Applied Geostatistics in R: 7. Conditional Inference Trees for Discrete Facies Prediction given Well Logs and Core data Measurements
Watheq J. Al-Mudhafar, Craft and Hawkins Department of Petroleum Engineering, Louisiana State University
August 15, 2015
Conditional Inference Trees (CITs) is popular tool for regression analysis. CITs estimate a regression relationship by binary recursive partitioning in a conditional inference framework. Different relationships between data can be described with directed and undirected graphs. Based on ts concept, CITs can be used to model categorical variables responses given continuous predictors.
Therefore, CITs was adopted her to predict the discrete Distribution of Facies in a sandstone formation through Karpur Dataset.
Install the packages required to implement CITs algorithm with their functions.
require(party)## Loading required package: party
## Loading required package: grid
## Loading required package: mvtnorm
## Loading required package: modeltools
## Loading required package: stats4
## Loading required package: strucchange
## Loading required package: zoo
##
## Attaching package: 'zoo'
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
##
## Loading required package: sandwichrequire(ipred)## Loading required package: ipredrequire(doParallel)## Loading required package: doParallel
## Loading required package: foreach
## Loading required package: iterators
## Loading required package: parallelrequire(foreach)
require(rgenoud)## Loading required package: rgenoud
## ## rgenoud (Version 5.7-12, Build Date: 2013-06-28)
## ## See http://sekhon.berkeley.edu/rgenoud for additional documentation.
## ## Please cite software as:
## ## Walter Mebane, Jr. and Jasjeet S. Sekhon. 2011.
## ## ``Genetic Optimization Using Derivatives: The rgenoud package for R.''
## ## Journal of Statistical Software, 42(11): 1-26.
## ##require(ggplot2)## Loading required package: ggplot2
##
## Attaching package: 'ggplot2'
##
## The following object is masked _by_ '.GlobalEnv':
##
## mpgrequire(MASS)## Loading required package: MASSrequire(lattice)## Loading required package: latticelibrary(party)
library(ipred)
library(doParallel)
library(foreach)
library(rgenoud)
library(ggplot2)
library(MASS)
library(lattice)Call the dataset and show the dataset head: -
## depth caliper ind.deep ind.med gamma phi.N R.deep R.med SP
## 1 5667.0 8.685 618.005 569.781 98.823 0.410 1.618 1.755 -56.587
## 2 5667.5 8.686 497.547 419.494 90.640 0.307 2.010 2.384 -61.916
## 3 5668.0 8.686 384.935 300.155 78.087 0.203 2.598 3.332 -55.861
## 4 5668.5 8.686 278.324 205.224 66.232 0.119 3.593 4.873 -41.860
## 5 5669.0 8.686 183.743 131.155 59.807 0.069 5.442 7.625 -34.934
## 6 5669.5 8.686 109.512 75.633 57.109 0.048 9.131 13.222 -39.769
## density.corr density phi.core k.core Facies
## 1 -0.033 2.205 33.9000 2442.590 F1
## 2 -0.067 2.040 33.4131 3006.989 F1
## 3 -0.064 1.888 33.1000 3370.000 F1
## 4 -0.053 1.794 34.9000 2270.000 F1
## 5 -0.054 1.758 35.0644 2530.758 F1
## 6 -0.058 1.759 35.3152 2928.314 F1Summary of the dataset.
## depth caliper ind.deep ind.med
## Min. :5667 Min. :8.487 Min. : 6.532 Min. : 9.386
## 1st Qu.:5769 1st Qu.:8.556 1st Qu.: 28.799 1st Qu.: 27.892
## Median :5872 Median :8.588 Median :217.849 Median :254.383
## Mean :5873 Mean :8.622 Mean :275.357 Mean :273.357
## 3rd Qu.:5977 3rd Qu.:8.686 3rd Qu.:566.793 3rd Qu.:544.232
## Max. :6083 Max. :8.886 Max. :769.484 Max. :746.028
##
## gamma phi.N R.deep R.med
## Min. : 16.74 Min. :0.0150 Min. : 1.300 Min. : 1.340
## 1st Qu.: 40.89 1st Qu.:0.2030 1st Qu.: 1.764 1st Qu.: 1.837
## Median : 51.37 Median :0.2450 Median : 4.590 Median : 3.931
## Mean : 53.42 Mean :0.2213 Mean : 24.501 Mean : 21.196
## 3rd Qu.: 62.37 3rd Qu.:0.2640 3rd Qu.: 34.724 3rd Qu.: 35.853
## Max. :112.40 Max. :0.4100 Max. :153.085 Max. :106.542
##
## SP density.corr density phi.core
## Min. :-73.95 Min. :-0.067000 Min. :1.758 Min. :15.70
## 1st Qu.:-42.01 1st Qu.:-0.016000 1st Qu.:2.023 1st Qu.:23.90
## Median :-32.25 Median :-0.007000 Median :2.099 Median :27.60
## Mean :-30.98 Mean :-0.008883 Mean :2.102 Mean :26.93
## 3rd Qu.:-19.48 3rd Qu.: 0.002000 3rd Qu.:2.181 3rd Qu.:30.70
## Max. : 25.13 Max. : 0.089000 Max. :2.387 Max. :36.30
##
## k.core Facies
## Min. : 0.42 F8 :184
## 1st Qu.: 657.33 F9 :172
## Median : 1591.22 F10 :171
## Mean : 2251.91 F1 :111
## 3rd Qu.: 3046.82 F5 :109
## Max. :15600.00 F3 : 55
## (Other): 17Visualize the dataset:
Sample data and split it into two parts: train and test:
## [1] 571 14## [1] 248 14Modeling the Facies given well logs and core data through CITs model for the train partision:
##
## Conditional inference tree with 16 terminal nodes
##
## Response: Facies
## Inputs: depth, caliper, ind.deep, ind.med, gamma, phi.N, R.deep, R.med, SP, density.corr, density, phi.core, k.core
## Number of observations: 571
##
## 1) depth <= 5723.5; criterion = 1, statistic = 468.77
## 2) phi.core <= 26.7824; criterion = 1, statistic = 38.59
## 3)* weights = 7
## 2) phi.core > 26.7824
## 4)* weights = 83
## 1) depth > 5723.5
## 5) density <= 2.21; criterion = 1, statistic = 372.606
## 6) depth <= 5982.5; criterion = 1, statistic = 231.673
## 7) depth <= 5856; criterion = 1, statistic = 165.411
## 8) ind.med <= 84.463; criterion = 1, statistic = 73.293
## 9)* weights = 50
## 8) ind.med > 84.463
## 10) R.med <= 6.419; criterion = 0.989, statistic = 16.707
## 11)* weights = 30
## 10) R.med > 6.419
## 12)* weights = 7
## 7) depth > 5856
## 13) phi.core <= 28.3; criterion = 1, statistic = 79.691
## 14)* weights = 7
## 13) phi.core > 28.3
## 15) density <= 2.078; criterion = 1, statistic = 46.679
## 16) phi.N <= 0.228; criterion = 1, statistic = 20.956
## 17)* weights = 7
## 16) phi.N > 0.228
## 18)* weights = 120
## 15) density > 2.078
## 19)* weights = 7
## 6) depth > 5982.5
## 20) k.core <= 3650; criterion = 1, statistic = 77.488
## 21) depth <= 6069; criterion = 1, statistic = 19.795
## 22)* weights = 115
## 21) depth > 6069
## 23)* weights = 7
## 20) k.core > 3650
## 24)* weights = 12
## 5) density > 2.21
## 25) R.med <= 4.672; criterion = 1, statistic = 50.428
## 26) depth <= 5891.5; criterion = 1, statistic = 35.205
## 27) density <= 2.271; criterion = 0.969, statistic = 9.205
## 28)* weights = 39
## 27) density > 2.271
## 29)* weights = 66
## 26) depth > 5891.5
## 30)* weights = 7
## 25) R.med > 4.672
## 31)* weights = 7Head & Sumary of predicted discrtet distributions of Facies for train partision:
## [1] F1 F1 F1 F1 F1 F1
## Levels: F1 F10 F2 F3 F5 F7 F8 F9Boxplot of observed and predicted Facies for the train data:
CITs Modeling Validation by computing the total correct percent for train data.
##
## qq F1 F10 F2 F3 F5 F7 F8 F9
## F1 87 3 0 0 0 0 0 0
## F10 0 101 0 9 0 0 0 2
## F2 0 0 0 0 0 0 0 0
## F3 0 10 2 23 0 2 0 0
## F5 0 1 1 2 70 0 0 2
## F7 0 0 0 0 1 3 3 0
## F8 0 2 0 0 3 0 129 0
## F9 0 0 0 0 0 0 0 115## F1 F10 F2 F3 F5 F7 F8
## 1.0000000 0.8632479 0.0000000 0.6764706 0.9459459 0.6000000 0.9772727
## F9
## 0.9663866Total percent correct that reflects the CITs accuracy of classificationin train data:
## [1] 0.9246935Total percent correct that reflects the CITs accuracy of classificationin test data based on train modeling:
##
## testPred F1 F10 F2 F3 F5 F7 F8 F9
## F1 24 0 0 0 0 0 0 0
## F10 0 47 2 11 0 0 0 0
## F2 0 0 0 0 0 0 0 0
## F3 0 2 2 8 1 0 0 0
## F5 0 4 1 2 27 0 0 2
## F7 0 0 0 0 3 4 2 0
## F8 0 1 0 0 4 0 49 0
## F9 0 0 0 0 0 0 1 51## F1 F10 F2 F3 F5 F7 F8
## 1.0000000 0.8703704 0.0000000 0.3809524 0.7714286 1.0000000 0.9423077
## F9
## 0.9622642## [1] 0.8467742Decison Tree Plots:
Scattermatrix plot of Lithofacies Classification by CITs:
Visualizing the predicted discrete distribution of the Eight Facies for the full dataset:
## Warning in bxp(structure(list(stats = structure(c(5667, 5680.75, 5694.5, :
## some notches went outside hinges ('box'): maybe set notch=FALSE## Warning in bxp(structure(list(stats = structure(c(5667, 5681, 5695.25,
## 5709.5, : some notches went outside hinges ('box'): maybe set notch=FALSE
References
Hothorn, T. K. Hornik and A. Zeileis. (2006). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651–674. Preprint available from http://statmath.wu-wien.ac.at/~zeileis/papers/Hothorn+Hornik+Zeileis-2006.pdf
Al-Mudhafar, W. J. (2015). Integrating Component Analysis & Classification Techniques for Comparative Prediction of Continuous & Discrete Lithofacies Distributions. Offshore Technology Conference. doi:10.4043/25806-MS.
Karpur, L., L. Lake, and K. Sepehrnoori. (2000). Probability Logs for Facies Classification. In Situ 24(1): 57.
Al-Mudhafer, W. J. (2014). Multinomial Logistic Regression for Bayesian Estimation of Vertical Facies Modeling in Heterogeneous Sandstone Reservoirs. Offshore Technology Conference. doi:10.4043/24732-MS.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 1. Naive Bayes Classifier for Lithofacies Modeling in a Sandstone Formation. RPubs.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 2. Applied Geostatistics in R: 2. Logistic Boosting Regression (LogitBoost) for Multinomial Lithofacies Classification in a Sandstone Formation. RPubs.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 3. Linear Discriminant Analysis (LDA) for Multinomial Lithofacies Classification in a Sandstone Formation. RPubs.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 4. Applied Geostatistics in R: 4. Multinomial Logistic Regression (MLR) for Posterior Lithofacies Probability Prediction in a Sandstone Formation. RPubs.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 5. Improved Reservoir Characterization through Facies Tree-Based Classification Models. RPubs.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 6. Integrating Well Logs and Core Data into Facies Classification through Kernel Support Vector Machine. RPubs.