## 4 Results and Discussion  
All prior electromagnetic (EM) responses were generated using the computer simulation technology (CST) software. Nine seabed logging (SBL) models were parameterized with the same input properties, except for its depth of hydrocarbon, which were 200 m-1000 m with a gap of 100 m each. It must be noted that these EM responses were evaluated using the finite element (FE) method, which was used exclusively by the CST software  
Figure 3: Methodological flow of Gaussian process (GP)-based inverse modeling. Note that all the seabed logging (SBL) models replicated by the computer simulation technology (CST) software are target models (i.e., with hydrocarbon layer). Hence, determining the presence of hydrocarbon is not discussed in this work. HC stands for hydrocarbon and w.r.t. represents with respect to. for the low-frequency applications. In this work, only magnitude of electric (E)-field was considered as the corresponding output. Figure 4 shows the magnitude versus offset plot for all nine SBL datasets. Based on Figure 4, the \(x\)-axis represents the offset distances from approximately 11,840.80 m to 19,004.97 m and the \(y\)-axis represents the magnitude of E-field with a logarithmic scale. This figure reveals that the CST was capable of simulating the SBL application in the deep marine environment. The generated EM responses behave similarly to the real behavior of EM signals in media with various conductivities. The EM signals travel through a high-resistive body with less attenuation. Thus, a model with higher hydrocarbon depth generates a much smaller magnitude of E-field due to the factor of far EM signal propagation. Next, these EM responses were fully utilized by the GP regression in order to provide more EM profiles at \"untried\" depths. The contour plot of the two-dimensional (2D) GP model is depicted in Figure 5.  
Based on Figure 5, the \(x\)-axis is the offset distance and the \(y\)-axis is the 41 depths of hydrocarbon from 200 m to 1000 m, while the magnitudes of the E-field are represented  
Figure 4: Magnitude of electric (E-)-field versus offset for nine different depths of hydrocarbon from 200 m to 1000 m with an increment of 100 m each. Figure 5: Two-dimensional (2D) forward Gaussian process (GP) model with 41 different electromagnetic (EM) datasets with depths from 200 m to 1000 m with an increment of 20 m.  
in color codes. This forward GP model is a combination of EM profiles at \"tried\" and \"untried\" hydrocarbon depths. The purpose of this GP modeling was to evaluate as many EM responses as possible at various depths of hydrocarbon for the inversion scheme, for which generating all these EM responses using the CST software could take high computational time. Simulating and generating all these 41 datasets using the CST could require around 3 h and 30 min, whereas the GP modeling only took 45 min for the prior knowledge acquisition and less than 1 min for developing the forward GP model and evaluating 41 profiles. In this work, three random observational datasets were generated separately using the CST software where the depths of hydrocarbon were assumed to be \"unknown\", i.e., 350, 650, and 950 m. Here, the goal was to find the best estimates of hydrocarbon depths of the observational datasets with the smallest MSE values. In other words, a small MSE value indicates that the EM profile evaluated by the forward GP model gives the most likely values for the observational dataset, thereby giving the best depth information. As discussed before, the step size of the optimization was determined by the learning rate. For this work, three different learning rates were used for every inversion scheme. The first scheme (1  
Figure 8: Mean squared error (MSE) versus hydrocarbon depth plot (3 rd observational dataset). Figure 7: Mean squared error (MSE) versus hydrocarbon depth plot (2 nd observational dataset). Figure 9: Convergence test (1 st observational dataset).