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Siyao Xu, Andre Jung Tapan Mukerji and Jef Caers

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1 Siyao Xu, Andre Jung Tapan Mukerji and Jef Caers
Annual Meeting 2013 Stanford Center for Reservoir Forecasting Statistical Similarity of Stacking Patterns: Linking Tank Experiments to Real Scale Siyao Xu, Andre Jung Tapan Mukerji and Jef Caers

2 Background - Statistics and Rules
Advantage & Challenge of Surface-based Model After Bertoncello et. al. 2011 Statistics & Rules Generate & Place Geometry Sequentially T Stack Surfaces for 3D Realization

3 Background - Tank Experiment
Source of Statistics and Rules (Xu et. al. 2012) T Sequential Measurement Deposition-Erosion Pattern Erosion Rules and Statistics Sedimentology Group, SAFL

4 … New Questions Given Field Data Tanks Which tank? What part?
Thickness Maps Seismic Sections Well Logs Saller et. al. 2008 … Tanks Sedimentology Group, SAFL Which tank? What part?

5 Problem – Quantify Heirarchy
at small scale 5 Lobes In Tanks Lobes at different scales Interpretation infeasible Automatic algorithm needed at large scale 2 Lobes

6 Problem – Statistical Similarity
Stacking Patterns as the Link From the Field Saller et. al. 2008 From the Tank Statistical Similarity Sedimentology Group, SAFL

7 Methodology - Preprocessing
Crop Lobes From Overhead Photo Series T Sedimentology Group, SAFL

8 Distances of 4 Parameters
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Distances of 4 Parameters Between Source Point Between Orientation Between Shape (Procrustes Analysis) Between Polygon (Haussdorf Distance)

9 𝑤 𝑆𝑜𝑢𝑟𝑐𝑒 =0.35; 𝑤 𝑂𝑟𝑖𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 =0.2;
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Geological Distance between Lobes Weighted sum of 4 parameters d= 𝑤 𝑆𝑜𝑢𝑟𝑐𝑒 ∗𝑆𝑜𝑢𝑟𝑐𝑒𝐷𝑖𝑠𝑡+ 𝑤 𝑂𝑟𝑖𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 ∗𝑂𝑟𝑖𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛𝐷𝑖𝑓𝑓+ 𝑤 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 ∗𝑃𝑜𝑙𝑦𝑔𝑜𝑛𝐷𝑖𝑠𝑡+ 𝑤 𝑆ℎ𝑎𝑝𝑒 ∗𝑆ℎ𝑎𝑝𝑒𝐷𝑖𝑓𝑓 Empirical weights 𝑤 𝑆𝑜𝑢𝑟𝑐𝑒 =0.35; 𝑤 𝑂𝑟𝑖𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 =0.2; 𝑤 𝑃𝑜𝑙𝑦𝑔𝑜𝑛 =0.35; 𝑤 𝑆ℎ𝑎𝑝𝑒 =0.1;

10 Agglomerative Hierarchical Clustering
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Agglomerative Hierarchical Clustering Using Geological Distance Repeat till all points are in one group Group Closest Pairs

11 Acceptable NOT acceptable Acceptable
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Clustering With Temporal Constraints d13=d12+d So d13 > d12 & d13 > d23 Time Space t1 d12 d23 t2 t3 Acceptable NOT acceptable Acceptable

12 Reachability Plot dAB A B Lobe Hierarchy Choose Scale Lobes to Point
Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Reachability Plot dAB A B Hierarchical Clustering

13 Reachability Plot A valley is a cluster Choose Scale Lobes to Point
Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Reachability Plot A valley is a cluster

14 Scale Reachability Plot
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Reachability Plot Put a threshold on y-axis (Scale Of Interpretation) Scale

15 Scale Reachability Plot Each cut valley is a big lobe Choose Scale
Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Reachability Plot Each cut valley is a big lobe Scale

16 Mark lobes by source points
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity Stacking Patterns  Point Process Mark lobes by source points

17 ECDF of Proximity to Nearest Neighbor (NN)
Choose Scale Lobes to Point Statistics of Pattern Compare Patterns Lobe Hierarchy Geobody Proximity ECDF of Proximity to Nearest Neighbor (NN) Degree of local clustering NN Angle NN Polygon Distance NN Shape Similarity NN Source Distance Statistical Similarity

18 G Function & Attributes
Choose Scale Lobes to Point G Function & Attributes Compare Patterns Lobe Hierarchy Geobody Proximity 2 Sample Kolmogorov-Smirnov Test Inputs: 2 ECDFs Outputs: P-value Higher  More similarity 0.067 Sample 1 Subset of 1 Sample 2 >>

19 Case Study - Patterns from Real Systems
Jegoua et. al. 2008 Amazon – 14 Lobe Complexes Borneo – 18 Lobes Saller et. al. 2008

20 Case Study – Patterns from Tanks
Tank B – 184 lobes Tank A – 424 lobes Sedimentology Group, SAFL

21 Case Study – Application of Method
Scale of Interpretation … 2. Hierarchical Clustering (Reachability Plot) 4. Compare 4 ECDFs Respectively 3. Choose a Scale 1. Measured Finest Scale

22 Case Study – Application of Method
5. Repeat for All Scales Scale of Interpretation …

23 Case Study – Application of Method
5. Repeat for All Scales Scale of Interpretation …

24 Case Study – Source CDF (Tanks vs. Borneo)
20 40 60 80 0.2 0.4 0.6 0.8 1 Scale of Interpretation (km) Similarity (P-Value) Tank A – More Significant Tank B - Less Significant Range of Interest For Surface-based Modeling X-axis: Calibrated to Real Scale Reservoir

25 Case Study – Angle CDF(Tanks vs. Borneo)
20 40 60 80 0.2 0.4 0.6 0.8 1 Scale of Interpretation (km) Similarity (P-Value) Tank B - Less Significant Tank A – More Significant Range of Interest

26 Case Study – Polygon Distance CDF(Tanks vs. Borneo)
20 80 0.2 0.4 0.6 0.8 1 Scale of Interpretation (km) Similarity (P-Value) 40 60 Tank A – More Significant Tank B - Less Significant Range of Interest

27 Case Study – Shape Similarity CDF(Tanks vs. Borneo)
20 80 0.2 0.4 0.6 0.8 1 Scale of Interpretation (km) Similarity (P-Value) 40 60 Tank A & Tank B – Approximate Significance

28 Case Study – 4 ECDFs (Tanks vs. Amazon)
Source Point Distance 0.2 0.4 0.6 0.8 1 100 200 Angle 0.2 0.4 0.6 0.8 1 100 200 Similarity (P-Value) Tank B - better Tank A – better 0.2 0.4 0.6 0.8 1 Polygon Distance 100 200 Shape Similarity 0.2 0.4 0.6 0.8 1 100 200 Tank A – better Tank B - better Scale of Interpretation (km)

29 Case Study - Summary Borneo  Tank A more similar Amazon  Neither
Different parameters  Different scale of interest Scale of interest  Assist surface-based modeling

30 Conclusion Statistical similarity
 Relative proximity Data mining with geological constraints  Hierarchy of geology Compare Stacking Patterns  Most similar tank & scale of interest Assist Surface-based Modeling  Patterns at scale of interests

31 Future Works Geological Side Engineering Side Geological validation
Calibrate method on different tanks Engineering Side Given a stacking pattern  How to simulate?

32 Acknowledgement Professor Chris Paola
Sedimentology Group, San Anthony Falls Laboratory, University of Minnesota

33 Conclusion Statistical similarity
 Relative spatial relationships Data mining with geological constraints  Hierarchy of geology Compare Stacking Patterns  Most similar tank & scale of interest Assisting Real Scale Modeling  Patterns at scale of interests

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