Applied Geostatistics in R: 1. Naive Bayes Classifier for Lithofacies Modeling in a Sandstone Formation

Naive Bayes Classifier (NBC) is bayesian algorithm that is used to compute the conditional posterior probabilities of a categorical class variable (Lithofacies) given independent predictor variables (core and well logs data) using the Bayes rule.

NBC was adopted here to model the Lithofacies given core analysis and well logs data from Karpur Dataset: -

Install the packages required to implement NBC algorithm with their functions.

require(e1071)

## Loading required package: e1071

require(MASS)

## Loading required package: MASS

library(e1071)
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

Modeling Lithofacies given the other independent variables. Also, predict the 1st 10 observations and plot the boxplot of the predicted lthofacies.

##  [1] F10 F3  F3  F1  F1  F1  F1  F1  F1  F1 
## Levels: F1 F10 F2 F3 F5 F7 F8 F9

Modeling Validation by computing the total correct percent.

##      
## pred   F1 F10  F2  F3  F5  F7  F8  F9
##   F1  107   3   0   0   0   0   0   0
##   F10   1 143   0  28   2   0   0   0
##   F2    1   1   8   0   0   0   0   0
##   F3    2  20   0  26   1   0   0   0
##   F5    0   1   0   1 100   0   4   2
##   F7    0   2   0   0   0   9   3   0
##   F8    0   1   0   0   0   0 171   0
##   F9    0   0   0   0   6   0   6 170

##        F1       F10        F2        F3        F5        F7        F8 
## 0.9727273 0.8218391 0.8000000 0.5306122 0.9259259 0.6428571 0.9941860 
##        F9 
## 0.9340659

## [1] 0.8962149

Visualizing the predicted posterior distribution of the Eight Facies.

Combining the posterior distribution of the eight Lithofacies in one plot.

References

Murphy, K. P. (2006). Naive bayes classifiers. University of British Columbia.

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.