Chlorite minerals can form in a variety of different environments or conditions. They can mineralize through rock alteration due to high pressure and/or high temperature burial, converging plates, hydrothermal activity, contact or retrograde metamorphism (Wang et al., 2022). Chlorite is also associated with propylitic alteration facies, which is very common in magmatic hydrothermal ore deposits, such as porphyry systems (Fulignati, 2020).

Chlorite is a group comprising 10 mineral species according to the International Mineralogical Association (rruff.info/ima; date accessed: July 2023). The chlorite mineral group has the general chemical formula A _5-6 T ₄ Z ₁₈, where A can incorporate many elements, including Mg, Fe²⁺, Al, Fe³⁺ Mn, and Zn, T is generally Si and Al, but is also known to contain Fe³⁺; and Z is O or OH. It is into these A, T, or Z sites that the elements that can be used to vector towards porphyry mineralization substitute. Which sites these elements enter depends on their size and charge.

Chlorite chemistry data was acquired from literature research, ScienceDirect, and GeoScienceWorld. Analyses went through extensive filtering to ensure that they can be confidently considered as chlorite (Freij et al., 2023). After these data were processed and filtered, 1,679 analyses remained from five papers studying five distinct areas: porphyry Cu-Au deposits in the Northparkes District in Australia (Pacey et al., 2020) and the Batu Hijau district in Indonesia (Wilkinson et al., 2015), Cu-Mo deposits in the Superior district of Arizona (Cooke et al., 2020) and El Teniente in Chile (Wilkinson et al., 2020), and a Cu-Mo-W deposit in Tongshankou, China (Chu et al., 2020).

The Northparkes district is located in New South Wales, Australia, and hosts Cu-Au deposits totaling 472 million tonnes at 0.56% Cu and 0.19 g/t Au (Pacey et al., 2019). The host rocks consist of volcanic and volcaniclastic rocks with intercalations of marine sediments locally (Krynen et al., 1990; Simpson et al., 2005). Mineralization is hosted in comagmatic intrusive rocks and show magmatic-hydrothermal activity from the Late Ordovician to earliest Silurian (Lickfold et al., 2007). Ore minerals include bornite and chalcopyrite (Pacey et al., 2020).

The Batu Hijau district in Indonesia hosts 1.64 billion tonnes of ore at 0.44% Cu and 0.35 g/t Au on average (Chu et al., 2020). It formed at ∼ 3.7 Ma. Batu Hijau consists of strongly mineralized tonalite emplaced into homogeneous intermediate volcanics (Chu et al., 2020) with quartz vein-hosted bornite and chalcopyrite as the primary copper ore minerals (Imai and Ohno, 2008).

The Cretaceous to Paleocene Cu-Mo deposit (Cooke et al., 2020) of the Superior District in Arizona hosts 1.787 billion tonnes at a grade of 1.53% Cu and 0.039% Mo (Rio Tinto, 2018). Host rocks consist of highly reactive dolerites and limestones and permeable breccias with chalcopyrite being the dominant ore mineral (Cooke et al., 2020).

El Teniente is located in the Andean Cordillera (Wilkinson et al., 2020) and hosts approximately 95 million tonnes of fine Cu grading 0.5% and 2.5 million tonnes of Mo (Camus, 2002). The host rock consists of a late Miocene volcano-plutonic complex which occurs with a sequence of extrusive and intrusive rocks of basaltic to rhyolitic composition (Skewes et al., 2002; Cannell et al., 2005) and was intruded by rocks of diorite to granodiorite (Wilkinson et al., 2020). Ore minerals include chalcopyrite, pyrite, and molybdenite (Wilkinson et al., 2020).

Tongshankou is a porphyry-related Cu–Mo–W skarn deposit in Eastern China and contains 0.55 Mt Cu at 0.86%, 0.01 Mt Mo at 0.10% and 0.12 Mt WO₃ at 0.19% (Chu et al., 2020). The deposit formed near the contact between Lower Triassic carbonate rocks and the granodiorite porphyry (Chu et al., 2020). Ore minerals are chalcopyrite, pyrite and molybdenite (Chu et al., 2020).

Data was filtered after the methods of Freij et al. (2023), and a summary of the process is provided here. The first step in processing the data was to determine whether the data acquired from literature sources was chemically consistent with chlorite. This was done by converting the ppm data to wt% oxide (Al to Al₂O₃, Ca to CaO, Cr to Cr₂O₃, Fe to FeO, K to K₂O, Mg to MgO, Mn to MnO, Na to Na₂O, Si to SiO₂, and Ti to TiO₂). Total wt% (including the wt% of H₂O) were then summed to determine whether the total was between 98.5% and 101.5%. If they were not, the analysis was rejected. In analyses without reported H₂O, the total wt% was subtracted from 100% and the difference was assumed to be H₂O. In this case if the H₂O was not between 9% and 18% the analysis was discounted as not being confidently chlorite. Similarly, if neither H₂O or SiO₂ were reported then H₂O was assumed to be 12% and the sum of the other cation oxides was subtracted from 88% (100%–12% water) to estimate the SiO₂ abundance. Next, the structural formula of each analysis was determined using a similar method to Deer et al. (2013). Any analysis that did not conform to chlorite’s structural formula, A_5–6T₄Z₁₈ (where A = Al, Fe, Mg, Mn; T = Al, Si; Z = OH, O) within 0.5 cations in each site, was rejected.

Some datasets contained both LA-ICP-MS and EMPA data. Upon converting the LA-ICP-MS data from ppm to wt% oxide for the chlorite test, the conversions sometimes differed from the corresponding values given in the EMPA data, and the analyses from LA-ICP-MS analyses had failed the chlorite test (above). In this case, the LA-ICP-MS data was corrected using a conversion factor. The conversion factor was determined for each analysis and defined as the ratio between the total wt% from the EMPA data and the total wt% from the converted LA-ICP-MS data for each analysis. Any analysis that had a ratio less than 0.8 or contained too little data to calculate an accurate ratio were discarded. The element concentrations for each analysis were then multiplied by this factor and in many cases successfully passed the chlorite test. Additionally, not all analyses had wt% oxide data as the LA-ICP-MS analyses differed in location to the EMPA analyses. Some of these analyses were still accepted as chlorite if they had similar spot IDs to other analyses from the same dataset that passed the chlorite test. Finally, analyses with irregularly high Ti and P (over ∼30,000 ppm and ∼5,000 ppm, respectively), were also excluded as values this high are indicative of micro inclusions of Ti or P bearing minerals respectively.

The chlorite test confidently classified 2,942 analyses as chlorite from 3,317 originally compiled analyses. Additionally, not all analyses had wt% oxide data as the LA-ICPMS analyses differed in location to the EMPA analyses. Some of these analyses were still accepted as chlorite if they had similar spot IDs to other analyses from the same dataset that passed the chlorite test.

After the filtering process, the data was trimmed to prepare for analysis. Analyses that calculated total elemental concentration from multiple different isotopes of the same element were merged by taking the average. In the case of analyses with missing data, if there were other analyses from the same dataset with similar spot IDs, then their reported values were averaged and reported for the missing data. Any case where the detection limit was not given for “not detected” (ND) values, the lowest value detected for an element in a dataset was used as the minimum detection limit. In some cases, the reported values were given as a range. These cells were changed to be less than the maximum value given in the range. Finally, any column with less than 64% number-containing cells were removed as this achieved a balance between amounts of data that needed to be excluded and number of data points with values for most elements, further it retained most of the elements used as a vectoring tool by previous authors. After this trimming, 23 elements remained: Al, As, B, Ba, Ca, Co, Cr, Cu, Fe, K, Li, Mg, Mn, Na, Ni, Pb, Si, Sn, Sr, Ti, V, Y, and Zn.

The data was then prepared for cluster analysis in R which is a programming language often used for statistical analysis (R Core Team, 2020). Each row of data that had missing values of the elements listed above was removed, leaving 1,679 rows for analysis. The remaining analyses are from deposits in Australia (Pacey et al., 2020), Indonesia (Wilkinson et al., 2015), China (Chu et al., 2020), United States (Cooke et al., 2020), and Chile (Wilkinson et al., 2020), representing a wide spatial coverage. Values below the detection limit were imputed using a multiplicative lognormal replacement function from the R package “zCompositions” as this has been shown to provide more accurate approximations for elemental values below detection limits (Dmitrijeva et al., 2020). Distributions of the element concentrations showed that elements Cr, Pb and Y were uniformly quite low in concentration and had little variance, thus they were removed from the data for cluster analysis. No log transformations were performed because most of the data approximated a normal distribution as shown in Appendix A. We then standardized the data (subtracted element concentration by the mean and then divided it by the standard deviation) and conducted principal component analysis (PCA) on this standardized dataset. Component 1 and component 2 explained 18.3% and 11.2% of the variance, respectively. Aluminum and Ca were the biggest contributors to component 1, whereas Fe and Mg were the biggest contributors to component 2. In order to evaluate the dataset for its tendency to contain meaningful clusters, we calculated the Hopkins Statistic (Banerjee and Dave, 2004), which assesses the data’s spatial randomness through computing the distances between nearest neighbor data points. The calculated Hopkins Statistic was found to be 0.96, indicating performing cluster analysis on the data is feasible.

Two different clustering algorithms (k-means clustering, and hierarchical clustering) were used to categorize our scaled element concentration data into reasonable clusters. K-means clustering works well with large datasets and is generally more scalable. It is relatively easy to implement and interpret. Hierarchical clustering can be computationally intensive and less efficient for large datasets, but it allows for more detailed output (i.e., a whole dendrogram) and selection of different distance measurement methods. For k-means clustering, once the number of desired clusters (k) is defined, the algorithm first creates k number of centroids at random locations. Then each point in the dataset is assigned to the nearest centroid. Once all the data points are assigned to a centroid and the clusters are defined, new centroids are determined for each cluster by the mean of all the points in each cluster. This process is repeated until none of the clusters change. For hierarchical clustering, data points that are close to each other are first individually grouped into their own cluster. Then, similar clusters are merged together after each iteration until the desired number of clusters is achieved. For both methods, to obtain the final clustering results from these algorithms, we need to choose the number of clusters or components (K). The silhouette (Rousseeuw, 1987) and elbow method (Thorndike, 1953) were both used to determine the best number of clusters for k-means and hierarchical clustering. The silhouette method measures the average silhouette width which determines how similar a sample is to its own cluster (cohesion) compared to other clusters (separation). A high average silhouette width indicates good clustering (Figure 1). The elbow method utilizes the within-cluster sum of squares (WSS), which is the sum of distances between the points and centroid of a cluster, to determine the best number of clusters. The elbow method calculates the total WSS for different amounts of clusters. The best number of clusters should have a small total WSS and should not be significantly higher than the total WSS when adding another cluster. The bend or inflection, “elbow,” in the total-within-cluster sum of squares curve vs. number of clusters usually indicates the optimal number of clusters (Figure 2). For k-means, the silhouette and elbow method both showed that the best number of clusters was 2. For hierarchical clustering, the best number of clusters was not as clear and thus different values were tested in the clustering algorithm.

The two clustering algorithms were performed on the scaled data; for k-means 50 iterations were used. To compare the clustering results with the environmental/geological properties of the data themselves, our data were grouped into bins based on their distance from a hydrothermal center. Different amounts and ranges of bins were compared with the clustering results to assess different outcomes. Most of the ranges of the bins were determined to spread out the distance data somewhat equally. From the filtered and trimmed 2,942 analyses, the minimum and maximum distances to the respective deposit center was 5.5 and 19,051 m respectively.

For the k-means algorithm, runs of different ranges of four and five bins were created. The first run used four bins based on the 25th, 50th and 75th percentiles of the 2,942 distance data points (i.e., d ≤ 1,375; 1,375 < d ≤ 1,813; 1,813 < d ≤ 3,682; d > 3,682). Other bins and ranges were varied to test what natural groupings of data could be found that also provide useful distances from mineralization (Table 1).

For hierarchical clustering, runs 1 and 3 were used as well as some additional runs with new bins. The new bins were created by splitting the first bin of the percentile-determined bins in different ways. This is summarized in Table 2. After hierarchical clustering of the entire data set hierarchical cluster analysis was also performed on the data set using only trace elements and major elements that did not vary based on parent mineral (Co, Cr, Cu, Li, Ni, Pb, Si, Sn, Sr, Ti, V, Y, and Zn) to test whether by utilizing only these elements the effects of inheritance of trace elements from the mineral the chlorite is replacing could be avoided.

Lastly, independent hierarchical cluster analyses were conducted on data from two different deposits. One used data from the Northparkes district and one used data from the Batu Hijau district. Both used all elements and the same methodology described above.

The k-means clustering algorithm was performed with k = 2, resulting in two clusters. The various runs of distinct bins allow for different views and interpretations of the clustering results. Figure 3A shows the clustering results compared against the 25th, 50th, and 75th percentile distance bins (run 1). Cluster 1 consists mostly of chlorite further away from the deposit center (85% of the analyses in cluster 1 are from >1,813 m from the deposits), whereas cluster 2 contains more proximal chlorite (70% of analyses in cluster 2 are from <1,813 m from the deposits). Albeit some overlap occurs in both clusters, as the two nearest and furthest bins are not perfectly segregated from each other, but the results show a general separation between proximal and distal chlorite. Figure 3B shows the same clustering results compared against the bins of run 2. The range of these bins are compressed in comparison to those in Figure 3A (run 1). With a narrower range of bins, cluster 1 now comprises most of one bin (85% of chlorite analyses are from greater than 1,800 m away from the deposit center), whereas cluster 2 contains a significant amount of each bin. There is more overlap in Figure 3B and not as clear of a distinction between the proximal and distal bins. Figure 3C compares the clustering results with the set of bins from run 3, which are broader than in Figure 3B (run 2) but still narrower than in Figure 3A (run 1). Similar to Figure 3B, cluster 1 still comprises mostly samples from the furthest bin, however there are more analyses from the second most distal bin as well (70% of analyses in cluster 1 >3,000 m from the deposits and 15% from 1,800 to 3,000 m from the deposit). Cluster 2 contains analyses from all four bins, similar to the results in Figure 3B. Figure 3D compares the clustering results binned by run 4, which has a set of five distance bins. All the figures and binning schemes show a small portion of the most proximal chlorite grouped in cluster 1, where most of the distal chlorite reside. For example, 14% of the chlorite in the most proximal distance bin in Figure 3A is grouped in cluster 1. There is also some chlorite from the most distal bin grouped with the nearer bins in cluster 2. Although there exists some overlap in the clusters among the different bins, overall, there is somewhat of a distinction between proximal and distal chlorite in the clusters.

The hierarchical clustering algorithm was performed using different k values, because the elbow method and silhouette method gave no clear indication of an optimal k value. Because of this 2, 3, and 4 clusters were tested against different bins. Figure 4 shows scatter plots of trace elements with results of hierarchical clustering and distance to mineralization. Figure 5A shows the clustering results compared against the 25th, 50th, and 75th percentiles distance bins (run 1). The chlorite data seems to be spread more evenly among the two clusters in this run using the hierarchical algorithm. Cluster 1 contains most chlorite from the two most proximal bins (77% of cluster 1), with some inclusion of chlorite from the two most distal bins. The two most distal chlorite bins are grouped mostly within cluster 2 (79% of the analyses from >1,813 m in cluster 2), with some overlap as well from the two most proximal bins. Although significant overlap of the bins is present in run 1, the hierarchical algorithm better separates proximal chlorite from distal chlorite than from the k-means algorithm in Figure 3A.

Figure 5B shows run 1 again but split across four clusters (k = 4). Ideally the four chlorite bins would segregate into their own cluster, however in these results there is significant contribution from each group in 2 of the 4 clusters. Cluster 3 consists primarily of the most proximal chlorite bin, with minor inclusions of the second most proximal bin. Cluster 1 consists more of the two most proximal chlorite bins (74% of cluster 1 < 1,813 m), while grouping some of the distal chlorite in as well. Cluster 2 contains predominantly chlorite from the two most distal bins (79% of cluster 2 > 1,813 m), with some overlap from the two most proximal bins, while cluster 4 is almost entirely chlorite from the two most distal bins. There is clear segregation of the proximal and distal chlorite across clusters 3 and 4, whereas clusters 1 and 2 contain overlap across all bins.

Figure 5C shows groupings of the data from hierarchical clustering with k = 3 of run 3. There is good segregation of chlorite from the most distal bin in cluster 3, however in cluster 2 there is significant overlap across all bins albeit the majority is chlorite from the two most distal bins (74% of cluster 2 from analyses >1,813 m). Cluster 1 also contains most of the chlorite from the two most proximal bins (75% from <1,813 m), and again, some overlap is still seen from the groupings of chlorite in the two most distal bins.

Figure 5D shows the clustering results against run 5 with two clusters. This shows similar results to Figure 5A, where cluster 1 and cluster 2 seem to segregate proximal chlorite and distal chlorite respectively, yet both clusters still contain some minor overlap with one another.

Figure 5E shows the results of run 6 using 4 clusters. These results are similar to Figure 5B. Again, there is a cluster containing solely chlorite from the most proximal bin, and another cluster with chlorite from the most distal bins, clusters 3 and 4 respectively. Cluster 1 consists mostly of chlorite from the proximal bins (77% of the analyses from <1,813 m), yet still grouping a smaller portion of chlorite from the distal bins. This is seen for cluster 2 as well, but distal chlorite dominates with less inclusions of proximal chlorite (79% of analyses from >1,813 m).

Figure 5F shows the clustering results compared against bins from run 7 using 3 clusters. This depicts similar results to Figure 5C. Cluster 3 segregates solely a portion of chlorite from the two most distal bins, however chlorite from these bins are still present in clusters 1 and 2. Cluster 1 is able to mostly differentiate proximal chlorite from distal (79% of analyses from <1,813 m), but still incorporates some chlorite from the distal bins. This is seen in cluster 2 but with distal chlorite dominating (74% of analyses from >1,813 m). In all, comparing the clustering results across different algorithms and bins, most results show somewhat of a segregation between proximal and distal chlorite but cannot fully differentiate them as the clusters depict a portion of overlap across all bins.

Additionally, when investigating the deposits individually, there appears to be bias in the interpretation when only distance to deposit is investigated in the different clusters. The classifier separates the deposits based on metal contained within the deposit with the same or better segregation than distance to the deposit. The analyses from Cu-Au deposits make up 91% of cluster 1 while the analyses from Cu-Mo deposits make up 76% of cluster 2 (Table 3).

An additional cluster analysis was conducted using only trace elements and major elements less dependent on parent mineral (Co, Cr, Cu, Li, Ni, Pb, Si, Sn, Sr, Ti, V, Y, and Zn). This gave relatively poor results in that the majority of the analyses were contained within cluster 1 (80% in cluster 1). While the majority of the analyses in cluster 2 were from the samples from greater distance to the deposit (85% of analyses in cluster 2 from >1,810 m from the deposit), approximately twice as many analyses from these distances were grouped into cluster 1 (Table 4).

The cluster analysis of the individual deposits (Northparkes and Batu Hijau districts) was less successful (Figure 6). While they did generally separate the distal samples preferentially into cluster 2 (100% of analyses in cluster 2 are from >3,681 m at Northparkes and 47% of analyses in cluster 2 from Batu Hijau from >3,681 m) most of the analyses from both deposits were grouped into cluster 1 (88% of analyses from Northparkes in cluster 1 and 83% of analyses from Batu Hijau in cluster 1).