Support Vector Machine for 3D Geological Modelling

Support Vector Machine for 3D Geological
Modelling
Alex Smirnoff, Eric Boisvert, Serge J. Paradis
Geological Survey of Canada, Quebec
Groundwater
Groundwater flow dynamics in an Abitibi esker with
3D geological and hydrological modelling
2
Objectives
Find or develop a tool capable of re-constructing
volumes from sparse geological information
Test the tool on available data sets
Make conclusions about its use
3
Potential Input Data
Well data
Surface geology
Cross-sections
4
Interpolation vs. Classification
Point-by-Point InterpolationBoundary Classification
?
?
?
?
Class 2
Class 1
Geology:
-Unit 1
-Unit 2
-Unknown
5
The SVM
Support Vector Machine
Boundary Classification Method
Based on Statistical Learning Theory
Developed by V. Vapnik(1995)
Becomes increasingly popular
6
xi
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Class 1
Class 2
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SVM Algorithm (Linear)
Feature 1
Feature2
Feature 1
Feature2
Class 1
Class 2
wT
x + b < 0
wT
x + b >0
SH
∆
∆
w
T
x
i
+

b

=

0
wT
xi
+ b < 0
wT
xi
+ b >0
SH
∆
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x
3.
x
1.
Class 1Class 2
SVM Algorithm (Non-Linear)
Class 1
x2
x
2.
Class 1
Class 2
Class 1
Class 2
Class 1
8
Multi-Class SVM
Class 1
Class 2
Feature 1
Feature2
Class 3
SH 1
SH 2
SH 3
9
3D Modelling with SVM
Y
X
Z
Feature3
F
e
a
t
u
r
e

1
F
e
a
t
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r
e

2
Training Set:
-Class 1
-Class 2
-Class 3
To Classify:
-Unknown
10
SVM Implementation
LIBSVM –From National University of Taiwan
Non-Linear SVM
Radial Basis Function (RBF) kernel
Controlled by only two parameters
11
Saint-Mathieu –Berry Esker
Binary Reconstruction
X
Z
Y
Training Set
Original Model
SVM Output
12
Input Data and Results
INPUT DATA:
Total points: 389235
Training Set: 17452 (4.48%) –2 units on 11 sections
RESULTS:
Total Classified: 371783
Success: 361909 (97.34%)
Failure: 9874 (2.66%)
13
Success in Class 1 (Esker)
0
10
20
30
40
50
60
70
80
90
100
0
240
All Sections
Success Rate (%)
Section 2
Section 1
Section 3
Section 4
Section 5
Section 6
Section 7
Section 8
Section 9
Section 10
Section 11
Training Sections
10
230
220
210
200
190
180
170
160
150
140
130
120
110
90
80
70
60
50
40
30
20
100
SouthNorth
14
Saint-Mathieu –Berry Esker
Multi-Class Reconstruction
1 -Organic
2 -Littoral
3 -Clay
4 -Esker
5 -Till
6 -Bedrock
15
Esker: Input & Output
16
Unit Comparison
O
r
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g
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a
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Bedrock
O
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a
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R
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o
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Till
O
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a
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R
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Esker
O
r
i
g
i
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a
l
R
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c
o
n
s
t
r
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d
20
Clay
O
r
i
g
i
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a
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R
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o
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s
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Littoral
O
r
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a
l
R
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c
o
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s
t
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Organic
O
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g
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a
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R
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o
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s
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Reconstruction Statistics
95.453.81148413199056. Bedrock
89.87
4.48
17452
371783
7. All
45.720.19747151185. Till
67.650.26995193054. Esker
57.100.16628126673. Clay
37.200.0519336262. Littoral
18.760.014811621. Organic
Success %
% of Total
Training
Set
To Classify
Class
24
Success per Class
0
20
40
60
80
100
0.010.1
1
10
Training Points (%)
Success(%)
Organic
Littoral
Till
Clay
Esker
Bedrock
1
25
Surface Area
1.00E+08
1.00E+09
1.00E+071.00E+081.00E+09
Original
Reconstructed
1.00E+07
Bedrock
Esker
Till
Clay
Littoral
Organic
26
Volume
1.00E+07
1.00E+08
1.00E+09
1.00E+10
1.00E+11
1.00E+071.00E+081.00E+091.00E+101.00E+11
Original
Reconstructed
Bedrock
Esker
Till
Clay
Littoral
Organic
27
Adjusting the Output
SVM
Training
Set
C
γ
RBF KernelParameter
Penalty Parameter
Prediction
Model
28
HMSH vs. SMSH
Class 1
Class 2
Feature 1
Feature2
HMSH
∆
High C
Class 1
Class 2
Feature 1
Feature2
∆
Low C
SMSH
29
Penalty in Modelling
30
High Penalty vs. Low Penalty
High C
Low C
31
Best Pair of Parameters?
lg(C)
lg(γ)
-3-10-2-4-5-8-7-6213945781061112131415
-1
6
12
11
10
9
8
7
5
4
3
2
1
0
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-Best Overall Result (97.79%)
-Previous Example (97.34%)
All Experiments
Range
C=2-3-2
15;
γ
= 24-2
9
-3-10-2213945781061112131415
lg(C)
6
9
8
7
5
4
lg(γ)
32
Influence of C & γ
Low
γ
C
High
Low
High
33
Portneuf: Input & Output
34
Portneuf: Geological Units
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
35
Bedrock
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
36
Till
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
37
Deep Marine
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
38
Deltaic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
39
Littoral
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
40
Proglacial
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
41
Fluvio-Glacial
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
42
Alluvial
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
43
Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
4 -Deltaic
3 -Deep Marine
1 -Bedrock
2 -Till
5 -Littoral
6 -Proglacial
7 -Fluvio-Glacial
8 -Alluvial
9 -Organic
44
Validation
1. Training Set
2. Validation Set
3. Success: 79%
45
Conclusions
SVM can be efficiently used in 3D geological
reconstructions
Reproducible 3D geological models can be built in a
single step with very few parameters set by the user
Number of units can vary from two to many
Data from wells, surface geology maps and arbitrarily
located cross-sections can be easily integrated in a
single model
46
References
Abe, S., 2005. Support Vector Machines for Pattern
Classification. Springer-Verlag, London, 343pp.
Cristianini, N., Shawe-Taylor, J., 2000. Support
Vector Machines. Cambridge University Press,
189pp.
Vapnik, V., 1995. The Nature of Statistical Learning
Theory. Springer-Verlag, New York, 311pp.
3D Geological Modeling: Solving as a Classification
Problem with the Support Vector Machine –
presentation at DMT-2006