## 3 Dynamic Adaptive Rock Physics Model (DARPM)
Step 6: Apply the Brown-Korringa theory to introduce water into inorganic pores [33]. The quantitative relationship between the anisotropic dry rock matrix and its effective modulus after being filled with fluid can be expressed as follows:  
\[S_{ijkl}^{(dry)}-S_{ijkl}^{(sat)}=\frac{\Big{(}S_{jka}^{(dry)}-S_{jika}^{0} \Big{)}\Big{(}S_{kla}^{(dry)}-S_{kla}^{0}\Big{)}}{\Big{(}S_{a\beta\beta}^{( dry)}-S_{a\alpha\beta\beta}^{0}\Big{)}+\Big{(}\beta_{fl}-\beta_{0}\Big{)}\Phi} \tag{11}\]  
\[\beta_{fl}=1/K_{fl},\ \ \ \beta_{0}=1/K_{0} \tag{12}\]  
Here, \(S_{ijkl}^{(dry)}\), \(S_{ijkl}^{(sat)}\), and \(S_{ijkl}^{0}\) represent the effective elastic compliance tensors of the rock skeleton, the pore fluid-saturated rock, and the constituent minerals. \(\beta_{fl}\) and \(\beta_{0}=S_{\alpha\alpha\beta\beta}^{0}\) are the compressibility coefficients of the pore fluid and minerals, \(\Phi\) is the porosity, and \(K_{fl}\) and \(K_{0}\) are the bulk moduli of the pore fluid and minerals. Then, we merge the organic matter mixture model with the equivalent VTI anisotropic medium model. Step 7: Apply anisotropic equivalent field theory [34] to introduce the organic matter mixture into the rock matrix with VTI anisotropic characteristics, resulting in an equivalent VTI anisotropic RPM of the shale reservoir target layer in the study area. For a VTI anisotropic media, when the inclusions can be fully filled with a shape and orientation identical to the associated pores, the formula for the equivalent elastic stiffness tensor \(\mathbf{C}_{ijkl}^{eff}\) of the VTI anisotropic medium derived by Sevostianov can be written as follows:  
\[\mathbf{C}_{ijkl}^{eff}=\mathbf{C}_{ijkl}^{(0)}+q\left[\mathbf{C}_{ijkl}^{(1)^{-1}}+(1-q) \mathbf{P}_{ijkl}\right]^{-1} \tag{13}\]  
where \(\mathbf{C}_{ijkl}\) represents the elastic stiffness tensor, the superscripts 0 and 1 refer to the matrix and the difference between the matrix and the inclusions, \(q\) is the volume fraction of the inclusions, and \(\mathbf{P}_{ijkl}\) represents the tensor representing the VTI anisotropic matrix. Specifically, the equivalent elastic stiffness tensor can be expressed as follows:  
\[\mathbf{C}^{eff}=\mathbf{C}_{1}^{eff}\mathbf{U}^{(1)}+\mathbf{C}_{2}^{eff}\mathbf{U}^{(2)}+\mathbf{C}_{ 3}^{eff}\mathbf{U}^{(3)}+\mathbf{C}_{4}^{eff}\mathbf{U}^{(4)}+\mathbf{C}_{5}^{eff}\mathbf{U}^{(5)}+ \mathbf{C}_{6}^{eff}\mathbf{U}^{(6)} \tag{14}\]where the subscripts _ijkl_ are simplified for clarity, and the matrix \(\mathbf{U}\) is related to \(\mathbf{C}^{(0)}\), \(\mathbf{C}^{(1)},q\), and \(\mathbf{P}\). Finally, we introduce the dip angle into the VTI anisotropic model to construct an equivalent TTI anisotropic RPM. Step 8: With the assistance of the Bond matrix [35], the dip angle can be incorporated into the initial VTI anisotropic RPM, thereby yielding the TTI anisotropic RPM. In the coordinate system defined by \(\alpha x_{1}x_{2}x_{3}\), the elastic coefficient matrix \(\mathbf{C}_{ij}\) can be represented as \(\mathbf{C}_{ij^{\prime}}\) after a coordinate transformation, where \(\mathbf{M}\) is defined as a 6 \(\times\) 6 transformation matrix. \[\mathbf{C}_{  
The PSO optimization rock physics inversion method is applied to perform calculations in two scenarios: one without considering dip angles in the geological formations and the other considering dip angles. In the first scenario, only the VTI anisotropic RPM is used to implement the inversion method. In the second scenario, the DARPM is used to conduct an adaptive inversion method. By comparing the results obtained in these two scenarios, the accuracy and applicability of the DARPM proposed in this paper are validated. Furthermore, the rock physics inversion results obtained when considering dip angles are integrated into a deep-learning algorithm for fusion and training. This inversion method provides a foundation and basis for research in quantitative seismic characterization methods.