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Abstract

Anisotropy of variations of Polish mineral deposit parameters is rarely the subject of interest of geologists who carry on the assessment projects . However, if the anisotropy is strong its description and mathematical modeling are rational and justified as it may affect the accuracy of many calculations suitably for mining geology and mining engineering, e.g. estimation of resources and grade of particular raw-material, interpolation of deposit parameters values and construction of their contour maps, designing of optimum grade mining operations or densification of sampling grid. In geostatistics anisotropy is described with directional semivariograms which represent average variability of values of particular deposit parameter in various directions, depending on the distance between sampling sites. Convenient graphic presentation of anisotropy is map of directional semivariograms and good mathematical presentation are functions describing the anisotropy models.

The paper presents the results of geostatistical descriptions of various anisotropy types in selected examples of Polish mineral deposits. Taking into account the spherical variability model, the influence of anisotropy on the results of deposit parameters estimations has been theorized for both the interpolation point and calculation block (area). It was found that anisotropy is effective for parameters estimation if three mutually interrelated factors are considered: power of directional diversification of parameters variation, contribution of random component to total, observed variation of parameters and the range of semivariograms (autocorrelation) of parameter referred to the average sampling grid density.

The results demonstrate that anisotropy influences much more the estimations of parameters value in interpolation points than those of average values of parameters calculated for particular parts of deposit (calculation blocks). Moreover, anisotropy is unimportant when the random component of variability dominates the overall variability of analyzed parameter. Therefore, the simpler, isotropic variability model can be applied to geostatistical estimations of deposit parameters.

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Authors and Affiliations

Jacek Mucha
ORCID: ORCID
Monika Wasilewska-Błaszczyk
ORCID: ORCID
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Abstract

In our article the ordinary kriging interpolation method was used for a spatial presentation of PM2.5 concentrations. The data used in the research was obtained from the unique PM2.5 measuring system, based on low-cost optical sensors for PM2.5 concentration measurements, working on Wroclaw University of Science and Technology campus area. The data from this system was used as an input for the interpolations that were made for three different days characterized by the highest measured values of PM2.5 – 20.01.2019, 17.02.2019 and 30.03.2019. For each of the selected days, variants with the maximum and minimum PM2.5 values recorded on a given measurement day were presented. In the analyses performed, the ordinary kriging technique and cross-validation, was used as the interpolation and the validation method, respectively. Parameters determining the quality of performed interpolation were Mean Error, Mean Standardized Error, Root Mean Square Error, and Average Standard Error. As the main indicator of quality of interpolation RMSE parameter was used. Analysis of that parameter shows that the higher variability of the data used for interpolation affects its quality. The Root Mean Square Error parameter reached 0.64, 0.94 and 1.71 for the lowest concentrations variants characterized by low spatial variability, and 6.53, 7.51, 11.28 for the highest one, which were characterized by high spatial variability. The obtained results of the research with the use of GIS tools shows that the ordinary kriging method allowed for the correct spatial presentation of the PM2.5 concentration variability in areas not covered by the measurement system.
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Authors and Affiliations

Izabela Sówka
1
ORCID: ORCID
Marek Badura
1
Marcin Pawnuk
1
ORCID: ORCID
Piotr Szymański
2
Piotr Batog
3

  1. Wroclaw University of Technology, Faculty of Environmental Engineering
  2. Wrocław University of Science and Technology, Faculty of Computer Science and Management
  3. INSYSPOM, Wrocław

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