## 3 Dynamic Adaptive Rock Physics Model (DARPM)
In the case where the dip angle is not considered, rock physics inversion was conducted for the entire interval based on the VTI anisotropic RPM, and the inversion results are shown in Figure 8. In Figure 8a,b, the black curves represent well log data, and the red curves represent the results obtained during the inversion process. Figure 8c-e show the inversion results for the negative logarithm of the organic matter mixture aspect ratio-log10(\(\alpha_{k}\)), organic matter porosity \(\Phi_{k}\), and the anisotropy parameters \(\varepsilon\) and \(\gamma\), respectively. In the scenario where the dip angle is considered, rock physics inversion was conducted for the entire interval based on the DARPM, and the inversion results are shown in Figure 9. In Figure 9a,b, the black curve represents the well log data, and the red curve represents the results obtained during the inversion process. Figure 9c-e show the inversion  
Figure 7: The flowchart of the adaptive rock physics inversion method. In figure: \(\alpha_{k}\) (organic matter mixture aspect ratio), \(\Phi_{k}\) (organic matter porosity), \(\varepsilon\) and \(\gamma\) (anisotropy parameters), \(\Phi\) (total porosity), \(Vp_{m}\) (measured longitudinal wave velocity), \(Vp_{c}\) (calculated longitudinal wave velocity), \(Vs_{m}\) (measured shear wave velocity), \(Vs_{c}\) (calculated shear wave velocity), VTI (vertically transversely isotropic), TTI (tilted transversely isotropic). results for the negative logarithm of the organic matter mixture aspect ratio \(-\)log10(\(\alpha_{k}\)), organic matter porosity \(\Phi_{k}\), and the anisotropy parameters \(\varepsilon\) and \(\gamma\), respectively. To assess the accuracy of the RPMs and inversion methods, a comparison was made by calculating the misfit of longitudinal wave velocity and shear wave velocity in both scenarios. Figures 10 and 11 show the inversion results and mis  
Figure 8: Inversion results in the first scenario (with VTI anisotropic RPM): (**a**) Well log measured longitudinal wave velocity \(Vp_{m}\) (black) and calculated longitudinal wave velocity \(Vp_{c}\) (red); (**b**) Well log measured shear wave velocity \(V_{Sm}\) (black) and calculated shear wave velocity \(V_{Sc}\) (red); (**c**) Organic matter mixture aspect ratio \(\alpha_{k}\); (**d**) Organic matter porosity \(\Phi_{k}\); (**e**) Anisotropy parameters \(\varepsilon\) and \(\gamma\). \[\mu_{m}=K_{m}\mu_{s}/K_{s} \tag{10}\]0 Inversion results in the first scenario (with DAPM): (**a**) Well log measured longitudinal wave velocity \(Vp_{m}\) (black) and calculated longitudinal wave velocity \(Vp_{c}\) (red); (**b**) Well log measured shear wave velocity \(Vs_{m}\) (black) and calculated shear wave velocity \(Vs_{c}\) (red); (**c**) Organic matter mixture aspect ratio \(\alpha_{k}\); (**d**) Organic matter porosity \(\Phi_{k}\); (**e**) Anisotropy parameters \(\varepsilon\) and \(\gamma\). The misfit reveals that the VTI anisotropic RPM established without considering the dip angle still cannot accurately describe the reservoir structure and has significant errors. These errors may be due to the absence of dip angle consideration. In contrast, the DARPM established while considering the dip angle provides a more accurate description of the subsurface structure of shale gas reservoirs with smaller errors. Therefore, the proposed DARPM and the associated adaptive rock physics inversion method in this paper exhibit a high level of accuracy and applicability. \[\mu_{m}=K_{m}\mu_{s}/K_{s} \tag{10}\]1 Misfit of \(Vp\) and \(Vs\) in the first scenario (with DARPM): (**a**) Well log measured longitudinal wave velocity \(Vp_{m}\) (black) and calculated longitudinal wave velocity \(Vp_{c}\) (red); (**b**) Well log measured shear wave velocity \(Vs_{m}\) (black) and calculated shear wave velocity \(Vs_{c}\) (red); (**c**) Misfit of longitudinal wave velocity \(Vp\); (**d**) Misfit of shear wave velocity \(Vs\).