gautier laurent - implicit modelling and volume deformation

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This presentation was delivered at the June 10 (2014) 3D Interest Group Meeting at the Centre for Exploration Targeting, UWA.

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  • 1. 0/31 Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 CONTROLLING FOLDS WITH AN IMPLICIT MODELLING APPROACH AND RIGID ELEMENT METHOD FOR GEOLOGICAL STRUCTURAL MODELLING Gautier Laurent Laurent Aillres Lachlan Grose Guillaume Caumon Monash GeoRessources

2. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Expert-driven approach Sparse Data Qualitative Models Modelling Geological Structures The modellers approach: Honour data One state = current state The geologists approach: Geological scenario Multiple phases Approaches to GeomodellingIntroduction 1/31 Data (current state) time Geological structures (current state) Geological scenario Tectonics / kinematics concepts Need to reconcile these two approaches Data-driven approach Lots of Data Quantitative Models Part I: Provide tools to implement interactive Deformation Events Part II: Better integrate Structural Data for Folding 3. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Interactive deformation tool ReedPart I 2/31 Part I - Rigid Element Embedding Deformation 4. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Deformation algorithm for Geomodelling ReedPart I 3/31 Our specifications:Usage: Physical Consistency: looks like natural deformations Interactive: fast and handy Robustness: dont break during computation Adapted Scale: dont loose details but dont compute too finely Parsimony: limited number of parameters Why? 1. Rely more on geologist interpretation 2. Allow easier automation 3. Ease meshing problems 4. And we dont have enough information anyway Editing Forward modelling Restoration 5. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Another world of deformation tools Computer Graphics: Physically-based deformable models Extensive literature with active research Eg. Adaptive space deformations based on rigid cells [Botsch et al, 2007] Transfer to Geosciences [Laurent, 2013] ReedPart I 4/31 Eg. [Nealen et al., 2006] Rigid Element Embedding Deformation eed 6. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Reed in Geosciences [Laurent, 2013] Using this interactive tool in Geoscience: Dynamic editing of Folding structures ReedPart I 5/31 7. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 How does Reed work? Four main steps: ReedPart I 6/31 Object to be deformed Deformation tool Reed 1: Encapsulation in Rigid Elements Cost Function0 1 3: Deformation computation = Optimisation of a cost function 4: Displacement Interpolation Deformed object 2: Define Boundary Conditions 8. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Cost function Neighbourhood constraint: Minimise difference of displacement Integrated over elements volume ReedPart I 7/31 Ri Ti Rj Tj x Dij ci cj 9. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Displacement interpolation The displacement of the rigid elements is Interpolated on the embedded objects Only once at the end (performance) Locate each point to deform Compute displacement for each element Combine linearly ReedPart I 8/31 10. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 A more complete example [Laurent, 2013] Deformation history modelling (as in Noddy [Jessell and Valenta, 1996]) ReedPart I 9/31 11. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 A more complete example [Laurent, 2013] ReedPart I 10/31 12. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 A more complete example [Laurent, 2013] Parameters: Shortening Axial surfaces Amplitude ReedPart I 11/31 13. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 A more complete example [Laurent, 2013] ReedPart I 12/31 14. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Reed Pros and Cons ReedPart I 13/31 Cons: Some missing behaviours (eg. No Poisson effect) No Faults Pros: Interative Space Deformation Robust to extreme deformation Good approximation of flexural behaviour until now! [Molino et al., 2004] Question: How to introduce faults in Reed? Any lead in Computer Graphics? [OBrien and Hodgins, 1999] Not really 15. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Requirements: Being able to evaluate anywhere in 3D The distance to the fault The direction towards the fault Result: Defining a cost function for faults ReedPart I 14/31 f = 0 f = 1 f = -1 f = -2 f = 2 f Init i i+1 16. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Implicit Folding Implicit modelling Part II - Modifying Implicit Methods To Actually Model Folds Part II 15/31 17. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Defining the problems Time: 1st event: S0 (stratigraphy) 2nd event: F1 (folding) may have more fold interference Current geometry = result of complex (multi event) history Data/ Measurements: Bedding observation: Stratigraphy Position of a contact Orientation of a contact Other structural observations: Hinges and Limbs Axial surfaces (+Fold axis) Vergence Fold type (Similar/parallel) Opening, Cylindricity ProblemsPart II 16/31 [Hudleston and Treagus, 2010] Where Geomodelling packages stops. What we are adding. 18. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Implicit Modelling overview Stratigraphy Data Control Points + Regularisation term BasicsPart II 17/31 Stratigraphic value Orientation Continuous values Gradient vary progressively Stratigraphy 19. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Discrete Implicit Modelling overview Discretised Region of Interest Mesh Stratigraphy = piecewise-linear scalar field How to take fold measurements into account? How to overcome constant gradient limitations? limits folding and promotes parallel fold style BasicsPart II 18/31 Stratigraphy x x0 v0 x1 v1 x2 v2 f(x) = i vi f = T . v Build a global system of linear equations Solve to build the scalar field 20. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Geological structures parameterisation How are geological structures taken into account? Faults: Described by structural parameters Centre, Azimuth, Dip, Slip Locality alter the mesh interpolation Fold: Result of the smoothing of data Not really controlled Proposal: Fold structure additional fields: Axial surface field F1: Related (parallel) to foliation field S1 Easier to measure (visible in the limbs) Relatively consistent over the whole area Fold Intensity field: Derived from vergence and S0 observation Quantitative version of the vergence Fold axis field P1: Vectorial field to impose non cylindricity MethodPart II 19/31 Vergence: Hey, Next antiform is this way! 21. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Fold Interpolation Process Interpolate S1 Analyse the vergence to infer the Fold Intensity field Infer gradient direction: Rotation around fold axis direction P1 Interpolate S0 MethodPart II 20/31 S1 Fold intensity 22. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Fold parameter control Fold centre position MethodPart II With classic constraints 21/31 23. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Fold parameter control Fold centre position Inter-limb angle MethodPart II With classic constraints 22/31 24. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Fold parameter control Fold centre position Inter-limb angle Axial surface orientation MethodPart II With classic constraints 23/31 25. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Fold parameter control Fold centre position Inter-limb angle Axial surface orientation Wavelength MethodPart II With classic constraints 24/31 26. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Fold parameter control Fold centre position Inter-limb angle Axial surface orientation Wavelength Tightness MethodPart II With classic constraints 25/31 27. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Regularisation term Constant gradient (classic) Parallel Fold Similar Fold: Conservation: Normalisation: MethodPart II 26/31 Z X X0 X1 f0 f1 f0X0 . f1 = 0- X1 . fi = LXi . 28. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 What can we do with that? Actually simulate folds instead of smoothing stratigraphy. Eg. Somebody said this is not possible (yet): ie. Interpolator smooth the folds. But with our constraints: Need to infer fold parameter. Optimisation/simulation process instead of simple interpolation. ResultPart II 27/31 29. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 What else can we do? Fold parameters simulation: To infer uncertainty related to structural parameters ResultsPart II 28/31 Measurement-related uncertainty Structural uncertainty 30. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 What else can we do? Interference patterns: Fold is defined by scalar field Use deformed geometries as S1 Produce a deformed fold Strategy: Model latest folds first Constrain the geometry Fn-1 based on Fn observations ResultsPart II 29/31 S1 (deformed by F2) S0 (deformed by F1 and F2) 31. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Some 3D The formulation is fully 3D so no problem to go in 3D Implementation in 3D packages to come soon (StructuralLab/Gocad) ResultsPart II 30/31 32. Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014 Contributions: Tools to model 3D folded geometries: Take advantage of complete structural observations Time-aware approaches: Reed: simulate deformation sequence Implicit Folding: use latest events to constrain previous ones Take fully advantage of implicit approaches and extend them. Thank you for your attention. Any questions? conclusionsConclusion 31/31