## 5 Conclusions and Prospects  
From the review of the field of the interrelationships between dynamic and static rock mechanics parameters. In general, both linear and nonlinear relationships can fit data of different types of rocks well. Therefore, the performance discrepancy between linear and power-law empirical equations is minimal. In light of the research outcomes presented in this review, we hold the following view:  
1. Based on comprehensive statistical analysis and theoretical framework research on the correlation between the static and dynamic elastic moduli of various rock types, a new method for estimating static elastic modulus based on a single parameter has been proposed while also considering the previous general form of the prediction equation. 2. Considering the correlation between static and dynamic moduli: In terms of different types of rocks, for igneous and metamorphic rocks, the optimal relationship between static and dynamic moduli of elasticity is a power-law correlation, with a value of (igneous R\({}^{2}\) = 0.97, metamorphic R\({}^{2}\) = 0.93), and for sedimentary rocks, a linear and nonlinear logarithmic correlation, with a value of (R\({}^{2}\) = 0.91). 3. Predictive equations obtained by previous researchers may have errors in practical applications, some of which may be appropriate for specific rock types. Therefore, it is necessary to calibrate the constant values, and any calibration may imply new correlations. 4. The discrepancy between the dynamic and static moduli of elasticity can be summarized as follows. The external factors include the amount of stress, strain amplitude, test confining pressure, test temperature, and the test frequency of the rock specimen. The internal factors are mainly the mineral composition, content, pore development degree, pore fluids, microfractures or microcracks, coupling between rock particles, cementation type and anisotropy of the rock, and so on. The existence of microfractures and pores in the rocks is the main reason for the differences. 5. Many factors affect the mechanical properties of rocks, and the experimental results often show inevitable fluctuations. To obtain more representative results, research should be carried out based on the inclusion of a large number of empirical data for regression analysis. Future research can focus on the following aspects: Firstly, the reasons for the discrepancy between dynamic and static mechanical parameters are analyzed from the micro-mechanism of test conditions and rock structure characteristics, and then other methods to make up for the reasons for these differences, to accurately grasp the correlation between the dynamic and static elastic parameters. Secondly, experiments should be conducted on the dynamic and static elastic parameters of rocks under reservoir circumstances. This is so because the validity of these relations is limited and local. So, in the future, it is possible to establish a faster, more accurate, and more efficient prediction model for obtaining static parameters without distinguishing rock types within an acceptable range of error, and then determine the conversion correlation between dynamic and static elastic parameters. Finally, an excellent linear relationship exists between the dynamic and static moduli of elasticity, which can be directly fitted. However, the relationship between the dynamic and static Poisson's ratios is more complex. In practice, it is necessary to consider parameters such as strain amplitude, test temperature, acoustic frequency, and porosity to improve the fitting relationship between the dynamic and static Poisson's ratios. This provides a basis for evaluating formation compressibility and fracturing design schemes. In summary, this review offers important references and insights to understand better the problems and challenges in dynamic and static elastic parameters.