# Estimation of Litho-Fluid Facies Distribution from Zero-Offset Acoustic and Shear Impedances
## 5 Results and Discussion
This phenomenon appears in the abrupt change in facies, as shown in Figure 23, where the black rectangle shows high contrast boundaries between layers coinciding with significant fluctuations in the Epsilon parameter. The same conclusion is mentioned by [PERSON] [76], who plotted the anisotropy parameters, Epsilon and Delta, versus the depth for a laminated shaly sand succession, as shown in Figure 24. The magnitude of the anisotropy is low for the water-saturated sand (Figure 24a), which has Lame's parameters that are similar to those of shale. On the other hand, the Lame's parameters of the gas-saturated sand (Figure 24b) and shale are significantly different, resulting in a high magnitude of the anisotropy parameters. Most of the previous studies stated that Epsilon is always positive or zero. However, the resulting Epsilon, as shown in Figure 21a, has a negative sign in some zones. This is matching with [PERSON]'s study [76], which stated that Epsilon can be negative in laminated shaly gas sand layers, as shown in the anisotropy-depth plot (Figure 24b), where the depth interval is divided into three zones, (A), (B), and (C), which are the shallow, compaction, and diagenesis regimes, respectively. Epsilon is significantly fluctuating around zero in the gas-saturated sand such that it becomes negative at the shallow and diagenesis zones. The Epsilon and Delta sections are plotted in Figure 25, showing a strong positive correlation between them. The color legend represents the two-way time value for each observation. The best-fit line gives the following linear relationship between Epsilon and Delta:  
\[\delta=0.31e+0.004 \tag{65}\]  
Interestingly, the observed relationship is mostly similar to that obtained by [PERSON] [73], who implemented the following equation:  
Figure 18:0  
Figure 18:1 Plots of the anisotropy parameters, Epsilon (blue curve) and Delta (red curve), on the X-axes versus the depth on the Y-axes, for both the water- and gas-saturated sand (**a** and **b**, respectively). The depth range is divided into three zones, (A), (B), and (C), which are the shallow, compaction, and diagenesis regimes, respectively [76]. The next step is to transform the \(Z_{P}\) and \(Z_{S}\) into the elastic properties from which the lithology and fluid distributions should be forecasted. The facies integrated model was firstly applied to logging data at the well (\(\times 1\)) for training and then used to predict the facies distribution from the elastic volumes. The lithology model was postulated by using R, based on logistic regression, to forecast the sand probability from the near and far elastic impedances. Similarly, the fluid model was created to predict the gas probability from the Mu-Rho, Lambda-Rho/Mu-Rho, and Poisson's ratios [52]. Finally, the two models were merged by a decision tree to obtain the distribution of each facies class. The predicted sand and gas probabilities (Phi-sand and Phi-gas-sand, respectively) of the training data were plotted versus the lithology and fluid variables, respectively, as shown in Figure 18:2 As expected, the sand probability values are high where the lithology variable is closer to 1, indicating sandstone, and low where the lithology variable is closer to 0, indicating shale (Figure 26a). Like the sand probability, the gas probability is high where the fluid variable is 1, indicating gas sand, and generally low where the fluid variable equals 0, indicating wet sand (Figure 26b). The best cut-off values were selected to differentiate between the sand and shale observations in the lithology model as well as the gas sand and wet sand in the fluid model. A decision tree was created to estimate the litho-fluid classes from the sand probability, gas probability, and depth. The total data points are 1084, starting from depth 1300 m to 1851 m. According to the facies log of the well (\(\times 1\)), the data consist of 75 gas sand, 286 wet sand, and 723 shale data points. The data were divided into three parts for training (80%), testing, (10%), and validation (10%).