Gautier Laurent - Implicit Modelling and volume deformation

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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 Aillères
Lachlan Grose
Guillaume Caumon
Monash
GeoRessources

 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)
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

Interactive deformation tool
ReedPart I
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Part I
-
Rigid Element Embedding Deformation

Deformation algorithm for Geomodelling
ReedPart 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 automation
3. Ease meshing problems
4. And we don’t have enough information
anyway…
Editing
Forward modelling
Restoration

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]
Rigid
Element
Embedding
Deformation
eed

Reed in Geosciences [Laurent, 2013]
 Using this interactive tool in Geoscience:
• Dynamic editing of Folding structures
ReedPart I
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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
Cost
Function0 1
3: Deformation computation
= Optimisation of a cost function
4: Displacement
Interpolation
Deformed object
2: Define Boundary Conditions

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

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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A more complete example [Laurent, 2013]
 Deformation history modelling (as in Noddy [Jessell and Valenta, 1996])
ReedPart I
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ReedPart I
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 Parameters:
• Shortening
• Axial surfaces
• Amplitude
ReedPart I
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ReedPart I
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Reed Pros and Cons
ReedPart 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

 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
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f = 0
f = 1
f = -1 f = -2
f = 2
f
Init
i
i+1

Implicit Folding
Implicit modelling
Part II
-
Modifying Implicit Methods
To Actually Model Folds
Part II
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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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[Hudleston and Treagus, 2010]
Where
Geomodelling
packages
stops.
What we are adding.

Implicit Modelling overview
Stratigraphy  Data Control Points + Regularisation term
BasicsPart II
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 Stratigraphic value
 Orientation
 Continuous values
 Gradient vary progressively
Stratigraphy

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
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Stratigraphy
x
x0
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

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!

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

Fold parameter control
 Fold centre position
MethodPart II
With classic constraints
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 Inter-limb angle
MethodPart II
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 Axial surface orientation
MethodPart II
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 Wavelength
MethodPart II
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 Wavelength
 Tightness
MethodPart II
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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 .

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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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

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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S1 (deformed by F2) S0 (deformed by F1 and F2)

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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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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Gautier Laurent - Implicit Modelling and volume deformation

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Gautier Laurent - Implicit Modelling and volume deformation

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