## 3 Results
### GRNN Model  
This article uses MATLAB's built-in _newgrnn_ function to build the GRNN model for porosity, water saturation and the volume of shale prediction for the study of seismic and well log datasets. The GRNN model is trained and optimized using Well one near and far seismic date traces as the training input and petrophysical log (porosity, water saturation and the volume of shale) as the training target. A total of 188 samples covering the zone of interest are selected to conduct the training. The GRNN smoothing factor (identified as _spread_ in the _newgrnn_ function syntax) is estimated by taking the absolute mean of the difference between the inverted EEI for each of the petrophysical data (porosity, water saturation and the volume of shale) and its mean. The smoothing factor of 4e-15, 6e-15 and 4e-15 is obtained, correspondingly, for porosity, water saturation and the volume of shale. To validate the estimated smoothing factors, experimental simulation is conducted to take the R-squared (R\({}^{2}\)) value between the estimated petrophysical properties versus the targeted log for smoothing factors between zero and two, including the guest smoothing factors. Figure 8 shows the diagram of a _newgrnn_ training that was conducted to determine one GRNN model for the petrophysical properties from one inverted EEI with one smoothing factor in the selected range. Figure 8 informs that there are four layers and 191 neurons, in total, involved during a sort of training. Figure 7: Stochastic process of EEI porosity enhancement. (**a**) porosity log reflectivity; (**b**) EEI porosity signature at Well-1 location; (**c**) initial prior EEI reflectivity extracted from EEI signature; (**d**) applied wavelet statistically extracted from EEI signature; (**e**) 50 prior perturbed EEI reflectivity models (thin colorful curves) overlaid by its associated posterior (thick blue curve) and log porosity reflectivity (thick red curve); (**f**) 50 prior EEI signature models, associated with the 50 EEI prior reflectivity (**e**), overlaid by its associated posterior EEI signature (thick blue curve) and the observed EEI signature (thick red curve); (**g**) 50 EEI reflectivity posterior models collected from 50 independent Bayesian-MCMC simulations; (**h**) 50 EEI signature posterior models associated with the 50 EEI reflectivity prior models (**f**). Figure 9 shows a comparison between predicted petrophysical properties and their associated log target for various values of the smoothing factor (\(\sigma\)). The smoothing factor of low, middle and high is taken for simulation. Figure 9 shows how the accuracy R\({}^{2}\) varies with the changing of a smoothing factor value. Comparing the R\({}^{2}\) given by the three smoothing factors, it indicates that the porosity prediction has maximum R\({}^{2}\) at the middle smoothing factor value, while water saturation and the volume of shale predictions achieve their maximum R\({}^{2}\) at low and high smoothing factor values. Figure 8: The GRNN training diagram built using MATLAB built-in _newgrnn_ function; (**a**) 1 neuron input layer; (**b**) 188 neurons radial basis layer; (**c**) 1 neuron summation layer; and (**d**) 1 neuron output layer. Figure 9: Effect of smoothing factor (\(\sigma\)) to the petrophysical prediction accuracy (R\({}^{2}\)), Porosity prediction (1 st row), water saturation prediction (2 nd row), and volume of shale (3 rd row). To obtain the optimum smoothing factor, a denser simulation is conducted for the smoothing factor values between zero and two, and the accuracy R\({}^{2}\) and smoothing factor is then cross plotted. Figure 10 shows the cross plot of R\({}^{2}\) for the estimated petrophysical properties (porosity, water saturation and the volume of shale) with the scanned smoothing factor between zero and two. As shown in Figure 10, the maximum R\({}^{2}\) for porosity, water saturation and the volume of shale is, respectively, about, 0.81 (achieved at smoothing factor 1.1), 0.9 and 0.8 (achieved at smoothing factor in 0 to 0.2 range).