tao zhao*, vikram jayaram, bo zhang and kurt j. marfurt, university of oklahoma huailai zhou,...

Tao Zhao*, Vikram Jayaram, Bo zhang and Kurt J. Marfurt, University of Oklahoma

Huailai Zhou, Chengdu University of Technology

Lithofacies Classification in the Barnett Shale Using Proximal Support Vector Machines

Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

2

Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

3

Introduction

What is the problem?

• Huge amount of data

• High dimensionality

• Nonlinear relation

4

Introduction

What is a proximal support vector machine (PSVM)?Proposed by Fung and Mangasarian (2001, 2005)

A recent variant of support vector machine (SVM) (Cortes and Vapnik, 1995)

Supervised machine learning technique that can recover the latent relation between existing properties and measurements

Height

Hair length

P1 P2

6’2’’ 5’7’’

1 in. 20 in.

Classification between male and female

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Introduction

What is a proximal support vector machine (PSVM)?Proposed by Fung and Mangasarian (2001, 2005)

A recent variant of support vector machine (SVM) (Cortes and Vapnik, 1995)

Supervised machine learning technique that can recover the latent relation between existing properties and measurements

Height

Hair length

5’8’’

15 in.

Classification between male and female

6

?IT Specialist Need more dimensions!

Introduction

Why we use PSVM?

1. Explicit geologic meaning for each class

2. Faster than traditional SVM

3. Superior than ANNs

7

Introduction

How we use PSVM?

We applied PSVM to delineate shale and limestone in the Barnett Shale from both seismic and well log data.

General stratigraphy of the Ordovician to Pennsylvanian section in the FWB through a well in the study area (After Loucks and Ruppel, 2007).

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Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

9

Theory and Formulations

Why we use PSVM?

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Sphericity

ColorRed Yellow Green Blue Purple

Hig

hM

ediu

mLo

w

AttributeSample Color Sphericity

1 Red High

2 Red Mid-Low

3 Green Mid-Low

4 Purple Medium

5 Blue Mid-Low

6 Yellow-Green Low

7 Green Low

8 Red-Yellow Low

9 Blue-Purple Medium

10 Red-Yellow High10

1

2

3

4

5

6

7

8

9

Low Vitamin C?

High Vitamin C?

Medium Vitamin C?

Medium-High Vitamin C?

Low Vitamin C High Vitamin C Medium Vitamin C

Unsupervised learning

Theory and Formulations

Why we use PSVM?

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Sphericity

ColorRed Yellow Green Blue Purple

Hig

hM

ediu

mLo

w

AttributeSample Color Sphericity

1 Red High

2 Red Mid-Low

3 Green Mid-Low

4 Purple Medium

5 Blue Mid-Low

6 Yellow-Green Low

7 Green Low

8 Red-Yellow Low

9 Blue-Purple Medium

10 Red-Yellow High10

1

2

3

4

5

6

7

8

9

Low Vitamin C

Medium Vitamin C

High Vitamin C

Low Vitamin C High Vitamin C Medium Vitamin C

Supervised learning

Theory and Formulations

Cartoon illustration for a 2D PSVM classifier

Fundamentals for PSVM

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Theory and Formulations

Cartoon illustration for a 3D PSVM classifier

Fundamentals for PSVM

13

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

14

Denotes “A”Denotes “B”

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

15

Denotes “A”Denotes “B”

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

16

Denotes “A”Denotes “B”

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

17

Denotes “A”Denotes “B”

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

18

Denotes “A”Denotes “B”

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

19

Denotes “A”Denotes “B”

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

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Denotes “A”Denotes “B”

These two classes are now separable by a 3D plane.

Decision-boundary

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

21

Denotes “A”Denotes “B”

Decision-boundary

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑦 , 𝑥2+ 𝑦2)

Theory and Formulations

Cartoon illustration for an linearly inseparable problem

Mapping into higher dimensional space

22

Denotes “A”Denotes “B”

Decision-boundary

𝑥2+𝑦2=1

𝑥2+𝑦2=2

A:

B:

(𝑥 , 𝑦 )

(𝑥 , 𝑥2+ 𝑦2)

Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

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Testing and Classification

Binary classification between shale and limestone in a Barnett Shale play

Seismic waveform classification

dim12345678

t.1 t.2 …

shale

limestone

PSVM classifier

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Testing and Classification

Sample traces are selected by interpreters across the survey

Seismic waveform classification

Time slice at 1376 ms 25

14 ms tim

e

window

Testing and Classification

Testing the robustness

Seismic waveform classification

Percentage of Traces Used in Training

Number of Training Traces Number of Testing Traces Correctness (%)

10% 16 145 83.45

20% 32 129 87.6

30% 48 113 84.1

40% 64 97 80.41

50% 80 81 90.12

50% 81 80 93.75

60% 97 64 93.75

70% 113 48 93.75

80% 129 32 90.63

90% 145 16 93.75 26

Testing and Classification

Classification result

Seismic waveform classification

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N

Marble Falls Limestone

Upper Barnett Shale

Forestburg Limestone

Lower Barnett Shale

Lower Barnett Shale Upper Barnett Shale

Forestburg Limestone

Marble Falls Limestone

Inlin

e

Crossline

Time (ms)1370

1384

shale

limestone

0.5 miles

Testing and Classification

Well base map

Well log classificationin

line

crossline

25

50

75

100

125

150

175

25 50 75 100 125 150 175 200

Training well Testing well

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0.5 miles

well A

well B

well C

well D

Testing and Classification

Well log classification correlating with lithologic interpretation

Well log classification

Lithology from well log interpretation

Blue: LimestoneGreen: Shale

Lithology from PSVM

Blue: LimestoneGreen: Shale

Marble Falls Limestone

Upper Barnett Limestone

Upper Barnett Shale

Lower Barnett Shale

Forestburg Limestone

5000 P-wave (ft/s) 20000

0 Gamma Ray (API) 150

1.5 Density (g/cc) 3

Training correctness: 89% Testing correctness: 88%

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7800

Depth (ft)

8000

8400

8200

8600

Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

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Discussions

The boundary between two PSVM classes matches the interpreted formation boundary nicely.

Seismic waveform classification

A zoom-in view of the previous PSVM classification map

Reliable classification rate can be achieved by training with as little as 0.2% of the data.

It can provide a reliable reference when human interpretation is tedious.

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Forestburg Limestone

Upper Barnett Shale

Lower Barnett Shale

0.3 miles

Discussions

Blind well testing correctness (88%) is close to the training correctness (89%), which indicates the PSVM classifier is capable of generalizing to a well with distance.

Three fundamental well logs are used as inputs instead of more advanced elastic properties, which can still guarantee a reliable classification.

Well log classification

A segment from the previous PSVM well log classification result

It can provide a fast and reliable reference when human interpretation is tedious.

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Discussions

One step further?Originally SVMs are built to solve binary classification problems.

Multiclass PSVM has been proposed by researchers, and we improved the classification robustness.

We then applied multiclass PSVM for brittleness index estimation in the Barnett Shale and it has provided promising result.

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Discussions

Brittleness index estimation

34Brittleness index (BI) estimation using PSVM on well logs from four rock properties

BI_N BI_Cσ

Depth (ft)

Discussions

Brittleness index estimation

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Normalized Brittleness index

6600 6800 7000 7200 7400 7600 7800 80000

0.1

0.2

0.3

0.4

0.5

0.6

0.7 BI_N = 10

BI_N = 9

BI_N = 8

BI_N = 7

BI_N = 6

BI_N = 5

BI_N = 4

BI_N = 3

BI_N = 2

BI_N = 1

Bri

ttle

ness

Ind

ex

Depth (ft)

Discussions

Brittleness index estimation

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Estimated brittleness index (BI) using PSVM on seismic prestack inversion

1.2

1.3

1.4

30 60 12090

t 0 (

s)

CDP Number

180

BI_C

Miles

0 0.2

10

0

150

Marble Falls

Upper Barnett

Forestburg

Lower Barnett

Viola

Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

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Conclusions

PSVM lithofacies classification showed promising results in both seismic and well log data.

Multiclass PSVM classifiers are also available and ready for more complicated applications.

Brittleness index estimation proves the capability of PSVM in a 3D multi-attribute classification using a vector of seismic attributes.

We also anticipate comparisons between PSVM and other supervised (e.g. artificial neural networks or ANN) and unsupervised (e.g. SOM, generative topographic mapping or GTM) classification algorithms.

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Outlines

Introduction

Theory and Formulations

Testing and Classification

Discussions

Conclusions

Acknowledgements

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Acknowledgement

Thanks to Devon Energy for providing the data, all sponsors of Attribute Assisted Seismic Processing and Interpretation (AASPI) consortium group for their generous sponsorship, and colleagues for their valuable suggestions.

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THANKS

Questions and suggestions?

ReferencesCortes, C. and V. Vapnik, 1995, Support-vector networks: Machine Learning, 20, 273-297.

Fung, G. and O. L. Mangasarian, 2001, Proximal support vector machine classifiers: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM 2001, 77-86.

Fung, G. M. and O. L. Mangasarian, 2005, Multicategory proximal support vector machine classifiers: Machine Learning, 59, 77-97.

Loucks, R. G. and S. C. Ruppel, 2007, Mississippian Barnett Shale: Lithofacies and depositional setting of a deep-water shale-gas succession in the Fort Worth Basin, Texas: AAPG Bulletin, 91, 579-601.

Mangasarian, O. L. and E. W. Wild, 2006, Multisurface proximal support vector machine classification via generalized eigenvalues: IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 69-74.

Platt, John C., Nello Cristianini, and John Shawe-Taylor, 1999, Large margin DAGs for multiclass classification: nips, 12, 547-553.

Roy, A., B. J. Dowdell, and K. J. Marfurt, 2013, Characterizing a Mississippian tripolitic chert reservoir using 3D unsupervised and supervised multiattribute seismic facies analysis: An example from Osage County, Oklahoma: Interpretation, 1, SB109-SB124.

Roy, A., A. S. Romero-Peláez, T. J. Kwaitkowski, and K. J. Marfurt, 2014, Generative topographic mapping for seismic facies estimation of a carbonate wash, Veracruz Basin, southern Mexico: Interpretation, 2, SA31-SA47.

Torres, A. and J. Reveron, 2013, Lithofacies discrimination using support vector machines, rock physics and simultaneous seismic inversion in clastic reservoirs in the Orinoco Oil Belt, Venezuela: SEG Technical Program Expanded Abstracts 2013, 2578-2582.

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Multiclass classification?How we assign a class to an unknown sample A B C D

A 0.3 -1.2 2.3

B -0.3 0.8 -1.1

C 1.2 -0.8 -1.9

D -2.3 1.1 1.9

Example of a classification factor table

Examine the binary PSVM classification factor (CF) of the current pilot class against every other active classes.

Find the class corresponds to the most negative CF value, then assign that class as the new pilot class, and turn the current pilot class into inactive.

All CFs are positive?

Yes Assign the current pilot class to this sample and exit

Set class “A” as the pilot class

Turn all classes into active

No

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Appendix

Appendix

Multiclass classification?Testing results for multiclass classification

Dataset Sample size

Testing size Dimension Number of class nu delta Sample

reduced to (%)Training

correctnessTesting

correctnessPendigits 7494 3498 16 10 2000 0.0001 10 97.72% 97.11%Pendigits 7494 3498 16 10 2000 0.0001 20 99.25% 97.20%Pendigits 7494 3498 16 10 2000 0.0001 30 99.56% 98.20%Pendigits 7494 3498 16 10 2000 0.0001 40 99.64% 97.71%Pendigits 7494 3498 16 10 2000 0.0001 50 99.73% 97.94%letter_scale 15000 5000 16 26 20000 0.1 10 82.69% 82.06%letter_scale 15000 5000 16 26 20000 0.1 20 89.70% 89.42%letter_scale 15000 5000 16 26 20000 0.1 30 93.23% 91.86%letter_scale 15000 5000 16 26 20000 0.1 40 94.83% 93.44%

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