design program for geological applications. Three-dimensional modeling with geoscientific information systems (pp. 123–141). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Mao, X., & Chen, G. (1991). Three-dimensional mathematical models of Xianghualing Tin deposit and prognosis of blind ore bodies occurring in margins and depths. Journal of Central-South Institute of Mining and Metallurgy, 22(4), 351–360.

    Google Scholar 

  • Mao, X., Ren, J., Liu, Z., Chen, J., Tang, L., Deng, H., & Liu, C. (2019). Three-dimensional prospectivity modeling of the Jiaojia-type gold deposit, Jiaodong Peninsula, Eastern China: A case study of the Dayingezhuang deposit. Journal of Geochemical Exploration, 203, 27–44.

    Article  Google Scholar 

  • Mao, X., Zhang, B., Deng, H., Zou, Y., & Chen, J. (2016). Three-dimensional morphological analysis method for geological bodies and its parallel implementation. Computers and Geosciences, 96, 11–22.

    Article  Google Scholar 

  • Mao, X., Zhao, Y., Deng, H., Zhang, B., Liu, Z. K., & Chen, J. (2018). Quantitative analysis of intrusive body morphology and its relationship with skarn mineralization—A case study of Fenghuangshan copper deposit, Tongling, Anhui, China. Transactions of Nonferrous Metals Society of China, 28(1), 151–162.

    Article  Google Scholar 

  • Matheron, G. F. P. M. (1975). Random sets and integral geometry. Wiley.

    Google Scholar 

  • Mejía-Herrera, P., Royer, J. J., Caumon, G., & Cheilletz, A. (2015). Curvature attribute from surface-restoration as predictor variable in Kupferschiefer copper potentials. Natural Resources Research, 24(3), 275–290.

    Article  Google Scholar 

  • Ord, A., Hobbs, B. E., Zhang, Y., Broadbent, G. C., Brown, M., Willetts, G., & Zhao, C. (2002). Geodynamic modelling of the century deposit, Mt Isa Province, Queensland. Australian Journal of Earth Sciences, 49(6), 1011–1039.

    Article  Google Scholar 

  • Pan, Y., & Dong, P. (1999). The Lower Changjiang (Yangzi/Yangtze River) metallogenic belt, east central China: Intrusion-and wall rock-hosted Cu–Fe–Au, Mo, Zn, Pb, Ag Deposits. Ore Geology Reviews, 15(4), 177–242.

    Article  Google Scholar 

  • Payne, C. E., Cunningham, F., Peters, K. J., Nielsen, S., Puccioni, E., Wildman, C., & Partington, G. A. (2015). From 2D to 3D: Prospectivity modelling in the Taupo volcanic zone, New Zealand. Ore Geology Reviews, 71, 558–577.

    Article  Google Scholar 

  • Pearce, M. A., Jones, R. R., Smith, S. A., McCaffrey, K. J., & Clegg, P. (2006). Numerical analysis of fold curvature using data acquired by high-precision GPS. Journal of Structural Geology, 28(9), 1640–1646.

    Article  Google Scholar 

  • Pike, R. J. (2000). Geomorphometry-diversity in quantitative surface analysis. Progress in Physical Geography, 24(1), 1–20.

    Google Scholar 

  • Pirajno, F. (2012). The geology and tectonic settings of China’s mineral deposits. Berlin: Springer Science and Business Media.

    Google Scholar 

  • Porwal, A., & Carranza, E. J. M. (2015). Introduction to the Special Issue: GIS-based mineral potential modelling and geological data analyses for mineral exploration. Ore Geology Reviews, 71, 477–483.

    Article  Google Scholar 

  • Porwal, A., Gonzalez-Alvarez, I., Markwitz, V., McCuaig, T. C., & Mamuse, A. (2010). Weights-of-evidence and logistic regression modeling of magmatic nickel sulfide prospectivity in the Yilgarn Craton, Western Australia. Ore Geology Reviews, 38(3), 184–196.

    Article  Google Scholar 

  • Qin, Y., & Liu, L. (2018). Quantitative 3D association of geological factors and geophysical fields with mineralization and its significance for ore prediction: An example from Anqing orefield China. Minerals, 8(7), 300.

    Article  Google Scholar 

  • Robb, L. (2020). Introduction to ore-forming processes. John Wiley and Sons.

    Google Scholar 

  • Sams, M. S., & Thomas-Betts, A. (1988). Models of convective fluid flow and mineralization in south-west England. Journal of the Geological Society, 145(5), 809–817.

    Article  Google Scholar 

  • Serra, J. (1986). Introduction to mathematical morphology. Computer Vision, Graphics, and Image Processing, 35(3), 283–305.

    Article  Google Scholar 

  • Song, M. C., Li, S. Z., Santosh, M., Zhao, S., Yu, S., Yi, P. H., & Zhou, M. L. (2015). Types, characteristics and metallogenesis of gold deposits in the Jiaodong Peninsula, Eastern North China Craton. Ore Geology Reviews, 65, 612–625.

    Article  Google Scholar 

  • Sörensen, R., Zinko, U., & Seibert, J. (2006). On the calculation of the topographic wetness index: Evaluation of different methods based on field observations. Hydrology and Earth System Sciences, 10(1), 101–112.

    Article  Google Scholar 

  • Sorjonen-Ward, P., Zhang, Y., & Zhao, C. (2002). Numerical modelling of orogenic processes and gold mineralisation in the southeastern part of the Yilgarn Craton, Western Australia. Australian Journal of Earth Sciences, 49(6), 935–964.

    Article  Google Scholar 

  • Sprague, K., de Kemp, E., Wong, W., McGaughey, J., Perron, G., & Barrie, T. (2006). Spatial targeting using queries in a 3-D GIS environment with application to mineral exploration. Computers and Geosciences, 32(3), 396–418.

    Article  Google Scholar 

  • Squire, R. J., Robinson, J. A., Rawling, T. J., & Wilson, C. J. (2008). Controls on ore shoot locations and geometries at the Stawell Gold Mine, Southeastern Australia: Contributions of the volcanosedimentary, alteration, and structural architecture. Economic Geology, 103(5), 1029–1041.

    Article  Google Scholar 

  • Teagle, D. A., Norris, R. J., & Craw, D. (1990). Structural controls on gold-bearing quartz mineralization in a duplex thrust system, Hyde-Macraes Shear Zone, Otago Schist, New Zealand. Economic Geology, 85(8), 1711–1719.

    Article  Google Scholar 

  • Wang, G., Zhang, S., Yan, C., Song, Y., Sun, Y., Li, D., & Xu, F. (2011). Mineral potential targeting and resource assessment based on 3D geological modeling in Luanchuan region, China. Computers and Geosciences, 37(12), 1976–1988.

    Article  Google Scholar 

  • Wilson, C. J., Osborne, D. J., Robinson, J. A., & Miller, J. M. (2016). Structural constraints and localization of gold mineralization in Leather Jacket Lodes, Ballarat, Victoria, Australia. Economic Geology, 111(5), 1073–1098.

    Article  Google Scholar 

  • Wilson, J. P., & Gallant, J. C. (2000). Digital terrain analysis. Terrain Analysis: Principles and Applications, 6(12), 1–27.

    Google Scholar 

  • Xiao, K., Li, N., Porwal, A., Holden, E. J., Bagas, L., & Lu, Y. (2015). GIS-based 3D prospectivity mapping: A case study of Jiama copper-polymetallic deposit in Tibet, China. Ore Geology Reviews, 71, 611–632.

    Article  Google Scholar 

  • Yang, L., Zhao, R., Wang, Q., Liu, X., & Carranza, E. J. M. (2018). Fault geometry and fluid-rock reaction: Combined controls on mineralization in the Xinli gold deposit, Jiaodong Peninsula, China. Journal of Structural Geology, 111, 14–26.

    Article  Google Scholar 

  • Yuan, F., Li, X., Zhang, M., Jowitt, S. M., Jia, C., Zheng, T., & Zhou, T. (2014). Three-dimensional weights of evidence-based prospectivity modeling: A case study of the Baixiangshan mining area, Ningwu Basin, Middle and Lower Yangtze Metallogenic Belt, China. Journal of Geochemical Exploration, 145, 82–97.

    Article  Google Scholar 

  • Zhang, M., Zhou, G., Shen, L., Zhao, W., Liao, B., Yuan, F., Li, X., Hu, X., & Wang, C. (2019). Comparison of 3D prospectivity modeling methods for Fe-Cu skarn deposits: A case study of the Zhuchong Fe-Cu deposit in the Yueshan orefield (Anhui), eastern China. Ore Geology Reviews, 114, 103126.

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank the editors and anonymous reviewers for their constructive comments. We are also grateful to Dr. Jeffrey Dick who helped us to improve the manuscript. This research was funded by the National Natural Science Foundation of China (Nos. 42030809, 72088101, 41972309, 41772349, and 42072325) and the National Key RandD Program of China (Nos. 2017YFC0601503 and 2019YFC1805905).

Author information

Authors and Affiliations

  1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Ministry of Education), School of Geosciences and Info-Physics, Central South University, Changsha, 410083, China

    Hao Deng, Xiaofu Huang, Xiancheng Mao, Shuyan Yu, Jin Chen, Zhankun Liu & Yanhong Zou

Authors
  1. Hao Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaofu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiancheng Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuyan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhankun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yanhong Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiancheng Mao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, H., Huang, X., Mao, X. et al. Generalized Mathematical Morphological Method for 3D Shape Analysis of Geological Boundaries: Application in Identifying Mineralization-Associated Shape Features. Nat Resour Res 31, 2103–2127 (2022). https://doi.org/10.1007/s11053-021-09975-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-021-09975-6

Keywords

Search

Navigation