Unstructured grid modelling to create 3-D Earth models that unify geological and geophysical information

Transcription

1 Unstructured grid modelling to create 3-D Earth models that unify geological and geophysical information Peter Lelièvre, Angela Carter-McAuslan, Cassandra Tycholiz, Colin Farquharson and Charles Hurich Memorial University, Department of Earth Sciences, St. John s, Newfoundland, Canada GAC-MAC Annual Meeting, SS14, May 28, 2012

2 The common Earth model Geological and geophysical models Instructured meshes Motivation: The common Earth model Lelièvre et al., Unstructured grid modelling (2 / 24)

3 The common Earth model Geological and geophysical models Instructured meshes Motivation: The common Earth model Earth models used for mineral exploration or other subsurface investigations should be consistent with all available geological and geophysical information Lelièvre et al., Unstructured grid modelling (2 / 24)

4 The common Earth model Geological and geophysical models Instructured meshes Motivation: The common Earth model Earth models used for mineral exploration or other subsurface investigations should be consistent with all available geological and geophysical information provides the means to unify geological and geophysical data towards the development of a common Earth model Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (2 / 24)

5 The common Earth model Geological and geophysical models Instructured meshes Forward problem Earth model (e.g. density) Survey data (e.g. gravity) Inverse problem Lelièvre et al., Unstructured grid modelling (3 / 24)

6 The common Earth model Geological and geophysical models Instructured meshes Incorporation of geological and geophysical data into inversions is always an iterative process Lelièvre et al., Unstructured grid modelling (4 / 24)

7 The common Earth model Geological and geophysical models Instructured meshes Incorporation of geological and geophysical data into inversions is always an iterative process Geophysical Data Inversion Earth Model Geological Data Lelièvre et al., Unstructured grid modelling (4 / 24)

8 The common Earth model Geological and geophysical models Instructured meshes Incorporation of geological and geophysical data into inversions is always an iterative process Geophysical Data Inversion Earth Model Geological Data More information reduce non-uniqueness higher potential to resolve deeper features Lelièvre et al., Unstructured grid modelling (4 / 24)

9 Geological models Motivation The common Earth model Geological and geophysical models Instructured meshes 3D geological ore deposit models are commonly created during delineation drilling: Lelièvre et al., Unstructured grid modelling (5 / 24)

10 Geological models Motivation The common Earth model Geological and geophysical models Instructured meshes 3D geological ore deposit models are commonly created during delineation drilling: visualization calculate volumes of ore reserves accuracy is crucial to determine if deposit is economical Lelièvre et al., Unstructured grid modelling (5 / 24)

11 Geological models Motivation The common Earth model Geological and geophysical models Instructured meshes 3D geological ore deposit models are commonly created during delineation drilling: visualization calculate volumes of ore reserves accuracy is crucial to determine if deposit is economical typically comprise wireframe surfaces of connected triangles that represent geological contacts Lelièvre et al., Unstructured grid modelling (5 / 24)

12 Geophysical models The common Earth model Geological and geophysical models Instructured meshes In contrast, most current 3D geophysical modelling is performed on rectilinear meshes: Lelièvre et al., Unstructured grid modelling (6 / 24)

13 Geophysical models The common Earth model Geological and geophysical models Instructured meshes In contrast, most current 3D geophysical modelling is performed on rectilinear meshes: simplifies the development of numerical methods Lelièvre et al., Unstructured grid modelling (6 / 24)

14 Geophysical models The common Earth model Geological and geophysical models Instructured meshes In contrast, most current 3D geophysical modelling is performed on rectilinear meshes: simplifies the development of numerical methods incompatible with wireframe geological models: - can be impossible to adequately model complicated geology - produce pixellated representations 55x82x31=139,810 cells and stair-casing still evident Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (6 / 24)

15 Geophysical models The common Earth model Geological and geophysical models Instructured meshes In contrast, most current 3D geophysical modelling is performed on rectilinear meshes: simplifies the development of numerical methods incompatible with wireframe geological models: - can be impossible to adequately model complicated geology - produce pixellated representations 55x82x31=139,810 cells and stair-casing still evident Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (7 / 24)

16 Why unstructured meshes? The common Earth model Geological and geophysical models Instructured meshes Incompatibility: most current 3D geological Earth models comprise wireframe surfaces (tessellated triangles) most current 3D geophysical modelling is performed on rectilinear meshes (rectangular prisms) Lelièvre et al., Unstructured grid modelling (8 / 24)

17 Unstructured meshes The common Earth model Geological and geophysical models Instructured meshes Unstructured meshes provide: efficient generation of complicated geometries significant reduction in problem size (57,132 vs. 139,810) Lelièvre et al., Unstructured grid modelling (9 / 24)

18 Unstructured meshes The common Earth model Geological and geophysical models Instructured meshes Unstructured meshes provide: efficient generation of complicated geometries significant reduction in problem size (57,132 vs. 139,810) Lelièvre et al., Unstructured grid modelling (9 / 24)

19 Unstructured meshes The common Earth model Geological and geophysical models Instructured meshes Unstructured meshes provide: efficient generation of complicated geometries significant reduction in problem size (57,132 vs. 139,810) Lelièvre et al., Unstructured grid modelling (10 / 24)

20 Unstructured meshes The common Earth model Geological and geophysical models Instructured meshes Advantages: efficient generation of complicated geometries significant reduction in problem size Lelièvre et al., Unstructured grid modelling (11 / 24)

21 Unstructured meshes The common Earth model Geological and geophysical models Instructured meshes Advantages: efficient generation of complicated geometries significant reduction in problem size Challenges: create, manipulate and visualize Earth models mathematics of numerical modelling Lelièvre et al., Unstructured grid modelling (11 / 24)

22 Creation and manipulation Forward modelling Inverse modelling Computational challenges Wireframe creation, manipulation and visualization Gocad FacetModeller (FacetModeller) Blender ParaView (ParaView) Lelièvre et al., Unstructured grid modelling (12 / 24)

23 Creation and manipulation Forward modelling Inverse modelling Computational challenges Volumetric discretization of wireframes 2D: Triangle (J. R. Shewchuck) 3D: TetGen (H. Si) Lelièvre et al., Unstructured grid modelling (13 / 24)

24 Creation and manipulation Forward modelling Inverse modelling Computational challenges Volumetric discretization of wireframes 2D: Triangle (J. R. Shewchuck) 3D: TetGen (H. Si) the triangular wireframe surface facets become the faces of tetrahedra in the volumetric model Lelièvre et al., Unstructured grid modelling (13 / 24)

25 Creation and manipulation Forward modelling Inverse modelling Computational challenges Volumetric discretization of wireframes 2D: Triangle (J. R. Shewchuck) 3D: TetGen (H. Si) the triangular wireframe surface facets become the faces of tetrahedra in the volumetric model geological and geophysical models can share the same modelling mesh; they can be the same model Lelièvre et al., Unstructured grid modelling (13 / 24)

26 Creation and manipulation Forward modelling Inverse modelling Computational challenges Forward modelling on unstructured meshes We have developed modelling methods for various data types: gravity (Hormoz Jahandari) gravity gradiometry (Cassandra Tycholiz) magnetics (Cassandra Tycholiz) seismic first-arrivals (Peter Lelièvre) geoelectric (Amir Javaheri) electromagnetic (Hormoz Jahandari, Masoud Ansari) Lelièvre et al., Unstructured grid modelling (14 / 24)

27 Creation and manipulation Forward modelling Inverse modelling Computational challenges Standard deterministic inversion approach Objective function Φ = Φ d + βφ m Data misfit Φ d = i ( d pred i ) 2 (m) di obs σ i Model structure (regularization) Φ m = [smallness term] + [smoothness term] Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (15 / 24)

28 Regularization Motivation Creation and manipulation Forward modelling Inverse modelling Computational challenges The same regularization is possible on unstructured or rectilinear meshes provided that appropriate matrix operators can be created regular rectilinear triangular unstructured Lelièvre et al., Unstructured grid modelling (16 / 24)

29 Computational challenges Creation and manipulation Forward modelling Inverse modelling Computational challenges Algorithms can be designed that exploit mesh structure: sparsity structure of spatial matrix operators compression of full sensitivity matrices regular rectilinear triangular unstructured Lelièvre et al., Unstructured grid modelling (17 / 24)

30 Voisey s Bay example Voisey s Bay Gravity gradiometry data Inversion results nickel-copper-cobalt sulfide deposit north-east coast of Labrador, Canada Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (18 / 24)

31 Gravity gradiometry (tensor) data Voisey s Bay Gravity gradiometry data Inversion results noisy zz-component noise plus signal from extension Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (19 / 24)

32 True model Motivation Voisey s Bay Gravity gradiometry data Inversion results Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (20 / 24)

33 Unconstrained inversion Voisey s Bay Gravity gradiometry data Inversion results (gravity gradiometry data only) Recovery of shallow sulphide body only Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (21 / 24)

34 Geologically-constrained inversion Voisey s Bay Gravity gradiometry data Inversion results (gneiss-troctolite surface and appropriate bounds) Indication of extension refine geological model; collect downhole data Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (22 / 24)

35 Motivation Acknowledgements most current 3D geological Earth models comprise wireframe surfaces Lelièvre et al., Unstructured grid modelling (23 / 24)

36 Motivation Acknowledgements most current 3D geological Earth models comprise wireframe surfaces in contrast, most current 3D geophysical modelling is performed on rectilinear meshes Lelièvre et al., Unstructured grid modelling (23 / 24)

37 Motivation Acknowledgements most current 3D geological Earth models comprise wireframe surfaces in contrast, most current 3D geophysical modelling is performed on rectilinear meshes working with unstructured meshes allows for efficient incorporation of complicated a priori geometries (forward modelling; constrained inversions) Lelièvre et al., plelievre@mun.ca Unstructured grid modelling (23 / 24)

38 Acknowledgements Motivation Acknowledgements ACOA (Atlantic Canada Opportunities Agency) NSERC (Natural Sciences and Engineering Research Council of Canada) Vale Lelièvre et al., Unstructured grid modelling (24 / 24)

39 Additional Slides Follow Lelièvre et al., Unstructured grid modelling (25 / 24)

40 Rectilinear meshes may require infeasibly many cells for adequate representation pixellated representation 256 cells Lelièvre et al., Unstructured grid modelling (26 / 24)

41 Quadtree & octree meshes need fewer cells and are still structured pixellated representation 946 cells (4096 in underlying regular mesh) Lelièvre et al., Unstructured grid modelling (27 / 24)

42 Unstructured triangular & tetrahedral meshes efficient generation of complicated geometries significant reduction in problem size 183 cells Lelièvre et al., Unstructured grid modelling (28 / 24)