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0/31Dr 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 LaurentLaurent Aillères
Lachlan GroseGuillaume
Caumon
Monash
GeoRessources
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Expert-driven approach Sparse Data Qualitative Models
Modelling Geological Structures The modeller’s approach:• Honour data• One state = current state
The geologist’s approach:• Geological scenario• Multiple phases
Approaches to GeomodellingIntroduction
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Data(current state)
timeGeological 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
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Interactive deformation toolReedPart I
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Part I-
Rigid Element Embedding Deformation
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Deformation algorithm for GeomodellingReedPart I
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Our specifications:Usage: Physical Consistency: looks like natural
deformations Interactive: fast and handy
Robustness: don’t break during computation
Adapted Scale: don’t loose details but don’t compute too finely
Parsimony: limited number of parameters
Why?
1. Rely more on geologist interpretation
2. Allow easier automation3. Ease meshing problems4. And we don’t have enough
information anyway…
Editing
Forward modelling
Restoration
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
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Eg. [Nealen et al., 2006]
RigidElementEmbeddingDeformation
eed
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
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
How does Reed work? Four main steps:
ReedPart I
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Object to be deformed
Deformation tool Reed
1: Encapsulation in Rigid Elements
CostFunction0 1
3: Deformation computation= Optimisation of a cost
function
4: Displacemen
t Interpolation
Deformed object
2: Define Boundary Conditions
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Cost function Neighbourhood constraint:• Minimise difference of displacement• Integrated over element’s volume
ReedPart I
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Ri
Ti
Rj
Tj
x
Dij
ci cj
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
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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
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
A more complete example [Laurent, 2013]
ReedPart I
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
A more complete example [Laurent, 2013]
Parameters:• Shortening• Axial surfaces• Amplitude
ReedPart I
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
A more complete example [Laurent, 2013]
ReedPart I
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Reed Pros and ConsReedPart I
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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?
[O’Brien and Hodgins, 1999]
Not really
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 faultsReedPart I
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f = 0
f = 1
f = -1 f = -2
f = 2
f
Init
i
i+1
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Implicit FoldingImplicit modelling
Part II-
Modifying Implicit Methods To Actually Model Folds
Part II
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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
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2010]
Where Geomodelling packages stops.
What we are adding.
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Implicit Modelling overviewStratigraphy Data Control Points + Regularisation term
BasicsPart II
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Stratigraphic value Orientation
Continuous values Gradient vary progressively
Stratigraphy
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
18/31Stratigraphy
xx0
v0 x1
v1
x2
v2
f(x) = λi vi
f = T . v
Build a global system of linear
equations
Solve to build the scalar field
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
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Vergence: Hey, Next antiform is
this way!
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
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S1
Fold intensity
Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Fold parameter control Fold centre position
MethodPart II
With classic constraints
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Fold parameter control Fold centre position Inter-limb angle
MethodPart II
With classic constraints
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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
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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
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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
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Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014
Regularisation term Constant gradient (classic) Parallel Fold Similar Fold:• Conservation:• Normalisation:
MethodPart II
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Z
X
X0
X1
f0
f1
f0X0 . f1 = 0- X1 .
fi = LXi .
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
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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
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Measurement-related uncertainty Structural uncertainty
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
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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
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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
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