Refining 3D Earth models by unifying geologicaland geophysical information on unstructured
meshes
Peter Lelievre, Angela Carter-McAuslan, Cassandra Tycholiz,Colin Farquharson and Charles Hurich
Memorial University,Department of Earth Sciences,
St. John’s, Newfoundland, Canada
EGU GA, ERE3.1, April 26, 2012
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Motivation: The common Earth model
Earth models used for mineral exploration or other subsurfaceinvestigations should be consistent with all available geologicaland geophysical information
Geophysical inversion provides the means to unify geologicaland geophysical data towards the development of a commonEarth model
Lelievre et al., [email protected] Inversion on unstructured meshes (2 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Geophysical inversion
Forward problem
Earth model (e.g. density) Survey data (e.g. gravity)
Inverse problem
Lelievre et al., [email protected] Inversion on unstructured meshes (3 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Geophysical inversion
Incorporation of geological and geophysical data intoinversions is always an iterative process
Geophysical Data
Geological Data
Inversion Earth Model
More information ⇒ reduce non-uniqueness ⇒ higherpotential to resolve deeper features
Lelievre et al., [email protected] Inversion on unstructured meshes (4 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Geological models
3D geological ore deposit models are commonly created duringdelineation drilling:
visualization
calculate volumes of ore reserves
accuracy is crucial to determine if deposit is economical
typically comprise wireframe surfaces of connected trianglesthat represent geological contacts
Lelievre et al., [email protected] Inversion on unstructured meshes (5 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Geophysical models
In contrast, most current 3D geophysical modelling is performedon 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
Lelievre et al., [email protected] Inversion on unstructured meshes (6 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Geophysical models
In contrast, most current 3D geophysical modelling is performedon 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
Lelievre et al., [email protected] Inversion on unstructured meshes (7 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Why unstructured meshes?
Incompatibility:
most current 3D geological Earth models comprise wireframesurfaces (tessellated triangles)
most current 3D geophysical modelling is performed onrectilinear meshes (rectangular prisms)
Lelievre et al., [email protected] Inversion on unstructured meshes (8 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Unstructured meshes
Unstructured meshes provide:
efficient generation ofcomplicated geometries
significant reduction inproblem size(57,132 vs. 139,810)
Lelievre et al., [email protected] Inversion on unstructured meshes (9 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Unstructured meshes
Unstructured meshes provide:
efficient generation ofcomplicated geometries
significant reduction inproblem size(57,132 vs. 139,810)
Lelievre et al., [email protected] Inversion on unstructured meshes (10 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
The common Earth modelGeophysical inversionGeological and geophysical modelsInstructured meshes
Unstructured meshes
Advantages:
efficient generation of complicated geometries
significant reduction in problem size
Challenges:
create, manipulate and visualize Earth models
mathematics of numerical modelling
Lelievre et al., [email protected] Inversion on unstructured meshes (11 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Creation and manipulationForward modellingInverse modellingComputational challenges
Wireframe creation, manipulation and visualization
Gocad
FacetModeller
Blender
ParaView
(FacetModeller)
(ParaView)
Lelievre et al., [email protected] Inversion on unstructured meshes (12 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Creation and manipulationForward modellingInverse modellingComputational challenges
Volumetric discretization of wireframes
2D: Triangle (J. R. Shewchuck)
3D: TetGen (H. Si)
the triangular wireframe surface facets become the faces oftetrahedra in the volumetric model
geological and geophysical models can share the samemodelling mesh; they can be the same model
Lelievre et al., [email protected] Inversion on unstructured meshes (13 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Creation and manipulationForward modellingInverse modellingComputational 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 Lelievre)
geoelectric (Amir Javaheri)
electromagnetic (Hormoz Jahandari, Masoud Ansari)
Lelievre et al., [email protected] Inversion on unstructured meshes (14 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Creation and manipulationForward modellingInverse modellingComputational challenges
Standard deterministic inversion approach
Objective functionΦ = Φd + βΦm
Data misfit
Φd =∑i
(dpredi (m)− dobs
i
σi
)2
Model structure (regularization)
Φm = [smallness term] + [smoothness term]
Lelievre et al., [email protected] Inversion on unstructured meshes (15 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Creation and manipulationForward modellingInverse modellingComputational challenges
Regularization
The same regularization is possible on unstructured or rectilinearmeshes provided that appropriate matrix operators can be created
regular rectilinear triangular unstructured
Lelievre et al., [email protected] Inversion on unstructured meshes (16 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Creation and manipulationForward modellingInverse modellingComputational challenges
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
Lelievre et al., [email protected] Inversion on unstructured meshes (17 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Voisey’s BayGravity gradiometry dataInversion results
Voisey’s Bay example
nickel-copper-cobalt sulfide deposit
north-east coast of Labrador, Canada
Lelievre et al., [email protected] Inversion on unstructured meshes (18 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Voisey’s BayGravity gradiometry dataInversion results
Gravity gradiometry (tensor) data
noisy zz-component noise plus signal from extension
Lelievre et al., [email protected] Inversion on unstructured meshes (19 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Voisey’s BayGravity gradiometry dataInversion results
True model
Lelievre et al., [email protected] Inversion on unstructured meshes (20 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Voisey’s BayGravity gradiometry dataInversion results
Unconstrained inversion
(gravity gradiometry data only)
Recovery of shallow sulphide body only
Lelievre et al., [email protected] Inversion on unstructured meshes (21 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
Voisey’s BayGravity gradiometry dataInversion results
Geologically-constrained inversion
(gneiss-troctolite surface and appropriate bounds)
Indication of extension ⇒ refine geological model; collect downhole data
Lelievre et al., [email protected] Inversion on unstructured meshes (22 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
ConclusionAcknowledgements
Conclusion
most current 3D geological Earth models comprise wireframesurfaces
in contrast, most current 3D geophysical modelling isperformed on rectilinear meshes
working with unstructured meshes allows for efficientincorporation of complicated a priori geometries(forward modelling; constrained inversions)
Lelievre et al., [email protected] Inversion on unstructured meshes (23 / 24)
MotivationWorking with unstructured meshes
Inversion exampleConclusion
ConclusionAcknowledgements
Acknowledgements
ACOA(Atlantic Canada Opportunities Agency)
NSERC(Natural Sciences and Engineering Research Council of Canada)
Vale
Lelievre et al., [email protected] Inversion on unstructured meshes (24 / 24)
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