Abstract
The number of boreholes investigated by geotechnical methods in long-term urban geological surveys can reach tens of thousands or even hundreds of thousands. These borehole data form a globally discrete and locally concentrated spatial distribution pattern. How to combine a large amount of unevenly distributed borehole data and large-scope geological expert knowledge to efficiently and accurately build 3D geological models is an urgent problem in urban 3D geological modelling. This paper presents a parallel and efficient Hermite radial basis function (HRBF) implicit 3D geological modelling method that can handle a large amount of borehole data while considering geomorphic unit constraints. The fast and stable solution of the HRBF implicit geological interface is completed based on the block parallel solution. The marching tetrahedron (MT) method is used to visualize the geological model. Finally, this paper conducts 75 standard strata and 18 h of automatic fine-scale 3D geological modelling based on 28,071 borehole data and conducts section spatial analysis. This paper and SKUA-GOCAD software have carried out several sets of comparative modelling experiments at the same data level, and the results show that the proposed modelling process improves the efficiency of geological modelling and geological analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The sample data used in this study are available from the corresponding author upon reasonable request.
References
Benetatos C, Giglio G (2021) Coping with uncertainties through an automated workflow for 3D reservoir modelling of carbonate reservoirs. Geosci Front 12(6):15. https://doi.org/10.1016/j.gsf.2019.11.008
Calcagno P, Chiles JP, Courrioux G et al (2008) Geological modelling from field data and geological knowledge Part I. Modelling method coupling 3D potential-field interpolation and geological rules. Phys Earth Planet Inter 171(1–4):147–157. https://doi.org/10.1016/j.pepi.2008.06.013
Casciola G, Lazzaro D, Montefusco LB et al (2006) Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants. Comput Math Appl 51(8):1185–1198. https://doi.org/10.1016/j.camwa.2006.04.002
Casciola G, Montefusco LB, Morigi S (2010) Edge-driven image interpolation using adaptive anisotropic radial basis functions. J Math Imaging Vis 36(2):125–139. https://doi.org/10.1007/s10851-009-0176-8
Caumon G (2010) Towards stochastic time-varying geological modelling. Math Geosci 42(5):555–569. https://doi.org/10.1007/s11004-010-9280-y
Caumon G, Grey G, Antoine C et al (2013) Three-dimensional implicit stratigraphic model building from remote sensing data on tetrahedral meshes: theory and application to a regional model of La Popa Basin, NE Mexico. IEEE Trans Geosci Remote Sens 51(3):1613–1621. https://doi.org/10.1109/TGRS.2012.2207727
Che DF, Wu LX, Yin ZR et al (2009) 3D spatial modeling for urban surface and subsurface seamless integration. In: 2009 IEEE International Geoscience and Remote Sensing Symposium, Cape Town, South Africa, pp III-392-III-395. https://doi.org/10.1109/IGARSS.2009.5417787
Chen QY, Liu G, Ma XG et al (2020) 3D stochastic modeling framework for Quaternary sediments using multiple-point statistics: a case study in Minjiang Estuary area, southeast China. Comput Geosci 136:14. https://doi.org/10.1016/j.cageo.2019.104404
Chen QY, Zhou RH, Liu C et al (2023) pyMPSLib: a robust and scalable open-source Python library for mutiple-point statistical simulation. Earth Sci Inform 12. https://doi.org/10.1007/s12145-023-01086-5
Cuomo S, Galletti A, Giunta G et al (2017) Reconstruction of implicit curves and surfaces via RBF interpolation. Appl Numer Math 116:157–171. https://doi.org/10.1016/j.apnum.2016.10.016
de la Varga M, Schaaf A, Wellmann F (2019) GemPy 1.0: open-source stochastic geological modelling and inversion. Geosci Model Dev 12(1):1–32. https://doi.org/10.5194/gmd-12-1-2019
Fouedjio F, Scheidt C, Yang L et al (2021) A geostatistical implicit modeling framework for uncertainty quantification of 3D geo-domain boundaries: application to lithological domains from a porphyry copper deposit. Comput Geosci 157:22. https://doi.org/10.1016/j.cageo.2021.104931
Guo JT, Wu LX, Zhou WH (2016) Automatic ore body implicit 3D modelling based on radial basis function surface. J China Coal Soc 41:2130–2135. https://doi.org/10.13225/j.cnki
Guo JT, Wu LX, Zhou WH et al (2018) Section-constrained local geological interface dynamic updating method based on the HRBF surface. J Struct Geol 107:64–72. https://doi.org/10.1016/j.jsg.2017.11.017
Guo JT, Wang JM, Wu LX et al (2020) Explicit-implicit-integrated 3-D geological modelling approach: a case study of the Xianyan Demolition Volcano (Fujian, China). Tectonophysics 795:16. https://doi.org/10.1016/j.tecto.2020.228648
Guo JT, Wang XL, Wang JM et al (2021a) Three-dimensional geological modelling and spatial analysis from geotechnical borehole data using an implicit surface and marching tetrahedra algorithm. Eng Geol 284:14. https://doi.org/10.1016/j.enggeo.2021.106047
Guo JT, Li YQ, Jessell MW et al (2021b) 3D geological structure inversion from Noddy-generated magnetic data using deep learning methods. Comput Geosci 149:11. https://doi.org/10.1016/j.cageo.2021.104701
Hillier MJ, Schetselaar EM, de Kemp EA et al (2014) Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions. Math Geosci 46(8):931–953. https://doi.org/10.1007/s11004-014-9540-3
Houlding S (2012) 3D geoscience modeling: computer techniques for geological characterization. Springer Science & Business Media, New York
Jacquemyn C, Jackson MD, Hampson GJ (2019) Surface-based geological reservoir modelling using grid-Free NURBS curves and surfaces. Math Geosci 51(1):1–28. https://doi.org/10.1007/s11004-018-9764-8
Jessell M, Guo JT, Li YQ et al (2022) Into the Noddyverse: a massive data store of 3D geological models for machine learning and inversion applications. Earth Syst Sci Data 14(1):381–392. https://doi.org/10.5194/essd-14-381-2022
Jia QR, Che DF, Li WW (2019) Effective coal seam surface modelling with an improved anisotropy-based, multiscale interpolation method. Comput Geosci 124:72–84. https://doi.org/10.1016/j.cageo.2018.12.008
Guo JT, Wang ZX, Li CL et al (2022) Multiple-point geostatistics-based three-dimensional automatic geological modelling and uncertainty analysis for borehole data. Nat Resour Res 31(5):2347–2367. https://doi.org/10.1007/s11053-022-10071-6
Kearsey T, Williams J, Finlayson A et al (2015) Testing the application and limitation of stochastic simulations to predict the lithology of glacial and fluvial deposits in Central Glasgow, UK. Eng Geol 187:98–112. https://doi.org/10.1016/j.enggeo.2014.12.017
Kearsey TI, Whitbread K, Arkley SLB et al (2019) Creation and delivery of a complex 3D geological survey for the Glasgow area and its application to urban geology. Earth Environ Sci Trans R Soc Edinb 108(2–3):123–140. https://doi.org/10.1017/S1755691018000270
Li J, Liu PR, Wang XY et al (2022) 3D geological implicit modeling method of regular voxel splitting based on layered interpolation data. Sci Rep 12(1):14. https://doi.org/10.1038/s41598-022-17231-x
Li XH, Xue C, Chen YH et al (2023) 3D convolutional neural Network-based 3D mineral prospectivity modeling for targeting concealed mineralization within Chating area, middle-lower Yangtze River metallogenic Belt, China. Ore Geol Rev 157:20. https://doi.org/10.1016/j.oregeorev.2023.105444
Li JH, Cai YM, Li XY, Zhang LM (2019) Simulating realistic geological stratigraphy using direction-dependent coupled Markov chain model. Comput Geotech 115:103147. https://doi.org/10.1016/j.compgeo.2019.103147
Liu JJ, Liu JC (2022) Integrating deep learning and logging data analytics for lithofacies classification and 3D modelling of tight sandstone reservoirs. Geosci Front 13(1):14. https://doi.org/10.1016/j.gsf.2021.101311
Liu H, Chen SZ, Hou MQ et al (2020) Improved inverse distance weighting method application considering spatial autocorrelation in 3D geological modelling. Earth Sci Inf 13(3):619–632. https://doi.org/10.1007/s12145-019-00436-6
Liu Z, Zhang ZL, Zhou CY et al (2021) An Adaptive Inverse-Distance Weighting Interpolation Method Considering Spatial Differentiation in 3D Geological Modelling. Geosciences 11(2), 51. https://doi.org/10.3390/geosciences11020051
Lobatskaya RM, Strelchenko IP (2016) GIS-based analysis of fault patterns in urban areas: a case study of Irkutsk city, Russia. Geosci Front 7(2):287–294. https://doi.org/10.1016/j.gsf.2015.07.004
Lyu MM, Ren BY, Wu BP et al (2021) A parametric 3D geological modelling method considering stratigraphic interface topology optimization and coding expert knowledge. Eng Geol 293. https://doi.org/10.1016/j.enggeo.2021.106300
Mallet JL (1997) Discrete modelling for natural objects. Math Geol 29(2):199–219. https://doi.org/10.1007/BF02769628
Manchuk JG, Deutsch CV (2019) Boundary modelling with moving least squares. Comput Geosci 126(MAY):96–106. https://doi.org/10.1016/j.cageo.2019.02.006
Martin R, Boisvert JB (2017) Iterative refinement of implicit boundary models for improved geological feature reproduction. Comput Geosci 109:1–15. https://doi.org/10.1016/j.cageo.2017.07.003
Mints MV, Glaznev VN, Muravina OM et al (2020) 3D model of Svecofennian Accretionary Orogen and Karelia Craton based on geology, reflection seismics, magnetotellurics and density modelling: geodynamic speculations. Geosci Front 11(3):999–1023. https://doi.org/10.1016/j.gsf.2019.10.003
Nonogaki S, Masumoto S, Nemoto T et al (2021) Voxel modelling of geotechnical characteristics in an urban area by natural neighbour interpolation using a large number of borehole logs. Earth Sci Inf 14(2):871–882. https://doi.org/10.1007/s12145-021-00600-x
Olierook HKH, Scalzo R, Kohn D et al (2021) Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models. Geosci Front 12(1):479–493. https://doi.org/10.1016/j.gsf.2020.04.015
Olivier R, Cao H (2012) Nearest neighbour value interpolation. Int J Adv Comput Sci Appl 3(4):25–30. https://doi.org/10.14569/IJACSA.2012.030405
Paul JD (2016) High-resolution geological maps of central London, UK: Comparisons with the London Underground. Geosci Front 7(2):273–286. https://doi.org/10.1016/j.gsf.2015.05.004
Randle CH, Bond CE, Lark RM et al (2018) Can uncertainty in geological cross-section interpretations be quantified and predicted?. Geosphere 14(3):1087–1100. https://doi.org/10.1130/GES01510.1
Shi TD, Zhong DY, Wang LG (2021) Geological modeling method based on the normal dynamic estimation of sparse point clouds. Mathematics 9(15):16. https://doi.org/10.3390/math9151819
Shuku T, Phoon KK (2021) Three-dimensional subsurface modelling using Geotechnical Lasso. Comput Geotech 133, 104068. https://doi.org/10.1016/j.compgeo.2021.104068
Skala V (2017) RBF Interpolation with CSRBF of large data sets. Procedia Comput Sci 108:2433–2437. https://doi.org/10.1016/j.procs.2017.05.081
Slomka JM, MacCormack KE, Eyles CH (2019) Preservation of local high-resolution data in a regional low-resolution dataset: A “nested” 3D modelling approach using an example from a Quaternary glacial stratigraphy (Ontario, Canada). Eng Geol 248:309–329. https://doi.org/10.1016/j.enggeo.2018.12.007
Sun H, Zhong DY, Wu ZH, Wang LG (2023) Multi-labeled regularized marching tetrahedra method for implicit geological modeling. Math Geosci 30. https://doi.org/10.1007/s11004-023-10075-9
Thanh HV, Sugai Y, Nguele R et al (2019) Integrated workflow in 3D geological model construction for evaluation of CO2 storage capacity of a fractured basement reservoir in Cuu Long Basin, Vietnam. Int J Greenhouse Gas Control 90:14. https://doi.org/10.1016/j.ijggc.2019.102826
Torres CE, Barba LA (2009) Fast radial basis function interpolation with Gaussians by localization and iteration. J Comput Phys 228(14):4976–4999. https://doi.org/10.1016/j.jcp.2009.03.007
Wang GW, Huang L (2012) 3D geological modelling for mineral resource assessment of the Tongshan Cu deposit, Heilongjiang Province, China. Geosci Front 3(4):483–491. https://doi.org/10.1016/j.gsf.2011.12.012
Wang GW, Ma ZB, Li RX et al (2017) Integration of multi-source and multi-scale datasets for 3D structural modeling for subsurface exploration targeting, Luanchuan Mo-polymetallic district, China. J Appl Geophys 139:269–290. https://doi.org/10.1016/j.jappgeo.2017.02.027
Wellmann JF, Lindsay M, Poh J et al (2014) Validating 3-D structural models with geological knowledge for improved uncertainty evaluations, General Assembly of the EGU Division on Energy, Resources and the Environment (ERE), Elsevier Science Bv, Vienna, AUSTRIA, pp. 374–381. https://doi.org/10.1016/j.egypro.2014.10.391
Wu LX (2004) Topological relations embodied in a generalized tri-prism (GTP) model for a 3D geoscience modelling system. Comput Geosci 30(4):405–418. https://doi.org/10.1016/j.cageo.2003.06.005
Xu NX, Tian H, Kulatilake PHSW et al (2011) Building a three dimensional sealed geological model to use in numerical stress analysis software: a case study for a dam site. Comput Geotech 38(8):1022–1030. https://doi.org/10.1016/j.compgeo.2011.07.013
Yang YS, Li YY, Liu TY et al (2011) Interactive 3D forwards modelling of total field surface and three-component borehole magnetic data for the Daye iron-ore deposit (Central China). J Appl Geophys 75(2):254–263. https://doi.org/10.1016/j.jappgeo.2011.07.010
Yang L, Achtziger-Zupancic P, Caers J (2021) 3D modeling of large-scale geological structures by linear combinations of implicit functions: application to a large banded iron formation. Nat Resour Res 30(5):3139–3163. https://doi.org/10.1007/s11053-021-09901-w
Yang BR, Ding YL, Zhu Q et al (2023) Implicit modelling and dynamic update of tunnel unfavourable geology based on multi-source data fusion using support vector machine. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 18. https://doi.org/10.1080/17499518.2023.2239778
Yokota R, Barba LA, Knepley MG (2010) PetRBF — A parallel O(N) algorithm for radial basis function interpolation with Gaussians. Comput Methods Appl Mech Eng 199(25–28):1793–1804. https://doi.org/10.1016/j.cma.2010.02.008
Zhong DY, Wang LG, Bi L et al (2019) Implicit modelling of complex orebody with constraints of geological rules. Trans Nonferrous Met Soc China 29(11):2392–2399. https://doi.org/10.1016/S1003-6326(19)65145-9
Zhong DY, Wang LG, Wang JM (2021) Combination constraints of multiple fields for implicit modeling of ore bodies. Appl Sci-Basel 11(3):15. https://doi.org/10.3390/app11031321
Funding
This work was financially supported by the National Natural Science Foundation of China [grant number: 42172327]; the Fundamental Research Funds for the Central Universities [grant number: N2201022]; the Shenyang Municipal Development and Reform Commission Project [2019–210100-64–01-056666]. We are very grateful to the editor and anonymous reviewers for their insightful comments and suggestions, which led to the improvement of the manuscript.
Author information
Authors and Affiliations
Contributions
Xulei Wang and Jiateng Guo conceived of the manuscript; Jiateng Guo provided funding support and ideas; Xulei Wang was responsible for the research method and program development; Shaohua Fu, Hengbing Zhang, Shengchuan Liu, Limin Dun and Xinbei Zhang provided the data used in this research and standardized the data; Xulei Wang, Jiateng Guo, Lixin Wu, and Zhibin Liu helped to improve the manuscript. All authors have read and agreed to the submitted version of the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Communicated by G. Liu
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wang, X., Guo, J., Fu, S. et al. Towards automatic and rapid 3D geological modelling of urban sedimentary strata from a large amount of borehole data using a parallel solution of implicit equations. Earth Sci Inform 17, 421–440 (2024). https://doi.org/10.1007/s12145-023-01164-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-023-01164-8