## 4 Results and Discussion
### Construction of a Quantitative Optimization Model for Prospecting Target Areas
There are 332 preferred ore-bearing units in level III, of which 23 are known ore-bearing units, and the Ratio of known ore-bearing units to preferred units is 6.92%, which is 15.72 times higher than Proportion of units with minerals (0.44%) (Table 4). Therefore, the model constructed in level II is highly effective in quantitatively selecting target areas for prospecting Au deposits in the Beishan area of Gansu Province. 3. The effectiveness of optimal model III  
Mathematical validity analysis: The results of the F-test for optimal model III are shown in Table 2. \(\mathrm{F_{P}}=0.47\), which is much smaller than \(\mathrm{F_{0.01}}=3\), The constructed discriminant model is mathematically ineffective (optimal model I for F-test calculation and parameters). In Table 2, preferred model III has a positive prediction rate of 85.7% for the ore-bearing units and a positive prediction rate of 94.6% for the non-ore-bearing units. This model identifies 85.7% of the known ore-bearing units as preferred ore-bearing units, and it \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Class of** & **Number of** & **Ratio of Preferred** & **Number of** & **Ratio of Known** & **Increase Multiplier** \\
**Preferred Units** & **Preferred Units** & **Units to Total** & **Known** & **Ore-Bearing Units** & **or Proportion of** \\  & & **Projected Units** & **Ore-Bearing Units** & **to Preferred Units** & **Units with Minerals** \\ \hline
**Level I** & 127 & 0.51\% & 20 & 15.75\% & 35.79 \\
**Level II** & 205 & 0.83\% & 35 & 17.07\% & 38.71 \\
**Level III** & 332 & 1.34\% & 23 & 6.92\% & 15.72 \\
**Total** & 665 & 2.68\% & 78 & 11.73\% & 26.66 \\ \hline \hline \end{tabular} 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 4: Statistics of quantitative optimization results of model II. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Class of** & **Number of** & **Ratio of Preferred Units** & **Number of** & **Ratio of Known** & **Increase Multiplier** \\
**Preferred Units** & **Preferred Units** & **Units to Total** & **Known** & **Ore-Bearing Units** & **to Preferred Units** & **Units with Minerals** \\ \hline
**Level I** & 89 & 0.36\% & 24 & 26.97\% & 61.29 \\
**Level II** & 144 & 0.58\% & 28 & 19.44\% & 44.18 \\
**Level III** & 233 & 0.94\% & 8 & 3.43\% & 7.80 \\
**Total** & 467 & 1.88\% & 60 & 12.85\% & 29.20 \\ \hline \hline \end{tabular} 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 3: Statistics of quantitative optimization results of model I.  
is considered that the model has a high reliability in regard to identifying the mineralization of each exploration unit. However, due to its poor F-test result, its preferred results should be used with caution. Analysis of the validity of the preferred results: Optimal model III identified 550 research units as preferred ore-bearing units, including 21 known ore-bearing units, with a ratio of known ore-bearing units of 3.81%, which is 8.68 times higher than the proportion of units with minerals (0.44%). Using preferred model III to optimize each research unit can result in 19.3% of the known ore-bearing units being distributed in 2.2% of the research units, which to some extent narrows the scope of the preferred target area for regional prospecting. The preferred ore-bearing units are arranged in ascending order of R3 value, from smallest to largest, and divided into three categories using the \"golden section\" method. The summary of the preferred statistical parameters at each level is presented in Table 5.  
There are 105 preferred ore-bearing units at level I, of which 6 are known ore-bearing units, representing 5.71% of the total.