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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.
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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.
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