## 4 Results and Discussion
### \(k\)-Fold Cross-Validation  
\(k\)-Fold cross-validation was conducted to verify the LSTM model's consistency [50]. For 13 wellbores, \(k\) was set to 10, which is typical for cross-validation. Figure 10 depicts the composition of the training, validation, and test datasets. Each fold was composed of training data from nine wellbores, validation data from two wellbores, and test data from two wellbores. Wellbores UBGH2-2_2 and UBGH2-6 were fixed as the test data for a fair comparison of the test performance according to the training and validation performance variation. Figure 11 compares the performance of the LSTM model for each fold of the 10-fold cross-validation. The performance of each fold was assessed in terms of \(R^{2}\) and RMSE. The model's consistency was quantified in terms of two statistical parameters: the average (\(\mu\)) and standard deviation (\(\sigma\)) of each indicator (e.g., \(\mu\) + \(\sigma\)). The performance of every experiment was satisfactory for generating synthetic Vp using the LSTM model. The average \(\mu\) + \(\sigma\) of the \(R^{2}\) values were 0.932 + 0.006 for the training data, 0.872 + 0.091 for the validation data, and 0.853 + 0.002 for the test data. The average \(\mu\) + \(\sigma\) of the RMSE were 0.200 + 0.277 for the training data, 0.322 + 0.254 for the validation data, and 0.288 + 0.003 for the test data. For the training data, \(R^{2}\) ranged from 0.922 to 0.943. For the validation data, \(R^{2}\) ranged from 0.673 to 0.959. For the test data, \(R^{2}\) ranged from 0.851 to 0.856. For the test data, Fold 3 had the highest performance among the 10 folds. Its \(R^{2}\) values were 0.931, 0.920, and 0.856 for the training, validation, and test data, respectively. Table 3 summarizes the ranges of the scaled logging data in each fold. The values were calculated using the robust scaler (Equation (8)). A high \(R^{2}\) value accompanied a low RMSE. The training data range covered that of the validation data except for Folds 1 and 2. These two folds had larger RMSEs and smaller \(R^{2}\) values than the other folds because the range of validation data exceeded that of the training data, as indicated in Figures 7 and 8. Figure 9: Sensitivity analysis results on the learning rate and batch size for the LSTM model. In contrast, Folds 3 to 10 obtained \(R^{2}\) values greater than 0.85 for both the training and validation data because the training range included the validation range. Folds 1 and 2 yielded \(R^{2}\) values of 0.812 and 0.789 for validation. Although the coincidence in the data range is desirable, the acceptable performance from the cross-validation implies the robustness of the proposed approach for generating synthetic logs using LSTM to estimate parameters in distant wellbores. Figure 12 illustrates the synthetic Vp logs at the training, validation, and test wellbores against their reference data for Fold 1. All the synthetic and reference data were expressed in scaled values using Equation (8). Among the nine training wellbores, UBGH2-5 obtained the highest \(R^{2}\) of 0.938, while UBGH2-4 obtained the lowest \(R^{2}\) of 0.854. The overall trend of our estimation was comparable to the reference except for the mismatch at the depth near 140 m b.s.f. in the validation data because the scaled Vp values rapidly decreased in both validation wellbores UBGH2-10 and UBGH2-11, as already captured in Figures 6 and 7. The mismatch was resolved by data swapping, as depicted in Figure 8. We confirmed that the synthetic Vp was generated at a high quality based on the two test wellbores. Therefore, the designed LSTM model and selected input variables were suitable for generating synthetic Vp with less-consolidated gas-hydrate-bearing sediments in the UBGH2 field.