###### Abstract  
Seabed logging (SBL) is an application of electromagnetic (EM) waves for detecting potential marine hydrocarbon-saturated reservoirs reliant on a source-receiver system. One of the concerns in modeling and inversion of the EM data is associated with the need for realistic representation of complex geo-electrical models. Concurrently, the corresponding algorithms of forward modeling should be robustly efficient with low computational effort for repeated use of the inversion. This work proposes a new inversion methodology which consists of two frameworks, namely Gaussian process (GP), which allows a greater flexibility in modeling a variety of EM responses, and gradient descent (GD) for finding the best minimizer (i.e., hydrocarbon depth). Computer simulation technology (CST), which uses finite element (FE), was exploited to generate prior EM responses for the GP to evaluate EM profiles at \"untrided\" depths. Then, GD was used to minimize the mean squared error (MSE) where GP acts as its forward model. Acquiring EM responses using mesh-based algorithms is a time-consuming task. Thus, this work compared the time taken by the CST and GP in evaluating the EM profiles. For the accuracy and performance, the GP model was compared with EM responses modeled by the FE, and percentage error between the estimate and \"untrided\" computer input was calculated. The results indicate that GP-based inverse modeling can efficiently predict the hydrocarbon depth in the SBL. seabed logging; electromagnetic data; hydrocarbon depth; inverse modeling; Gaussian process; gradient descent; computer simulation technology +
Footnote †: journal: Applied Sci. 2021, 11, 1492. [[https://doi.org/10.3390/app11041492](https://doi.org/10.3390/app11041492)]([https://doi.org/10.3390/app11041492](https://doi.org/10.3390/app11041492))  
Footnote †: journal: Applied Sci. 2021, 11, 1492. [[https://doi.org/10.33390/app11041492](https://doi.org/10.33390/app11041492)]([https://doi.org/10.33390/app11041492](https://doi.org/10.33390/app11041492))  
recording the returned EM signals [1]. Studies related to the commercial SBL application can be found in [1; 2; 3; 4; 5; 6; 7; 8; 9]. Figure 1 is adopted from [10] to depict the illustration of the SBL application in the offshore environment. Numerical modeling is a crucial task in geophysics problems since it provides prior knowledge and information of the potential reservoirs. Many powerful computational modeling techniques have been exploited for processing the EM responses, such as finite element (FE), finite difference (FD), finite volume (FV), integral equations (IE), etc. These numerical techniques are capable of modeling the subsurface realistically in the marine environment by defining grids or meshes. According to [11], the FE technique is highly preferred due to its ability to support unstructured meshes. These meshes are able to provide a quality geological representation by placing small grid elements in the areas where better resolution is highly needed, such as in large conductivity contrast areas [11]. However, as the consequence, the mesh-based algorithms require a very lengthy computational time to solve the linear system; in addition, these forward modeling techniques involve very complicated deterministic mathematical equations. According to [12; 13], the most time-consuming task in the algorithms is solving the integral and multiple linear equations, not to mention for the inversion scheme that requires multiple EM forward solutions [13]. Here, the corresponding forward modeling should be robust and capable of operating the EM simulation rapidly, especially for repeated use in the large number of iterations involved in the inversion scheme as well as for multiple source-receiver positions in the SBL application [14]. To address these problems, this work aimed to develop a novel Gaussian process-based inversion methodology to provide meaningful information where the hydrocarbon potentially resides underneath the seabed.