gautier laurent - implicit modelling and volume deformation

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0/31 Dr Gautier Laurent 3D Interest Group Meeting 10 th 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

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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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Page 1: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 2: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 3: Gautier Laurent - Implicit Modelling and volume deformation

Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014

Interactive deformation toolReedPart I

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Part I-

Rigid Element Embedding Deformation

Page 4: Gautier Laurent - Implicit Modelling and volume 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

Page 5: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 6: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 7: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 8: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 9: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 10: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 11: Gautier Laurent - Implicit Modelling and volume deformation

Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014

A more complete example [Laurent, 2013]

ReedPart I

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Page 12: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 13: Gautier Laurent - Implicit Modelling and volume deformation

Dr Gautier Laurent 3D Interest Group Meeting 10th June 2014

A more complete example [Laurent, 2013]

ReedPart I

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Page 14: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 15: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 16: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 17: Gautier Laurent - Implicit Modelling and volume deformation

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.

Page 18: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 19: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 20: Gautier Laurent - Implicit Modelling and volume deformation

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!

Page 21: Gautier Laurent - Implicit Modelling and volume deformation

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

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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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Page 23: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 24: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 25: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 26: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 27: Gautier Laurent - Implicit Modelling and volume deformation

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 .

Page 28: Gautier Laurent - Implicit Modelling and volume deformation

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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Page 29: Gautier Laurent - Implicit Modelling and volume deformation

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

Page 30: Gautier Laurent - Implicit Modelling and volume deformation

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

29/31S1 (deformed by F2) S0 (deformed by F1 and F2)

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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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Page 32: Gautier Laurent - Implicit Modelling and volume deformation

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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