{"id":4794,"date":"2026-05-02T16:42:55","date_gmt":"2026-05-02T08:42:55","guid":{"rendered":"\/jase\/?post_type=tkuisotope&p=4794"},"modified":"2026-06-28T23:34:17","modified_gmt":"2026-06-28T15:34:17","slug":"a-calculation-method-for-mineral-reserves-based-on-multi-point-geostatistics","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=a-calculation-method-for-mineral-reserves-based-on-multi-point-geostatistics","title":{"rendered":"A Calculation Method for Mineral Reserves based on Multi-point Geostatistics"},"content":{"rendered":"\n
\n
\n

<\/i> 2023<\/a><\/p>\n<\/div>\n\n\n\n

\n

<\/i> Volume 26, Issue 12<\/a><\/p>\n<\/div>\n\n\n\n

\n
\n
\n
\n

Yongzhi Wang1,2<\/sup><\/i><\/a>, Mengrou Yu2<\/sup>, Hui Wang3<\/sup>, and Baojuan Wang1<\/sup><\/p>\n\n\n\n

1<\/sup>School of Geography Science and Geomatics Engineering, Suzhou University of Science and Technology, Suzhou, China<\/p>\n\n\n\n

2<\/sup>School of Civil and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou, China<\/p>\n\n\n\n

3<\/sup>Provincial Geomatics Center of Jiangsu, Nanjing, China<\/p>\n<\/div>\n\n\n\n

\n

Received:\u00a0June 10, 2022
Accepted:\u00a0September 15, 2022
Publication Date:\u00a0May 2, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n

\"\u4e0a\u50b3\u5716\u7247\"\n\n\n

Grade model of regular hexahedron voxel of I-3.<\/p>\n<\/div>\n<\/div>\n\n\n\n

<\/i> Copyright <\/strong>The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n

Download Citation:  BibTeX <\/a>| http:\/\/dx.doi.org\/10.6180\/jase.202312_26(12).0013<\/a>  <\/p>\n\n\n\n

Download PDF<\/a><\/p>\n\n\n\n

<\/div>\n\n\n\n

To improve the accuracy of the calculation for the current mineral resource reserves, a calculation method for mineral resource reserves based on multi-point geostatistics was proposed. The new method, including four major steps, focuses on calculating resource reserves of ore body accurately for rational development and utilization of mineral resources. To represent the spatial geometric relationship of the ore body accurately, a three-dimensional irregular tetrahedron voxel (3D ITV) model construction method for the ore body is proposed first. Second, a tetrahedron voxel grade model built by the mineral reservation calculation oriented multi-point geostatistics method is proposed. The construction of 3D training image, definition of data template with N-order adjacency voxels, construction of search trees and conditional probability extraction of data event are conducted in this step. Finally, the resource reserves of the ore body are calculated on the basis of the tetrahedron voxel grade model. A calculation experiment of copper reserves is conducted to demonstrate the validity of the new method. The new method can be meaningful to the exploration, development, and utilization of mineral resources.<\/p>\n\n\n\n

Keywords:\u00a0Mineral reserve calculation, multi-point geostatistics, 3D irregular tetrahedron voxel model, 3D training images<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
\n
    \n
  1. [1] X. Huang, X. Li, K. Hu, Y. Liu, and D. Liu, (2012) \u201cStatus and Achievement of the Green Mine in China” International Proceedings of Chemical Biological & Environmental Science and Development (ICESD):<\/li>\n
  2. [2] A. Valero, A. Valero, and G. M. Mudd. \u201cExergy-a useful indicator for the sustainability of mineral resources and mining\u201d. In: SDIMI Conference Gold Coast. 2009.<\/li>\n
  3. [3] F.-W. Wellmer, J. D. Becker-Platen, D. J. Shields, J. A. Briskey, K. J. Schulz, J. P. Mosesso, L. R. Horwitz, C. G. Cunningham, P. F. Langhammer, W. J. Bawiec, et al., (2007) \u201cProceedings for a Workshop on Deposit Modeling, Mineral Resource Assessment, and Their Role in Sustainable Development” Guizhou Ethnic Studies: DOI: 10.3133\/cir1294.<\/li>\n
  4. [4] M. Khaidir Noor. \u201cOre Reserve Estimation of Saprolite Nickel Using Inverse Distance Method in PIT Block 3A Banggai Area Central Sulawesi\u201d. In: 979. 1. Cited by: 0; All Open Access, Gold Open Access. 2018. DOI: 10.1088\/1742-6596\/979\/1\/012047.<\/li>\n
  5. [5] R. d. S. Machado and J. F. C. L. Costa, (2019) \u201cField parametric geostatistics-an alternative to tackle gold grade estimations” Revista Escola de Minas 72(1): 167\u2013172. DOI: 10.1590\/0370-44672018720085.<\/li>\n
  6. [6] B. Samanta, S. Bandopadhyay, and R. Ganguli, (2002) \u201cData segmentation and genetic algorithms for sparse data division in Nome placer gold grade estimation using neural network and geostatistics” Exploration and Mining Geology 11(1-4): 69\u201376. DOI: 10.2113\/11.1-4.69.<\/li>\n
  7. [7] D. Silva and J. Almeida, (2017) \u201cGeostatistical methodology to characterize volcanogenic massive and stockwork ore deposits” Minerals 7(12): DOI: 10.3390\/min7120238.<\/li>\n
  8. [8] S. Strebelle, (2002) \u201cConditional simulation of complex geological structures using multiple-point statistics” Mathematical Geology 34(1): 1\u201321. DOI: 10.1023\/A:1014009426274.<\/li>\n
  9. [9] C. Casta\u00f1\u00f3n, D. Arias, I. Diego, A. Martin-Izard, and Y. Ruiz, (2017) \u201cResource and reserve calculation in seam-shaped mineral deposits; a new approach: \u201cThe pentahedral method\u201d” Minerals 7(5): DOI: 10.3390\/min7050072.<\/li>\n
  10. [10] H. Anhar and F. Khalifani. Evaluation of Mineral Reserves. 2018.<\/li>\n
  11. [11] R. Wang, L. Li, D.-W. Zhou, Z.-G. Lu, H.-M. Deng, and S.-A. Ke, (2019) \u201cCalculation of Rare Earth Ore Reserves by Geostatistics” Chinese Rare Earths 40(2): 35\u201341. DOI: 10.16533\/J.CNKI.15-1099\/TF.20190001.<\/li>\n
  12. [12] S. Haldar. \u201cChapter 8 – Mineral Resource and Ore Reserve Estimation\u201d. In: Mineral Exploration. Ed. by S. Haldar. Boston: Elsevier, 2013, 137\u2013155. DOI: https:\/\/doi.org\/10.1016\/B978-0-12-416005-7.00008-8.<\/li>\n
  13. [13] L. Shu, Y. Cheng, L. Wang, J. Jiang, Q. Zhai, and S. Kong, (2011) \u201cResearch on influence of geological factors on gas storage in coal seam” China Safety Science Journal 21(02):<\/li>\n
  14. [14] J. Hou and G. Guo, (1993) \u201cTheory and Apply of Statistical Prediction of Deposits and Geostatistics” Metallurgical Industry Press: 325\u2013327.<\/li>\n
  15. [15] X. Gong, (2019) \u201c3D Geological Modeling and Resource Estimation of Laotianzhuang Manganese Deposit in Chongqing” Chengdu University of Technology:<\/li>\n
  16. [16] L. Coppa, E. Green, and C. Quan, (1984) \u201cGeostatistics for Resource\/Reserve Estimation.”<\/li>\n
  17. [17] F. Bastante, J. Taboada, L. Alejano, and C. Ord\u00f3\u00f1ez, (2005) \u201cEvaluation of the resources of a slate deposit using indicator kriging” Engineering Geology 81(4): 407\u2013418. DOI: 10.1016\/j.enggeo.2005.08.003.<\/li>\n
  18. [18] G. Wang, Z. Pang, J. B. Boisvert, Y. Hao, Y. Cao, and J. Qu, (2013) \u201cQuantitative assessment of mineral resources by combining geostatistics and fractal methods in the Tongshan porphyry Cu deposit (China)” Journal of Geochemical Exploration 134: 85\u201398. DOI: 10.1016\/j.gexplo.2013.08.004.<\/li>\n
  19. [19] A Study of Coupling Surface Network to Reservoir Simulation Model in a Large Middle East Field. All Days. SPE North Africa Technical Conference and Exhibition. SPE-127976-MS. 2010. DOI: 10.2118\/127976-MS. eprint: https:\/\/onepetro.org\/SPENATC\/proceedings-pdf\/10NATC\/All-10NATC\/SPE -127976-MS\/1764218\/spe-127976-ms.pdf.<\/li>\n
  20. [20] S. KASMAEE, J. GHOLAMNEJAD, A. YARAHMADI, and H. MOJTAHEDZADEH, (2010) \u201cReserve estimation of the high phosphorous stockpile at the Choghart iron mine of Iran using geostatistical modeling” Mining Science and Technology (China) 20(6): 855\u2013860. DOI: https:\/\/doi.org\/10.1016\/S1674-5264(09)60295-7.<\/li>\n
  21. [21] A. E. Tercan, B. \u00dcnver, M. A. Hindistan, G. Ertun\u00e7, F. Atalay, S. \u00dcnal, and Y. Killio\u011flu, (2013) \u201cSeam modeling and resource estimation in the coalfields of western Anatolia” International Journal of Coal Geology 112: 94\u2013106. DOI: 10.1016\/j.coal.2012.10.006.<\/li>\n
  22. [22] K. Modis, S. Stavrou, N. Terezopoulos, and D. Vattis, (2008) \u201cGeostatistics versus inverse distance squares in ore reserves estimation: Comparative case study in copper ore body in Cyprus” Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology 117(1): 48\u201352. DOI: 10.1179\/174328607X228866.<\/li>\n
  23. [23] S. Talesh Hosseini, O. Asghari, S. A. Torabi, and M. Abedi, (2020) \u201cAn Optimum Selection of Simulated Geological Models by Multi-Point Geostatistics and MultiCriteria Decision-Making Approaches; a Case Study in Sungun Porphyry-Cu deposit, Iran” Journal of Mining and Environment 11(2): 481\u2013503. DOI: 10.22044\/JME.2020.8710.1757.<\/li>\n
  24. [24] L. Hu and T. Chugunova, (2008) \u201cMultiple-point geostatistics for modeling subsurface heterogeneity: A comprehensive review” Water Resources Research 44(11): DOI: 10.1029\/2008WR006993.<\/li>\n
  25. [25] G. Mariethoz and J. Caers. Multiple-point Geostatistics: Stochastic Modeling with Training Images. 9781118662755. Cited by: 313. 2014, 1\u2013364. DOI: 10.1002\/9781118662953.<\/li>\n
  26. [26] T. ZHANG, (2008) \u201cIncorporating Geological Conceptual Models and Interpretations into Reservoir Modeling Using Multiple-Point Geostatistics” Earth Science Frontiers 15(1): 26\u201335. DOI: https:\/\/doi.org\/10.1016\/S1872-5791(08)60016-0.<\/li>\n
  27. [27] P. W. Mirowski, D. M. Tetzlaff, R. C. Davies, D. S. McCormick, N. Williams, and C. Signer, (2009) \u201cStationarity scores on training images for multipoint geostatistics” Mathematical Geosciences 41(4): 447\u2013474. DOI: 10.1007\/s11004-008-9194-0.<\/li>\n
  28. [28] S. Strebelle, (2002) \u201cConditional simulation of complex geological structures using multiple-point statistics” Mathematical Geology 34(1): 1\u201321. DOI: 10.1023\/A:1014009426274.<\/li>\n
  29. [29] H. Si, (2015) \u201cTetGen, a delaunay-based quality tetrahedral mesh generator” ACM Transactions on Mathematical Software 41(2): DOI: 10.1145\/2629697.<\/li>\n
  30. [30] Y. Wang, H. Zhao, Y. Sheng, and N. Kang, (2015) \u201cConstruction and application of 3d geological models for attribute-oriented information expression” Journal of Applied Science and Engineering 18(4): 315\u2013322. DOI: 10.6180\/jase.2015.18.4.01.<\/li>\n
  31. [31] P. Boguslawski, C. M. Gold, and H. Ledoux, (2011) \u201cModelling and analysing 3D buildings with a primal\/dual data structure” ISPRS Journal of Photogrammetry and Remote Sensing 66(2): 188\u2013197. DOI: 10.1016\/j.isprsjprs.2010.11.003.<\/li>\n
  32. [32] Y. Yin, C. Zhang, and S. Li, (2013) \u201cPrinciple, method and application of multi-point geostatistics” Geology press:<\/li>\n
  33. [33] J. Li, M. Wang, F. Wang, P. Yao, J. Liang, G. Tang, X. Zhu, G. Ma, G. Zou, Z. Shen, et al., (2010) \u201cCharacteristics of ductile shear-type disseminated ores in Heiniudong copper deposit, Jiulong County, Sichuan Province” Mineral Deposits 29(5): 853\u2013868. DOI: 10.1360\/972010-741.<\/li>\n
  34. [34] M. Chen, J. Ding, X. Zhu, G. Ma, P. Yao, and J. Li, (2013) \u201cGeological and geochemical characteristics and its ore-forming mechanism of Heiniudong copper deposit, Jiulong, Sichuan” Mineral Resources and Geology 27(6): 479\u2013486.<\/li>\n
  35. [35] F. Cao, (2016) \u201cThe study on Geological characteristics and Genesis of Heiniudong Cu deposit in Jiulong country, Sichuan Province, China” Chengdu University of Technology:<\/li>\n<\/ol>\n<\/div>\n\n\n\n

    <\/p>\n","protected":false},"author":3,"template":"wp-custom-template-detail-4-aricles","meta":{"_uag_custom_page_level_css":""},"categories":[740,6,752],"tags":[933],"acf":[],"uagb_featured_image_src":[],"uagb_author_info":{"display_name":"\u6797\u923a\u6db5","author_link":"\/jase\/?author=3"},"uagb_comment_info":0,"uagb_excerpt":" Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited. Download Citation:  BibTeX | http:\/\/dx.doi.org\/10.6180\/jase.202312_26(12).0013   Download PDF To improve the accuracy of the calculation for the current mineral…","_links":{"self":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope\/4794"}],"collection":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope"}],"about":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/types\/tkuisotope"}],"author":[{"embeddable":true,"href":"\/jase\/index.php?rest_route=\/wp\/v2\/users\/3"}],"wp:attachment":[{"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4794"},{"taxonomy":"post_tag","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}