## 4 Results and Discussion
### Construction of a Quantitative Optimization Model for Prospecting Target Areas
This is 12.98 times higher than the proportion of units with minerals (0.44%), with 5.71% of known ore-bearing units spread over only 0.42% of the exploration units. There are 170 preferred ore-bearing units in level II, of which 4 are known ore-bearing units, and the proportion of known ore-bearing units is 2.35%, which is 5.34 times higher than the proportion of units with minerals (0.44%). There are 275 preferred ore-bearing units in level III, of which 11 are known ore-bearing units, and the proportion of known ore-bearing units is 4%, which is 9.09 times higher than the proportion of units with minerals (0.44%) (Table 5). Therefore, the constructed model III has a certain effect on the quantitative optimization of the prospecting target area for Au deposits in the Beishan area of Gansu Province. 4. Discussion of a series of models for the optimization of prospecting target areas in the Au mining area  
In models I and II, \(\rm F_{P}>F_{0.01}\), which means that models I and II are highly effective in a statistical sense. Although \(\rm F_{P}<F_{0.01}\) in model III, each of the three models has a very high positive prediction rate for both sample types. Furthermore, the proportion of ore-bearing units in each model and classification is greater than the proportion of units with minerals (0.44%). Therefore, all three models are considered to have a very good optimization effect. The results of the validity test, the optimization outcomes, and the analysis of the ore-bearing rate in each classification of each model indicate that model I displays the most optimal results, model II is the second most optimal, and model III exhibits relatively poor optimization effects. The application of the optimization results of each model should be treated differently. Optimal models I, II, and III are all based on the theoretical foundation of mathematical statistics. The determination of each model is based on the correlation between different variables and the existing Au deposits (points) in the area. This approach eliminates the \begin{table}
\begin{tabular}{c c c c c c} \hline
**Class of** & **Number of** & **Ratio of Preferred Units** & **Number of Units to Total** & **Ratio of Known** & **Increase Multiplier** & **for Proportion of** \\
**Preferred Units** & **Preferred Units** & **Ore-Bearing Units** & **to Preferred Units** & **Units with Minerals** \\ \hline
**Level I units** & 105 & 0.42\% & 6 & 5.71\% & 12.98 \\
**Level II units** & 170 & 0.68\% & 4 & 2.35\% & 5.34 \\
**Level III units** & 275 & 1.11\% & 11 & 4\% & 9.09 \\
**Total** & 550 & 2.22\% & 21 & 3.81\% & 8.68 \\ \hline \end{tabular}
\begin{tabular}{c c c c c} \hline
**Description: Total number of projected units: 24.824. The number of known ore-bearing units: 109. Proportion of units with minerals (ratio of known ore-bearing units to total projected units): 0.44%.**  
\end{table} 
Table 5: Statistics of quantitative optimization results of model III. influence of subjective human factors and the uncertainties and differences inherent in geological and metallogenic theories. Of the 109 known ore-bearing units in the entire region, 102 known ore-bearing units (representing 93.6% of the total) are distributed across the three preferred models. It is postulated that 93.6% of the ore-bearing units in the entire region can be clearly delineated into three categories within the 42-dimensional space (comprising 39 geochemical elements, 2 aeromagnetic variables, and 1 fitted value of the Au element). Preferred model I: A total of 60 known ore-bearing units are highly separated from other non-ore-bearing units in 10 dimensional spaces, such as SiO\({}_{2}\), \(\Delta\)Tx, \(\Delta\)Td, Al\({}_{2}\)O\({}_{3}\), and Au. Typical mineral deposits include the Xiaoxi Gong medium-sized gold deposit in Subei County and the Laojin Chang medium-sized gold deposit in Guazhou County (Table 2). Further study is required to determine whether this type of Au deposit has a different genesis than other Au deposits in the study area.