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Supervised Multiattribute Classification
Kurt J. Marfurt (The University of Oklahoma)
3D Seismic Attributes for Prospect Identification and Reservoir Characterization
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Course OutlineIntroductionComplex Trace, Horizon, and Formation AttributesMultiattribute DisplaySpectral Decomposition
Geometric AttributesAttribute Expression of Geology
Tectonic DeformationClastic Depositional EnvironmentsCarbonate Deposition EnvironmentsShallow Stratigraphy and Drilling HazardsIgneous and Intrusive Reservoirs and Seals
Impact of Acquisition and Processing on AttributesAttribute Prediction of Fractures and StressData ConditioningInversion for Acoustic and Elastic ImpedanceImage Enhancement and Object Extraction
Interactive Multiattribute AnalysisStatistical Multiattribute AnalysisUnsupervised Multiattribute ClassificationSupervised Multiattribute Classification
Attributes and Hydraulic Fracturing of Shale ReservoirsAttribute Expression of the Mississippi Lime
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Multiattribute Analysis Tools
• Statistical Pattern Recognition
• Support Vector Machine
• Projection Pursuit
• Artificial Neural Networks
Supervised Learning
• K-means
• Mixture Models
• Kohonen Self-Organizing Maps
• Generative Topographical Maps
Unsupervised Learning
Machine Learning Attribute AnalysisInterpreter-Driven Attribute Analysis
• Cross-correlation on Maps
• Cross-plotting and Geobodies
• Connected Component Labeling
• Component Analysis
• Image Grand Tour
Interactive Analysis
• Analysis of Variance (ANOVA, MANOVA)
• Multilinear Regression
• Kriging with external drift
• Collocated co-kriging
Statistical Analysis
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Artificial Neural Nets (ANN)
Neurons
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Artificial Neural Nets (ANN)
Objective: From continuous input measurements (e.g. seismic attributes):
• Predict a continuous output (e.g. porosity)
• Predict discrete lithologies (e.g. wet sand, gas sand, limestone, shale,…)
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Artificial Neural Nets (ANN)
Attributes
Looks like a duck?
Quack like a duck?
Walk like a duck?
Observations+1
0
yes
no
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Linear Neurons used in Predictive Deconvolution
(Courtesy Rock Solid Images)
OutputOutputPerceptron,r
N
iiiawy
1
a1
a2
a3
aN
w3
w2
w1
wN
a0=1 (Bias)
w0
N-long operator, w
Prediction
0 1 2 3Time (s)
Prediction distance
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The Perceptron
w2 wnw1
w0
a2ana1
. . .
Input attributes, ai
N
iiiawy
0
1 if y > +0.50 if y < -0.5{Output, r =
yer 1
1
Unknown weights, wia0=1
r
y0.0
0.5
1.0
0.0+1.0 +1.5+0.5-0.5-1.0-1.5
yes
no
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input a1
output r
0 11 0
y
a1
w1= -11
w0= 0.5
r
y0.0
0.5
1.0
0.0+1.0 +1.5+0.5-0.5-1.0-1.5
yes
no
y=-1*0+0.5*1= +0.5
-1*1+0.5*1= -0.5
Inverter
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r
y0.0
0.5
1.0
0.0+1.0 +1.5+0.5-0.5-1.0-1.5
yes
no
input a1
input a2
outputr
0 0 0
0 1 1
1 0 1
1 1 1 a2
y
a1
w2=1w1=1
w0= -0.5
1
y=1*0+1*0-0.5*1= -0.5
y=1*0+1*1-0.5*1= +0.5
y=1*0+1*1+0.5*1= +0.5
y=1*1+1*1-0.5*1= +1.5
Boolean OR
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r
y0.0
0.5
1.0
0.0+1.0 +1.5+0.5-0.5-1.0-1.5
yes
no
input x1
input x2
outputr
0 0 0
0 1 0
1 0 0
1 1 1 a2
y
a1
w2=1w1=1
w0= -1.5
1
Boolean AND
input a1
input a2
outputr
0 0 00 1 01 0 01 1 1
y=1*0+1*0-1.5*1= -1.5
y=1*0+1*1-1.5*1= -0.5
y=1*0+1*1-1.5*1= -0.5
y=1*1+1*1-1.5*1= +0.5
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Boolean XOR
input a1
input a2
outputr
0 0 00 1 11 0 11 1 0 a2
y
a1
Doesn’t work!
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a1
a2
a1
a2
Linear Separability
a1
a2
AND
10
1 1
OR
00
0 1
10
1 0
XOR
OK! OK! Can’t separate!
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a2
h2
w2=1
w1=1 w0= -1.5
1
Boolean ANDh1
a1
w2=1
w1=1
w0= -0.5
1
Boolean OR
y w0= -0.5
1w1=1 w1=-1
input a1
input a2
outputr
0 0 0
0 1 1
1 0 1
1 1 0
r
y0.0
0.5
1.0
0.0+1.0 +1.5+0.5-0.5-1.0-1.5
yes
noy=1*h1-1*h2+-0.5*1=-0.5
y=1*h1-1*h2+-0.5*1=0.5
y=1*h1-1*h2+-0.5*1=0.5
y=1*h1-1*h2+-0.5*1=-0.5
Boolean XOR
the hidden layer!
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(Ross, 2002)
A typical neural network
hidden layer!input layer! output layer!
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Decision workflow
1. Choose the classes you wish to discriminate
2. Choose attributes that differentiate these classes
3. Train using calibrated or “truth” data
4. Validate with “truth” data not used in the training step
5. Apply to the target data
6. Interpret the results
(van der Baan and Jutten, 2000)15-16
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Alternative perceptrons
Discrete output classese.g. lithology
Continuous output classes (e.g. porosity)Intermediate results (in hidden layer)
(van der Baan and Jutten, 2000)
differentiable
differentiable
r(w) r(w)r(w)
fs[r(w)]fG[r(w)]fh[r(w)]
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Attributes Weights Perceptron Output
0 or 1
r(w)
a1
a2
w0
w2
w1
y
2-attribute example with a single decision boundary
(van der Baan and Jutten, 2000)
Decision boundary
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Example of two attributes with a single decision boundary
(van der Baan and Jutten, 2000)
a1
a 2
Class 1
Class 2
Decision boundary
a 2=-w 1
/w 2*a 1
+w 0/w 1
Brad
Brad says: “We could have more than one decision boundary!”
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Attributes Weights Perceptron Output
0 or 1
Weights
Explicit representation
Hidden
Layer
(van der Baan and Jutten, 2000)
Example of two attributes with three decision boundaries
Decision boundaries
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Attributes Weights Perceptron Output
0 or 1
This is a more compact representation of the previous image
Hidden
Layer
(van der Baan and Jutten, 2000)
Example of two attributes with three decision boundaries
Decision boundaries
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a1
a2
Class 2
Class 2 Class 2
Class 1
Class 2 Class 2
boundary 1
boundary 3
boundary 2 Class 2
(van der Baan and Jutten, 2000)
Example of two attributes with three decision boundaries
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The danger of too many boundaries (hidden neurons)
(courtesy Brad Wallet, OU)
Brad
Brad says: “You can overfit your data by putting in too many
decision boundaries, thereby overdividing your attribute space!”
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7th order polynomial
The danger of too many degrees of freedom (polynomial fitting)
a1
a 2
Prediction error
2nd order polynomial
1st order polynomial
Prediction errorPrediction error
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The danger of too many attributes
a1
a 2
4D hyperplane
a3
2D hyperplane (a line)
3D hyperplane (a plane)
J
jjjawwy
10
Training data
Validation data
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A feed-forward network
One of several ways of estimating the weights, w(easily understood by Geophysicists). Use a Taylor Series expansion:
Let’s define
Initial guess based on random weights, w.a0=input attributesz0=output measurements
Prediction error given current weights, w.
Sensitivity of output to the weights (Jacobian matrix) (note that f must be differentiable!)
Equation predicting the output from the input
(van der Baan and Jutten, 2000)
Δw
w
r(w),afw),afz 0
00
(
00 zr(w),afΔz
w
w,afA(w) 0
)(r
ww,A(aΔz 0 )
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J
jj
j
kkk s
s
ttt
1
0 )( Δ(s)
s
Tomography
Known output (measurements)
Differentiable model system
Unknown model parameters
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Known previous model resultl
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j
j
Δww
r(w),azr(w),azz 0
00
Neural networks
Known output (“truth” data)
Known input (attributes)
Unknown weights
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Differentiable model system
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Computing the weights, w
(van der Baan and Jutten, 2000)
w)Δ),A(aΔz 0
w
w,afw),A(a 0
0
)(r
Differentiable preceptron!
f[r(w)]
r(w)
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zwAIwAwAw TT )()()(1
Iterative least-squares solution using the normal equations
Levenberg-Marquardt (or Tikhonov)
Regularization
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(Ross, 2002)
A typical neural network
hidden layer!input layer! output layer!
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Example 1. Mapping a stratigraphic depositional system
(Ruffo et al., 2009)15-32
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Seismic line perpendicular to channel system
(Ruffo et al., 2009)15-33
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Seismic facies classification using a neural network classifier
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Use 4-way averaged vertical 2D GLCM attributes parallel to dip at a suite of azimuths
(Ruffo et al., 2009)15-35
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Seeding the facies classification algorithm
(Ruffo et al., 2009)15-36
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Lithofacies classification
(Ruffo et al., 2009)15-37
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Lithofacies classification scheme
(Ruffo et al., 2009)15-38
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Lithofacies classification
(Ruffo et al., 2009)15-39
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Seismic facies overlain on seismic data
(Ruffo et al., 2009)15-40
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Horizon slice
(Ruffo et al., 2009)15-41
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Example 2. Clustering of - and - volumes
-
(Chopra and Pruden, 2003)15-42
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Neural network estimation
Gamma ray response Porosity(With mask generated from gamma
ray response)
(Chopra and Pruden, 2003)15-43
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San Luis Pass weather prediction exercise
August 24, 2005 – sunnyAugust 25, 2005 - storms August 26, 2005 - sunnyAugust 27, 2005 - sunnyAugust 28, 2005 - sunnyAugust 29, 2005 - storms
Exercise: flip 6 coins: Heads=sunny Tails=stormy
Read out your correlation rate:0/6 = -1.00 3/6 = -0.00 1/6 = -0.67 4/6 = +0.33 2/6 = -0.33 5/6=+0.67 6/6 = 1.00
heads tails
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San Luis Pass weather prediction exercise
Which coins best predict the weather in San Luis Pass?Should Marfurt go fishing?
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(Kalkomey, 1997)
Potential risks when using seismic attributes as predictors of reservoir properties
When the sample size is small, the uncertainty about the value of the true correlation can be large. • given 10 wells with a correlation of r=0.8, the 95%
confidence level is [0.34,0.95]
• given only 5 wells with a correlation of r=0.8, the 95% confidence level is [-0.28,0.99] !
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(Kalkomey, 1997)
Spurious Correlations
A spurious correlation is a sample correlation that is large in absolute value purely by chance.
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(Kalkomey, 1997)
The more attributes, the more spurious correlations!
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(Kalkomey, 1997)
Risk = expected loss due to our
uncertainty about the truth * cost of
making a bad decision
Cost of a Type I Error (using a seismic attribute to predict a reservoir property which is actually uncorrelated) is:• Inaccurate prediction biased by the attribute.• Inflated confidence in the inaccurate prediction — apparent prediction errors are small.
Cost of a Type II Error (rejecting a seismic attribute for use in predicting a reservoir property when in fact they are truly correlated) is:• Less accurate prediction than if we’d used the seismic attribute.• Larger prediction errors than if we’d used the attribute.15-49
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Validation of Attribute Anomalies
1. Basic QC• is the well tie good?• are the interpreted horizons consistent and accurate?• are the correlations statistically meaningful?• is there a physical or well-documented reason for an attribute to correlate
with the reservoir property to be predicted?
2. Validation • does the prediction correlate to control not used in training?• does the prediction make geologic sense?• does the prediction fit production data?• can you validate the correlation through forward modeling?
(Hart, 2002)15-50
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Validation of Attribute Anomalies(Porosity prediction in lower Brushy Canyon)
Right map has higher statistical significance and is geologically more realistic
From probabilistic neural network. From multivariate linear regression
(Hart, 2002)15-51
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Validation of Attribute Anomalies(Through modeling the Smackover formation)
Seismic
Instantaneous frequency
Envelope
Field data Model data
Seismic Attribute Correlations: “Trust, but verify!”(Hart, 2002)15-52
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Validation of Attribute Anomalies(Through engineering and geology)
Neural Net. R=0.96
Multivariate Linear Regression. R=0.89
Dip map. Engineering and geologic analyses indicate fractures, associated with high dip areas, play an important role in enhancing gas production from these tight carbonates. Stars indicate locations of wells drilled in 1999
(Hart, 2002)15-53
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Neural Networks
In Summary
• Neural networks find linear and nonlinear trends in the seismic data that can help correlate well control to maps and formations.
• Avoid using cyclical attributes (phase, strike,…) with neural networks.
• A good neural network application will mimic the interpreter who trains it.
• Don’t ask a poor interpreter to train a neural network!
• Lack of sufficient control or use of too many attributes can lead to false positive and false negative predictions!
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“Understand your assumptions!Quality control your results!
Avoid Mindless Interpretation!”(Bob Sheriff, 2004)
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