## 4 Results and Discussion
### Construction of a Quantitative Optimization Model for Prospecting Target Areas
This model identifies 82.2% of the known ore-bearing units as preferred ore-bearing units. Therefore, the authors believe that this model can be used to reliably identify the mineralization of all research units [65; 66; 67]. Analysis of the effectiveness of the target area optimization results: Optimal model I identified 467 exploration units as preferred ore-bearing units, of which 60 were known ore-bearing units, with a mineralized unit ratio of up to 12.85%, which is 29.2 times higher than the proportion of units with minerals (0.44%). Utilizing preferred model I to optimize each exploration unit can result in 55.05% of known ore-bearing units being distributed within 1.88% of the exploration units, significantly reducing the size of the preferred target area for regional prospecting. The researcher ranks each preferred mineral unit in ascending order of R1 value and divides it into three levels using the \"golden section\" method [68]. We provide a summary of the preferred statistical parameters at all levels, as presented in Table 3. A total of 89 preferred ore-bearing units have been identified in level I, of which 24 are known ore-bearing units, representing 26.97% of all units. This figure is 61.29 times higher than the proportion of units with minerals (0.44%). A total of 144 level-II preferred ore-bearing units have been identified, of which 28 are known ore-bearing units. This represents 19.44% of the total, which is 44.18 times higher than the proportion of units with minerals (0.44%). A total of 233 preferred ore-bearing units have been identified in level III, of which 8 known ore-bearing units have been confirmed. This represents a known ore-bearing unit proportion of 3.43%, which is 7.8 times higher than the proportion of units with minerals (0.44%) (Table 3). Consequently, the model constructed in this study is highly effective in quantitatively optimizing the prospecting target area for the Au deposit in the Beishan region of Gansu Province. 2. The effectiveness of optimal model II  
Mathematical validity analysis: The results of the \"F-test\" for preferred model II are shown in Table 2. F\({}_{\text{P}}\) = 6.45, which is much greater than F\({}_{0.01}\) = 3, indicating that the constructed discriminant model is highly effective. Table 2 shows that optimal model II has a positive prediction rate of 100% for the ore-bearing units and 88.1% for the non-ore-bearing units. This model identifies 100% of the known ore-bearing units as preferred ore-bearing units, and it is considered that the model has a high reliability for identifying the ore-bearing characteristics of all the exploration units. Analysis of the validity of the preferred results: Preferred model II identified 665 exploration units as preferred ore-bearing units, of which 78 were known to contain minerals, with a proportion of ore-bearing units as high as 11.73%, which is 26.66 times higher than the proportion of units with minerals (0.44%). Using preferred model II to optimize each exploration unit, 71.6% of the known ore-bearing units can be distributed into 2.68% of the exploration units, significantly reducing the size of the preferred target area for regional prospecting. The preferred ore-bearing units are sorted in ascending order of R2 value from small to large and divided into three levels using the \"golden section\" method. The statistical parameters of the preferred units at each level are summarized (Table 4). There are 127 level-I preferred ore-bearing units, of which 20 are known ore-bearing units, accounting for 15.74% of the total. This is 35.79 times higher than the proportion of units with minerals (0.44%) and means that 15.74% of the known ore-bearing units are spread over only 0.51% of the exploration units. There are 205 preferred ore-bearing units in level II, of which 35 are known ore-bearing units, accounting for 17.07% of the total. This is 38.71 times higher than the proportion of units with minerals (0.44%).