## 3 Methods
### Derivation of Rock Mechanics Parameters  
There are generally two approaches to acquiring rock mechanics parameters. One approach involves statically determining rock mechanics parameters by observing rock deformation under controlled confining pressure in the laboratory [5; 35]. The alternative approach involves using logging data to establish continuous dynamic profiles of rock mechanics parameters [35]. Static mechanical parameters measured in the laboratory simulate the magnitude of confining pressure during rock formation, the rate and amplitude of pressure loading, and the pressure changes during subsequent formation stages. Consequently, laboratory-measured static mechanical parameters provide a more accurate representation of the true mechanical properties of rocks [36; 37]. A plunger sample with a diameter of 2.5 cm and a height of 5 cm was selected for rock mechanics experiments. The experimental equipment was commissioned to the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences for measurement. The test standards adopted for this experiment are Part 7 of GB/T 23561.7-2009 [38] and Part 8 of GB/T 23561.8-2009 [39]: Methods for determining the uniaxial compressive strength and deformation parameters of coal and rock. The triaxial mechanical parameters of tight sandstone from the Chang 7 memberwere measured using a digital triaxial testing machine with a load capacity ranging from 100 to 400 kN. The testing was conducted under either displacement or pressure control, and a high-precision pressure sensor, capable of measuring up to 100 MPa with an accuracy of \(\pm\)0.1%, was used. Displacement measurements were recorded with a sensor that had a resolution of 0.001 mm or higher. The temperature during testing was maintained between 20 \({}^{\circ}\)C and 80 \({}^{\circ}\)C, with a precision of \(\pm\)0.1 \({}^{\circ}\)C. Axial stress was applied at a rate of 0.01 to 0.1 MPa/s, while confining pressures were set at 0, 5, 10, and 15 MPa. Data acquisition was conducted in real time using a high-frequency system. However, measuring rock mechanics parameters in the laboratory necessitates sample preparation and incurs relatively high costs [40]. Given the unique characteristics of rock samples, it is necessary to obtain multiple samples. Acquiring dynamic rock mechanics parameters through logging conserves financial and material resources and enables the creation of continuous rock mechanics profiles. Therefore, investigating the relationship between dynamic and static rock mechanics parameters is essential [41]. Typically, static rock mechanics parameters obtained in the laboratory are used to calibrate dynamic parameters. The method for acquiring dynamic rock mechanics parameters is as follows:  
\[E_{d}=\rho{v_{s}}^{2}\frac{3{v_{p}}^{2}-4{v_{s}}^{2}}{{v_{p}}^{2}-{v_{s}}^{2}} \tag{4}\]  
\[\mu_{d}=\frac{{v_{p}}^{2}-2{v_{s}}^{2}}{2\big{(}{v_{p}}^{2}-{v_{s}}^{2}\big{)}} \tag{5}\]  
where \(E_{d}\) is the dynamic [PERSON]'s modulus, Gpa; \(\mu_{d}\) is the dynamic Poisson's ratio; \(v_{s}\) is the shear wave velocity, m/us; \(v_{p}\) is the compressional velocity, m/us; and \(\rho\) is the rock density, kg/m\({}^{3}\).