Developments in Geometry Uncertainty Jing Bai Geometric Uncertainty

Developments in Geometry Uncertainty Jing Bai

Geometric Uncertainty •

Multiple Imputation •

The Steps of Multiple Imputation • 1. Forming the distributions – Primary distribution for elevation (spatial) – Secondary distribution for thickness (spatial) • 2. Transforming the distribution – Thickness to Elevation (collocated) • 3. Merging the distributions – Primary and Transformed • 4. Drawing from the distribution Carvalho, D. , & Deutsch, C. V. (2017). Imputation of Tabular Vein Geometry Data for Tonnage Uncertainty Assessment. Centre for Computational Geostatistics Annual Report 19, Paper 313

2. Imputation, Transforming Distributions •

3. Imputation，Merging Distributions •

Case Study 1 True data generated by specifying distributions and variograms. Transformation based on the estimated distribution and calculated variograms. Absolute Error RMSE Hangingwall EE: 2. 39% BU: 2. 73% EE: 1. 277 BU: 1. 653 Footwall EE: 21. 6% BU: 23. 5% EE: 5. 33 BU: 5. 83 Thickness EE: 31. 04% BU: 30. 77% EE: 10. 77 BU: 11. 06

Case Study 2 • True data generated by specifying distributions and variograms. • Transformation based on the known distribution and known variograms. Absolute Error RMSE Hangingwall BU: 6. 9% EE: 6. 3% BU: 4. 11 EE: 3. 91 Footwall BU: 7. 7% EE: 7. 6% BU: 2. 97 EE: 2. 93

Discussion • Combining distributions: Bayesian updating and Error Ellipses provide similar results. • Highly influenced by the transformation methods; Having a known distribution can increase the performance, but it really depends on the distributions • Gaussian variograms are susceptible to being singular. • Dependency between variables • Performance increases with high tolerance angle (less imputation number), known variograms • Future works: have more control on the results by understanding parameters’ influence; improve the performance and algorithm

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