uncertainty in geological mapping - lachlan grose (monash uni.)

School of Geosciences

Investigating uncertainty in geological maps using geological variability and geodiversity

Lachlan Grose, Laurent Ailleres, Gautier Laurent and Peter Betts

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What are geological maps? how do we create them?

• A topological representation of geological interactions eg. Lithological boundaries, structures.

• Essentially a 2D model

• Human interpolation between outcrops guided by knowledge and experience

• Interpolation is similar to how implicit 3D models are built

• Studies looking into uncertainty in 3D models have used implicit scheme, we used 40 students

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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This study

Geological variability as a proxy for geological uncertainty

40 geological maps of the Eldee Structure, Broken Hill

Locate and quantifying geological variability between maps

Identify how maps vary geologically and geometrically due to variability

Classifies geological maps into “species” using the concept of biodiversity

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Three types of uncertainty (Mann, 1993)

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

a.Error, bias and imprecision

b.Inherent randomness

c.Imprecise knowledge

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A sample map of the Eldee structure

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

Metasediments

– Clast-Bearing-Biotite-Gneiss (CBBG)– Interbedded Pelite and psamopelitic schist

(IPP) Large intrusive

– Pegmatite Smaller intrusive

– Felsic gneiss– Amphibolite

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Visualising variability Stratigraphic variability (Lindsay et al. 2012)

– Maximal when most common lithology is least well known– Assesses the quality of the average map

Information entropy (Shannon, 1958; Wellmann et al., 2012)

– Determines amount of information missing from a system– Maximal when all lithologies are equally likely to occur

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Stratigraphic variability (P)

All maps2011 2012+ =

Stratigraphic variability

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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All maps2011 2012+ =

Confidence map 70% cutoff

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

CBBG IPP PEG

FELS AMPH

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Entropy (H)

All maps2011 2012+ =

Information entropy

Information entropy (H)

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Probability

Felsic gneiss

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

All maps2011 2012+ =

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Probability

Amphibolite

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

All maps2011 2012+ =

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Lawrence, 2008; Lindsay et al., 2013

Comparing maps using geodiversity• Biodiversity allows for;

• Diversity of species described by a number of metrics• Trends in dataset to be identified

• Geodiversity

• Built on the concept of biodiversity• Geometrical and geological metrics can be used to

analyse the diversity of a set of geological maps/models• Trends between maps can be found highlighting different

“species” of maps/models

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Analysing geodiversity• Principal Component Analysis (PCA)

• Used by Lindsay et al. 2013• Identifies linear trends in the dataset• A common dimension reduction technique• However many of the geodiversity metrics don’t follow

standard distributions - which can introduce error!• May bias towards modal map (modal geodiversity values)

• Self Organising Maps (SOMs) (Kohonen, 1982)

• Fits a deformable mesh to the dataset capturing more details about the distribution of the original dataset

• Also provides dimension reduction• Can be used to categorise groups of similar maps

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Sml Med Lge Legs Feathers

Hair Hooves

Mane

Run Swim Hunt Fly

dove 1 0 0 2 1 0 0 0 0 0 0 1

hen 1 0 0 2 1 0 0 0 0 0 0 0

duck 1 0 0 2 1 0 0 0 0 1 0 0

goose 1 0 0 2 1 0 0 0 0 1 0 1

owl 1 0 0 2 1 0 0 0 0 0 1 1

hawk 1 0 0 2 1 0 0 0 0 0 1 1

eagle 0 1 0 2 1 0 0 0 0 0 1 1

fox 0 1 0 4 0 1 0 0 0 0 1 0

dog 0 1 0 4 0 1 0 0 1 0 1 0

wolf 0 1 0 4 0 1 0 1 1 0 1 0

cat 1 0 0 4 0 1 0 0 0 0 1 0

tiger 0 0 1 4 0 1 0 0 1 0 1 0

lion 0 0 1 4 0 1 0 1 1 0 1 0

horse 0 0 1 4 0 1 1 1 1 0 0 0

zebra 0 0 1 4 0 1 1 1 1 0 0 0

cow 0 0 1 4 0 1 1 0 0 0 0 0

A quick example of SOMs

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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SOMs component maps

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Animal groups

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

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Geodiversity metrics

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

Aspect ratio

Geological Complexity

Contact relationships

Surface area and number of regionsOrientation

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SOMs geodiversity results

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

Number of regions PEGMATITE

Number of regions FELSIC GNEISS

Contact between INTERBEDDED AND

FELSIC GNEISS

Maximum surface area PEGMATITE

Number of regions INTERBEDDED

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Map “species”

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

Species 1 Species 2 Species 3

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Probability

The modal map

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

All maps2011 2012+ =

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Conclusion

6th Febuary 2014Geological uncertainty in geological maps using variability and geodiversity

Variability observed between students interpretation of the geometry of lithological domains

The felsic gneiss and amphibolite were rarely mapped consistently in the one location

◦ We identified three distinct clusters highlight different mapping styles; lumpers, blobbers and the outliers!

◦ Self Organising Maps should be considered for further geodiversity analysis