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Supervised Multiattribute Classification Kurt J. Marfurt (The University of Oklahoma) Kurt J. Marfurt (The University of Oklahoma) 3D Seismic Attributes for Prospect Identification and Reservoir Characterization 15-1

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Course Outline Introduction Complex Trace, Horizon, and Formation Attributes Multiattribute Display Spectral Decomposition Geometric Attributes Attribute Expression of Geology Tectonic Deformation Clastic Depositional Environments Carbonate Deposition Environments Shallow Stratigraphy and Drilling Hazards Igneous and Intrusive Reservoirs and Seals Impact of Acquisition and Processing on Attributes Attribute Prediction of Fractures and Stress Data Conditioning Inversion for Acoustic and Elastic Impedance Image Enhancement and Object Extraction Interactive Multiattribute Analysis Statistical Multiattribute Analysis Unsupervised Multiattribute Classification Supervised Multiattribute Classification Attributes and Hydraulic Fracturing of Shale Reservoirs Attribute Expression of the Mississippi Lime 15-2

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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 15-3

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Artificial Neural Nets (ANN) Neurons 15-4

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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 a continuous output (e.g. porosity) Predict discrete lithologies (e.g. wet sand, gas sand, limestone, shale,…) Predict discrete lithologies (e.g. wet sand, gas sand, limestone, shale,…) 15-5

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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 15-6

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Linear Neurons used in Predictive Deconvolution (Courtesy Rock Solid Images) Output Perceptron,r a1a1a1a1 a2a2a2a2 a3a3a3a3 aNaNaNaN w3w3w3w3 w2w2w2w2 w1w1w1w1 wNwNwNwN a 0 =1 (Bias) w0w0w0w0 N-long operator, w Prediction 0 1 2 3 Time (s) Prediction distance 15-7

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The Perceptron w2w2 wnwn w1w1 w0w0 a2a2 anan a1a1... Input attributes, a i 1 if y > +0.5 0 if y < -0.5 { Output, r = Unknown weights, w i a 0 =1 r y 0.0 0.5 1.0 0.0 +1.0+1.5+0.5-0.5-1.5 yes no 15-8

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input a 1 output r 01 10 y a1a1a1a1 w 1 = -1 1 w 0 = 0.5 r y 0.0 0.5 1.0 0.0 +1.0+1.5+0.5-0.5-1.5 yes no y=-1*0+0.5*1= +0.5 -1*1+0.5*1= -0.5 Inverter 15-9

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r y 0.0 0.5 1.0 0.0 +1.0+1.5+0.5-0.5-1.5 yes no input a 1 input a 2 outputr 000 011 101 111 a2a2a2a2 y a1a1a1a1 w 2 =1 w 1 =1 w 0 = -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 15-10

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r y 0.0 0.5 1.0 0.0 +1.0+1.5+0.5-0.5-1.5 yes no input x1 input x2 outputr 000 010 100 111 a2a2a2a2 y a1a1a1a1 w 2 =1 w 1 =1 w 0 = -1.5 1 Boolean AND input a 1 input a 2 outputr000 010 100 111 y=1*0+1*0-1.5*1= -1.5 y=1*0+1*1-1.5*1= -0.5 y=1*1+1*1-1.5*1= +0.5 15-11

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Boolean XOR input a 1 input a 2 output r 000 011 101 110 a2a2a2a2 y a1a1a1a1 Doesn’t work! 15-12

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a1a1a1a1 a2a2a2a2 a1a1a1a1 a2a2a2a2 Linear Separability a1a1a1a1 a2a2a2a2 AND 10 11 OR 00 01 10 10 XOR OK! OK! Can’t separate! 15-13

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a2a2a2a2 h2h2h2h2 w 2 =1 w 1 =1 w 0 = -1.5 1 Boolean AND h1h1h1h1 a1a1a1a1 w 2 =1 w 1 =1 w 0 = -0.5 1 Boolean OR y w 0 = -0.5 1 w 1 =1 w 1 =-1 input a 1 input a 2 outputr 000 011 101 110 r y 0.0 0.5 1.0 0.0 +1.0+1.5+0.5-0.5-1.5 yes no y=1*h 1 -1*h 2 +-0.5*1=-0.5 y=1*h 1 -1*h 2 +-0.5*1=0.5 y=1*h 1 -1*h 2 +-0.5*1=-0.5 Boolean XOR the hidden layer! 15-14

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(Ross, 2002) A typical neural network hidden layer! input layer! output layer! 15-15

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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 classes e.g. lithology Continuous output classes (e.g. porosity) Intermediate results (in hidden layer) (van der Baan and Jutten, 2000) differentiable differentiable r(w) f s [r(w)] f G [r(w)] f h [r(w)] 15-17

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AttributesWeightsPerceptron Output 0 or 1 r(w) a1a1a1a1 a2a2a2a2 w0w0w0w0 w2w2w2w2 w1w1w1w1 y 2-attribute example with a single decision boundary (van der Baan and Jutten, 2000) Decision boundary 15-18

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Example of two attributes with a single decision boundary (van der Baan and Jutten, 2000) a1a1a1a1 a2a2a2a2 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!” 15-19

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Attributes Weights Perceptron Output 0 or 1 Weights Explicit representation Hidden Layer Layer (van der Baan and Jutten, 2000) Example of two attributes with three decision boundaries Decision boundaries 15-20

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Attributes Weights Perceptron Output 0 or 1 This is a more compact representation of the previous image Hidden Layer Layer (van der Baan and Jutten, 2000) Example of two attributes with three decision boundaries Decision boundaries 15-21

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a1 a1 a1 a1 a2 a2 a2 a2 Class 2 Class 2 Class 1 Class 1 Class 2 Class 2 boundary 1 boundary 1 boundary 3 boundary 3 boundary 2 boundary 2 Class 2 Class 2 (van der Baan and Jutten, 2000) Example of two attributes with three decision boundaries 15-22

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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!” 15-23

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7 th order polynomial The danger of too many degrees of freedom (polynomial fitting) a1a1a1a1 a2a2a2a2 Prediction error 2 nd order polynomial 1 st order polynomial Prediction error 15-24

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The danger of too many attributes a1a1a1a1 a2a2a2a2 4D hyperplane a3a3a3a3 2D hyperplane (a line) 3D hyperplane (a plane) Training data Validation data 15-25

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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. a 0 =input attributes z 0 =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) 15-26

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Tomography Known output (measurements) Differentiable model system Unknown model parameters 15-27 Known previous model resultl

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Neural networks Known output (“truth” data) Known input (attributes) Unknown weights 15-28 Differentiable model system

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Computing the weights, w (van der Baan and Jutten, 2000) Differentiable preceptron! f[r(w)] r(w) 15-29

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Iterative least-squares solution using the normal equations Levenberg-Marquardt (or Tikhonov) Regularization 15-30

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(Ross, 2002) A typical neural network hidden layer! input layer! output layer! 15-31

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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 (Ruffo et al., 2009) 15-34

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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 – sunny August 25, 2005 - storms August 26, 2005 - sunny August 27, 2005 - sunny August 28, 2005 - sunny August 29, 2005 - storms Exercise: flip 6 coins: Heads=sunny Heads=sunny Tails=stormy 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 6/6 = 1.00 heads tails 15-44

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San Luis Pass weather prediction exercise Which coins best predict the weather in San Luis Pass? Should Marfurt go fishing? 15-45

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(Kalkomey, 1997) Potential risks when using seismic attributes as predictors of reservoir properties 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 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] ! given only 5 wells with a correlation of r=0.8, the 95% confidence level is [-0.28,0.99] ! 15-46

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(Kalkomey, 1997) Spurious Correlations A spurious correlation is a sample correlation that is large in absolute value purely by chance. 15-47

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(Kalkomey, 1997) The more attributes, the more spurious correlations! 15-48

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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. Inaccurate prediction biased by the attribute. Inflated confidence in the inaccurate prediction — apparent prediction errors are small. 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. Less accurate prediction than if we’d used the seismic attribute. Larger prediction errors than if we’d used the attribute. Larger prediction errors than if we’d used the attribute. 15-49

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Validation of Attribute Anomalies 1. Basic QC 1. Basic QC is the well tie good? is the well tie good? are the interpreted horizons consistent and accurate? are the interpreted horizons consistent and accurate? are the correlations statistically meaningful? 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? is there a physical or well-documented reason for an attribute to correlate with the reservoir property to be predicted? 2. Validation 2. Validation does the prediction correlate to control not used in training? does the prediction correlate to control not used in training? does the prediction make geologic sense? does the prediction make geologic sense? does the prediction fit production data? does the prediction fit production data? can you validate the correlation through forward modeling? 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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15-54 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.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.Avoid using cyclical attributes (phase, strike,…) with neural networks. A good neural network application will mimic the interpreter who trains it.A good neural network application will mimic the interpreter who trains it. Don’t ask a poor interpreter to train a neural network!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!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) 14-55

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