## 5 Conclusions  
This work proposed Gaussian process (GP)-based inverse modeling to predict the depth of hydrocarbon in the seabed logging (SBL) application. The capability of computational modeling and inversion of the SBL data with good accuracy and low computational effort is one of the main concerns in electromagnetic (EM) problems. Thus, this work used machine learning-based approaches, namely GP, as the forward modeling of EM profiles and the gradient descent (GD) method as the optimizer for finding the input parameter of the hydrocarbon (e.g., depth) in the SBL data processing. This work utilized three datasets generated through the computer simulation technology (CST) software with random \"unknown\" hydrocarbon depths as the observational responses. Based on the results, GP regression can provide accurate EM profiles at various depths of hydrocarbon with low computational time (45 min for the prior data acquisition) and less than 2 min for the GP-based inversion methodology. We believed that if the forward modeling performed by the GP could be done rapidly for the repeated use, the inverse modeling (by the GD) would not significantly affect the total computational time of the inversion methodology. Next, the resulting mean absolute deviations (MADs), mean absolute percentage errors (MAPEs), and root mean squared errors (RMSEs) between the GP model and the data modeled by finite element (FE) method were very small. Furthermore, the GP-based inverse modeling could also predict the depth of hydrocarbon for each observation dataset accurately. All the calculated percentage errors between the estimates (by the GP-based \begin{table}
\begin{tabular}{c c c} \hline \hline
**True Depth (m)** & **Estimate (m)** & **Percentage Error (\%)** \\ \hline
350.0000 & 349.9172 & 0.0237 \\
650.0000 & 650.2015 & 0.0310 \\
950.0000 & 950.2225 & 0.0234 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Percentage errors of hydrocarbon depth prediction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hydrocarbon Depth (m)** & **MAD** & **MAPE (\%)** & **RMSE** \\ \hline
200 & \(1.39\times 10^{-9}\) & 0.0849 & \(2.63\times 10^{-9}\) \\
300 & \(1.84\times 10^{-9}\) & 0.1027 & \(4.25\times 10^{-9}\) \\
400 & \(1.48\times 10^{-9}\) & 0.1035 & \(3.26\times 10^{-9}\) \\
500 & \(1.64\times 10^{-9}\) & 0.1144 & \(3.49\times 10^{-9}\) \\
600 & \(1.68\times 10^{-9}\) & 0.1168 & \(4.28\times 10^{-9}\) \\
700 & \(1.21\times 10^{-9}\) & 0.1270 & \(2.33\times 10^{-9}\) \\
800 & \(1.37\times 10^{-9}\) & 0.1204 & \(3.57\times 10^{-9}\) \\
900 & \(1.85\times 10^{-9}\) & 0.1346 & \(5.79\times 10^{-9}\) \\
1000 & \(9.64\times 10^{-9}\) & 0.1212 & \(1.81\times 10^{-9}\) \\ Average & \(1.49\times 10^{-9}\) & 0.1140 & \(3.49\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Validation of the Gaussian process (GP) model. inversion methodology) and the true depth values (computer input) were very small as well. Therefore, it can be concluded that the GP-based inverse modeling was successfully developed to predict the depth of hydrocarbon in the SBL. This attempt could help marine EM data processing, especially in order to de-risk hydrocarbon exploration in the deep marine environment. Conceptualization, H.D. and S.C.D. ; methodology, M.N.M.A. and S.C.D. ; software, M.N.M.A. and H.D. ; validation, S.C.D. and K.A.M.N. ; writing--original draft preparation, M.N.M.A. and K.A.M.N. ; writing--review and editing, M.N.M.A. and K.A.M.N. ; supervision, H.D., K.A.M.N., and S.C.D. ; funding acquisition, H.D. and S.C.D. All authors have read and agreed to the published version of the manuscript. This work was funded by Yayasan Universiti Teknologi PETRONAS-Fundamental Research Grant (YUTP-FRG) with cost center of 015 LC0-055. Not applicable. The data presented in this study are openly available in Mendeley Data at 10.17632/bvwf54j2d.1.