Providing a suitable model for estimating the percentage of minerals and their spatial Study in the study area using microscopic images (Case study: Skarn in southwest of Taft(

Introduction
Most software produces models based on a pre-constructed grid. A grid network in 3-D modeling is an assemblage of voxels or cells of equal size. The number of cells producing is related to the spacing of the available data. The smaller the differences in the real data, the lower the dimensions of the cell unit, thus increasing the number of cells. The intersection of the lines formed by this network is called the node of the network and is calculated using the given data. These values are used for calculating each cell quantity and evaluating different cell values in the three-dimensional spaces. If one part is deleted based on operator order, the percent of remaining volume can easily be calculated by dividing the residual volume to total volume of the model. This study shows how to model spatial form and determine the quantity of mineral in the rock through the application of a small -scale high precision calculation. By paying attention to the used modeling method and using a high amount of data, the result will be as close as possible to the real distribution of minerals in the rock.
In this research, to introduce the method and due to the full range of studies, the area 4 of metamorphism (Figure 1) Skarn Hassan Abad was selected for this research and was evaluated (mineralogy diversity is one of the essential reasons for this choice).
 
Fig 1. Geological map of the studied area located in the south west of Yazd City.
 
Methodology
In this study, serial section images are used for the modeling of the rocks. Five minerals (Clintonite, Diopside, Vesuvianite, garnet, and epidote) were selected and examined. The sampling is to cover all parts of the metamorphosed area and have a uniform distribution in the area, as well as all samples,  should be safe and identifiable and not be used for displaced specimens. Thirty-three samples were prepared according to the principles from different skarn ranges. At first, all specimens were cut in a few centimeters and then thin sections were prepared, and a fixed camera took a digital image of the surface on a polarizing microscope. A layer with one-centimeter thickness was removed, and the above procedure was repeated. Figure 2 shows images of serial sections of one rock samples.
For total calculations and producing the network of image coordination, MATLAB software was used, and for final modeling, RockWorks software was used. Closest point method was used for modeling. In this method, each unknown point gets the value of the sharp boundaries (Wylie, 2005).
 
 
 
Fig 2. Serial thin section of one studied samples (Xpl, Vesu: Vesuvianite).
 
Results and Discussion
Consequently, each image is identified by an m×n×3, matrix where m and n are length and width of the image respectively and dependent on the number of pixels per image. Numerical three is indicative of the red, green and blue colour bands. Matrixes of successive images are arranged as a column, and the Z value of each image in successive sections and the fourth value related to the numerical value of the green color was added. The final matrix with four columns X, Y, Z, and G is stored in a standard ASCII file.
Finally, 33 models were prepared for 33 rock samples. The obtained models show a complete distribution of color band value for each mineral with the corresponding color scale. After calculating the statistical parameters, for each of the five minerals desired in all models, by the filtering, the amount of each mineral was determined. Other parts other than the minerals in question should be removed from the model, to do this. For this purpose, the normal distribution curve of the prepared models was used. According to the desired tables, depending on the increase or decrease of selected minerals in all profiles, it is possible to determine the zoning of minerals around the intrusive rock accurately.
For other minerals, these values are calculated and listed separately in the tables, and due to the amounts obtained from this mineral and the presence or absence of specific skarner minerals, the conditions of temperature and pressure governing the metamorphic region with a higher probability of Measurement. The normal distribution curve for each reaction zone (skarn zone) is shown on average from all four zones in Fig. 3. According to the volumetric tables of 5 minerals selected, the total amount of garnet, diopside, vesuvianite, clintonite and epidote minerals is 58.77%. As a result, the remaining volumetric percentages are (according to microscopic examination and XRD tests, these minerals have been confirmed in the region): apatite, quartz, low thermolite, wollastonite, significant calcite, and metal ores. These turning points coincide with the “average ± standard deviation” on the normal distribution curve. In this study, all models were filtered based on the two numbers average ± standard deviation. Since the rock matrix volume is always more extensive than that of the mineral, distribution values around the average ± standard deviation of the data reflect the values related to the rock. Mineral amounts can be obtained by subtracting these amounts from the total population of the model (Fig.4). The relative amount of minerals in the rock can be obtained by dividing volume of the mineral in the rock to the volume of the rock. Equation (1) shows the percentage of mineral in the rock. 
   (1)
Where FMV is the volume of filtered model (volume of minerals) and MV is total volume of model.
 
Fig 3. The mean distribution curve for the normal distribution is in the range of 105 meters (1); 105-222 meters (2); 222-320 meters (3); 320-450 meters (4).
 
Fig 4. Filtered models of the minerals.
 
Conclusions
Calculating mineral quantities and the determination of the three-dimensional distribution of minerals is necessary for the petrological and economic geology investigations. The total volumes of 5 selected minerals are 58.77%. As a result, the remaining volumetric percentages are Apatite, quartz, thermolite in a small amount; Wollastonite and calcite significantly and metallic minerals.
By extensive sampling of ores in different areas, it is possible to use this method in ore body volume determination. Also, this method has many applications such as studying of the fluid inclusions, calculation of the type, and amount of porosity in oil reservoirs and studying the tectonic of the selected area.
 
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