Florian Wellmann: Uncertainties in 3D Models

Uncertainties in 3-D Structural Models

A Probabilistic Perspective and some Considerations to include AdditionalGeological Knowledge

Centre for Exploration Targeting (CET)

Geomodelling seminar presentation

March 1, 2014

(3D Interest Group) Uncertainties in 3-D Structural Models March 1, 2014 1 / 55

Overview of Presentation

3-D GeologicalModelling

Uncertainties

Probabilistic frameworkfor multiple constraints

Model validation andgeological “rules”

Application: NorthPerth Basin

Future work

Uncertainties

Future work

Uncertainties

Future work

Uncertainties

Future work

Uncertainties

Future work

Part 1: Geological Modelling and Uncertainties

Uncertainties

Future work

Why 3-D Modelling?

Why make 3-D models?

To spin them around andimpress (“cyber-kineticart”)

As an act of learningwhile modelling

3-D extension of maps

As basis for simulations(property distributions)

Prospectivity analysis

Multiple methods and approaches

SKUA%Earthvision% Geomodeller%

Noddy%

Explicit(

Implicit(

Kinema/c/(Mechanical(

Geophysical(Inversion(

Kine3D%

Vulcan%(old)%

Why 3-D Modelling?

Noddy%

Explicit(

Implicit(

Kine3D%

Vulcan%(old)%

Why 3-D Modelling?

Noddy%

Explicit(

Implicit(

Kine3D%

Vulcan%(old)%

Why 3-D Modelling?

Noddy%

Explicit(

Implicit(

Kine3D%

Vulcan%(old)%

Why 3-D Modelling?

Noddy%

Explicit(

Implicit(

Kine3D%

Vulcan%(old)%

Why 3-D Modelling?

Noddy%

Explicit(

Implicit(

Kine3D%

Vulcan%(old)%

Challenges in 3-D Modelling

Challenges depend on the application and the specific scale,some general points:

What is a good model?

Usability (beyond pretty pictures)

Reproducibility and extensibility

Separation of data and interpretation

Consideration of uncertainty

Uncertainties in 3-D Geological Modelling

Types of uncertainty

Mann (1993):

Error, bias, imprecision

Inherent randomness

Incomplete knowledge

Bardossy and Fodor (2001):

Sampling andobservation error

Variability andpropagation error

Conceptual and modeluncertainty

Mann (1993):

Inherent randomness

Mann (1993):

Inherent randomness

Mann (1993):

Inherent randomness

Geological Uncertainties are real

Field example by Courrioux et al.: comparing multiple 3-D models,created for same region, by different teams of students

Yellow lines: surface contacts White lines: faults

(From: Courrioux et al., 34th IGC, Brisbane, 2012)

Unfortunately, quite infeasible in real applications...

Stochastic Geological Modelling

Stochastic modelling approach

Primary Observations

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

Principal Component 10

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

2 Lithologies per voxel 6

Gravity misfit

-2.5 mgal 1.5

Figure 2

(Jessell et al., submitted)

Start with primaryobservations

Assign probabilitydistributions to observations

Randomly generate newobservation sets

Create models for all sets

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Analysis and visualisation

Analysis and visualisation of uncertainties

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Stochastic modelling works, but important further questions:

How to best analyse and visualise uncertainties?

How to ensure that models are valid?

How to include additional geological constraints and knowledge?

How to combine stochastic geological modelling with geophysicalinversions?

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Realisation 1

Realisation n

Realisation 3

Realisation 2

Model 1

Model n

Model 3

Model 2

0.40.30.2

-0.1-0.2-0.3-0.4

0.5-0.5

Initialmodel

Model spaceboundary

Gravity misfit

-2.5 mgal 1.5

Figure 2

Part 2: Model Validation and Geological “Rules”

Uncertainties

Future work

Geological rules and model validation

Problem outline

Initial model and input points and their uncertainties

Reasonable model realisation Failure of model construction Failure of geological constraint

Problem outline

Simple model: Graben

Model of a simple graben (essentially 2-D)

Interpolation with Geomodeller,automation with Python; 3-D view

Geological parameters:

fault positions (•)

surface contact points (•)Uncertainties assigned to points asnormal distributions:

Faults: σ = 100 m in EWdirection

Surfaces: σ = 75 m in zdirection

Geological knowledge: graben,normal faulting, three layers

fault positions (•)surface contact points (•)

Uncertainties assigned to points asnormal distributions:

Model realisations - all models

Consideration of geological knowledge

Encapsulating geological knowledge not taken into account bythe model interpolation method

Fault offset

Regional thickness continuationand variation

Combined effect of syntectonicsedimentation

Implementation of rules in Python package wrapping stochasticgeological uncertainty simulation and rejection sampling

Fault offset

Additional constraints

Additional constraints for Graben model

Additional constraints:

Min/max values for objects

Layer thickness

Fault offset

Thickness variation acrossfault compartments

In total: 27 constraints based onthese geometric relationships defined.

Layer thickness

Fault offset

Layer thickness

Fault offset

Layer thickness

Fault offset

Layer thickness

Fault offset

Model realisations - validated models only

Conclusion

Conclusion from model validation step

First results show that automatic model validation step with additionalconstraints is feasible

However:

Constraints are fixed values, whereas they might actually be highlyuncertain themselves!

Inefficient sampling, high rejection rate (> 99% in this case!)

Conclusion

However:

Conclusion

However:

Conclusion

However:

Part 3: Probabilistic Framework for Multiple Constraints

Uncertainties

Future work

Probabilistic framework - concept

A flexible method is required to handle multiple, possiblyuncertain, additional constraints

Interesting scientific questions:

Which rules led to rejections?Which parameter values led to valid models?How are these parameters correlated?

Additional theoretical considerations:

Efficiency of algorithmPossibility to explore wide range of parameter space (non-linearities)

Hypothesis: probabilistic Bayesian framework and combination withMarkov Chain Monte Carlo (MCMC) sampling suitable to address thesequestions.

Which rules led to rejections?

Which parameter values led to valid models?How are these parameters correlated?

Which rules led to rejections?Which parameter values led to valid models?

How are these parameters correlated?

Efficiency of algorithm

Possibility to explore wide range of parameter space (non-linearities)

Interpretation in the context of Geological Modelling

Bayes’ Rule – linking posterior through prior and likelihood

p(θ|y) =p(y |θ)p(θ)

p(y)(1)

We want to know how geological knowledge (“rules”) reduces theuncertainty of the geological model, therefore:

The (uncertain) geological data are the model, p(θ)

The geological rules are the (additional) data, p(y)

We want to know the posterior p(θ|y): probability (uncertainty) of ageological parameter set, given geological rules

We need to define the likelihood functions p(y |θ): probability of arule, given geological data set

p(y)(1)

Simple example

From simple graben to even simpler example

Reduce the simple graben model to its bare minimum:

From 3-D...

(which is essentially 2-D)

Some random x-range

Thickness (t1)

Depth of surface 1 (d1)

From 3-D (which is essentially 2-D) to 2-D (which is actually even 1-D...)

Simple example

From simple graben to even simpler example

Reduce the simple graben model to its bare minimum:

From 3-D...

(which is essentially 2-D)

Some random x-range

Thickness (t1)

From 3-D (which is essentially 2-D) to 2-D (which is actually even 1-D...)

Prior distribtuions

Prior distributions for depths and thickness: all parametersindependent

0 50 100 150 200 250 300 350Depth [m]

prior d1

prior d2

0 50 100 150 200Depth [m]

prior thickness

Sampling from the posterior

Rejection sampling from posterior, determination of “probable”geological models

0 50 100 150 200 250 300Some random x-range

Selection of prior samples (N=30)

0Selection of accepted samples (N=30)

Sampling from the posterior

Rejection sampling from posterior, determination of “probable”geological models

Selection of prior samples (N=30)

0Selection of accepted samples (N=30)

Posterior distribtuions

Posterior distributions: how did combining the information changeuncertainty?

0 50 100 150 200 250 300 350Depth [m]

prior d1

prior d2

posterior d1

posterior d2

0 50 100 150 200Depth [m]

prior thickness

posterior thickness

Parameter correlation

Parameter correlations: prior and posterior

Parameter correlation

Parameter correlations: prior and posterior

Conclusion from probabilistic approach

What does posterior distribution tell us?

Valid range of model results

Parameter uncertainty reduction!

Insights into parameter correlations

Next steps for probabilistic framework

Use Markov Chain Monte Carlo sampling (with pymc) instead ofrejection algorithm (and compare efficiency)

Implement additional constraints (e.g. off-surface observations)

Detailed analysis of posterior distribution using information theory

Possibly analyse as Bayesian network

Part 3: Application: North Perth Basin

Uncertainties

Future work

Application to North Perth Basin

North Perth Basin probabilistic model – work in progress!

Regional scale model as basis forgeothermal resource estimations

Based on previous GSWA studies andlegacy data

Significant uncertainties at depth

“...owing to the poor quality ofseismic data [...] [the top] Permianis commonly only a phantomhorizon.” (Mory and Iasky, 1996)

How uncertain is the model and how can additional information andgeological knowledge reduce these uncertainties?

Model setup

Initial 3-D geological model

(Mory and Iasky, 1996)

Extent: 34 km EW, 38 km NS, Depth to 7.5 km

Interpolation with Geomodeller,input data discretised as:

Surface contact points

Orientation measurements

Plus: definition of stratigraphyand fault interaction

Model setup

Initial 3-D geological model

(Mory and Iasky, 1996)

Extent: 34 km EW, 38 km NS, Depth to 7.5 km

Interpolation with Geomodeller,input data discretised as:

Surface contact points

Orientation measurements

Plus: definition of stratigraphyand fault interaction

Uncertainties and constraints in cross-sections

Contact points in cross-sections and definition of fault compartments

Cross Section C

Cross Section B

Litho-stratigraphic Column

Yarragadee Formation

Cadda & Cattamarra Formation

Eneabba Member

Woodada and Leseuer Sandstone

Kockatea Shale

Undifferentiated Permian

Undifferentiated Early Permian

PreCambrian_Basement

Fault compartments

7.5 km

(Jonathan Poh et al. in prep.)

Uncertainties and constraints in cross-sections

Contact points in cross-sections and definition of fault compartments

Cross Section C

Cross Section B

Litho-stratigraphic Column

Yarragadee Formation

Cadda & Cattamarra Formation

Eneabba Member

Woodada and Leseuer Sandstone

Kockatea Shale

Undifferentiated Permian

Undifferentiated Early Permian

PreCambrian_Basement

Fault compartments

7.5 km

From tectonic and sedimentary evolution to geological rules

SedimentaryLow High

Tectonics

Low High

akup o

Geological Evolution Combination Applicable Rules Fault Offset Result

Multiple cycles of syn-tectonic sedimentary deposition with

a decrease in effect from sedimentary processes

(Early Permian sequence)

Syn-depositional tectonics with a strong normal faulting

component and a gradually increasing sedimentary process

(Late Permian Sequence)

Syn-depositional tectonics with a decrease in tectonic strength

(reverse faulting took place), sedimentary processes is

assumed to be stablised (Kockatea Shale)

Syn-sedimentary tectonics with a low tectonic strength

(reverted to normal faulting), sedimentary processes have

stablised (Woodada Formation)

Syn-tectonic sedimentary with an slight increased strength

from minor fault event (Eneabba Formation)

Normal Fault + Sedimentary + Normal Fault

(Cattamarra Coal Formation)

Inferred weak sedimentary and tectonic sedimentary

(Cadda Formation)

Syn-sedimentary tectonics with inferred strong sedimentary

and regional tectonic forces (Yarragadee Formation)

Synchronous Rule II (a)

Synchronous Rule II (b)

Synchronous Rule III (b)

Synchronous Rule I, IV or

even sedimentary deposition

Synchronous Rule I

Discrete Rule VI

Synchronous Rule I

(with litho-stratigraphic unit)

Fault offset becomes more

pronounced

Fault offset has increased and

should be greater than the fault

offset during the Early Permian

Fault offset has decreased

Fault offset has increased

Fault offset has increased greatly

Fault offset should remain

unchanged

Sedimentary Key EventsTectonics Key Events

4) Basin organisation with reverse faulting and sinistral transpressional

event (Harris 1994)

1) Neo-proterzoic basement have undergone a series of structural events

that involved syn-rift sequences (Harris 2000, Song & Cawood 2000)

2) End of Syn-rift megasequence I found through an unconformity

at Caryngina Formation and the start of syn-rift II meagsequence

(Norvick 2004)

3) Start of syn-rift II meagsequence (Norvick 2004)

6) Mild tectonism during the Pliensbachian (Norvick 2004)

5) No record of structural near NPB but only in regional scale (Harris 1994)

Tectonic forces is inferred and interpreted to be decreasing in strength

7 & 8) Fault activity found at the start and finish (Norvick 2004)

9) Syn-deposition tectonics during the formation of the

Yarragadee Formation at the Dandaragan Trough

(Norvick 2004, Mory & Iasky 1994)

10) No further information found in literature relating to study area

1) Pre-Cambrian structural activity on the basement which may

have a potential effect on the upcoming Permian units

(Harris 2000, Song & Cawood 2000)

3) Abrupt change in sediment source, resulting in the start of the

deposition of Kockatea Shale (Cawood and Nemchin 2000)

5) Deposition should have appeared in between two discrete fault

events (Norvick 2004)

4) Local thickening of units over the Mid-Triassic period

(Norvick 2004)

at Caryngina Formation and the start of syn-rift II

megasequence (Cawood and Nemchin 2000)

Regional Thickening

Direction

Legend

Data found in paleo-current studies and isopach maps

in Mory & Iasky 1996

Sedimentary Events

Tectonic Events

SW to NE

(700m - 1000m)

S to NE

(50m - 200m)

NW to SE

(50m - 200m)

N-NW to S-SE

(150m - 200m)

N to S

(150m - 200m)

Slight syn-sedimentary tectonics due to the presence of fault

controlled thickening (Leseur Sandstone Formation)

Synchronous Rule I or

even sedimentary depositionFault offset has increased

N to S

(300m - 400m)

E to W

(1500m - 2500m)

SedimentaryLow High

Tectonics

Low High

akup o

(Cadda Formation)

Synchronous Rule I

Discrete Rule VI

Synchronous Rule I

pronounced

unchanged

event (Harris 1994)

(Norvick 2004)

Regional Thickening

Direction

Legend

Sedimentary Events

Tectonic Events

SW to NE

(700m - 1000m)

S to NE

(50m - 200m)

NW to SE

(50m - 200m)

N-NW to S-SE

(150m - 200m)

N to S

(150m - 200m)

N to S

(300m - 400m)

E to W

(1500m - 2500m)

SedimentaryLow High

Tectonics

Low High

akup o

(Cadda Formation)

Synchronous Rule I

Discrete Rule VI

Synchronous Rule I

pronounced

unchanged

event (Harris 1994)

(Norvick 2004)

Regional Thickening

Direction

Legend

Sedimentary Events

Tectonic Events

SW to NE

(700m - 1000m)

S to NE

(50m - 200m)

NW to SE

(50m - 200m)

N-NW to S-SE

(150m - 200m)

N to S

(150m - 200m)

N to S

(300m - 400m)

E to W

(1500m - 2500m)

North Perth Basin - first results, unvalidated models

Next step: parameterise and add constraints

Combining probabilistic modelling with resourceestimations

Probabilistic geothermal resource assessment

Geothermal resource estimation forNorth Perth Basin model withestimation of uncertainty:

Simulate temperature field forall valid models

calculate geothermal resource(heat in place)

Preliminary results, presented at

Australian Geothermal Energy Conference

Conclusion from application to NPB

Possible to separate significant phases from geological evolution toderive constraints

Python workflow for stochastic simulations works for (reasonably)complex models

Combination with geothermal resource estimation feasible

Next steps

Define probability distributions for all data points

Quantify geological rules

Perform rejection sampling for automatic model validation

Compare differences in geothermal resource estimation

Next steps

Outlook and Future Work

Uncertainties

Future work

Consideration of additional constraints

Additional geologically motivated constraints

Geometric constraints

Min/max extent

On-surface

Off-surfaceCorrelation

Thickness

Volume

Curvature

Lateral Extent

Stratigraphic relationships

Lateral Extent

Consideration of additional constraints

Additional geologically motivated constraints

Geometric constraints

Min/max extent

On-surface

Off-surfaceCorrelation

Thickness

Volume

Curvature

Lateral Extent

Stratigraphic relationships

thLateral Extent

Fault network constraints

Fault shape and interaction

Fault shape and effect

Direction Angle

Listric

Thickness variation

Lateral Extent

Fault interaction

Lateral Extent Lateral Extent

Fault network constraints

Fault shape and interaction

Fault shape and effect

Direction Angle

Listric

Thickness variation

Lateral Extent

Fault interaction

tLateral Extent Lateral Extent

Curvature analysis

Curvature analysis of surfaces

80100 0

0 50 100 150 200 2500

250Shape index

1.0 0.5 0.0 0.5 1.00

6000 Synclasticsynform

Anticlasticsynform

Anticlasticantiform

Synclasticantiform

Geologic topology

Considerations of geological topology vs. geometric topology

How to characterise topologicalelements with a geologic meaning?

Fault surfaces

Discontinuities

Geologic topology

Fault surfaces

Discontinuities

Geologic topology

Fault surfaces

Discontinuities

Geologic topology

Fault surfaces

Discontinuities

... ?(3D Interest Group) Uncertainties in 3-D Structural Models March 1, 2014 51 / 55

Combination with kinematic modelling

Using Noddy for kinematic modelling to parameterise geologicalknowledge

Start with a stratigraphicpile

Add geological historyevents, for example:

FoldingFaulting

Idea: use as stochastic model to generate typical probabilitydistributions expected for specific events (simplest case: fault offset, asused before!)

Folding

Faulting

FoldingFaulting

Combining geological modelling and multiphase flowsimulations

Combined inversion of structural interpolation and fluid flowsimulation

Combination with Seismics: Madagascar

Combining implicit geological modelling with seismic simulations

Thank you

Florian Wellmann: Uncertainties in 3D Models

Self Improvement

Transcript of Florian Wellmann: Uncertainties in 3D Models