Uncertainty analysis and visualization of geological subsurface and its application in metro station construction

doi:10.1007/s11707-021-0897-6

Front. Earth Sci.

2021, Vol. 15

Issue (3) : 692-704 https://doi.org/10.1007/s11707-021-0897-6

RESEARCH ARTICLE

Uncertainty analysis and visualization of geological subsurface and its application in metro station construction

Weisheng HOU^1,^2,³(

), Qiaochu YANG^4,¹, Xiuwen CHEN¹, Fan XIAO^1,^2,³, Yonghua CHEN⁵

¹. School of Earth Sciences and Engineering, Sun Yat-sen University, Guangzhou 510275, China
². Guangdong Provincial Key Lab of Geodynamics and Geohazards, Guangzhou 510275, China
³. Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519080, China
⁴. Sichuan Highway Planning, Survey, Design and Research Institute Ltd., Chengdu 610041, China
⁵. Guangzhou Metro Design & Research Institute Co. Ltd., Guangzhou 510010, China

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Abstract

To visualize and analyze the impact of uncertainty on the geological subsurface, on the term of the geological attribute probabilities (GAP), a vector parameters-based method is presented. Perturbing local data with error distribution, a GAP isosurface suite is first obtained by the Monte Carlo simulation. Several vector parameters including normal vector, curvatures and their entropy are used to measure uncertainties of the isosurface suite. The vector parameters except curvature and curvature entropy are visualized as line features by distributing them over their respective equivalent structure surfaces or concentrating on the initial surface. The curvature and curvature entropy presented with color map to reveal the geometrical variation on the perturbed zone. The multiple-dimensional scaling (MDS) method is used to map GAP isosurfaces to a set of points in low-dimensional space to obtain the total diversity among these equivalent probability surfaces. An example of a bedrock surface structure in a metro station shows that the presented method is applicable to quantitative description and visualization of uncertainties in geological subsurface. MDS plots shows differences of total diversity caused by different error distribution parameters or different distribution types.

Keywords uncertainty geological sub-surface model vector parameters multiple-dimensional scaling

Corresponding Author(s): Weisheng HOU

Online First Date: 02 August 2021 Issue Date: 17 January 2022

Cite this article:

Weisheng HOU,Qiaochu YANG,Xiuwen CHEN, et al. Uncertainty analysis and visualization of geological subsurface and its application in metro station construction[J]. Front. Earth Sci., 2021, 15(3): 692-704.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-021-0897-6
https://academic.hep.com.cn/fesci/EN/Y2021/V15/I3/692

Fig.1 Bedrock geology map. 1—Lower section of Dalangshan Group of Cretaceous; 2—Upper section of Sanshui Group of Cretaceous; 3—Donghu section of Sanshui Group of Cretaceous; 4—Xihao section of Sanshui Group of Cretaceous; 5—Lower section of Sanshui Group of Cretaceous; 6—Upper section of Baihedong Group of Cretaceous; 7—Subrhyolite; 8—Guangsan Fault; 9—Burried Fault; 10—Metro Line and metro stop; 11—Modeling area.

Fig.2 Flowchart of vector parameters-based uncertainty analysis for 3D geological subsurface.

Fig.3 Standard deviation on different points of the surface network. Points marked with ① and ③ are the longest distance and the shortest distance from the nearest sample point respectively in the left image. The color bars in the right illustrated the standard deviation distribution along the z direction at three points ①, ②, and ③.

Fig.4 Uncertainties distribution on subsurface with different distance factors and standard variation is 1.0 at the sample points. The left image shows the relationship between standard deviation variation with regularization distance, in which different distance factors are 1(blue line), 7(green line), and 13 (red line). The standard variation with different distance factors is shown in the middle image. The GAP values in green, brown, and blue in the right image are 0.1, 0.5, and 0.95, respectively, in which the distance factors are same to the middle images.

Fig.5 Typical surface with their vectors and a local effect graph. (a) Vector parameters on four typical surfaces (After Lindsay et al., 2013). (b) Local effect graph of vector parametric system on a surface triangle network.

Fig.6 Curvature and its entropy of subsurface. (a) and (b) are mean curvature and its entropy of subsurface, respectively; (c) and (d) are Gaussian curvature and its entropy of subsurface respectively.

Fig.7 Uncertainty visualization methods based on normal vector.

Fig.8 Uncertainty visualization with principal curvature vectors. The red circle marked out the variation of principal curvature vectors change of the same point on different GAP iso-surface.

Fig.9 MDS plots of results with different parameters. Four images with σ = 0.7, 1.0, 1.2, and 1.5 in each row are MDS plots of normal vector, mean curvature, mean curvature entropy, Gaussian curvature and Gaussian curvature entropy respectively. Images of each column are MDS plots of different parameters with the same standard deviation value. The dark cycle in the image is the best-guessed model. Other symbols represent models with different distance factors (A). Color bar in the legend is the scalar of GAP values,

Fig.10 MDS plots of GAP iso-surfaces with different standard deviation values when distance factor is 1.0. Images from (a) to (f) are different vector parameters of normal vector, mean curvature, mean curvature entropy, Gaussian curvature, Gaussian.

Fig.11 MDS plots of GAP iso-surfaces with one perturbed point where distance factor is 3.0, standard deviations of the perturbed point are 0.5, 1.0, and 1.5 and other points are 1.0. Images from (a) to (f) are different vector parameters of normal vector, mean curvature, mean curvature entropy, Gaussian curvature, Gaussian curvature entropy, and the principal vector, respectively.

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