Behavior of Gold, Arsenic, and Antimony Elements

Table of contents

Abstract

1 Introduction

2 The study area

3 The study method

4 Results and discussion

5 The prediction of the gold grade

6 Conclusion

7 Acknowledgement

Bibliography

Abstract

Tarq geochemical 1:100,000 Sheet is located in Isfahan province which is investigated by Iran's Geological and Explorations Organization using stream sediment analyzes. This area has stratigraphy of Precambrian to Quaternary rocks and is located in the Central Iran zone. According to the presence of signs of gold mineralization in this area, it is necessary to identify important mineral areas in this area. Therefore, finding information is necessary about the relationship and monitoring the elements of gold, arsenic, and antimony relative to each other in this area to determine the extent of geochemical halos and to estimate the grade. Therefore, a well-known and useful K-mean method is used for monitoring the elements in the present study, this is a clustering method based on minimizing the total Euclidean distances of each sample from the center of the classes which are assigned to them.In this research, the clustering quality function and the utility rate of the sample have been used in the desired cluster (S(i)) to determine the optimum number of clusters. Finally, with regard to the cluster centers and the results, the equations were used to predict the amount of the gold element based on four parameters of arsenic and antimony grade, length and width of sampling points.

Keywords: Gold, Tarq, K-Means clustering method, Estimation of the elements grade, K-means

1 Introduction

In recent years, due to the high dependence of mineral projects on the precise determination of the tonnage of mineral materials, the various methods have been developed to estimate the grade such as geometric methods based on distance and geostatistics. [1,2].

Each method has limitations and disadvantages which affect the accuracy of estimation 3. One of the new methods is the grade estimation using the clustering. The cluster analysis methods are widely used in the earth sciences. The cluster grouping method is used to classify geochemical data 4.

The cluster analysis connects the observations to each other which together have many similarities, then, the observations consecutively connect them which are most similar to previous observations 5. In other words, in clustering, we try to divide the data into clusters that the similarity is maximized between the data within each cluster and it is minimized between the data within the different clusters 6. No classes already exist in the clustering method and in fact, the variables are not divided independently and dependently, but here, the search is performed to access groups of data which are similar to each other and the behaviors can be better identified by discovering these similarities and it can be operated to achieve a better result based on them 7. The clustering method is an indirect method; this means that it can be used even when there is no previous information from the internal structure of the database. This method can be used to discover hidden patterns and improve the performance of direct methods 8.

The k-means method is one of the methods for clustering the data in data mining. It is an exclusive and planar method which has been widely studied by different researchers and attempts to cluster the samples with the specified number of k classes so that the total Euclidean intervals of each sample are minimized from the center of the class which has been assigned to it 9.

The k-means methods are used to properly analyze the data behavior and available analyses to each other. Some of its applications include: the division of the geological terrain 10, the classification of the effect of vegetation and the recovery of water health in the Mediterranean coast forests 11, the presentation of geochemical patterns in mineral areas 12, predicting the organic carbon in the intelligent systems 13, and determining the effect of gas diffusion in urban environments 14.

In this article, the behavior of the gold, arsenic, and antimony elements has been evaluated using k-means method, MATLAB and SPSS software based on the data collected from the drainage sediments and then, the gold grade is estimated using the results.

2 The study area

The study area is the geochemical sheet 1:100.000 of stream sediments called Tarq which is provided by the Geological Survey of Iran with code 6356 and it is located in the geographic latitudes are 24° 51° to 24° 52°, and the latitudes are 55° 32° to 33° 33° 15.

This area is located in Isfahan province as well as the area divides into two distinct eastern and western parts by the Kohroud Mountain range with the west bank and Karkas Mountain with a height of 3895 m. Northeast low altitude plain has an average height of 1000 m which is outside the studied area and the southwest plain called Robat Sultan has nearly 1650 m altitude and there will be farming more or less in it 16.

Kahroud and Garrison Mountains divided the drainages of an area into two distinct networks from each other. Eastern network flows to the sabulous and southwest drainages join the Zayandehrood River in the east of Isfahan. Tame rivers have a constant flow on the eastern hillside of Karkas Mountain and most of the springs are on the hillsides of this mountain (Figure 1). Some springs have Calcium bicarbonate to a great extent which they create the sediment of travertine stone in the area. The annual rainfall was reported at 51.8 mm 17.

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Figure 1: Location of samples and stream in the area 15

2.1 General geology of the area

The stratigraphy of the zone consists of Precambrian to Quaternary rocks, which are described from the old to the new, respectively. The upper Precambrian and the former Cambrian units are yellow-tufted dolomites which in the shale and lime layers are observed. This unit has a thickness of about 360 m [17, 18].

The sedimentary rocks are more clastic and the lower part of them is related to Cambrian and Ordovician which are located in the sequence of red sandstone layers. Generally, this unit consists of yellow silicified dolomite rocks, red shale, bright yellow or gray Trilobite Limestone, Red and green sandy shale [18, 19].

The doleritic rocks are formed in the Silurian and Devonian unit and red cement clay and hematite sandstones are located in these dolerites. In the following, the alternation of yellow sandstone layers and dark dolomite are created with interlayers of red shale. In the upper part, the layers of limestone and dolomite have been made with a thickness of 140 which contain brachiopod, trilobite, coral, and tentaculite fossils [18.19]. This unit is bright gray which turns into black brachiopod limestone in the upper part and it has an interlayer of oolite and pizzolite (Figure 2).

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Figure 2: Tarq geology sheet 1: 100,000, Isfahan 19

3 The study method

637 samples of drainage sediments have been collected from the area and have been analyzed using ICP-MS method. In this paper, in order to estimate the gold grade and to study the behavior of arsenic, antimony, and gold elements, only these three elements have been investigated due to being paragenesis as well as the correlation coefficient. As can be seen from Table 1, the values of the correlation coefficient of these three elements are good and indicate the relationship of these three elements with each other. Also, given that most geochemical data are either closed or compound, if proper conversion is not performed for data expansion, the wrong results are obtained. Therefore, data must be separated before doing any processing on the data. In this study, ilr method 20 was used to separate the data.

Table 1: Spearman correlation coefficients matrix for gold, arsenic, and antimony elements

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3.1 The k-means algorithm

The k-means algorithm starts with a given value for K (number of classes) and tries to estimate the following cases:

Finding the points as centers of clusters, in fact, these points are the same average points of each cluster.

Assigning each sample data to a cluster that data has the smallest distance to the center of that cluster 9. In the simple form of this method, first, the points are selected randomly as much as needed clusters. Then, the data is assigned to one of these clusters according to the similarity and so, new clusters are obtained 21.

New centers can be calculated for them in each of iterations by repeating the same steps and averaging of data and again the data can be attributed to new clusters 22. The important steps of this algorithm are summarized as follows [23, 24]:

1. First, k members randomly are selected as the number of clusters among the n members (k is the number of clusters)
2. vector is calculated based on equation 1 which represents the center of each class Cj.

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3. In this equation, x represents the vector of a sample which is a member of Cj and #Cj represents the number of samples which are members of the Cj class. It should be noted that relation (1) is used to calculate the center of each class during solving and usually, k samples are randomly selected at the start of the algorithm and are considered as the center of each class 24.
4. Calculate the target function of the classification {C1, C2, …, Ck}based on equation (5) which calculates the total distance of samples from the center of the classes.

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5. Minimize the objective function of equation (2) and find the proper classification on the M set with the number k of classes. and a software has been introduced by the author to speed up the operation above. 37

4 Results and discussion

4.1 Results and discussion on the results

In various studies, such as the relationship of altered diorite with magnetite mineral in the iron belt of Chile 25, the relationship between copper and molybdenum of porphyry copper ore 26, and the relationship between elements of the platinum group of porphyry copper ore 27, the behavior of elements has been measured relative to each other in various methods. In the current study, k optimum value has been calculated using the K-means method for clustering the drainage sediment data in the Tarq area with three grade value of elements of gold, arsenic, and antimony (taking into account the coordinates of the sampling points), because the elements of arsenic and antimony are important elements in determining the geochemical halos of the gold element.

In this study, two appropriate criteria have been used to determine the appropriate value of k to determine the number of clusters. The first used benchmark is the S(i) that the number of clusters is changed from 3 to 10 based on it and then, the obtained results are analyzed to select optimal k using the above benchmark 28.

An appropriate benchmark has been determined according to equation (3) for determining optimum k. The obtained classifications are measured based on the benchmark.

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In the above equation, S(i) expresses the utility rate of the ith sample in its class, the parameter Aveg_within (i) represents the average distance between the ith sample and the other samples in that class which ith sample is a member of that class and the parameter Aveg_Between (i.k) represents the average distance between the ith sample and the other samples which are members of another class such as k [24.28].

The results are analyzed by calculating the utility rate as an average utility. The utility rate varies between -1 and +1; as this value approaches to +1, the sample is a member of more appropriate classification and as it approaches -1, it has an inappropriate classification and the zero number means that the presence of the sample is not very important in the current classification or another classification. So, the value of equation (6) is calculated for each sample and then the obtained results are analyzed by calculating the average numbers as the average utility rate of the classification.

The second used benchmark is the quality function. According to the information, the best cluster maximizes the total similarity between the cluster center and all cluster members and minimizes the total similarity between cluster centers. First, a range is determined for the number of clusters to select the best cluster which is between 3 and 10 in this research. Then p (k) is calculated for each value k.

The k value is selected as the optimal number of clusters which maximizes p (k). In this way, the number of clusters can be selected for which the distance is maximized between cluster centers and the similarity of cluster centers with the members within each cluster. The quality of clustering results is defined with k clusters as follow 29:

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In these equations, O is set of cluster centers; Cn is centers of clusters; On is the set of elements which has not been selected as cluster centers; Tc is the set of all elements which is clustered; ηn is the average similarity the between the center of the cluster Cn and all the cluster elements of On, ηm is the average similarity the between the center of the cluster Cm and all the elements of the cluster Om and finally, δnm is defined as the similarity of Cn and On 29.

4.2. The monitoring of gold, arsenic, and antimony elements relative to each other

In order to study the behavior of the elements relative to each other, the cluster profile and the utility rate of each sample were determined in pair for classifications k=3 and k=10 for the elements of Gold, Arsenic, and Antimony, and the results of the utility rate of the classes have been compared together, the best class is determined according to the utility rate of the classes, and then the centers of the clusters of each class are determined according to it.

As shown in Fig. 3, class 4 is selected as the best class according to the class profile diagrams and the utility rates of best class for the two gold and arsenic elements, because as much as the utility rate is close to 1, the samples are more correctly located in the class. According to the diagram, the little negative values are also found in this classification.

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