## 1 Introduction  
The mechanical properties of formation rocks are the foundation of oil/gas engineering design and development, during which these issues hinder the oil/gas recovery effect and safety a great deal, such as in the stability of wellbore, pay zones, and cap rocks, and the surface subsidence/uplift. For instance, the constitutive model can control the wellbore stability and reservoir compression/expansion capacity. Rock strength parameters can determine the reservoir stability and well drilling stability. The deformation parameters describing stress-strain behaviors, such as the elastic modulus (\(E\)) and Poisson's ratio (\(\mu\)), can impact the surface subsidence or uplift, and the safety of underground structures in exploration areas. In addition, these mechanical parameters above can not only play a critical role in the concentration, dispersion, propagation, and attenuation of geo-stress but also can provide an indispensable basis for the well drilling, well completion, and the numerical simulation of geo-mechanical stimulation in oil and gas reservoirs [1, 2]. To date, the commonly used test methods of rock mechanical parameters include static and dynamic methods [3]. The static parameters can be obtained by measuring the degree of deformation of the rock sample under static loading, and the dynamic parameters can be obtained from the conversion of the ultrasonic propagation speed in the rock sample. The static test method is limited by the number of core wells and the cost,so the experimental data are limited. Although the static method is relatively accurate, the process is complex, costly, and requires specific downhole test equipment. Dynamic test methods (e.g., logging and seismic surveys) can obtain the continuous rock dynamic mechanical parameters along the depth, and the acquisition is convenient, economical, and reliable, so the dynamic method can usually overcome these shortcomings of the static method. However, taking the elastic modulus (\(E\)) as an instance, there is a challenging and meaningful study on the relation between static and dynamic elastic moduli. The earliest suggestion that there is a discrepancy between the dynamic (\(E_{\text{d}}\)) and static (\(E_{\text{s}}\)) elastic moduli was made by [PERSON] [4] at Harvard University. After that, many researchers conducted some experimental or analytical studies, and most of the results showed that the dynamic elastic modulus (\(E_{\text{d}}\)) is larger than the static elastic modulus (\(E_{\text{s}}\)) [5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. There is an acceptable linear or nonlinear relationship between the dynamic (\(E_{\text{d}}\)) and static (\(E_{\text{s}}\)) elastic moduli. The dynamic elastic moduli can reach 1 to 10 times the static elastic moduli. There is no obvious relationship between the dynamic (\(\mu_{\text{d}}\)) and static (\(\mu_{\text{s}}\)) [PERSON]'s ratios. While there is a relationship between dynamic and static parameters, the substantial variations in their data are primarily influenced by several complex factors. The external factors include the amount of stress, strain amplitude, test confining pressure, test temperature, and the test frequency of the rock sample [15; 16; 17]. The internal factors are mainly the mineral composition, content, pore development degree, microfractures or microcracks, pore fluid, coupling between rock particles, cementation type, and anisotropy of rock [3; 6; 18]. The discrepancy between dynamic (\(E_{\text{d}}\)) and static (\(E_{\text{s}}\)) elastic moduli has been extensively addressed in rock engineering, and this difference can typically be attributed to microcracks and pores within the rocks. Because static test conditions are closer to the actual underground environments of rock [19], the static elastic parameters are frequently employed in practical engineering applications and can reflect formation properties more accurately [20; 21; 22; 23]. In general, oil and gas field engineers hope to predict static mechanical parameters through dynamic mechanical parameters.