Applied Geostatistics in R: 2. Logistic Boosting Regression (LogitBoost) for Multinomial Lithofacies Classification in a Sandstone Formation
Watheq J. Al-Mudhafar, Craft and Hawkins Department of Petroleum Engineering, Louisiana State University
August 3, 2015
LogitBoost is an efficient computational method for learning accurate classifiers and it has been applied successfully to a variety of classification problems. It is easy to implement, not requires external optimization tools. LogitBoost classification algorithm defines a classifier using an additive model as a family of weak learners. The weak classifiers are sequentially added to the model to minimize the residual loss. The strong (non-linear) classifier is built as the combination of all the weak (linear) classifiers. The Final classification based on weighted vote of weak classifiers. In this work, LogitBoost was adopted here to model Lithofacies given core analysis and well logs data in order to predict discrete and posterior probability distributions of the Lithofacies in Karpur Dataset.
Install the packages required to implement LogitBoost algorithm with their functions.
require(caTools)## Loading required package: caToolsrequire(MASS)## Loading required package: MASSlibrary(caTools)
library(MASS)Call the dataset and visualize it: -
## 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 F1## 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): 17
The following shows the modeling Lithofacies given well logs and core data. Also, predict the 1st 10 observations of discrete and posterior distribution in addtion to plot the boxplot of the predicted lthofacies by LogitBoost Algorithm.
## Lab F1 F10 F2 F3 F5
## [1,] 1 0.9999939 0.500000000 3.353501e-04 0.0003353501 6.144175e-06
## [2,] 1 0.9999992 0.119202922 3.353501e-04 0.0024726232 6.144175e-06
## [3,] 1 0.9999999 0.119202922 4.539787e-05 0.0024726232 4.539787e-05
## [4,] 1 0.9999992 0.017986210 4.539787e-05 0.1192029220 3.353501e-04
## [5,] 1 0.9999992 0.119202922 4.539787e-05 0.0179862100 2.472623e-03
## [6,] 1 0.9999992 0.017986210 3.353501e-04 0.0024726232 2.472623e-03
## [7,] 1 0.9999546 0.002472623 3.353501e-04 0.0024726232 3.353501e-04
## [8,] 1 0.9999992 0.002472623 3.353501e-04 0.0024726232 3.353501e-04
## [9,] 1 0.9999939 0.002472623 3.353501e-04 0.0024726232 3.353501e-04
## [10,] 1 0.9999939 0.002472623 3.353501e-04 0.0003353501 2.472623e-03
## F7 F8 F9
## [1,] 8.315280e-07 0.0003353501 0.0179862100
## [2,] 8.315280e-07 0.0179862100 0.0003353501
## [3,] 6.144175e-06 0.0003353501 0.0003353501
## [4,] 6.144175e-06 0.0003353501 0.0003353501
## [5,] 3.353501e-04 0.0003353501 0.0003353501
## [6,] 3.353501e-04 0.0003353501 0.0003353501
## [7,] 4.539787e-05 0.0024726232 0.0003353501
## [8,] 4.539787e-05 0.0024726232 0.0003353501
## [9,] 4.539787e-05 0.0024726232 0.0003353501
## [10,] 4.539787e-05 0.0024726232 0.0003353501## [1] F1 F1 F1 F1 F1 F1
## Levels: F1 F10 F2 F3 F5 F7 F8 F9
Modeling Validation by computing the total correct percent.
## Label
## F1 F10 F2 F3 F5 F7 F8 F9
## F1 111 0 0 0 0 0 0 0
## F10 0 146 0 4 0 0 0 0
## F2 0 0 6 0 0 0 0 0
## F3 0 8 0 43 0 0 0 0
## F5 0 2 0 0 102 0 1 0
## F7 0 0 0 0 0 7 1 0
## F8 0 2 0 0 0 0 181 0
## F9 0 0 0 0 0 0 0 171## F1 F10 F2 F3 F5 F7 F8
## 1.0000000 0.9733333 1.0000000 0.8431373 0.9714286 0.8750000 0.9890710
## F9
## 1.0000000## [1] 0.9770701Visualizing the predicted posterior distribution of the Eight Facies.
Combining the posterior distribution of the eight Lithofacies in one plot.
## 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, 5680.75, 5694.5, :
## some notches went outside hinges ('box'): maybe set notch=FALSE
References
Friedman, J., Hastie, T., & Tibshirani, R. (2000). Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors). The annals of statistics, 28(2), 337-407.
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). Integrating Component Analysis & Classification Techniques for Comparative Prediction of Continuous & Discrete Lithofacies Distributions. Offshore Technology Conference. doi:10.4043/25806-MS.
Al-Mudhafar, W. J. (2015). Applied Geostatistics in R: 1. Naive Bayes Classifier for Lithofacies Modeling in a Sandstone Formation. RPubs.