Mark Jessell - The topology of geology
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Transcript of Mark Jessell - The topology of geology
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