Spatial Modelling of Kaolin Deposit Demonstrated on the Jiml í kov-East Deposit, Karlovy Vary, Czech Republic

: The present study is focused on spatial modelling of a kaolin deposit in Karlovy Vary, Czech Republic, and the methodical procedure of development, evaluation and visualization of a 3D model are described step by step. The implementation of this methodology is performed in Visual Studio 2019 with use of the Surfer and Voxler objects from Golden Software. This methodology combined with the newly developed software (Kaolin_A and Kaolin_Viz programs) allow a user to create a variant dynamic model for the same or similar types of deposits. It enables a quick update of the model when changing the input data, based on the new mining exploration or when changing the modelling parameters. The presented approach leads to a more advanced evaluation of deposits, including various estimates of reserves according to pre-speciﬁed usability conditions. The efﬁciency of the developed methodology and the software for the evaluation of the deposit are demonstrated on the kaolin deposit Jiml í kov-East, located near the village Jiml í kov about 5 km west of Karlovy Vary in the Czech Republic.


Introduction
Research of critical and strategic minerals plays a crucial role in strategic planning on how to deal with these minerals in all countries, including the Czech Republic [1]. In the Czech Republic, kaolin, which is a key raw material for various industrial applications, was also included among the national critical raw materials [1]. For instance, it is used in the production of porcelain, washed kaolin, as a filler in the production of paper, and as an additive to paints and in refractory materials. It is also used in the cosmetics, pharmaceutical and food industries. The Czech Republic belongs to the leading states in Europe and the world, both in the mining of raw kaolin and in the production of washed kaolin. Other world's major sites with the occurrence of kaolin include USA, UK, Brazil, China, and Germany [2].
The problem of optimal kaolin mining was addressed in the paper by M. Koneshloo and J.-P. Chiles [3], where a method for selective mining was described on two kaolin deposits of the Charentes Basin in France. Ukraine also belongs to the world's major locations with significant kaolin deposits, and in the paper by R. Sobolevskyi et al., [4] an analysis of technological parameters of kaolin in this territory determining its quality was performed. The paper describes a method of calculating reserves in the Veliko Hadominetsky deposit, where mining began in 2017. E. Kogel [5] claimed that due to kaolin properties distinct from other minerals, new methods for mining and processing of kaolin are needed. Additionally, 3D models are increasingly required to perform selective mining.
Many authors have dealt with spatial modelling of deposits other than kaolin ones. The article by Xinyu Zhang et al. [6] deals with 3D geological modelling, which proposes a method for quickly processing papery borehole log information. Zhi-Wei Hou et al. [7] provided a systematic review of the state-of-the-art methods for preparing input data for 3D geological modelling. Other methods of spatial modelling of mineral deposits were described by Li et al. [8], whose modelling approach was to generate 3D predictive maps from 3D geological models. The mineral resource deposits are modelled and categorized by N. Battalgazy and N. Madani [9], who employed the projection pursuit multivariate transformation method, and then, the outputs are compared with conventional (co)-simulation methods. Li et al. [10] proposed multiple-point geostatistical simulation and local singularity analysis to identify regional geochemical anomalies and potential mineral resource areas. Liu et al. [11] constructed 3D geometric models for evaluating the Dawangding gold deposit in south China using the FLAC3D (fast Lagrangian analysis of continua in three dimensions) modelling. Hosseini and Asghari [12] described a multidimensional geostatistic simulation on block support in the presence of complex multidimensional relationships and compared their results with a common modelling approach. Li et al. [13] analyzed different 3D geological modelling processes. They considered dynamic updatability as one of the metrics to assess 3D geological modelling methods. Paithankar and Chatterjee [14] applied a multi-point geostatistical method and sequential Gaussian simulation to generate multiple equiprobable models of a selected deposit in Africa. Tao et al. [15] created a 3D geological model based on geological maps, geological plans, cross sections and boreholes. Subsequently, they used the weight of evidence method and fuzzy logic to integrate various predictor maps, in order to generate perspective maps. Mao et al. [16] performed multi-constraint geological modelling and spatial analysis involving 3D buffer analysis, shape analysis, and field analysis. The obtained spatial data were further integrated into three-dimensional prospectivity modelling by fuzzy weights of evidence and continuous methods to evaluate the mineral potential. Resource estimation of mineral deposits requires spatial modelling of orebody boundaries, based on a set of exploration borehole data. The use of multipoint statistics with the direct sampling algorithm and geostatistical simulation was described by Dagasan et al. [17] However, none of these researchers, aside those already mentioned in the previous paragraph, focused on kaolin deposits.
Currently, it is desirable to use mined kaolin deposits in an efficient way and in parallel, evaluate newly found kaolin stocks, to prepare suitable locations for future mining. This presupposes the construction of a 3D model of the kaolin deposit for the area of interest. This will allow for the determination of optimal kaolin mining not only based on historical data obtained from exploratory drills in the past but also from data obtained from any additional exploration and ongoing mining. Such a 3D model is the fundamental foundation for detailed local estimation of reserves according to the usability requirements. Kaolin has specific properties in mineralogical and chemical composition, as well as technological properties. In order to divide the reserves of kaolin in terms of their future use, it is necessary to classify these reserves into individual categories. In the case of the Czech Republic, these technological parameters are monitored and processed to categorize the reserves of kaolin deposits into so-called kaolin outwash (kaolin residue after kaolin washing out with the grain size up to 20 microns), Al 2 O 3 , Fe 2 O 3 , and TiO 2 (Table 1). To meet this target, a methodology for creating a digital model of a kaolin deposit and appropriate software for creating 3D grids for the distribution of technological parameters, for the visualization of the model in 2D and 3D, and for stock estimates, was created. Section 2 describes the individual steps of the methodological procedure for modelling the technological parameters of kaolin at a given deposit. Afterwards, the methodology is implemented in the Visual Studio 2019 [18] environment using the Surfer [19] and Voxler [20] objects from Golden Software in Section 3.

Materials and Methods
The Jimlíkov-East kaolin deposit has been formed by kaolinization of granites of the Karlovy Vary massif in the Cretaceous-to-Paleogene periods [21]. These are the remains of the original weathering barks, which were preserved before denudation. The Karlovy Vary massif, which is part of the extensive Ore Mountains pluton, forms the crystalline bedrock of the deposit (Figure 1). This section focuses on derivation and visualization of a 3D model of the deposit. The individual steps of the methodological procedure together with the developed software allow for the construction of various models of kaolin deposits. Each of the specific models will be the foundation for detailed local estimates of reserves according to the defined usability conditions. Additionally, models can be updated and modified according to the requirements of possible additional exploration and ongoing mining.
The modelling uses state-of-the-art available software: MS Excel, Surfer [19] and Voxler [20] from Golden Software, and the open-source program SGeMS [22]. Additional software implementation and its development is performed in the Visual Studio 2019 [18] environment with the support of the object-oriented programming language Visual Basic (VB.NET). MS Excel macros in VBA are used to ensure the compatibility of used programs. The steps of the methodological procedure can be summarized into the following list:

1.
Evaluation of all available archive materials. The first step consists of the collection of all available information of the geological composition of the area from the archives of the Geofond of the Czech Republic [23][24][25][26][27][28] and the revision of the obtained input data.

2.
Verification and correction of input data. Verification and correction of the input data are performed by the comparison of the data with information from archive reports using the visualization (in 2D and 3D), and the comparison with the corresponding archive horizontal and vertical sections (see Step 1). In the case of our example of the kaolin deposit Jimlíkov-East, many errors in the data were found. The sources of these errors are various. However, most of them were caused by typographical mistakes during the digitalization process. The calculation includes corrected data from 85 exploration drill holes ( Figure 2) and 1098 analyzed samples, for which the categories (classes) of the reserves according to Table 1 were calculated with respect to the content of kaolin outwash, Al 2 O 3 , Fe 2 O 3 , and TiO 2 .

3.
Calculation and visualization of spatial localization of the input data. Corrected and completed input data (geometric parameters of prospect holes and samples with the content of technological parameters) are divided into 10 cm sections using the created macro in a such a way that the data have the same carrier (in total 21,209), spatially located in the center of each section. The file of necessary data is created as a source for further processing (Figure 3): horizontal and vertical sections for statistical analyses, gridding, 2D and 3D visualization, etc. Another created macro converts the necessary data to the format GSLIB [29] for the processing program SGeMS. After the import into the environment SGeMS [22], these data can be visualized ( Figure 4).

4.
Statistical processing of the technological parameters. Basic statistical processing of the technological parameters is performed in the SGeMS environment [22]. An example of the output is given in Figure 5-histograms of the frequencies of individual technological parameters and their basic statistical characteristics.

5.
Modelling of the bottom and the top of the kaolin deposit and overall lithology.
To spatially limit the occurrence of kaolin in the model, it is necessary to model the rock interface of the deposit. Gradually, 2D grids of eight geological layers were created from the crystalline basement to the surface. Based on these 2D grids, the grids of both the bottom and top of the kaolin occurrence were created. These two grids bound the 3D model of the deposit. During mining, it will be necessary to regularly update the grid of the top of the kaolin occurrence.

6.
Three-dimensional visualization of the input data for the kaolin deposit in the Voxler environment, the construction of 3D grids based on technological parameters, and the export of the 2D grids in individual horizons to the grd Surfer format. Input data are processed by the implemented program Kaolin_A (see Section 3.2). This code generates 3D grids of individual parameters using the specified parameters of anisotropy, grid geometry, and the selection of samples for interpolation. Additionally, it also displays individual parameters in the Voxler environment. These parameters can be changed and tuned to construct variants of deposit models. The program also exports 2D grids in the format grd (Surfer) of individual horizontal layers of all parameters, which are further processed by the program Kaolin_Viz (see  (Table 1). Additionally, this module estimates kaolin deposits reserves in text form. In the case of updating the input data based on the exploratory mining, the data must be processed as described in Steps 2-4. During ongoing mining activities, it is also necessary to update the grid of the top of the kaolin deposit (see Step 5). Afterwards, everything is prepared for the model update and its visualization as described in Steps 6-10.

Results and Discussion
This section demonstrates the resulting implementation of the kaolin deposit processing methodology in the Visual Studio 2019 [18] environment using the Voxler automation object model [20] and the Surfer automation object model [19] published by the Golden Software Company, for the kaolin deposit Jimlíkov-East, Karlovy Vary, Czech Republic.

Working with Objects Voxler and Surfer in Visual Studio 2019
Voxler and Surfer can be called from any automation-compatible programming languages such as VB.NET. In our case, this approach is applied in the implementation of programs Kaolin_A and Kaolin_Viz in Visual Studio 2019 [18]. To utilize Voxler and Surfer in this environment, the implementation must include a reference to this application. Figure 6 describes the Voxler automation model. The model presents a flow chart to create the type of considered module using automation and shows which objects provide access to other objects in the hierarchy. At the top of the hierarchy, the "Application" object is located, and all objects are directly accessible from this root object. However, to access objects located deeper in the hierarchy, one has to traverse from the "Application" object through one or more layers of sub-objects. The "CommandApi" object contains all properties of the various modules in the Voxler program. "CommandApi" refers to accessing the commands from the "Application" programming interface. Using the "CommandApi" object requires accessing the property with the "Construct method", specifying any settings with the "Option method", and performing the action with the "Do" or "DoOnce" method. In Figure 7, the Surfer automation object model is presented. This chart shows objects that provide access to other objects. Surfer groups most objects in collections. Collection of objects are containers for groups of related objects. Although these collections contain different types of data, they can be processed using similar techniques. Non-container objects are very specific for Surfer. Several objects presented in Figure 7 share common features (e.g., "PlotDocument" provides "SaveAs", "Activate", and "Close" methods). The online Surfer help is the complete reference for all Surfer automation objects, their properties, and their methods. . Surfer automation object model [19], including collection objects (gray boxes) and objects (blue boxes).

Program Kaolin_A
The updated input data (see Section 2, Steps 2-5) is further processed by the program Kaolin_A. Figure 8 shows the application window for entering input parameters. It is necessary to check the input parameters of the directories and files specified in the initialization file. It is also important to check the input parameters for 3D interpolationanisotropy, grid geometry and selection of samples specified in the initialization file.
We chose the interpolation method of inverse distances with a significant length of the X-and Y-axes (in this example it is 200 m) and minimal length of the Z-axis (in this example it is 2 m) of a spatial ellipse of anisotropy ( Figure 9) and sampling ( Figure 10). This is because we could not find generic laws of spatial distribution in the monitored technological parameters, due to the origins of the raw material. The specified geometry parameters for the 3D gridding are presented in Figure 11.    Different input parameters of the Kaolin_A program calculation allow to create different variants of the model. By comparing the predictions of different model variants with the results of mining after commencing of works, it will be possible to select the optimal variant of the model. For each variant, the input parameters are defined in the initialization text file, which is the input for the Kaolin_A program. These parameters are displayed after the program execution (see Figures 8-11).
The program Kaolin_A limits 3D grids of the bottom and the top of the kaolin deposit with the help of the "Math" object. Moreover, the "Math" object exports (if the "Export 2D grids" button is checked-see Figure 8) 2D grids in the format grd (Surfer) of individual horizontal layers of all technological parameters to the directory specified in the initialization file for further processing by the program Kaolin_Viz.
The following VB.NET code sample ( Figure 12) using the Voxler automation object exports the resulting grids of the monitored technological parameters to the directory specified in the initialization file.

Program Kaolin_Viz
The program Kaolin_A creates 2D grids output in the format grd (Surfer) of individual horizontal layers of all technological parameters (see Section 2, Step 6). Afterwards, these data are further processed by the program Kaolin_Viz. Figure 16 demonstrates a window for entering user's input parameters. It is required to check the input parameters of the directories and files entered in the initialization file, the input parameters for categorizing inventory blocks, the inventory estimates and the visualization entered in the initialization file. By changing the input parameters for categorizing inventory blocks in the initialization file, different usability conditions can be set (different from the values listed in Table 1). In this way, variant stock estimates can be created according to the currently entered usability conditions. The program Kaolin_Viz contains four modules. The buttons for starting the individual program modules ( Figure 17) are displayed after entering the input parameters ( Figure 16) and pressing the "OK" button. After starting the first module with the button "Categorization of blocks-calculation of grids 2D, transfer to 3D", the categorization of blocks of reserves is performed, based on the grid kaolin outwash, Al 2 O 3 , Fe 2 O 3 , TiO 2 , and Fe 2 O 3 + TiO 2 exported by Kaolin_A and the entered parameters of categories of reserves in 2D and their transfer to 3D. A text file is generated (input for the "Displaying the blocks of categories in 3D" in the Voxler environment). Additionally, the first module creates the resulting stock of the deposit (text file). An example of part of this file is demonstrated in Figure 18. It is necessary to run this first module to create the grids used in the other three models. The second module of the program Kaolin_Viz performs the visualization of horizontal cuts in 2D in the Surfer environment (button "Displaying of the horizontal cuts specified layers"). Before starting, it is possible to enter the values Zmin and Zmax (both in meters above sea level) of the layers to be processed in the frame "Horizontal cutsvisualization parameters" (Figure 16) and then confirm these values by pressing the button "OK". Figure 19 shows a visualization of one of the 85 horizontal cuts generated in the Surfer environment.
The third module of the program Kaolin_Viz provides the visualization of the vertical sections in 2D in the Surfer environment. Before starting, it is possible to enter the values of the geometry of the network of vertical cuts to be processed in the frame "Vertical cuts" (Figure 16), and then to confirm these values by pressing the button "OK". Figures 20 and 21 demonstrate a visualization of the 9 XZ and 9 YZ vertical cuts, respectively, generated in the Surfer environment.     The estimation of kaolin reserves is commonly calculated in a simplistic way, which does not reflect the state-of-the-art computational methods developed and published in the technical literature. For instance, regarding the area considered in this paper, the most recent recalculations of the kaolin reserves have been performed by the method of geological blocks [21]. The method is based on the fact that the volume of stocks is equal to the product of the block area and the average thickness of the raw material. The mass is equal to the product of the volume and the density determined in the applicable conditions of usability. Blocks of stocks were determined based on the deposit evaluation of archive drill holes. The basic rule for interpolation was determined as 1/3 of the distance between the balance and negative drill holes for balance (economic) reserves, 1/2 of the distance between the balance and non-balance drill holes for balance (economic) reserves and 1/2 of the distance between non-balance and negative drill holes for non-balance (potentially economic) reserves [21]. It is obvious that such imprecisely defined boundaries of geological blocks lead to an inaccurate estimate of the volume of blocks and thus to an inaccurate estimation of reserves. Additionally, the rough method of determining the kaolin outwash content, Al 2 O 3 content, Fe 2 O 3 content and TiO 2 content (arithmetic average of the average values of these parameters in the wells located in the geological block) for the entire geological block leads to an inaccurate categorization of reserves.
For a more economical usage of the reserves novel methods are needed. The proposed methodological procedure and newly created software provide a way to achieve this goal. When we compare the estimates of reserves by the method of geological blocks [21] with the results based on our study, it is clear that the proposed methodological procedure and newly created software provide a much more reliable reflection of reality in the resulting model. A comparison of the reserves calculated by the geological block method [21] with the results of our study per type of kaolin shows that the volume of "kaolin for production of pottery" (categories K1, K2, K2A and K51) is 30% higher in the current study. The volume of "kaolin for the production of ceramics after reducing the TiO 2 content" (categories K2B, K3B and K4B) is 96% higher in the current study and the volume of "kaolin for other ceramic industry" (categories K3, K4J and K4) is 81% higher in the current study.
The approach presented in this study has the following advantages relative to the quality of the material extracted and the possible end use: • Detailed and precise spatial definition of categories of reserves (see Table 1), based on precisely determined spatial distribution of kaolin outwash content, Al 2 O 3 content, The possibility of targeted selective kaolin extraction according to the required stock category for different processing purposes (see Table 1).

Conclusions
The kaolin deposit modelling methodology (see Section 2) specifies the individual steps of the methodological procedure from the acquisition of the necessary input data from archival documentation, through the application of modern algorithms for creating a 3D bearing model, to inventory estimates and deposit visualization in 2D and 3D (including inventory categories). This methodology, together with the developed software (see Section 3), allows the creation of variant models of the kaolin deposit using different input parameters of the calculation and/or different usability conditions. It also allows quick updates of these models when adding input data from ongoing mining. Section 3 also shows the various outputs ( Figures 13-15 and 18-22) of a model variant with the setting of input parameters according to  and with the set usability conditions according to Table 1.
Comparison of variants of kaolin deposit models with results of mining after its start will allow to select the optimal setting of input parameters of the calculation. According to the model with the input parameters set in this way, the model will lead to an optimal selective extraction of kaolin of the required quality.