and transport pathways with pattern recognition algorithms Ryan Shaver Where is groundwater Heath RC 1984 Groundwater regions of the United States USGS WSP 2242 p 22 ID: 1039012
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1. Finding groundwater flow and transport pathways with pattern recognition algorithmsRyan Shaver
2. Where is groundwater?Heath, R.C. (1984). Ground-water regions of the United States. USGS, WSP 2242, p. 22.Porous media:Alluvium (e.g., soil)Sedimentary (e.g., sandstone)Fractured rock, e.g.:GraniteSlateBasalt
3. Fractured bedrock groundwater models:Discrete fracture networks (DFNs)1 kmStochastic GenerationMonte Carlo realizations: repeatedly sample possible fracture networksBertrand, L., et al. (2015). “A multiscale analysis of a fracture pattern in granite: A case study of the Tamariu granite, Catalunya, Spain”. Journal of Structural Geology, vol. 78, pp. 52-56.Aldrich, G., et al. (2017). “Analysis and visualization of discrete fracture networks using a flow topology graph”. IEEE Transactions on Visualization and Computer Graphics, vol. 23, no. 8, pp. 1896-1909.Own figure (unpublished).2D3D
4. Flow & transport solving: Very expensive!Darcy’s law (for flow q):Used to get flow field v(x) for transport2D: linear solution on each fractureSolution over DFN involves solving very large, very sparse matrix equationAx = b3D: non-linear, solve by meshing and using a finite volume methodTransport (Lagrangian approach):Trace individual particles starting at x0:Must trace many particles to get a distributionHyman, J. D., et al. (2018). “Identifying backbones in three-dimensional discrete fracture networks: A bipartite graph-based approach”. SIAM, vol. 16, iss. 4, pp. 1948-1968.
5. Flow & transport backbonesPreserve transport/flow pathways with as few fractures as possible (comp. PCA with data variance)Aldrich, G., et al. (2017).Easy to do after solving for flow/transportMuch harder to do before: requires a “filter” method
6. Classification problem: Backbone or not?Represent as a graph of vertices and edgesClassify vertices (or edges) as belonging to backbone or notCompare with “ground-truth” backboneValera, M., et al. (2018). “Machine learning for graph-based representations of three-dimensional discrete fracture networks”. Computational Geosciences, vol. 22, pp. 695-710.
7. Previous work: Valera et al. (2018)80 training graphsCross-validation w/ grid search20 testing graphs~7% backbone: emphasize recall over precisionBackbone is not unique---how should we measure accuracy?What if backbones are disconnected?SVMRadial basis kernelDifferent misclassification penalties (slack variables)Random Forest (RF)Main hyperparameter: min_samples_leafBreakthrough Curve (BTC)Valera, M., et al. (2018).
8. Alternative: Consider paths, not verticesEnsure connectivityConsider solutions as unions of simple pathsForget classification---just try to mimic the breakthrough curve (or some other flow/transport quantity)Perfect for: genetic algorithms (GAs)!Own figure (unpublished).
9. Very preliminary (promising) resultOriginal DFNGA-extracted backboneFocus on flow backbone instead of transport backboneInstead of BTC, use conductance (aperture / length)Own figures (unpublished).
10. ReferencesAldrich, G., et al. (2017). “Analysis and visualization of discrete fracture networks using a flow topology graph”. IEEE Transactions on Visualization and Computer Graphics, vol. 23, no. 8, pp. 1896-1909.Bertrand, L., et al. (2015). “A multiscale analysis of a fracture pattern in granite: A case study of the Tamariu granite, Catalunya, Spain”. Journal of Structural Geology, vol. 78, pp. 52-56.Heath, R.C. (1984). Ground-water regions of the United States. USGS, WSP 2242, p. 22.Hyman, J. D., et al. (2018). “Identifying backbones in three-dimensional discrete fracture networks: A bipartite graph-based approach”. SIAM, vol. 16, iss. 4, pp. 1948-1968.Valera, M., et al. (2018). “Machine learning for graph-based representations of three-dimensional discrete fracture networks”. Computational Geosciences, vol. 22, pp. 695-710.