## 5 Establishment of 3D Geological Model
### Analysis of Variation Function  
The variation function serves as a metric for quantifying the variability of regional variables within three-dimensional space. It captures the extent to which variables fluctuate with changes in distance, thereby delineating the spatial correlation among variables. This method is instrumental in precisely articulating the spatial variation patterns and attributes of geological parameters. There are three main types: spherical models, exponential models, and Gaussian models, which are generally used to describe geological parameters. In the assessment of the variation function, it is imperative to identify the predominant direction based on the sedimentary environment's characteristics, the orientation of material sources, and the distribution of sedimentary sand bodies. Once the primary direction is established, the search radius and step size must be adjusted to align the variation function curve withthe experimental regression curve, ensuring their fundamental consistency or convergence. The secondary direction, orthogonal to the primary one, is ascertained subsequent to the analysis of the main direction's variation function. The scope of variation for the secondary direction is set by replicating the aforementioned analytical process for the primary direction. The two rock facies types, mudstone and sandstone, are assigned values of 0 and 1, respectively, thus converting continuous parameters into discrete parameters (Table 1). Then, the attribute variation function under phase control is fitted hierarchically, and the characteristic parameters of the variation function (direction, variation range, nugget value, and base value) are adjusted until the actual variation function essentially conforms to the theoretical variation function. Subsequently, a three-dimensional spatial model for each rock facies in the southern Heshui area is formulated using the sequential Gaussian simulation method, complemented by the fitting of the variation function.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sub-** **Layers**} & \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Major Range**} & \multicolumn{3}{c}{**Minor Range**} & \multicolumn{3}{c}{**Vertical Range**} \\ \cline{3-10}  & & **Azimuth/\({}^{c}\)** & **Range/m** & **Nugget/m** & **Azimuth/\({}^{c}\)** & **Range/m** & **Nugget/m** & **Range/m** & **Nugget/m** \\ \hline Chang & Lithofacies & & & & & & & & \\ \(7_{1}\)1 & model & 30 & 3200 & 0 & 300 & 1700 & 0 & 4 & 0 \\ Chang & Lithofacies & & & & & & & & \\ \(7_{2}\)1 & model & 35 & 4000 & 0 & 305 & 2050 & 0 & 5 & 0 \\ Chang & Lithofacies & & & & & & & & \\ \(7_{2}\)2 & model & 40 & 4500 & 0 & 310 & 2300 & 0 & 6 & 0 \\ Chang & Lithofacies & & & & & & & & \\ \(7_{2}\)2 & model & 45 & 5100 & 0 & 315 & 2650 & 0 & 7 & 0 \\ Chang & Lithofacies & & & & & & & & \\ \(7_{3}\) & model & 50 & 5500 & 0 & 320 & 3000 & 0 & 8 & 0 \\ Chang & \(7_{1}\)1 & Porosity & & & & & & & \\ \(7_{1}\)2 & model & 30 & 1300 & 0 & 300 & 750 & 0 & 4 & 0 \\ Chang & \(7_{1}\)2 & Porosity & & & & & & & \\ \(7_{2}\)1 & model & 35 & 1600 & 0 & 305 & 1050 & 0 & 5 & 0 \\ \(7_{2}\)1 & Porosity & & & & & & & & \\ \(7_{2}\)1 & model & 40 & 1900 & 0 & 310 & 1400 & 0 & 6 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fitting parameter table of variation function of long 7 segments in Heshui South block.  
Figure 3: Three-dimensional (3D) structure model of each sublayer of the target layer: (**a**) structural model; (**b**) grid model.