The area is located in Yazd province and in central tectonic zone of Iran, which is a small part of the Poshtebadam-Bafq block. In terms of lithology, it has a wide range of alkaline (gabbro-diabaz) to acidic (rhyolitic and rhyodactic) rocks, and includes intrusive, semi-deep and extrusive types. Eastern view of the region and the position of the drilling equipments is shown in Figure 2.

In Figure 2, the locating of 1:1000 map of Sheytoor deposit and 1:20,000 map of the gazestan in the topographic map of 1:50,000 Sheytoor is shown [35] [37].

In terms of lithology, the area consists of the late precambrian to cambrian volcanic-sedimentary rocks and igneous rocks after that. In the central parts of the

region, diorite-gabbro and diabase masses occurs as dykes and sills, with porphyritic granite and granite-syenite which cut out older rocks and outcrop. Parts of the ore are covered by present sediments. Metasomatic rocks is as host of mineralization and that has occurred inside it [35] [37].

Mineralization of iron-phosphate is closely related to the region’s rocks including gabbro, monzo gabbro, diorite, syenite and diabase which is seen in dark green color. The main ore deposit is as apatite-magnetite mineralization.

Quartz and calcite constitute the main waste material of the mineral. The ore mainly consists of magnetite-apatite in the southern part, usually composed of quartz and calcite in the late stages after mineralization, and in different forms occur within volcanic rocks, microgranite and granodiorite intrusive masses.

Based on microscopic and XRD analysis, the ore minerals include: magnetite, hematite, limonite, goethite, lipidocrocyte, apatite, pyrite, chalcopyrite and rare earth elements minerals such as monazite which can be seen in conjunction with pyroxene, actinolite, thermolite, epidote, chlorite, quartz and calcite waste minerals (Figure 3) [35].

Before using raw data must identified and replaced censored and outlier data. Censored data is said to be data that among them, due to the high sensitivity limit of measuring devices, a number of data are found to be smaller than the device sensitivity limit. Such data can make statistical problems, because, firstly, statistical methods require a complete set of non-censored data, and secondly, in some cases, such as anomaly separation from background and relative

measurements, the existence of censored data leads to inappropriate evaluations. If the censored data are identified and replaced, the amount of background and intensity of the anomalies will be calculated more accurately [38].

As the existence of censored data among geochemical data leads to errors, outlier data also have the same effect on the results. In statistics, an outlier is an observation point that is distant from other observations [39] [40]. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set [41]. An outlier can cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they often indicate either measurement error or that the population has a heavy-tailed distribution.

Several methods can detect and replace censored and outlier data. In this study, a simple method is used to replace sensor data. In this method, the values of less than sensitivity limit are replaced by 3/4 of data value. The main problem of this method is that it is by no means influenced by the statistical parameters of the data society and is merely a function of the sensitivity limit of the measurement method [38] [42].

In order to identify and replace the outlier data, the doerffel method was used. Doerffel has prepared a graph for determining the threshold of outlier data values, which is provided for two levels of significance of 5% and 1% (see Figure 4) [35] [42].

To perform the doerffel test, the average ( x ¯ ) and standard deviation of the data (s) is calculated regardless of the largest amount of data. Then the largest amount of data (x_A) is considered to be outside of the row if it is true in the following Equation (1):

x A ≥ x ¯ + s ⋅ g (1)

where “g” is the threshold limit for outlier values which can be calculated by graph shown in Figure 4.

In this study, in order to grade estimation, methods kriging and inverse distance weighting (IDW) were used.

• Kriging: The basic idea of kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point. In geostatistical models, sampled data is interpreted as the result of a random process. The fact that these models incorporate uncertainty in their conceptualization doesn’t mean that the phenomenon—the forest, the aquifer, the mineral deposit—has resulted from a random process, but rather it allows one to build a methodological basis for the spatial inference of quantities in unobserved locations, and to quantify the uncertainty associated with the estimator. The kriging function is defined as follows (2):

z ^ ( x ) = ∑ i = 1 n λ i z ( x i ) (2)

λ_i is the weight associated with the value of the x-variable x at the point i in the case where Σλ = 1 [43].

• Inverse Distance Weighting (IDW): Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. IDW is an interpolation method in which estimation is performed based on the values of the nearest points to the point of the weighted inverted distance. The calculation method of the IDW is as follows Equations (3) and (4) [44]:

w ( x , y ) = ∑ i = 1 n λ i w i (3)

λ i = ( 1 d i ) p ∑ k = 1 N λ i ( 1 d k ) p (4)

3D modeling is one of the most common types of modeling to understand the mineralization model below the surface of the earth. This modeling, carried out by interpolation of the concentrations of borehole elements at different depths, results in a form of ore below the surface of the earth. Considering the threshold limit, it is possible to see the separated part of the deposit, which is considered as an anomaly. The most common type of 3D model for the description of the ore and the implementation design is “Regular 3D Fixed Block Model”. Figure 5 shows an example of a block model [45].

K-Means clustering is a method for classifying voluminous data. In this method, using clustering algorithm, data is divided into optimal classes. In this study, using the K-means method, the geochemical behaviors of iron interfering elements are also identified.

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 [12]. 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 [46].

• 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 [14].

The important steps of this algorithm are summarized as follows [47]:

1) First, k members randomly are selected as the number of clusters among the n members (k is the number of clusters).

2) Z_j vector is calculated based on Equation (5) which represents the center of each class C_j.

z j = ∑ x ∈ c j x # c j     for   j = 1 , ⋯ , k (5)

3) In this equation, x represents the vector of a sample which is a member of C_j and #C_j represents the number of samples which are members of the C_j class. It should be noted that relation (6) 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 [13].

4) Calculate the target function of the classification which calculates the total distance of samples from the center of the classes.

f ( C 1 , C 2 , ⋯ , C k ) = ∑ j − 1 k ∑ X ∈ C j | X − z j | 2 (6)

5) Minimize the objective function of Equation (6) and find the proper classification on the M set with the numberk of classes.

And a software has been introduced by the author to speed up the operation above [13] [48].

The C-V fractal model, which was proposed by Afzal et al. (2011) [49] for division of mineralized zones and barren host rocks in porphyry deposits, can be addressed as Equation (7):

V ( ρ ≤ v ) ∝ ρ − α 1 ;             V ( ρ ≥ v ) ∝ ρ − α 2 (7)

where V ( ρ ≤ v ) and V ( ρ ≥ v ) illustrate two volumes with concentration values less than or equal to and greater than or equal to the contour value ρ; v indicates the threshold value of a mineralized zone (or volume); and α 1 and α 2 are characteristic exponents. Elemental threshold values in this model represent boundaries between different mineralized zones and host rocks of mineral deposits. To calculate V ( ρ ≤ v ) and V ( ρ ≥ v ) which are the volumes enclosed by a contour level ρ in a 3D block model, the borehole data of ore element concentrations were interpolated by utilization of geostatistical estimation [49] [50].

The selection of breakpoints as threshold values appears to be an objective decision because geochemical populations are defined by different line segments in the C-V log-log plot. The straight fitted lines were obtained based on least-square regression [51] [52]. In other words, the intensity of element enrichment is depicted by each slope of the line segment in the C-V log-log plots [26].

In this study, information of 57 boreholes which are drilled in Sheytoor deposit were used. The depth of the boreholes was between 76 and 475 meters. 1550 samples from cores were systematically collected, the average sampling distance was about 2 meters. All samples were analyzed using ICP-AES method [35]. You can see the geolocations of boreholes in Figure 6.

The statistical parameters of the Fe, P and S elements such as mean, standard deviation, variance and etc. were calculated and are shown in Table 1 [37].

The explained method in Section 3.1 was used to replace the Fe censored data values. Using doerffel method for identifying outliers, data were analyzed. Regarding iron cadmium data, the values of 42.10% were considered as larger values and then calculated the average and standard deviations of data without considering these values, which was 24.78% and 9.91%, respectively.

According to the graph that is given in Figure 4 and number of samples (1550 samples), the amount of (g) parameter, was estimated “4.4”.

So using doerffel relationship (8):

x A ≥ x ¯ + s ⋅ g (8)

Outlierlimit ≥ 24.78 + ( 9.91 × 4.4 ) = 68.38 %

The highest Fe content in the analysis data is 65.5% which this value is less than outlier limit (68.38%). Therefore, it does not count as an outlier value. So some value is not removed from the raw data as outlier data.

In this section, the frequency distribution chart (histogram) is drawn to examine the various characteristics of our statistical society. The statistical society of the study is a set of geochemical information in the form of iron element concentration derived from systematic sampling of exploratory boreholes which are drilled in the Sheytoor mining area. The histogram of our statistical society is shown in Figure 7. The purpose of this study is geochemical modeling of iron interfering elements (Phosphor and Sulfur) and to identify the behavior of these elements in relation to the Fe.

The statistical parameters of the Iron, Phosphorus and Sulfur elements such as mean, standard deviation, variance and etc. were calculated and are shown in Table 1.

In this Model, by using the “Inverse Distance Weighting (IDW)” interpolation

method, interpolation and estimation of the iron element concentration according to the boreholes (Figure 8) were studied at all points of the study area. Then, 3D block model of subsurface mineralization was modeled.

In this section, using the K-Means clustering method, how the elements behave to each other is discussed. The elements associated with the mineralization of iron in Sheytoor area, are sulfur and phosphorus, which can be effective in the processing and extraction of pure metal. Therefore, in this section, the geochemical behavior of iron, phosphorus and sulfur in relation to each other was investigated in pairs.

The three-dimensional model of mineralization and dispersion of phosphorus and sulfur elements in exploratory boreholes in order to provide a better view of mineralization in the region is given in the figure below (Figure 15).

Using the Kriging interpolation method in confined space to exploratory boreholes, the estimated titers of phosphorus and sulfur elements were calculated at points where no borehole had been drilled. The mineralization of phosphorus and sulfur elements in the area of Sheytoor deposit was modeled in three dimensions. The 3D geochemical models of P and S elements are presented in Figure 16.