Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 4
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

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.

Go to article

Authors and Affiliations

Jacek Mucha
ORCID: ORCID
Monika Wasilewska-Błaszczyk
ORCID: ORCID
Download PDF Download RIS Download Bibtex

Abstract

The aim of the paper is the comparison of the least squares prediction presented by Heiskanen and Moritz (1967) in the classical handbook “Physical Geodesy” with the geostatistical method of simple kriging as well as in case of Gaussian random fields their equivalence to conditional expectation. The paper contains also short notes on the extension of simple kriging to ordinary kriging by dropping the assumption of known mean value of a random field as well as some necessary information on random fields, covariance function and semivariogram function. The semivariogram is emphasized in the paper, for two reasons. Firstly, the semivariogram describes broader class of phenomena, and for the second order stationary processes it is equivalent to the covariance function. Secondly, the analysis of different kinds of phenomena in terms of covariance is more common. Thus, it is worth introducing another function describing spatial continuity and variability. For the ease of presentation all the considerations were limited to the Euclidean space (thus, for limited areas) although with some extra effort they can be extended to manifolds like sphere, ellipsoid, etc.
Go to article

Authors and Affiliations

Marcin Ligas
Marek Kulczycki
Download PDF Download RIS Download Bibtex

Abstract

The article describes the influence of anomalous values and local variability on the structure of variability and the estimation of deposit parameters. The research was carried out using statistical and geostatistical methods based on the Pb accumulation index in the shale series in part of the Cu-Ag ore deposit, LGCD (Lubin-Głogów Copper District). The authors recommend the use of a geostatistical tool, the so-called semivariogram cloud to determine the anomalous values. Anomalous values determined by the geostatistical method and removed from the dataset have resulted in a significant reduction of the relative variability of data, which is still very large in the case of the analyzed parameter or parameters with similar statistical features such as extreme variability and strongly asymmetric distribution. Calculations of the resources of this element can be treated only as estimates and formally classified to category D. The hypothetical assumption of the absence of sampling errors, resulting in a decrease in the magnitude of local variation, leads to a certain reduction of the median error of resource estimates. However, they are still high (> 35%). This is due to the large natural variability of the accumulation index of Pb on the local observation scale. The current method for collecting samples from mine workings of the Cu-Ag deposits in the Lubin-Głogów Copper District (LGCD), aimed at the proper assessment of copper resources, the Cu content, and at estimating the quality of copper output, makes it impossible to achieve an accuracy of estimates of Pb resources similar to that obtained for the main metal. Theoretically, this effect can be achieved by a strong concentration of the sample collection points and thanks to a multiple increase in the samples weight; this, however, is unrealistic for both economic and organizational reasons. It is therefore to be expected that the assessment of Pb resources and other accompanying elements of similar statistical features (e.g. As), located in parts of the deposit where mining activities are to be carried out, will be subject to significant errors.

Go to article

Authors and Affiliations

Justyna Auguścik
Jacek Mucha
Download PDF Download RIS Download Bibtex

Abstract

Bełchatów lignite deposit is located in the central partof Poland in the tectonic Kleszczów graben. It is dividedinto several parts, which are mining fields: Kamieńsk area (eastern part of the deposit), Bełchatów area (central partof the deposit) and Szczerców area (western part of the deposit). The subject of this study was the Belchatow area.The main issue of the investigations was the dependence of local, regional and global, horizontal variability of selected lignite qualitative parameters (moisture, ash content, calorific value and sulfur content in the as receivedstate) is a function of viewing direction. There was applied the geostatistical analysis of the lignite variability parameters with use of semivariograms.

The researches which were conducted at different scales of observation: in the locale scale – in small field size8 ́8 m called experimental area (local analysis), in larger homogeneous separated parts of the Belchatow area(regional analysis) and in the whole Bełchatów area scale (general analysis). The results proved the visible anisotropy of variability mine lignite parametres. Anisotropy structure observed in regional and global scale isconnected with tectonic structure of the Bełchatów Graben. The detailed studies show the variated level of anisotropy observed in different areas of Bełchatów field.

However, no dependence of the relative level of ash and total sulfur content anisotropy on the environment of sedimentation of the main coal deposit in different parts of the Belhchatów field has been observed. Both parameters characterize with strong or medium anisotropy level in examined fields. Moreover, anisotropy is alsovisible in the local scale. Conducted researches confirmed the thesis that zonal anisotropy is prevalent kind of anisotropy in the regional scale. In the range of the whole deposit the total sulfur content showed zonal anisotropy,whereas the ash content revealed geometric anisotropy

Go to article

Authors and Affiliations

Tomasz Bartuś

This page uses 'cookies'. Learn more