## 3 Dynamic Adaptive Rock Physics Model (DARPM)  
Drawing from the geological and well log characteristics of the study area, SEM images of shale reservoirs, and structural figures, we can delineate the following key features of the target layer in the shale gas reservoirs: (a) Shale gas reservoirs display a macroscopic layered distribution, showcasing a stratified structure. The background matrix can be effectively considered as VTI (vertical transverse isotropic) anisotropic media. (b) Clay constitutes a significant proportion and is distributed within the rock matrix, exhibiting oriented arrangements correlated with the stratified nature of the reservoir. (c) The reservoir encompasses various pore types, including inorganic pores dispersed in the rock matrix and organic pores within the organic matter (kerogen). (d) The formation dip angle exhibits irregular changes with depth. Introducing the formation dip angle into a VTI anisotropic medium allows for its equivalent representation as a macroscopic TTI (tilted transverse isotropic) anisotropic medium. Based on this analysis, we present a schematic diagram illustrating the microstructure of shale gas reservoirs in Figure 4.  
Given the irregular variations in the dip angles of the strata in the study area, establishing a dynamic adaptive model becomes imperative. Initially, a comprehensive rock physics model (RPM) is devised by amalgamating various theories of rock physics for equivalent media. Subsequently, accounting for the irregular dip angle variations, a fixed sampling step size is employed. Sampling is conducted by moving a window from shallow to deep layers. When the window sampling reaches a layer with dip angles, a TTI (tilted transversely isotropic) rock physics model is applied. Conversely, if the window sampling reaches a layer without dip angles, a VTI (vertically transversely isotropic) rock physics model is utilized. Through the integration of VTI and TTI rock physics models using a moving window, an adaptive rock physics model dynamically takes shape. The construction of the rock physics model in this paper adheres to the following constraints: (1) The macroscopic horizontal bedding of shale reservoirs results from the oriented arrangement of clay. (2) Both the inorganic pores within the rock matrix and the contained fluids are considered isotropic media. (3) The organic mixture comprises kerogen and fluid within organic pores. (4) Kerogen, the fluid within organic pores, and the composite organic mixture are all treated as isotropic media. The consideration of dip angles leads to the dynamic adaptive rock physics model (DARPM) construction process, as illustrated in Figures 5 and 6. Figure 4: The schematic diagram of the microstructure of shale gas reservoirs. Figure 5: Flowchart of DARPM (dynamic adaptive rock physics model). In figure: VTI (vertically transversely isotropic), TTI (tilted transversely isotropic). Figure 6: Schematic diagram of DARPM (dynamic adaptive rock physics model). In figure: VTI (vertically transversely isotropic), TTI (tilted transversely isotropic). First, construct an organic matter mixture model. Step 1: Consider the organic matter pore fluids in the reservoir, which include shale gas and water. The acoustic velocity \(V\) of the gas and water mixture can be estimated with the Wood formula [29]:  
\[V=\sqrt{\frac{K_{R}}{\rho}} \tag{1}\]  
where \(K_{R}\) is the equivalent stress average of the mixture, and \(\rho\) is the average density of the equivalent medium. Step 2: Use the Kuster-Toksoz theory to mix kerogen and organic pore fluids. The stiffness coefficients of the kerogen and fluid mixture (referred to as organic matter mixture) can be calculated using fluid saturation.