Journal of Jilin University(Earth Science Edition) ›› 2019, Vol. 49 ›› Issue (5): 1496-1506.doi: 10.13278/j.cnki.jjuese.20180207

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An MPS-Based Simulation Algorithm for 3D Geological Structure with 2D Cross-Sections

Zheng Tiancheng1,2, Hou Weisheng1,2, He Sitong1,2   

  1. 1. School of Earth Sciences and Engineering, Sun Yat-Sen University, Guangzhou 510275, China;
    2. Key Laboratory of Geodynamic Action and Geological Hazards of Guangdong, Guangzhou 510275, China
  • Received:2018-09-29 Published:2019-10-10
  • Supported by:
    Supported by National Natural Science Foundation of China (41772345, 41472300)

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Abstract: Reconstructing 3D spatial distribution of geological phenomena with 3D geological simulation techniques is essential for natural resource management and risk assessment. Based on the spatial structural relationship of multiple points,and combined with stochastic simulation techniques to create different results, multiple-point statistics (MPS) can be used to reconstruct complicated geological phenomena. However, how to build an appropriate and effective training image is the key problem in MPS-based 3D geological simulations. The authors present a modified MPS algorithm, which combines sequential simulation and iterative methods to extend 2D training images into 3D training images, and applies the EM-like algorithm to optimize the simulation of 3D geological structures. The modeling examples show that the simulation grids are conditional to the training images; on which the stratigraphic sequence of the study area is simulated accurately, and the relationship of stratigraphic structures in 2D cross-sections is effectively reconstructed.

Key words: multiple-point statistics, 3D geological structures, 2D geological cross-sections, global optimization

CLC Number: 

  • P628.2
[1] Houlding S W. 3D Geoscience Modeling:Computer Techniques for Geological Characterization[M]. Berlin:Springer, 1994.
[2] Kaufmann O, Martin T. 3D Geological Modeling from Bore Holes, Cross Sections and Geological Maps, Application over for Mer Natural Gas Storages in Coal Mines[J]. Computers & Geosciences, 2008, 34:278-290.
[3] Pyrcz M, Deutsch C. Geostatistical Reservoir Modeling[M]. 2nd ed. New York:Oxford University Press, 2014.
[4] 尹艳树, 吴胜和, 张昌民,等. 用多种随机建模方法综合预测储层微相[J]. 石油学报, 2006, 27(2):68-71. Yin Yanshu, Wu Shenghe, Zhang Changmin, et al. Integrative Prediction of Microfacies with Multiple Stochastic Modeling Methods[J]. Acta Petrolei Sinica, 2006, 27(2):68-71.
[5] Turner A K. Challenges and Trends for Geological Modelling and Visualisation[J]. Bulletin of Engineering Geology & the Environment, 2006, 65(2):109-127.
[6] 武强, 徐华. 三维地质建模与可视化方法研究[J]. 中国科学:D辑:地球科学, 2004, 34(1):54-60. Wu Qiang, Xu Hua. Study of Geological Modeling and Visualization Method[J]. Scinece in China:Serious D:Earth Scinece, 2004,34(1):54-60.
[7] 朱合华, 郑国平, 吴江斌,等. 基于钻孔信息的地层数据模型研究[J]. 同济大学学报(自然科学版), 2003, 31(5):535-539. Zhu Hehua,Zheng Guoping, Wu Jiangbin, et al. Study on Ground Data Model Based on Drill Hole Information[J]. Journal of Tongji University(Natural Science), 2003, 31(5):535-539.
[8] 王靖波, 潘懋, 张绪定. 基于Kriging方法的空间散乱点插值[J]. 计算机辅助设计与图形学学报, 1999, 11(6):525-529. Wang Jingbo, Pan Mao, Zhang Xuding. The Kriging Interpolation Method for Scattered Data Points[J]. Journal of Computer-Aided Design & Computer Graphics, 1999, 11(6):525-529.
[9] 李晓军, 王长虹, 朱合华. Kriging插值方法在地层模型生成中的应用[J]. 岩土力学, 2009, 30(1):157-162. Li Xiaojun, Wang Changhong, Zhu Hehua. Kriging Interpolation and Its Application to Generating Stratum Model[J]. Rock and Soil Mechanics, 2009, 30(1):157-162.
[10] Calcagno P, Chilès J P, Courrioux G, et al. Geological Modelling from Field Data and Geological Knowledge:Part I:Modelling Method Coupling 3D Potential-Field Interpolation and Geological Rules[J]. Physics of the Earth & Planetary Interiors, 2008, 171(1):147-157.
[11] Chilès J P, Delfiner P. Geostatistics:Modeling Spatial Uncertainty[M]. 2nd ed. US:Wiley-Blackwell:John Wiley & Sons Ltd, 2012.
[12] Cowan E J, Beatson R K, Ross H J, et al. Practical Implicit Geological Modelling[C]//Fifth International Mining Geology Conference. Victoria:Australian Institute of Mining and Metallurgy Bendigo, 2003:17-19.
[13] Savchenko V V, Pasko A A, Okunev O G, et al. Function Representation of Solids Reconstructed from Scattered Surface Points and Contours[C]//Computer Graphics Forum. Edinburgh:Blackwell Science Ltd, 1995:181-188.
[14] Caumon G. Towards Stochastic Time-Varying Geological Modeling[J]. Mathematical Geosciences, 2010, 42(5):555-569.
[15] Caers J. Modeling Uncertainty in the Earth Sciences[M]. Wiley-Blackwell:John Wiley & Sons Ltd, 2011.
[16] Wellmann J F, Horowitz F G, Schill E, et al.Towards Incorporating Uncertainty of Structural Data in 3D Geological Inversion[J]. Tectonophysics, 2010, 490(3/4):141-151.
[17] Lindsay M D, Aillères L, Jessell M W, et al. Locating and Quantifying Geological Uncertainty in Three-Dimensional Models:Analysis of the Gippsland Basin, Southeastern Australia[J]. Tectonophysics, 2012, 546:10-27.
[18] Røe P, Georgsen F, Abrahamsen P. An Uncertainty Model for Fault Shape and Location[J]. Mathematical Geosciences, 2014, 46(8):957-969.
[19] Guardiano F B, Srivastava R M. Multivariate Geostatistics:Beyond Bivariate Moments[M]//Geostatistics Troia'92. Dordrecht:Springer, 1993:133-144.
[20] Strebelle S. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics[J]. Mathematical Geology, 2002, 34(1):1-21.
[21] Journel A, Zhang T. The Necessity of a Multiple-Point Prior Model[J]. Mathematical Geology, 2006, 38(5):591-610.
[22] 吴胜和, 李文克. 多点地质统计学:理论、应用与展望[J]. 古地理学报, 2005, 7(1):137-144. Wu Shenghe, Li Wenke. Multiple-Point Geostatistics:Theory, Application and Perspective[J]. Journal of Palaeogeography, 2005, 7(1):137-144.
[23] Jones P, Douglas I, Jewbali A. Modeling Combined Geological and Grade Uncertainty:Application of Multiple-Point Simulation at the Apensu Gold Deposit, Ghana[J]. Mathematical Geosciences, 2013, 45(8):949-965.
[24] Silva D A, Deutsch C V. A Multiple Training Image Approach for Spatial Modeling of Geologic Domains[J]. Mathematical Geosciences, 2014, 46(7):815-840.
[25] Mariethoz G, Caers J. Multiple-Point Geostatistics:Stochastic Modeling with Training Images[M]. Wiley-Blackwell:John Wiley & Sons Ltd, 2014.
[26] Zhang T. MPS-Driven Digital Rock Modeling and Upscaling[J]. Mathematical Geosciences, 2015, 47(8):937-954.
[27] 骆杨, 赵彦超. 多点地质统计学在河流相储层建模中的应用[J]. 地质科技情报, 2008, 27(3):68-72. Luo Yang, Zhao Yanchao. Application of Multiple-Point Geostatistics in Fluvial Reservoir Stochastic Modeling[J]. Geological Science and Technology Information, 2008, 27(3):68-72.
[28] 尹艳树, 吴胜和, 张昌民,等. 基于储层骨架的多点地质统计学方法[J]. 中国科学:D辑:地球科学, 2008,38(增刊2):160-167. Yin Yanshu, Wu Shenghe, Zhang Changmin, et al. Multi-Point Geostatistics Method Based on Reservoir Skeleton[J]. Scinece in China:Serious D:Earth Scinece, 2008,38(Sup. 2):160-167.
[29] Comunian A, Renard P, Straubhaar J. 3D Multiple-Point Statistics Simulation Using 2D Training Images[J]. Computers & Geosciences, 2012, 40:49-65.
[30] Linde N, Renard P, Mukerji T, et al.Geological Realism in Hydrogeological and Geophysical Inverse Modeling:A Review[J]. Advances in Water Resources, 2015, 86:86-101.
[31] Wu Y, Lin C, Ren L, et al.Reconstruction of 3D Porous Media Using Multiple-Point Statistics Based on a 3D Training Image[J]. Journal of Natural Gas Science and Engineering, 2018, 51:129-140.
[32] 林承焰,王杨,杨山,等. 基于CT的数字岩心三维建模[J]. 吉林大学学报(地球科学版), 2018, 48(1):307-317. Lin Chengyan, Wang Yang, Yang Shan, et al. 3D Modeling of Digital Core Based on X-Ray Computed Tomography[J]. Journal of Jilin University (Earth Science Edition), 2018, 48(1):307-317.
[33] Mustapha H, Dimitrakopoulos R. HOSIM:A High-Order Stochastic Simulation Algorithm for Generating Three-Dimensional Complex Geological Patterns[J]. Computers & Geosciences, 2011, 37(9):1242-1253.
[34] Hu L Y, Liu Y, Scheepens C, et al. Multiple-Point Simulation with an Existing Reservoir Model as Training Image[J]. Mathematical Geosciences, 2014, 46(2):227-240.
[35] Boucher A, Costa J F, Rasera L G, et al. Simulation of Geological Contacts from Interpreted Geological Model Using Multiple-Point Statistics[J]. Mathematical Geosciences, 2014, 46(5):561-572.
[36] Gueting N, Caers J, Comunian A, et al. Reconstruction of Three-Dimensional Aquifer Heterogeneity from Two-Dimensional Geophysical Data[J]. Mathematical Geosciences, 2018, 50(1):53-75.
[37] Mariethoz G, Renard P, Straubhaar J. The Direct Sampling Method to Perform Multiple-Point Geostatistical Simulations[J]. Water Resources Research, 2010, 46(11):1-14.
[38] Caers J. AGeneral Algorithm for Building 3D Spatial Laws from Lower Dimensional Structural Information[R]. Stanford:Stanford University, 2006.
[39] Journel A G. Combining Knowledge from Diverse Sources:An Alternative to Traditional Data Independence Hypotheses[J]. Mathematical Geology, 2002, 34(5):573-596.
[40] Tahmasebi P, Sahimi M. Enhancing Multiple-Point Geostatistical Modeling:2:Iterative Simulation and Multiple Distance Function[J]. Water Resources Research, 2016, 52(3):2099-2122.
[41] Yang L, Hou W, Cui C, et al. GOSIM:A Multi-Scale Iterative Multiple-Point Statistics Algorithm with Global Optimization[J]. Computers & Geosciences, 2016, 89:57-70.
[42] Feng W, Wu S, Yin Y, et al. A Training Image Evaluation and Selection Method Based on Minimum Data Event Distance for Multiple-Point Geostatistics[J]. Computers & Geosciences, 2017, 104:35-53.
[43] Hamming R W. Error Detecting and Error Correcting Codes[J]. Bell System Technical Journal, 1950, 29(2):147-160.
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