## 4 Results and Discussion
### Elastic Inversion Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**P-Wave Velocity**} & \multicolumn{6}{c}{**WELL No-6608-10-02**} \\ \cline{2-7}  & **INITIAL** & **ITER. 1** & **ITER. 2** & **ITER. 3** & **ITER. 4** & **FINAL** \\ \hline AVO Inversion & 0.7050 & 0.6508 & 0.7065 & 0.7505 & 0.7999 & 0.8332 \\ \hline BLI Inversion & 0.7865 & 0.6878 & 0.7154 & 0.8004 & 0.8289 & 0.8680 \\ \hline \multirow{2}{*}{**P-Wave Velocity**} & \multicolumn{6}{c}{**WELL No-6608-10-04**} \\ \cline{2-7}  & **INITIAL** & **ITER. 1** & **ITER. 2** & **ITER. 3** & **ITER. 4** & **FINAL** \\ \hline AVO Inversion & 0.6989 & 0.6604 & 0.7150 & 0.7515 & 0.8001 & 0.8021 \\ \hline BLI Inversion & 0.7059 & 0.6941 & 0.7180 & 0.8105 & 0.8320 & 0.8758 \\ \hline \multirow{2}{*}{**S-Wave Velocity**} & \multicolumn{6}{c}{**WELL No-6608-10-02**} \\ \cline{2-7}  & **INITIAL** & **ITER. 1** & **ITER. 2** & **ITER. 3** & **ITER. 4** & **FINAL** \\ \hline AVO Inversion & 0.6698 & 0.6183 & 0.6712 & 0.7130 & 0.7599 & 0.7915 \\ \hline BLI Inversion & 0.7472 & 0.6534 & 0.6796 & 0.7604 & 0.7875 & 0.8246 \\ \hline \multirow{2}{*}{**S-Wave Velocity**} & \multicolumn{6}{c}{**WELL No-6608-10-04**} \\ \cline{2-7}  & **INITIAL** & **ITER. 1** & **ITER. 2** & **ITER. 3** & **ITER. 4** & **FINAL** \\ \hline AVO Inversion & 0.6640 & 0.6274 & 0.6793 & 0.7139 & 0.7601 & 0.7620 \\ \hline BLI Inversion & 0.6706 & 0.6594 & 0.6821 & 0.7700 & 0.7904 & 0.8320 \\ \hline \multirow{2}{*}{\(\rho\)} & \multicolumn{6}{c}{**WELL No-6608-10-02**} \\ \cline{2-7}  & **INITIAL** & **ITER. 1** & **ITER. 2** & **ITER. 3** & **ITER. 4** & **FINAL** \\ \hline AVO Inversion & 0.6557 & 0.6052 & 0.6570 & 0.6980 & 0.7439 & 0.7749 \\ \hline BLI Inversion & 0.7314 & 0.6397 & 0.6653 & 0.7444 & 0.7709 & 0.8072 \\ \hline \multirow{2}{*}{\(\rho\)} & \multicolumn{6}{c}{**WELL No-6608-10-04**} \\ \cline{2-7}  & **INITIAL** & **ITER. 1** & **ITER. 2** & **ITER. 3** & **ITER. 4** & **FINAL** \\ \hline AVO Inversion & 0.6500 & 0.6142 & 0.6649 & 0.6989 & 0.7441 & 0.7459 \\ \hline BLI Inversion & 0.6565 & 0.6455 & 0.6677 & 0.7538 & 0.7738 & 0.8145 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The values of the correlation coefficients for \(V_{p}\), \(V_{S}\), and \(\rho\) are shown for each well and each iteration of the AVO and BLI inversion procedures. The final results are depicted in Figure 11.  
In Figure 10, we can see the results of the AVO and BLI inversion processes applied to two synthetic models: one without noise and the other with noise included. The AVO inversion process produces slightly higher velocities than the original model, while the BLI inversion process produces lower velocities very close to the original model. A comprehensive comparison between the AVO and BLI inversion processes was performed using various metrics, and the results are included in Table 2.  
These metrics together imply that, within this hypothetical scenario, Bayesian inversion is the option that provides a better definition of the investment compared to the AVO method. Figure 10 we can see that, specifically, both the amplitude versus offset inversion  
Figure 10: The results of the inversion performed using Bayesian Inversion (BLI) and Amplitude Versus Offset (AVO) methodologies are displayed. The inversion procedures were implemented on a synthetic model, which was used in two distinct scenarios: in the first, the model was utilized without any introduced noise; in the second, noise was introduced into the initial model. The purpose of deliberately introducing noise was to examine the inversion process’s behavior and enable a comparative analysis of the two. The inversion was executed on the \(V_{p}\) and density (\(\rho\)) models in the current case. (AVO) method and the Bayesian linear inversion (BLI) method exhibit an exceptional ability to recover values closely aligned with those of the original velocity model.