# Estimation of Litho-Fluid Facies Distribution from Zero-Offset Acoustic and Shear Impedances
## 5 Results and Discussion
The best minimum split value has been observed to be 10, which leads to the best performance of the tree. Figure 27 shows the graphical representation of the decision tree, which classifies the training data into gas sand in red, wet sand in blue, and shale in green. The input variables are the gas probability (Pg), sand probability (Ps), and depth (d). Figure 18:3 A linear regression plot between Epsilon, on the X-axis, and Delta, on the Y-axis. The data points were obtained from the Epsilon and Delta volumes, which were calculated by applying the MLFN-based \(Z_{P}\) and \(Z_{S}\) to the impedance-domain [PERSON]’s anisotropy equations. The accuracy of the tree was calculated for the training, testing, and validation data to be 91%, 89%, and 90%, respectively, and the average accuracy is 91%. These results show that the tree is accurate enough to be applied to the depth-converted seismic data. A function was created in R-Studio to transform the zero-offset \(Z_{P}\) and \(Z_{S}\) volumes, obtained from the isotropic inversion and MLFN, into elastic properties and then into sand and gas probabilities based on the facies model. Figure 18:4 The graphical representation of the decision tree model, which classifies the training data of the well (\(\times\)1) into gas sand in red, wet sand in blue, and shale in green. The input variables are the gas probability (Pg), sand probability (Ps), and depth (d). Figure 18:5 (**a**) Plot of the sand probability (Phi-sand) versus the lithology (facies) variable. (**b**) Plot of the gas probability (Phi-gas-sand) versus the fluid variable. Eventually, the decision tree was applied to predict the facies classes from the probabilities and depth. The composite traces of the facies volumes were extracted at the well (\(\times 1\)) to compare the isotropic simultaneous inversion and the anisotropic MLFN outputs, as shown in Figure 28, where the gas sand, wet sand, and shale are represented in the red, blue, and green colors, respectively. The CCR was calculated for each litho-fluid class for both the isotropic and anisotropic cases, as shown in Figure 18:6  
The CCR values of the gas sand are 51% and 97% for the isotropic and anisotropic cases, respectively. This improvement is evident in Figure 28, where the gas sand is correctly detected at the anisotropic case. Similarly, the CCR values of the shale are 55% and 73% for the isotropic and anisotropic cases, respectively. The CCR values of the wet sand are almost the same for the two cases, 82% and 83% for the isotropic and anisotropic cases, respectively. The average CCR value is 56% for the isotropic facies and 77% for the anisotropic case. This means that the accuracy of litho-fluid detection has been enhanced by about 21%. This improvement is not only due to the reduction in the anisotropy effect but also because the MLFN has normalized the inversion errors due to the tuning effect. These results seem comparable to those of another case study, from the Okoli field in the Sava depression, which aimed at predicting clastic facies using neural networks [107]. Although the lithology was estimated based on various logs, the results showed correlation levels ranging from 78.3% to 82.1%, which are close to the results of this study. A recent study set various ML algorithms to estimate four facies classes from seismic attributes [131]. The logistic regression showed encouraging success rates, up to 0.98, compared to other algorithms, such as the Gaussian process, linear discriminant analysis, and stochastic gradient descent. However, a high success rate does not indicate the model's stability, especially in heterogeneous fields. The advantage of the current study's facies model is that the litho-fluid probabilities as well as the depth variable are inserted into \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Gas Sand** & **Wet Sand** & **Shale** & **All Facies** \\ \hline Isotropic Inversion & 51\% & 82\% & 55\% & 56\% \\ MLFN & 97\% & 83\% & 73\% & 77\% \\ \hline \hline \end{tabular}
\end{table}