# Advanced Elastic and Reservoir Properties Prediction through Generative Adversarial Network
## 5 Results  
This section is organized as follows. Each figure contains 3 images: prediction from pix2 pix, prediction from MS-pix2 pix (proposed method) and the ground truth. The first 2 figures are the velocity prediction for Inline 1 and Inline 2. The next 2 figures are the porosity prediction, followed by density and lastly water saturation. The accuracy metrics used were correlation (Equation (5)) and the structural similarity index, SSIM (Equation (6)). The SSIM metric calculates the similarity between 2 images based on 3 key features: luminance, \(l\); contrast, \(c\); and structure, \(s\)[41]. Both metrics range between \(-1\), which means the 2 images are very different, and \(+1\), which means the 2 images are very similar. The results can be found in Table 2.  
\[CORR\big{(}y,y^{\prime}\big{)}=\frac{\sum\Big{(}(y-\overline{y})\Big{(}y^{ \prime}-\overline{y^{\prime}}\Big{)}\Big{)}}{\sqrt{\sum(y-\overline{y})^{2} \sum\Big{(}y^{\prime}-\overline{y^{\prime}}\Big{)}^{2}}} \tag{5}\]  
\[SSIM\big{(}y,y^{\prime}\big{)}=[l(y,y^{\prime})]\alpha\cdot[c(y,y^{\prime})] \beta\cdot[s(y,y^{\prime})]\gamma \tag{6}\]  
MS-pix2 pix managed to produce predictions of higher accuracy qualitatively and quantitatively compared to the pix2 pix network for all subsurface properties (Figures 9-16). Although the predictions were better, there are still some areas that require further attention. In Figures 9, 11, 13 and 15, for example, MS-pix2 pix improved the predictions of pix2 pix by a lot. However, there is a wrong prediction that is predicted as a salt body at a shallow depth. This could be due to the \"dimmed\" amplitude in the seismic data that resembles the salt body signature. In Figure 16, although the prediction from MS-pix2 pix is better, \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Properties** & \multicolumn{2}{c}{**Correlation**} & \multicolumn{2}{c}{**SSIM**} \\
**Model** & **Pix2 pix** & **MS-Pix2 pix** & **Pix2 pix** & **MS-Pix2 pix** \\ \hline Velocity Inline 1 & 0.70 & 0.91 & 0.77 & 0.93 \\ Velocity Inline 2 & 0.91 & 0.99 & 0.90 & 0.97 \\ Porosity Inline 1 & 0.40 & 0.83 & 0.54 & 0.90 \\ Porosity Inline 2 & 0.82 & 0.98 & 0.78 & 0.92 \\ Density Inline 1 & 0.97 & 0.99 & 0.93 & 0.99 \\ Density Inline 2 & 0.97 & 0.99 & 0.95 & 0.98 \\ Water saturation Inline 1 & 0.43 & 0.84 & 0.76 & 0.95 \\ Water saturation Inline 2 & 0.77 & 0.95 & 0.89 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The prediction accuracy was calculated using cross-correlation and SSIM. The MS-pix2 pix produced higher accuracy predictions for all properties and for all inlines. Figure 8: (**left**): Inline 1. Simple geological section with a small salt body, (**right**): Inline 2. Complex geological section with a bigger salt body. The color bar is exaggerated to make the sections clearer. it is over-predicted. There should not be a layer inside the salt body. As pix2 pix was conditioned on the input image, the layer might be carried over from the input seismic. It is also important to note that although both accuracy metrics gave high accuracy for water saturation, the network actually failed to detect the water layer. The high accuracy was given by the salt and non-salt formation of the water saturation model. The salt and non-salt formations must be removed from the training for a more accurate water saturation prediction. Figure 11: Porosity prediction results of Inline 1. **(a)**: Prediction from pix2 pix. **(b)**: Prediction from MS-pix2 pix. **(c)**: The ground truth. The same shallow artifact was observed in the porosity model. Figure 10: Velocity prediction results of Inline 2. **(a)**: Prediction from pix2 pix. **(b)**: Prediction from MS-pix2 pix. **(c)**: The ground truth. Although MS-Pix2 Pix produced better prediction, the pre-salt velocity requires further refinement. Figure 9: Velocity prediction results of Inline 1. **(a)**: Prediction from pix2 pix. **(b)**: Prediction from MS-pix2 pix. **(c)**: The ground truth. Visually, the MS-pix2 pix showed better results.