## 3 Methodology
### Model Modulation  
During this phase (which we call Phase II, see Figure 1), we meticulously crafted crucial models, most notably the seismic model, which played a pivotal role in calibrating and refining the overarching model responsible for estimating fundamental parameters. The seismic model was meticulously constructed through the interpretation of the target horizon interlinked with fault planes identified in the seismic section (see Figure 4a,b). This approach aimed to enhance the fidelity of seismic data, ensuring a more accurate representation of actual conditions and subsurface structures. The development of the low-frequency model paralleled this process. This model encapsulated the low-frequency components, serving as a detailed approximation of the subsurface model. These parts are very important because they show important subsurface properties and make it easier to describe large structures and low-contrast features below the surface. To augment the precision of this model, additional insights from well logs were incorporated. Well logs, offering detailed and highly precise information on subsurface properties at well locations, played a significant role in fine-tuning and validating the low-frequency model derived from seismic data. This integrated approach ensured a more comprehensive and accurate representation of the subsurface, blending the strengths of seismic data and well-log information. Again, machine learning (ML) algorithms are used at this stage. The RandomizedSearchCV algorithm was used to tune the hyperparameters of the models. Because the well logs in the vicinity of the site presented gaps (between 3300 and 3700 m), it was  
Figure 4: The interpretation of the target stratigraphic horizon was executed utilizing the seismic cube through two distinct workflows: (**a**) employing the automatic tracking algorithm integrated into the Opendtect software, devoid of the fault planes; and (**b**) utilizing a manual approach that integrates fault planes and geological reference markers to conduct the interpretation of the seismic horizon. necessary to develop regression models to extrapolate the missing data, and thus, reduce the possible errors present. For this, four different types of models were developed and tested: linear regression (LR), random forest (RF), K-nearest neighbors (KNN), and support vector regression (SVR); the initial settings of the models were determined by using the RandomizedSearchCV algorithm. The sensitivity of the initial data was then tested through a sensitivity analysis concerning the amount of data needed (see Figure 5). Likewise, an evaluation of the well logs was initially carried out to identify the type of underlying distribution of the data and optimize the results' quality. In particular, regression algorithms tend to exhibit improved performance when applied to datasets that exhibit a normal or Gaussian distribution pattern in the initial data (see Figure 6). Figure 5: The assessment of model performance was conducted on the regression models, and the displayed confidence intervals were calculated at a 95% confidence level. The figure depicts the behavior observed during the evaluation of the initial data size of the four selected algorithms (Linear Regression, Support Vector Machine, Random Forest, and K-neighbors regression). The error and uncertainty exhibit an inverse relationship with the number of elements or data evaluated, as the area of the confidence interval tends to decrease with an increase in the evaluated data. Figure 6: The graphs depict the evaluation of the well-log distribution type that served as the starting point for the inversion procedure. All of the used well logs (**a**–**d**) have a Gaussian or normal distribution, except one well log (**e**) that has an exponential distribution. Within this stage, the BLI inversion process was carried out.