## 3 Results and Discussion
### Empirical Correlations for the Rock Mechanical Properties
#### 3.3.2 Static Elasticity Parameters
Figure 11b also shows that Equations (15) and (17) tended to considerably underestimate the _E_s of the samples. Figure 11c indicates that the developed equation in this study (Equation (27)) calculated the _v_s, fitting 78.6% of the given data within \(\pm\)0.03. In previous works, however, Equations (19) and (20) fit 42.86% and 14.26% of the given data, respectively, within \(\pm\)0.03. Figure 11c also represents that Equation (19) appeared to greatly underestimate the _v_s of the samples, whereas Equation (20) seemed to overestimate the _v_s of the samples. Figure 11c indicates that the developed equation in this study (Equation (27)) calculated the _v_s, fitting 78.6% of the given data within \(\pm\)0.03. In previous works, however, Equations (19) and (20) fit 42.86% and 14.26% of the given data, respectively, within \(\pm\)0.03. Figure 11c also represents that Equation (19) tended to greatly underestimate the _v_s of the samples, whereas Equation (20) seemed to overestimate the _v_s of the samples. Figure 11d depicts that the developed equation in this study (Equation (24)) determined the _v_s of the given data within \(\pm\)3\({}^{\circ}\). In previous works, however, Equations (21) and (22) fit 42.86% and 7.14% of the given data, respectively, within \(\pm\)3\({}^{\circ}\). Figure 11d also displays that Equations (21) and (22) appeared to overestimate the \(v\) of samples, especially Equation (22). Based on the comparison results, the prediction performances of the newly developed equations are significantly higher than those of the equations suggested in previous works (Table 2), indicating that a set of empirical equations was unable to cover a wide range of geographical areas. This result is consistent with previous research conclusions [16]. This \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Empirical Equation** & _RMSE_ & _AARD_/\% \\ \hline \multirow{6}{*}{_UCS_} & Equation (10) & 49.36 MPa & 48.60 \\  & Equation (11) & 19.77 MPa & 22.28 \\  & Equation (12) & 38.10 MPa & 38.63 \\  & Equation (13) & 26.76 MPa & 24.16 \\  & Equation (14) & 27.82 MPa & 25.47 \\  & Equation (23) (in this study) & 9.72 MPa & 7.48 \\ \hline \multirow{6}{*}{_E_s} & Equation (15) & 4.59 GPa & 31.04 \\  & Equation (16) & 3.19 GPa & 29.00 \\ \cline{1-1}  & Equation (17) & 6.75 GPa & 47.71 \\ \cline{1-1}  & Equation (18) & 3.92 GPa & 48.20 \\ \cline{1-1}  & Equation (26) (in this study) & 1.54 GPa & 12.41 \\ \hline \multirow{6}{*}{_v_s} & Equation (19) & 0.06 & 19.22 \\  & Equation (20) & 0.10 & 44.38 \\ \cline{1-1}  & Equation (27) (in this study) & 0.02 & 8.58 \\ \hline \multirow{2}{*}{_C_} & Equation (24) (in this study) & 1.90 MPa & 5.52 \\ \cline{1-1}  & Equation (21) & 4.22\({}^{\circ}\) & 11.41 \\ \cline{1-1}  & Equation (22) & 11.58\({}^{\circ}\) & 32.88 \\ \cline{1-1}  & Equation (25) (in this study) & 3.14\({}^{\circ}\) & 6.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The _RMSE_ and _AARD_ of the equations in Table 2, estimating the rock mechanical parameters. may be attributed to the sample lithology and heterogeneities. In other words, the existing empirical equations for specific blocks or formation are not universal or applicable to other blocks. When using these empirical equations, the applicability of existing empirical equations should be checked first or the empirical relationships for a specific block established, to ensure that the results obtained can be used reasonably and reliably. Hence, local empirical correlations between rock mechanical and physical properties need to be determined, in order to provide correct information for future exploration in the same or close-by areas. Figure 11: Cont. On the basis of the above research, the new empirical equations (Equations (23)-(27)) can be used to calculate the rock mechanical properties for the Permian Lucaogou Formation shale oil reservoirs, which can be compared to the experimental data.