Lithofacies Classification in the Barnett Shale Using Proximal Support Vector Machines

Lithofacies Classification in the Barnett Shale Using Proximal Support Vector Machines Tao Zhao*, Vikram Jayaram, Bo zhang and Kurt J. Marfurt, University of Oklahoma Huailai Zhou, Chengdu University of Technology

Outlines Introduction Theory and Formulations Testing and Classification Discussions Conclusions Acknowledgements

Introduction What is the problem? • Huge amount of data • High dimensionality • Nonlinear relation

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 Classification between male and female P1 P2 Height 6’2’’ 5’7’’ Hair length 1in. 20 in.

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 Classification between male and female ? Height 5’8’’ Hair length 15 in. Need more dimensions! IT Specialist

Introduction Why we use PSVM? Explicit geologic meaning for each class Faster than traditional SVM Superior than ANNs

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).

Theory and Formulations Sphericity Unsupervised learning Why we use PSVM? Low Vitamin C? High 2 3 5 6 1 8 9 4 7 10 Medium Vitamin C? Medium High Vitamin C? Low Medium-High Vitamin C? Red Yellow Color Green Purple Blue Medium Vitamin C Low Vitamin C High Vitamin C

Theory and Formulations Sphericity Supervised learning Why we use PSVM? Low Vitamin C High 2 4 5 6 1 8 9 3 7 10 Medium High Vitamin C Medium Vitamin C Low Red Yellow Color Green Purple Blue Medium Vitamin C Low Vitamin C High Vitamin C

Theory and Formulations Fundamentals for PSVM Cartoon illustration for a 2D PSVM classifier

Theory and Formulations Fundamentals for PSVM Cartoon illustration for a 3D PSVM classifier

Theory and Formulations Mapping into higher dimensional space Denotes “A” Denotes “B” A: B: Cartoon illustration for an linearly inseparable problem

Theory and Formulations Mapping into higher dimensional space Denotes “A” Denotes “B” A: B: Decision-boundary These two classes are now separable by a 3D plane. Cartoon illustration for an linearly inseparable problem

Theory and Formulations Mapping into higher dimensional space Denotes “A” Denotes “B” A: B: Decision-boundary Cartoon illustration for an linearly inseparable problem

Testing and Classification Seismic waveform classification Binary classification between shale and limestone in a Barnett Shale play … dim t.1 t.2 1 2 shale 3 4 5 limestone 6 7 PSVM classifier 8

Testing and Classification Seismic waveform classification Sample traces are selected by interpreters across the survey 14 ms time window Time slice at 1376 ms

Testing and Classification Seismic waveform classification Testing the robustness

Testing and Classification shale Seismic waveform classification Time (ms) 1370 1384 Forestburg Limestone Marble Falls Limestone Lower Barnett Shale Upper Barnett Shale Classification result Crossline limestone N Upper Barnett Shale Forestburg Limestone Lower Barnett Shale Marble Falls Limestone Inline 0.5 miles

Testing and Classification Well log classification Well base map 175 150 125 well D well C inline 100 well B 75 50 25 Training well Testing well well A 200 175 150 100 125 50 75 25 crossline 0.5 miles

Testing and Classification Lithology from well log interpretation Blue: Limestone Green: Shale Lithology from PSVM Blue: Limestone Green: Shale 5000 P-wave (ft/s) 20000 Well log classification 0 Gamma Ray (API) 150 1.5 Density (g/cc) 3 Marble Falls Limestone Well log classification correlating with lithologic interpretation Training correctness: 89% Testing correctness: 88% Upper Barnett Limestone Depth (ft) Upper Barnett Shale 7800 Forestburg Limestone 8000 Lower Barnett Shale 8200 8400 8600

Discussions Seismic waveform classification The boundary between two PSVM classes matches the interpreted formation boundary nicely. Lower Barnett Shale 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. Upper Barnett Shale Forestburg Limestone A zoom-in view of the previous PSVM classification map 0.3 miles

Discussions Well log classification 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. It can provide a fast and reliable reference when human interpretation is tedious. A segment from the previous PSVM well log classification result

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.

Discussions σ BI_C BI_N Brittleness index estimation Depth (ft) Brittleness index (BI) estimation using PSVM on well logs from four rock properties

Discussions Brittleness index estimation BI_N = 10 BI_N = 9 BI_N = 8 BI_N = 7 BI_N = 6 Brittleness Index BI_N = 5 BI_N = 4 BI_N = 3 BI_N = 2 BI_N = 1 Depth (ft) Normalized Brittleness index

Discussions Brittleness index estimation CDP Number 60 120 90 30 180 150 BI_C 10 1.2 Marble Falls t0 (s) Upper Barnett Forestburg 1.3 Lower Barnett 0 Viola 1.4 Estimated brittleness index (BI) using PSVM on seismic prestack inversion 0.2 0 Miles

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.

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.

THANKS Questions and suggestions?

References • Cortes, 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., NelloCristianini, 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 tripoliticchert 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.

Appendix Multiclass classification? How we assign a class to an unknown sample Set class “A” as the pilot class Turn all classes into active Examine the binary PSVM classification factor (CF) of the current pilot class against every other active classes. Example of a classification factor table Yes All CFs are positive? Assign the current pilot class to this sample and exit No 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.

Appendix Multiclass classification? Testing results for multiclass classification

Lithofacies Classification in the Barnett Shale Using Proximal Support Vector Machines