Fig 1.
Methodology flowchart.
Table 1.
The optimized parameters of the proposed GPR method.
Table 2.
The most common machine learning methods to predict νs.
Fig 2.
The comparison of νs – RHOB trends models with experimental measurements.
Fig 3.
Trend analysis of the νs – RHOB in the range of data found in the dataset used for the optimized GPR.
Fig 4.
The comparison of νs – DTc trends models with experimental measured values for RHOB = 2.27 g/cc and DTs = 248.99 us/ft.
Fig 5.
The comparison of νs – DTc trends models with experimental measured values for RHOB = 2.02 g/cc and DTs = 265.03 us/ft.
Fig 6.
Trend analysis of the νs – DTc in the range found in the dataset used for the optimized GPR.
Fig 7.
The comparison of νs – DTs trends models with experimental measured values for RHOB = 2.72 g/cc and DTc = 51.47 us/ft.
Fig 8.
The comparison of νs – DTs trends models with experimental measured values for RHOB = 2.33 g/cc and DTc = 118.67 us/ft.
Fig 9.
Trend analysis of the νs – DTs in the range found in the dataset used for the optimized GPR.
Fig 10.
The optimized GPR approach’s cross-plotting for the training dataset.
Fig 11.
The optimized GPR approach’s cross-plotting for the validation dataset.
Fig 12.
The optimized GPR approach’s cross-plotting for the testing dataset.
Table 3.
Statistical error analyses of the proposed or optimized GPR model.
Fig 13.
Comparison of νs measured and predicted estimates of the optimized GPR approach for (a) training, (b) validation, and (c) testing datasets.
Fig 14.
The optimized GPR approach’s error histogram of the training dataset.
Fig 15.
The optimized GPR approach’s error histogram of the validation dataset.
Fig 16.
The optimized GPR approach’s errors histogram of the testing dataset.
Fig 17.
Group error analysis of bulk formation density for the proposed GPR and some previous approaches.
Fig 18.
Group error analysis of compressional time for the proposed GPR and some previous approaches.
Fig 19.
Group error analysis of shear time for the proposed GPR and some previous approaches.
Fig 20.
Cross-plots of (a) the proposed GPR, Ranjbar-Karaml et al. [14], Christaras et al. [52], Feng et al. [16], Gowida et al. [17] models and (b) Khandelwal et al. [13], Brandås et al. [15], and Kumar et al. [12].
Fig 21.
(a) Average absolute percentage relative error (AAPRE), and, (b) Coefficient of determination (R2) of the models.
Fig 22.
(a, b). The statistical error analyses for the models using the same dataset.
Fig 23.
(a) Taylor diagrams of Khandelwal et al. [13], Brabdas et al, Kumar et al. [12] models. (b) Taylor diagrams of Ranjbar-Karami et al. [14], Christaras et al. [52], Feng et al. [16], Gowida et al. [17], and the proposed GPR models.
Table 4.
P values of Kruskal–Wallis test at 95% significance level.
Fig 24.
Error boxplot and violin graphs for the previously published and proposed GPR models.
Fig 25.
Fracture pressure based on previous Poisson’s ratio models.
Fig 26.
Fracture pressure based on proposed GPR Poisson’s ratio model.
Fig 27.
Residual error of fracture pressure for all studied models.