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

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.