## 3 Results and Discussion
### Empirical Correlations for the Rock Mechanical Properties
#### 3.3.2 Static Elasticity Parameters  
The correlation between the static Young's modulus and the P-wave interval transit time is shown in Figure S8 (within the Supplementary Data), where the \(E_{\rm s}\) of the rocks was negatively correlated with the P-wave interval transit time, consistent with previous studies [19; 20; 29; 33; 34], suggesting that the \(E_{\rm s}\) of the rocks increased with the increasing P-wave velocity. The combination of parameters considering the P-wave interval transit time and density was adopted to develop the equation for estimating the \(E_{\rm s}\) of the rocks  
Figure 8: Relationship between \(C\) and \(\Delta t_{\rm c}/\)DEN. Figure 7: Relationship between UCS and \(\Delta t_{\rm c}\). because of the higher \(R^{2}\). The relationship between \(E_{\rm s}\) and \(\Delta t_{\rm c}\)/DEN is described in Figure 9. Here, it can be seen that the curve based on the exponential function had the best fit, with an \(R^{2}\) of 0.9137. The empirical equation for estimating the \(E_{\rm s}\) of the rocks is as follows:  
\[E_{\rm s}=195.12\mathrm{e}^{-0.091\times(\Delta t_{\rm c}/DEN)}\ \ R^{2}=0.9137 \tag{26}\]  
The correlation between the static Poisson's ratio and the P-wave interval transit time is shown in Figure S9. From Figure S9, the \(\
u_{\rm s}\) of the rocks was positively correlated with the P-wave interval transit time, which is consistent with previous studies [16; 17], indicating that the \(\
u_{\rm s}\) of the rocks increased with increasing P-wave velocity. The combination of parameters considering the P-wave interval transit time and density was adopted to develop the equation for estimating the \(\
u_{\rm s}\) of rocks because of the higher \(R^{2}\). The relationship between \(\
u_{\rm s}\) and \(\Delta t_{\rm c}\)/DEN is described in Figure 10, where we can observe that the curve based on the linear function had the best-fitting effect, with an \(R^{2}\) of 0.8782. The empirical equation for estimating the \(\
u_{\rm s}\) of rocks is as follows:  
\[\
u_{\rm s}=0.011\times(\Delta t_{\rm c}/DEN)-0.1281\ \ R^{2}=0.8782 \tag{27}\]  
The accuracy of the predicted rock mechanical properties for shale oil reservoirs based on the empirical equations was evaluated via statistical analysis. The values of the predicted rock mechanical properties (based on equations in Table 2 and Equations (23)-(27)) were compared with the corresponding measured values, and the corresponding error comparative analysis was carried out. The root mean square error (_RMSE_) and average absolute relative deviation (_AARD/%_) are shown in Table 3. Compared with the empirical equations suggested in previous works (Table 2), the empirical equations established in this study show the lowest  
Figure 10: Relationship between \(\
u_{\rm s}\) and \(\Delta t_{\rm c}\)/DEN. Figure 9: Relationship between \(E_{\rm s}\) and \(\Delta t_{\rm c}\)/DEN. _RMSE_ and _AARD_, indicating that the equations worked well for predicting rock mechanical properties for shale oil reservoirs with a comparatively small deviation. Furthermore, the histograms of the differences between the predicted rock mechanical properties and the corresponding measured values are presented in Figure 11. From Figure 11a, the equation in this study (Equation (23)) predicted the _UCS_ very well, fitting 85.71% of the given data within \(\pm\)15 MPa, whereas Equations (11), (13) and (14) only fitted 42.86%, 28.57%, and 21.43% of the given data within \(\pm\)15 MPa, respectively. Figure 11a also shows that Equation (11) tended to greatly overestimate the _UCS_ of the samples, whereas Equations (10) and (12)-(14) tended to underestimate the _UCS_ of the samples, especially Equations (10) and (12). From Figure 11b, we can observe that the developed equation in this study (Equation (26)) predicted the _E_s very well, fitting 92.86% of the given data within \(\pm\)3 GPa. In previous works, however, Equations (15)-(18) fit 42.86%, 64.29%, 28.57%, and 50% of the given data, respectively, within \(\pm\)3 GPa.