The Topology of Geology, a work in progress…Mark Jessell, Sam Thiele, Vitaliy Orgarko, Mark Lindsay, Evren Pakyuz-Charrier, Florian Wellmann

• What do I mean by topology… and what I don’t.• 2D• 2D->3D• 3D

Energy Sink

Energy Source

Potential Energy

Gradient Self-Organized System

Entropy (exported to

environment as diffuse heat)

Energy Flux – fed into system at a slow rate

Energy Flux –Released in transient “Avalanches”

Threshold Barrier

A B

Framing of new paradigms

Giant ore deposits are zones of focused mass and energy flux

Giant ore deposits are zones of focused mass and energy flux

So as geologists (and explorers) we need to understand spatial and temporal relationships:

• Fluid pathways & barriers• Thermal, structural, chemical overprinting relationships• Neighbourhood relationships

… we know this, and these concepts are already partially captured in prospectivity mapping as proximity buffers etc.

Chudasama et al., 2016, OGR

Geology Structures Prospectivity

How do we combine these ideas today?

= topologySpatial and temporal relationships

Egenhofer (spatial) relationships

K. L. Burns 1975 Analysis of Geological Events. Mathematical Geology, Vol. 7, No. 4,

Kerry Burns,1975

Non-overlapping spatial topology

What I don’t mean: Map topology

No topology control

2D topology control

What I don’t mean: Mesh topology Pellerin et al., 2011

Analysis of spatial topology

Adjacency Matrices

Network Diagrams Hive Diagram

2D map analytics• What do maps tells us about pathways, spatial

relationships, stratigraphic variation?

Geology Polygons

1:500 000 GSWA Geology Layer (Mount Bruce sub-set)

Potential for data mining (see EJ… )

UNITNAME GROUP MAX_AGE_MA MIN_AGE_MAAshburton Formation Wyloo Group 1806 1799Duck Creek Dolomite Wyloo Group 2010 1799Mount McGrath Formation Wyloo Group 2010 1799Beasley River Quartzite Shingle Creek Group 2208 2208Cheela Springs Basalt Shingle Creek Group 2208 2208Boolgeeda Iron Formation Hamersley Group 2445 2208Kazput Formation Turee Creek Group 2445 2208Koolbye Formation Turee Creek Group 2445 2208Kungarra Formation Turee Creek Group 2445 2208Turee Creek Group Turee Creek Group 2449 2208Woongarra Rhyolite Hamersley Group 2449 2445Weeli Wolli Formation Hamersley Group 2451 2450Brockman Iron Formation Hamersley Group 2494 2451Mount McRae Shale and Mount Sylvia Formation Hamersley Group 2541 2501Wittenoom Formation Hamersley Group 2597 2504Marra Mamba Iron Formation Hamersley Group 2629 2597Jeerinah Formation Fortescue Group 2715 2629Bunjinah Formation Fortescue Group 2718 2715Maddina Formation Fortescue Group 2718 2713Pyradie Formation Fortescue Group 2730 2718Boongal Formation Fortescue Group 2745 2730Hardey Formation Fortescue Group 2766 2749Mount Roe Basalt Fortescue Group 2775 2772Fortescue Group Fortescue Group 2780 2629Milli Milli Inlier metagranitic unit 3500 2830Rocklea Inlier metagranitic unit 3500 2830Milli Milli inlier greenstones 3520 2930Rocklea Inlier greenstones 3520 2930

Stratigraphic Relationships

Fault Relationships

Geology polygon & fault shapefiles converted to WKT format for easy of analysis

Need to distinguish between fault contacts and stratigraphic contacts

A is younger than B

Line width to contact length

Stratigraphic Contact

Relationships

Example unconformable contact relationships

Offlap?

Onlap?

Wyloo

Turee

Shingle Ck

Hamersley

Fortescue

Basement

Full Group topology of Mt Bruce sheet

UNITNAME topology of each group

Formation-level regional analysis

Formation-level polygon analysis

Marra Mamba Iron Formation

SW SE NW NEFormation-level Sub-regional analysis

Fault network1:500 000 GSWA Geology Layer

Strat

Fault

If we include fault contact relationships, this diagram represents the key topological aspects of a mineral system

2D->3D

With the harmonisation of digital geological data available via delivery systems such

as GeoVIEW, we can imagine a world where 3D models are available “on-demand”

2D->3DCurrent Workflow

Insert data into geomodeller

1. Topography

2. Stratigraphic contacts, with structural orientation data

3. Faults with structural orientation data

4. Stratigraphy

5. Fault-Fault age relationships

6. Fault-stratigraphy age relationships

3D model and/or cross-sections

Data availability?

1. Topography SRTM

2. Stratigraphic contacts, with structural orientation data Map + WAROX

3. Faults with structural orientation data Map + WAROX

4. Stratigraphy ? 2D Map Analytics

5. Fault-Fault age relationships ? 2D Map Analytics

6. Fault-stratigraphy age relationships 2D Map Analytics

+

+

+ = 3D

But what if we don’t have enough data to constrain the model (lack of fault dip information for example)?

Original Inputs

Perturbed Inputs 1

Perturbed Inputs 2

Perturbed Inputs 3

Perturbed Inputs 4

Perturbed Inputs N

• • •

Implicit Modelling

Engine

Wellman et al., 2010, 2011Jessell et al., 2010Lindsay et al., 2012,2013

Geological Topological Uncertainty & MC Simulation: Multiple Hypotheses

45

43

47

41

45

44

Could be uncertainty wrt orientation, position, nature, age relationship…

So now, instead on ONE model, we have as many models as our patience allows…

and the challenge changes from perfecting THE MODEL, to analysing the comonalities and differences between suites of geological models

Triple Domain InversionJ Giraud

Dept

h (k

m)

Geological Uncertainty

Density true model Magnetic – true model

Colour scale: likelihood

Contour lines: petrophysical distribution

Petrophysical Uncertainty

Unconstrained single inversion

Petrophys constrained single inversion

Petrophys + geol constrained single inversion

Petrophys constrained joint inversion

Petrophys + geol constrained joint inversion

3D Model topology

a) Connectivity• Flow simulations• Electrical measurementsMassively reduced dimensionality (>4000 x for this example)

b) Litho-structural contacts form the limiting containers for property simulations

c) Geophysical inversions often assume fixed topology to constrain the model space

d) Proxy for plumbing of mineral system Thiele et al., 2016a,b

350,000 voxels

82 elements

Mount Painter InlierArmit et al., Geophys. J. Int. (2014) 199, 253–275

50,000,000 voxels

Unique topologies (overall, structural and lithological) can be identified by comparing graphs using the Jaccard coefficient j (Jaccard, 1901; 1912).

Graphs are considered to be equivalent when the set of arcs defining each graph (A and B) are identical, and hence j=1

𝑗(A, B) = A B / A B

Thiele et al., 2016a,b J Struct Geol accepted

Spot the difference

Conclusions• Spatial and temporal topology have the potential to provide essential insights in to

minerals systems

• We can extract topology from 2D (maps) and 3D models

• In map view we can use the extracted topology to better understand scaling and spatial variation in lithostratigraphic and fault systems ( key Mineral System components)

• We can potentially use the map analytics to help automate the 2D map to 3D model transformation

• 3D model topologies are highly sensitive to small variations in input data and can be used to classify distinct topological classes