The Zhongdian belt lies in the southern Yidun terrane, between the Ganzi-Litang suture to the east and the Jinshajiang suture to the west (Figure 1(a), Figure 1(b)). The terrane forms part of the eastern Tethyan domain and records westward subduction of the Ganzi-Litang ocean beneath the Yidun block during the Late Triassic [12][13]. Arc magmatism produced a north-northwest-trending belt of intermediate to felsic intrusions and associated hydrothermal systems.

Upper Triassic volcanic, volcaniclastic, carbonate and clastic rocks, commonly assigned to the Tumugou Formation and related units, form the principal country-rock succession. These rocks were intruded by quartz diorite, granodiorite, monzodiorite and quartz monzonite porphyries (Figure 1(b)). Carbonate-bearing intervals favored skarn and replacement mineralization, whereas porphyry-style stockworks and disseminations are concentrated within and around the intrusive centers [13]-[15].

Ore formation was concentrated in the Late Triassic. Published geochronology places the Pulang and Songnuo intrusive systems broadly near 216 Ma, while the Xuejiping porphyry system is approximately 213 Ma [14]-[17]. Pulang is the largest known porphyry Cu-Au district in the belt and comprises several intrusive phases with potassic, phyllic and propylitic alteration and Cu-Au-bearing stockwork mineralization [15][16]. Smaller Cu-Mo, Cu-Au-Ag, Pb-Zn and polymetallic occurrences are distributed along intrusive and structural corridors.

The 13 validation targets include the Cu-dominant Pulang, Lannitang, Gaochiping, Chundu and Qiansui occurrences; Cu-Mo associations at Relin and Hongshan; Cu-Au-Ag associations at Xuejiping and Pulang; and Pb-Zn-Ag-Au-bearing targets such as Langdu, Yaza, Disuga and Songnuo (Supplementary Table S1). Their locations are clustered along several NNW-trending corridors, with a central group and more isolated northern and southern targets (Figure 1(c)). This spatial clustering is one reason why random validation folds would be misleading and why spatially separated testing was used below. Because the available inventory reports metal associations rather than verified genetic classes, the analysis does not assign individual targets to porphyry, skarn, or epithermal subsets.

The analytical surface contains 4307 grid cells at an exact 500 m spacing. It is a gridded geochemical product, not the original stream-sediment sample table. A 500 × 500 m square centered on each node produces a non-overlapping coverage of 1076.75 km². All 13 targets lie within this coverage, at distances of 108.0 - 322.3 m from the nearest grid node.

Coordinate values are consistent with a projected UTM zone 47N system. WGS 84/UTM zone 47N (EPSG:32647) was used as the working reference for display and area calculations, but the source CSV files do not store CRS metadata. The definitive datum and the interpolation history of the grid should therefore be confirmed from the originating GIS archive. This limitation does not affect relative distances and areas because the grid and target coordinates share the same meter-based system.

Figure 1.Regional geology and analytical coverage of the Zhongdian porphyry-skarn belt. (a) Regional location of the study area in southwestern China, based on the 2024 Standard Map of Yunnan Province issued by the Yunnan Provincial Department of Natural Resources. (b) Simplified geology, major intrusions, structures, and representative mineral occurrences of the Zhongdian-Yidun region, modified from Mondah et al., 2021 [18]. (c) Extent of the 4307-cell geochemical grid and the 13 validation targets in the working UTM zone 47N system.

Cu, Pb, Zn, Ag, Au, Mo and W are available for every grid cell. Cu, Pb, Zn, Ag, Mo and W are expressed in micrograms per gram, whereas Au is expressed in nanograms per gram. No coordinates are missing or duplicated. Three ratios were calculated on positive concentrations: RCu = Cu/(Pb + Zn), RMo = Mo/(Cu + W), and RAu = Au/Ag. Au was converted to micrograms per gram before RAu was calculated, so numerator and denominator share common mass units. Ratios were formed on the concentration scale, not by dividing logarithms. Each of the ten variables was thresholded at P85, P90, and P95.

The target table contains 13-point locations. One Au occurrence is unnamed and was retained as OID 13 so that the validation set was not altered. Eight records contain national catalogue codes and size-class attributes; the remaining five contain names, commodity associations and coordinates only. Discovery status, positional uncertainty and verified genetic type are not recorded. SupplementaryTable S1 reports on the available fields and nearest-grid distances. Commodity groups were not analyzed separately because the Pb-Zn, Au-only and polymetallic strata contain only two, one and one targets, respectively.

The study boundary B was generated as the union of the 4307 square cells and has an area of 1076.75 km². For every variable-threshold combination, selected cell centroids were buffered at 250, 500, 750, 1000, 1500 and 2000 m. Overlapping polygons were dissolved and intersected with B. The resulting union-buffer footprint therefore varies with the spatial arrangement of anomalous cells and with buffer radius.

For a configuration capturing nc of N = 13 targets within a clipped union-buffer area U_B, capture C, footprint A, and spatial efficiency SE were calculated as:

SE = 1 is the geometric expectation for a single configuration under uniformly distributed targets. Because 180 configurations were searched and the targets are clustered, statistical evidence was based on the max-statistic permutation test rather than on SE > 1 alone. Wilson 95% intervals were used for capture proportions [19].

Capture and footprint were also evaluated as a two-objective problem. A configuration was considered non-dominated when no alternative captured more targets within an equal or smaller footprint. The set of non-dominated configurations defines an efficiency frontier and separates selective first-pass rules from higher-recall rules.

Two spatial validation schemes were used. In spatial-exclusion leave-one-target-out validation, each target was withheld, and training targets within 5 km were excluded before the best configuration was selected. In the second scheme, 5 km spatial blocks were held out in turn. Selection was repeated globally across all ten variables and within each variable separately. Rank stability was assessed with 1000 spatial-block bootstrap replicates [20].

The search-corrected benchmark was obtained from 999 random sets of 13 points generated uniformly within the study boundary. Every random set was scored against all 180 configurations, and only the maximum SE was retained. The familywise p-value used the standard plus-one correction [21]. This procedure controls the fact that the reported maximum was selected from a search rather than specified in advance.

The selected Cu-P95 configurations were converted into two prospectivity products. The 250 m union-buffer footprint represents the most spatially selective screen, whereas the 750 m footprint represents the higher-recall alternative on the efficiency frontier. These polygons are follow-up target zones, not newly discovered deposits; their geological significance requires independent mapping, geophysics, geochemistry and field verification.

Processing was implemented in Python using pandas, GeoPandas, Shapely, NumPy, Matplotlib and PyProj, with the random seed fixed at 20260730. The input files, analysis script, metadata, and complete configuration table accompany the revision. The full analytical sequence is summarized in Figure 2.

Figure 2.Methodological workflow. The analysis proceeds from common-unit variables, percentile thresholds, and buffer radii to dissolved, boundary-clipped footprints; all 180 configurations are then evaluated by blocked validation, bootstrap stability, and max-statistic permutation testing. The workflow ends with an optimal threshold-plus-buffer rule and the corresponding prospectivity targets.

P85, P90 and P95 select approximately 15%, 10% and 5% of the grid cells, but these fractions are not the mapped areas produced after buffering. At 1000 m, P95 footprints range from 19.40% of the boundary for W to 35.89% for RAu; Cu occupies 25.57% (Table 1). At P85 and the same radius, single-element footprints range from 46.74% for Pb to 68.21% for Ag.

Using the selected-cell fraction in place of the true footprint inflates SE by 3.80 - 7.16 times at 1,000 m and P95, with a mean inflation factor of 5.48 (Table 2). For Cu, the approximation changes SE from 3.61 to 18.24. The difference is large enough to alter both variable ranking and the selected radius.

Table 1.Thresholds, anomalous-cell counts, clipped union-buffer footprints, target capture and spatial efficiency at the 1000 m reference radius. Concentrations are µg/g except Au (ng/g); ratios are dimensionless after common-unit conversion. CI = Wilson 95% confidence interval.

Table 2.Effect of the footprint denominator at 1000 m and P95. The selected-cell approximation divides capture by the fraction of selected cells; the corrected index uses the clipped union-buffer footprint.

Footprint growth explains why the denominator must respond to radius. For Cu-P95, 218 separate 250 m discs would cover 42.8 km² and the measured union covers 42.74 km², an overlap loss of only 0.2%. The loss rises to 30.3% at 500 m, 48.7% at 750 m, 59.8% at 1000 m, 72.8% at 1500 m and 79.9% at 2000 m. The same pattern occurs across all ten variables (Figure 3). At 250 m, the buffer diameter equals the grid spacing; beyond that distance, successive increments mainly fill gaps between neighboring anomalous cells.

Target capture rises monotonically with radius, but at different rates among variables and thresholds (Figure 4). Cu-P95 captures 46.2% of targets at 250 m, 61.5% at 500 m, and 92.3% at 750 m. The 1000 m radius adds no Cu-P95 target, and complete capture is reached only at 1500 m. Ag-P95 rises from 38.5% at 250 m to 92.3% at 1000 m, whereas Au-P95 rises from 23.1% to 84.6% over the same interval. W-P95 remains at or below 30.8% through 1500 m and reaches 61.5% only at 2000 m.

Figure 3.(a) Clipped union-buffer footprint against radius at P95. The dashed curve shows the nominal area of separate Cu buffers; the horizontal line marks the selected-cell fraction. (b) Overlap loss, expressed as the proportion of nominal disc area absorbed by buffer coalescence, for all ten variables at P95.

Figure 4. Target capture against buffer radius for the seven single elements at P85, P90 and P95. With 13 validation targets, capture changes in increments of 7.7 percentage points.

Figure 5.Spatial efficiency against buffer radius. The upper horizontal line is the 5% familywise threshold from the max-statistic permutation test (SE = 5.87); the lower line is the conventional single-configuration expectation (SE = 1).

Spatial efficiency changes in the opposite direction. Because footprint expands faster than capture, SE decreases with radius for every variable and threshold (Figure 5). Cu-P95 at 250 m is the maximum among all 180 configurations (SE = 11.63), capturing 6 of 13 targets inside 3.97% of the boundary. Pb-P95 (SE = 9.78), Ag-P95 (9.47), and RCu-P95 (7.82) at 250 m follow. The design contains no interior efficiency maximum: the statistical optimum lies at the shortest radius tested.

A single maximum does not summarize the operational trade-off because capture and efficiency favor different settings. Eight configurations are non-dominated: no alternative captures more targets within an equal or smaller footprint (Figure 6; Table 3). The frontier extends from Pb-P95 and Cu-P95 at 250 m, which are highly selective, to Cu-P90 at 750 m, which captures all 13 targets within 31.36% of the boundary. Cu-P95 at 750 m is the most attractive high-recall compromise, capturing 12 of 13 targets within 18.35% of the area.

Figure 6.Capture versus clipped footprint for all 180 configurations. Marker size increases with buffer radius. The heavy line joins the eight non-dominated configurations that form the efficiency frontier; the diagonal is the conventional random expectation.

Table 3.Efficiency frontier. Each row is non-dominated: no alternative captures more targets within an equal or smaller footprint.

At 1000 m and P95, the corrected ranking is Cu (SE = 3.61), RCu (3.36), Au (3.20), Ag (2.94), Pb (2.50), Mo (2.42), Zn (1.63), W (1.59), RAu (1.29) and RMo (1.22) (Figure 7;Table 1). None reaches the familywise threshold of 5.87. This radius is therefore useful only as a comparison with earlier practice; it is neither the efficiency optimum nor the most economical high-recall rule.

Figure 7.(a) Spatial efficiency at the 1000 m reference radius for all ten variables, calculated from true clipped footprints. (b) Target capture and (c) spatial-efficiency heat maps. No value reaches the familywise threshold of SE = 5.87.

The distribution of the maximum SE from 999 spatial permutations has a median of 2.93 and a 95th percentile of 5.87 (Figure 8(a)). The observed maximum of 11.63 yields a familywise p-value of 0.001. Seven configurations exceed the 5% familywise threshold; all occur at 250 m and involve Cu, Pb, Ag, or RCu (Table 4). The effect of correcting the footprint denominator and re-optimizing the configuration is summarized in Figure 8(d).

Table 4.Configurations exceeding the 5% familywise threshold (SE = 5.87) from 999 max-statistic spatial permutations.

Across 1000 spatial-block bootstrap replicates, Cu-P95-250 m is the global winner in 45.5% of replicates, Pb-P95-250 m in 33.6%, and Ag-P95-250 m in 9.5% (Figure 8(b)). Within Cu alone, the same configuration is selected in 97.8% of replicates. Its bootstrap median SE is 11.63 with a 95% interval of 5.81 - 17.44. Threshold and radius are stable; the leading variable is less certain because Pb and Ag together win more than 40% of global replicates.

Spatial-exclusion and regular-block validation recover P95 and 250 m as the modal setting for most variables; W favors P90 at 250 m. When the pathfinder variable is fixed in advance, out-of-fold capture is 46.2% for Cu, 38.5% for Pb, Ag, and W, and 30.8% for RCu. When selection is allowed across all ten variables, out-of-fold capture falls to 3 of 13 targets, or 23.1% (95% CI: 8.2% - 50.3%) (Figure 8(c); Table 5). The setting is stable between folds, but the full-data capture of the selected winner is optimistic.

Table 5.Spatially out-of-fold performance and configuration stability. Capture is from 5 km spatial-exclusion leave-one-target-out validation; the final column reports within-variable selection across 1000 spatial-block bootstrap replicates.

Figure 8.Validation and uncertainty. (a) Observed spatial efficiencies ranked against the max-statistic null. (b) Global winner frequencies across 1000 spatial-block bootstrap replicates. (c) Spatial-exclusion out-of-fold capture with Wilson 95% intervals. (d) Decomposition of the apparent performance into denominator choice, corrected 1000 m performance and the re-optimized maximum.

Figure 9.Prospectivity target footprints derived from Cu-P95. (a) The 250 m selective screen captures 6 of 13 targets within 3.97% of the boundary. (b) The 750 m higher-recall screen captures 12 of 13 within 18.35%. Filled circles mark captured validation targets; crosses mark targets outside the selected footprint.

The optimal settings were converted into two prospectivity footprints (Figure 9). The Cu-P95-250 m screen selects 3.97% of the belt and captures Langdu, Lannitang, Hongshan, Xuejiping, Pulang and Qiansui. The Cu-P95-750 m screen expands the footprint to 18.35% and captures 12 of the 13 targets; only the unnamed Au occurrence remains outside. The 750 - 1000 m expansion is not retained because it increases the footprint to 25.57% without adding a target.

Areas within these footprints that do not coincide with a documented target constitute the principal follow-up zones generated by the analysis. They should be ranked with geological contacts, intrusive centers, structures, alteration, and independent geophysical or geochemical evidence before field investigation. The maps are therefore prospectivity targets in an operational sense, not evidence that every buffered cell contains mineralization.

The analysis returns two defensible operating rules rather than one universal setting. Cu-P95 at 250 m is the most efficient rule and is supported by the bootstrap and permutation results. It is appropriate when the objective is to reduce a regional dataset to a small first-pass footprint. Its limitation is equally clear: only six of the thirteen targets are captured.

Cu-P95 at 750 m is the better rule when missing a mineralized center is more costly than investigating additional ground. It captures twelve targets within 18.35% of the belt and lies on the efficiency frontier. The move from 750 to 1000 m is not justified by this dataset because it adds approximately 7.2 percentage points of area without increasing capture. The frontier makes the decision transparent: the final choice is governed by follow-up cost and tolerance for false negatives, not by SE alone.

Cu is the most stable variable across full-data efficiency, bootstrap selection, and out-of-fold capture. That result is geologically reasonable in a belt dominated by porphyry Cu-Au and Cu-bearing skarn systems, and it is also influenced by the validation inventory, in which nine of thirteen targets are Cu-dominant. The ranking should therefore be read as performance against the available inventory rather than as an inventory-independent statement about the whole belt.

Pb and Ag are competitive at short radius, and both survive the familywise test. Their performance is consistent with the presence of polymetallic skarn, replacement, and peripheral hydrothermal signatures. At Lannitang, for example, published primary-halo workplaces show Cu-Mo closer to the mineralized core and Pb-Zn-Ag-related associations farther outward [22]. That comparison provides a plausible geological context, but the present pooled inventory is too small to test metal zonation directly.

RCu = Cu/(Pb + Zn) also performs well. Normalizing Cu by Pb + Zn may suppress broad polymetallic background while retaining Cu-dominant centers, but the mechanism remains an interpretation. RMo and RAu are weaker and less stable; large ratio values can be generated by small denominators as easily as by strong numerators [23]. Ratios should therefore be assessed individually rather than accepted or rejected as a class.

The conventional SE = 1 benchmark applies to a single rule specified in advance. Once 180 correlated configurations are searched, chance alone produces a much larger maximum. In the present permutation experiment, the median null maximum is 2.93, and the 95th percentile is 5.87. Comparing the selected winner with unity would therefore overstate the evidence even if the footprint denominator were correct.

The max-statistic test addresses this problem directly and identifies seven familywise-significant configurations. Spatial validation addresses a different question: how much of the selected performance transfers to locations not used in selection. The global out-of-fold capture of 23.1% is much lower than the 46.2% full-data capture of Cu-P95-250 m. The result remains useful as a selective screen, but it should not be presented as a fully predictive prospectivity model.

The 250 m optimum coincides with half the 500 m grid spacing. At that radius, neighboring buffers first touch and remain almost completely disjoint; spatial selectivity is therefore maximized by the geometry of the gridded surface. The optimized radius is not an estimate of stream-sediment dispersion length and should not be interpreted as a physical transport distance.

Hydrologically routed catchments would be more defensible for original stream-sediment samples because they follow upstream flow paths and drainage anisotropy [5]-[7]. Fractal and singularity methods could also be compared with percentile thresholds [24]-[26]. Any such comparison should retain the same clipped-footprint denominator, spatial blocking and familywise testing; otherwise, methodological complexity can mask the same validation bias identified here.

Figure 9 translates the statistical result into areas that an exploration team can inspect. The 250 m product is suited to rapid ranking because it isolates narrow Cu-rich neighborhoods around six known centers and a set of unvalidated anomaly patches. The 750 m product is broader and recovers nearly the full validation inventory, making it more appropriate for regional compilation, reconnaissance planning, or integration with structural and lithological layers.

Neither product should be treated as a stand-alone discovery map. The geochemical surface has already been gridded, the original catchments are unavailable, and some selected zones may be artifacts of interpolation or clustered cells. A defensible target-ranking stage should combine the optimized footprints with intrusive contacts, favorable stratigraphy, faults, alteration, geophysics, and access constraints. In that sense, the present workflow ends where geological targeting begins.