基于开源GemPy的城市地下空间三维隐式势场建模方法研究

doi:10.13745/j.esf.sf.2024.2.30

摘要/Abstract

摘要：

三维地质建模是城市地下空间规划和管理的重要基础工作。在地质科学大数据时代,当前三维建模逐渐转向三维隐式建模。常见的三维地质建模软件如GeoModeller、Surpac等都提供了隐式建模技术,但是上述商业软件均封装完好、并不开源。本文基于开源GemPy建模平台,重点实现了三维隐式势场建模技术与针对地层尖灭的建模方案,将算法方案加入GemPy底层建模架构,并以某城市地下空间为例,对三维地质精细化建模工程流程进行了验证。论文构建了基于研究区钻孔数据的建模数据集,采用势场法和泛克立格插值法建立城市三维地质模型,并针对城市地质中常见的地层尖灭进行了单独的布尔运算处理。为细致直观展示研究区三维地质模型地层界面的拟合情况,对共计18个工程地质层分别进行可视化。最后,对模型的精度采用分层K折交叉验证方法进行验证,并用皮尔逊相关系数(CC)等4种指标对建模效果进行衡量。对研究区的实验结果表明,基于开源GemPy的三维隐式势场地质建模方法针对城市地质构造具有一定通用性,并在精度上具有较好效果,可以为城市地下空间开发利用提供决策依据。

关键词: 三维地质建模, 隐式势场法, GemPy, 地层尖灭, 城市地下空间

Abstract:

Three-dimensional geological modeling is essential for urban subterranean space planning and management. In the era of geological big data, there is a shift towards implicit modeling techniques. While commercial software like GeoModeller and Surpac offer implicit modeling capabilities, they are proprietary and lack open-source accessibility. This paper focuses on the open-source GemPy modeling platform, utilizing three-dimensional implicit potential field modeling techniques and presenting an algorithmic solution for geological pinch-outs. The proposed approach is integrated into GemPy’s foundational modeling architecture. Through a case study of a specific urban area, the paper demonstrates the workflow for fine-scale three-dimensional geological modeling. A modeling dataset is created using borehole data and the potential field method, along with pan-Kriging interpolation, to establish a three-dimensional geological model of the urban area. Specialized techniques are employed to address urban pinch-outs. To visualize geological interfaces in the model, 18 engineering geological layers are individually displayed. The model’s accuracy is assessed using stratified K-fold cross-validation, including metrics like the Pearson correlation coefficient (CC). Experimental results show that the three-dimensional implicit potential field geological modeling method in GemPy is suitable for urban geological structures, providing a reliable foundation for decision-making in urban subterranean development.

Key words: three-dimensional geological modeling, implicit potential field method, GemPy, stratigraphic pinch-outs, urban subterranean space

中图分类号:

廖舟, 李梅. 基于开源GemPy的城市地下空间三维隐式势场建模方法研究[J]. 地学前缘, 2024, 31(3): 482-497.

LIAO Zhou, LI Mei. Research on the 3D implicit potential field modeling method for urban underground space based on the open-source GemPy[J]. Earth Science Frontiers, 2024, 31(3): 482-497.

图/表 16

图1 整体工作流程

Fig.1 Overall workflow

图2 研究区钻孔位置分布

Fig.2 Distribution of borehole locations in the study area

表1 研究区地层相关信息表

Table 1 Table of information related to the stratigraphy of the study area

地层单位				地层划分		岩性简述
系	统	阶	段	地层划分		岩性简述
第四系	全新统	上阶		SA1_0		杂填土、素填土吹填土、淤填土
		上阶		SA1_1	SA1_2	褐黄、灰黄粉质黏土、黏土	黄褐色、灰褐色粉土
		中阶		SA2		灰色淤泥质土,黄灰、灰色粉土、粉砂
		下阶		SA3_0		褐黄色黏土、粉质黏土,局部灰黄色粉细砂
		下阶		SA3		灰色淤泥质土、灰色黏性土
	上更新统	上阶	上段	SA4_1		褐黄、灰绿色黏性土,局部灰黄色粉细砂
				SA4_2		灰色黏性土,局部灰绿色粉土(第三软弱层)
				SA4_3		灰、灰黄色粉土、粉细砂
			下段	SA5_1		褐黄、灰绿色黏性土
				SA5_2		灰色黏性土
				SA5_3		灰、灰黄、灰绿色粉土、粉砂、砂,局部含砾
		下阶		SA6_1		褐黄、灰绿色黏性土
		下阶		SA6_3_4		灰、灰黄卵(砾石)、砾砂、砂
	中更新统	上阶		SA7_1		杂色黏性土层
		上阶		SA7_2		卵(砾石)、砾砂、砂
		下阶		SA8_1		杂色黏性土层,局部含砾
前第四系				SA10		不同时代不同类型岩石

图3 浅孔深部控制预处理示意剖面图

Fig.3 Schematic cross-section of shallow hole depth control pretreatment

图4 建模数据集的浅孔深部控制预处理 (a)—模型中出现浅孔深部控制异常的情况;(b)—Deep Surface的处理效果。

Fig.4 Shallow hole depth control preprocessing of modeling datasets (a) The abnormality of shallow hole depth control appears in the model; (b) the processing effect of Deep Surface.

图5 建模工作原理

Fig.5 Modeling working principles

图6 标量场及其梯度

Fig.6 Scalar field and its gradient

图7 研究区三维地质模型局部模型剖面 (a)—地层尖灭处理前;(b)—地层尖灭处理后。

Fig.7 Local model profile of the three-dimensional geological model in the research area (a) Before strata pinching treatment; (b) After strata pinching treatment.

图8 研究区建模数据集二维可视化结果 (a)—从x轴方向纵切;(b)—从y轴方向纵切。

Fig.8 Two-dimensional visualization results of the research area modeling data set (a) x-axis direction; (b) y-axis direction.

图9 研究区建模数据集三维空间分布

Fig.9 Three-dimensional spatial distribution of modeling data set in the study area

图10 研究区三维地质模型不同视角可视化结果 (a)等距视图;(b)-z;(c)+z;(d)-y;(e)+y;(f)-x;(g)+x。

Fig.10 Three-dimensional geological model results of the study area, visualized from different perspectives (a) isometric view; (b)-z;(c)+z;(d)-y;(e)+y;(f)-x;(g)+x

图11 研究区三维地质模型 (a)—模型地质界面集(A=100,e=2);(b)—线框模式。

Fig.11 Three-dimensional geological model of the study area (a) Model geological interface set (stretch exaggeration coefficient=2); (b) Wireframe mode.

图12 研究区三维地质模型每一层地层面可视化结果

Fig.12 Visualization results of each stratigraphic layer of the three-dimensional geological model of the study area

图13 不同条件下的全视图(overall view)和其他视图 (a)—体元大小:100×80×80,格网数=64 000;(b)—体元大小:50×40×30,格网数=60 000。

Fig.13 Overall view and other views under different conditions (a) Volume element size: 100×80×80, grid number=64000; (b) Volume element size: 50×40×30, grid number=60000.

图14 研究区三维地质模型部分地层深度图 (a)—地层SA0;(b)—地层SA1_1;(c)—地层SA1_2;(d)—地层SA2。

Fig.14 Depth map of each layer in the three-dimensional geological model of the study area (a)SA0; (b)SA1_1; (c) SA1_2; (d) SA2

表2 研究区三维地质模型精度验证

Table 2 Accuracy verification of the three-dimensional geological model of the study area

地层	精度指标(值域)
地层	CC [-1,1]	RMSE (0,+∞)	bias (-∞,0)∪ [0,+∞)	MAE (0,+∞)
SA0	0.898 293	3.477 853 651	-0.568 945	0.006 677 825 4
SA1_1	0.808 163	3.868 290 178	-0.734 876	0.008 604 348 6
SA1_2	0.790 859	4.373 820 489	-10.763 290	0.009 982 961 3
SA2	0.729 982	4.918 728 856	-11.793 872	0.011 946 271 0
SA3	0.657 102	5.972 010 837	-13.802 891	0.013 985 019 8
SA3_0	0.650 391	6.108 289 082	-14.082 647	0.014 074 550 1
SA4_1	0.550 829	9.289 107 576	16.290 184	0.028 476 845 3
SA4_2	0.550 021	9.587 408 083	17.208 371	0.029 081 209 7
SA4_3	0.548 902	9.718 018 476	17.937 659	0.030 128 748 9
SA5_1	0.530 827	10.278 377 632	18.628 746	0.039 475 665 1
SA5_2	0.553 805	9.037 486 502	16.750 385	0.028 947 630 6
SA5_3	0.529 104	10.910 471 291	19.056 821	0.040 129 479 5
SA6_1	0.528 576	10.983 465 825	19.856 625	0.040 146 286 4
SA6_3_4	0.519 865	11.746 208 264	20.047 652	0.041 846 567 2
SA7_1	-0.504 872	11.896 773 621	20.103 867	0.053 857 309 1
SA7_2	-0.504 635	11.907 857 693	20.859 261	0.062 947 565 8
SA8_1	0.503 748 3	13.294 876 507	21.907 703	0.082 056 328 2
SA10	0.502 837 6	16.205 873 628	23.287 659	0.094 859 287 5

参考文献 41

[1]	ELMQVIST T, ANDERSSON E, MCPHEARSON T, et al. Urbanization in and for the Anthropocene[J]. Urban Sustainability, 2021, 1(1): 6.
[2]	郝卉. 城市地下空间发展现状与前景[J]. 砖瓦, 2021(11): 85-86.
[3]	XIE H, ZHANG Y, CHEN Y, et al. A case study of development and utilization of urban underground space in Shenzhen and the Guangdong-Hong Kong-Macao Greater Bay Area[J]. Tunnelling and Underground Space Technology, 2021, 107: 103651.
[4]	OSWALD C, RINNER C, ROBINSON A. Applications of 3D printing in physical geography education and urban visualization[J]. Cartographica: The International Journal for Geographic Information and Geovisualization, 2019, 54(4): 278-287.
[5]	OLIEROOK H K H, SCALZO R, KOHN D, et al. Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models[J]. Geoscience Frontiers, 2021, 12(1): 479-493.
[6]	田玉培, 王俊, 刘文文. 城市地下空间三维地质建模的研究及实现[J]. 现代矿业, 2021, 37(8): 49-52, 55.
[7]	JING H, HANHAN H, GUISEN Z, et al. 3D geological modelling of superficial deposits in Beijing City[J]. Geology in China, 2019, 46(2): 244-254.
[8]	BIRCH C. New systems for geological modelling-black box or best practice?[J]. Journal of the Southern African Institute of Mining and Metallurgy, 2014, 114(12): 993-1000.
[9]	COWAN E J, BEATSON R K, FRIGHT W R, et al. Rapid geological modelling[C]//Applied structural geology for mineral exploration and mining, international symposium, Kalgoorlie, Australia: Kalgoorlie. 2002, 9: 23-25.
[10]	COWAN E J, BEATSON R K, ROSS H J, et al. Practical implicit geological modelling[C]//Proceedings of the 5th international mining geology conference. Bendigoe: Australasian Institute of Mining and Metallurgy Melbourne, 2003, 8: 89-99.
[11]	VOLLGGER S A, CRUDEN A R, AILLERES L, et al. Regional dome evolution and its control on ore-grade distribution: insights from 3D implicit modelling of the Navachab gold deposit, Namibia[J]. Ore Geology Reviews, 2015, 69: 268-284.
[12]	VON HARTEN J, DE LA VARGA M, HILLIER M, et al. Informed local smoothing in 3D implicit geological modeling[J]. Minerals, 2021, 11(11): 1281.
[13]	王权, 邹艳红. 基于轮廓线层间形态插值的三维地质隐式曲面重构[J]. 地质科技通报, 2023, 42(5): 293-300.
[14]	王权. 三维地质隐式建模形态不确定性分析与定量评价研究[D]. 长沙: 中南大学, 2022.
[15]	ZHONG D, WANG L, LIN B I, et al. Implicit modeling of complex orebody with constraints of geological rules[J]. Transactions of Nonferrous Metals Society of China, 2019, 29(11): 2392-2399. DOI
[16]	FRANK T, TERTOIS A L, MALLET J L. 3D-reconstruction of complex geological interfaces from irregularly distributed and noisy point data[J]. Computers & Geosciences, 2007, 33(7): 932-943.
[17]	CUOMO S, GALLETTI A, GIUNTA G, et al. Reconstruction of implicit curves and surfaces via RBF interpolation[J]. Applied Numerical Mathematics, 2017, 116: 157-171.
[18]	SKALA V. RBF interpolation with CSRBF of large data sets[J]. Procedia Computer Science, 2017, 108: 2433-2437.
[19]	MACÊDO I, GOIS J P, VELHO L. Hermite radial basis function simplicits[C]//Proceedings of computer graphics forum. Oxford: Blackwell Publishing Ltd, 2011, 30(1): 27-42.
[20]	GUO J, WU L, ZHOU W, et al. Section-constrained local geological interface dynamic updating method based on the HRBF surface[J]. Journal of Structural Geology, 2018, 107: 64-72.
[21]	FLEISHMAN S, COHEN-OR D, SILVA C T. Robust moving least-squares fitting with sharp features[J]. ACM Transactions on Graphics (TOG), 2005, 24(3): 544-552.
[22]	CARR J C, BEATSON R K, CHERRIE J B, et al. Reconstruction and representation of 3D objects with radial basis functions[C]//Proceedings of the 28th annual conference on computer graphics and interactive techniques (SIGGRAPH’01). New York: Association for Computing Machinery, 2001: 67-76.
[23]	STOCH B, ANTHONISSEN C J, MCCALL M J, et al. 3D implicit modeling of the Sishen Mine: new resolution of the geometry and origin of Fe mineralization[J]. Mineralium Deposita, 2018, 53(6): 835-853.
[24]	JONES M W, CHEN M. A new approach to the construction of surfaces from contour data[C]//Proceedings of computer graphics forum. Edinburgh: Blackwell Science Ltd, 1994, 13(3): 75-84.
[25]	曹勇, 苏晓慧, 孙梦梦, 等. 开源建模软件在水利工程BIM领域中的应用[J]. 水利规划与设计, 2021(8): 96-101, 126.
[26]	张志武. 三维矢量数据矿山模型算法研究及在Blender中的应用[D]. 武汉: 武汉科技大学, 2016.
[27]	赵勇, 许国, 卢鹏, 等. 基于GemPy的隐式三维地质建模方法[J]. 人民长江, 2023, 54(10): 98-104.
[28]	WU J, SUN B. Discontinuous mechanical analysis of manifold element strain of rock slope based on open source Gempy[C]//E3S Web of conferences. Hangzhou: EDP Sciences, 2021, 248: 03084.
[29]	BEN-SHABAT Y, GOULD S. DeepFit: 3D surface fitting via neural network weighted least squares[C]//Computer Vision-ECCV 2020: 16th European conference. Glasgow: Springer International Publishing, 2020: 20-34.
[30]	SCHAAF A, VARGA M, WELLMANN F, et al. Constraining stochastic 3-D structural geological models with topology information using approximate Bayesian computation in GemPy 2.1[J]. Geoscientific Model Development, 2021, 14(6): 3899-3913.
[31]	DE LA VARGA M, SCHAAF A, WELLMANN F. GemPy 1.0: open-source stochastic geological modeling and inversion[J]. Geoscience Model Development, 2019, 12 (32): 1-32.
[32]	CHEN G, ZHU J, QIANG M, et al. Three-dimensional site characterization with borehole data: a case study of Suzhou area[J]. Engineering Geology, 2018, 234: 65-82.
[33]	FISCHER M, PROPPE C. Enhanced universal kriging for transformed input parameter spaces[J]. Probabilistic Engineering Mechanics, 2023, 74: 103486.
[34]	熊前进, 柴小婷, 万翔, 等. 对数泛克立格法在东天山土屋—延东地区Cu、Au异常信息提取中的应用[J]. 资源环境与工程, 2021, 35(4): 536-540. DOI
[35]	LORENSEN W E, CLINE H E. Marching cubes: a high resolution 3D surface construction algorithm[J]. ACM SIGGRAPH Computer Graphics, 1987, 21(4): 163-169.
[36]	SANTOLARIA P, VENDEVILLE B C, GRAVELEAU F, et al. Double evaporitic décollements: influence of pinch-out overlapping in experimental thrust wedges[J]. Journal of Structural Geology, 2015, 76: 35-51.
[37]	苏栋, 黄茂隆, 韩文龙, 等. 考虑城市地质环境影响的深圳市地下空间开发适宜性评价[J]. 地学前缘, 2023, 30(4): 514-524. DOI
[38]	蒋旭, 王婷婷, 穆静. 地下空间开发利用适宜性与资源量的应用研究[J]. 地下空间与工程学报, 2018, 14(5): 1145-1153.
[39]	RATA M, DOUAOUI A, LARID M, et al. Comparison of geostatistical interpolation methods to map annual rainfall in the Chéliff watershed, Algeria[J]. Theoretical and Applied Climatology, 2020, 141: 1009-1024.
[40]	GUO J, WANG X, WANG J, et al. Three-dimensional geological modeling and spatial analysis from geotechnical borehole data using an implicit surface and marching tetrahedra algorithm[J]. Engineering Geology, 2021, 284: 106047.
[41]	BORGHI A, RENARD P, FOURNIER L, et al. Stochastic fracture generation accounting for the stratification orientation in a folded environment based on an implicit geological model[J]. Engineering Geology, 2015, 187: 135-142.