## 3 Dynamic-Static Conversion Relationship
### Relation Establishment
The results show that if dynamic values are used instead of static values, the influence of rock type must be considered to reduce errors between dynamic and static values. Dynamic elastic modulus can also be used to evaluate the deformation characteristics of elastic modulus, and they have established a correlation equation (Equation (11)) between the dynamic and static elastic parameters of the rock mass during drilling, but it is only applicable to Jurassic granites. \[E_{\rm s}=0.69E_{\rm d}+6.40\quad\quad\text{with R}^{2}=0.75\]  
[PERSON] et al. (2018) compared the data obtained from two different dynamic non-destructive testing methods (the first method employs P-wave and S-wave velocity measurements, while the second method utilizes mechanical resonance frequency detection) and standard static method on different types of rock samples, and the results showed good correlation. Moreover, they established relevant formulas (Equation (12)) between dynamic and static parameters. Although a non-destructive testing method was used, porosity was not considered as it has a great influence on the propagation of waves in rock masses. \[E_{\rm s}=1.05E_{\rm d}-3.16\quad\quad\text{with R}^{2}=0.99\]  
[PERSON] (2018) determined the correlation coefficient between static and dynamic data of sedimentary rocks by conducting triaxial and ultrasonic tests on 600 cores from 60 formations. He believed that dynamic core testing could significantly reduce costs and save time. The following relationships were obtained:  
\[E_{\rm s}=0.018E_{\rm d}\ ^{2}+0.422E_{\rm d}\quad\quad\text{with R}^{2}=0.7472\]  
\[E_{\rm s}=0.0293E_{\rm d}\ ^{2}+0.4533E_{\rm d}\quad\quad\text{with R}^{2}=0.7389\]  
\[E_{\rm s}=0.0428E_{\rm d}\ ^{2}+0.2334E_{\rm d}\quad\quad\text{with R}^{2}=0.9259\]  
[PERSON] et al. (2018) investigated the relationship between dynamic and static parameters of different types of composite resins under different light time conditions. They showed that the irradiation time leads to significantly increased dynamic elastic moduli and static elastic moduli of the test material. They found that a high correlation exists between the dynamic and static elastic moduli, and observed that the dynamic modulus of elasticity is higher than the static modulus of elasticity. They established a correlation equation between the dynamic and static parameters (Equation (20)). This suggests a correlation between dynamic and static parameters, which is observed not only in the field of rock but also in other domains. \[E_{\rm s}=0.8069E_{\rm d}\quad\quad\text{with R}^{2}=0.92\]  
[PERSON] et al. (2018) tested the acoustic and mechanical properties of 400 rock samples from carbonate reservoirs under triaxial stress conditions. They believed that rock mechanical parameters are mainly influenced by porosity, mineral types, structure, and pore structure, and established a correlation equation between dynamic and static parameters:  
\[E_{\rm s}=0.541E_{\rm d}+12.852\quad\quad\text{with R}^{2}=0.60\][PERSON] et al. [32] obtained new correlations by testing 10 different carbonate rocks extracted in Spain. Because carbonate rocks are rocks with fractures, voids, and/or weathering, conventional ultrasonic testing indirectly measures mechanical parameters, which can cause errors in the results. Therefore, the variable of spatial attenuation was introduced because they are highly sensitive to the existence of rock defects. They used Equation (34) to ascertain the spatial attenuation of dynamic elastic modulus and compression wave to provide an accurate prediction of the static elastic modulus. This empirical formula is very useful for rocks with fractures, voids, and/or weathering, filling the gap in our collective knowledge with regard to this issue. In Figure 4, they conclude that in most situations. The dynamic modulus of elasticity exceeds the static modulus of elasticity. The symbols in the Figure 4 are explained as follows.