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.

The correlation-regression method, as one of the indirect sampling methods, is only sporadically used in geological and mining activities. Theoretically, it should be particularly useful for predicting the content of some chemical components in limestone and marl deposits due to the correlation between them. The results of simple and multiple correlation and regression analysis for 5 selected components (CaO, SiO2, Al2O3, MgO, and SO3), determined in samples from exploratory boreholes and blast holes carried out in the Barcin-Piechcin-Pakość deposit, are presented in the article. The determination coefficients were used as a measure of the correlation power and the quality of the regression models. A very strong linear correlation between CaO and SiO2 content and strong linear correlations between CaO and Al2O3 and SiO2 with Al2O3 have been found. The correlation relationships of the remaining pairs of oxides are weak or very weak and do not provide a basis for prediction of their content based on regression models binding them with the content of other components. The use of nonlinear models for these pairs of oxides results in only a slight improvement in the quality of regression, insignificant from a practical point of view. The application of multiple regression models, linking the content of the mentioned components (with the exception of CaO), leads to similar conclusions. Compared to the determination coefficients of a simple linear correlation, a strong increase in determination coefficients obtained in two cases was found to be artificial and caused by a correlation between the content of the selected components acting as independent variables. From the geological and mining point of view, the results of the analysis indicate the possibility of a fully reliable prediction of SiO2 content and the limited reliability of the Al2O3 content prediction when the CaO content is determined using simple linear regression models.

The main source of information on the abundance of polymetallic nodules (APN) is the results of direct seafloor sampling, mainly using box corers. Due to the vast spread of nodule occurrence in the Pacific, the distances between successive sampling sites are significant. This makes it difficult to reliably estimate the nodule resources, especially in parts of the deposit with small areas corresponding to the areas scheduled for extraction in the short term (e.g. within one year). It seems justified to try to increase the accuracy of nodule resource estimates through the use of information provided by numerous photos of the ocean floor taken between sampling stations. In particular, the percentage of nodule coverage of the ocean floor (NC), the data on fraction distribution of nodules (FD) and the coverage of nodules with sediments (SC) are important here. In the presented study, three regression models were used to predict the nodule abundance from images: simple linear regression (SLR), multiple regression (MR), and general linear model (GLM). The GLM provides the most accurate prediction of nodule abundance (APN) due to the ability of this model to simultaneously take into account both quantitative variable (NC) and qualitative variables (FD, SC). The mean absolute errors of APN prediction are in the range of 1.0–1.7 kg/m2, which is 7–13% of the average nodule abundance determined for training or testing data sets. This result can be considered satisfactory for predicting the abundance in ocean floor areas covered only by photographic survey.

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.

In the world-class Cu-Ag deposits of the Legnica-Głogów Copper District (LGCD), constant bulk density values are adopted to estimate the ore and metal resources within them based on the results of previous studies of the LGCD deposits carried out at the stage of their exploration and documentation: 2.6 Mg/m3 for the carbonate series, 2.5 Mg/m3 for the shale series, and 2.3 Mg/m3 for the sandstone series. The main purpose of research was to analyze the range of possible differences at local scale of observation between constant values of bulk densities (hereinafter referred to as reference values) assigned during deposit documentation to the main lithological units and bulk densities of these units determined based on the results of experimental sampling of individual lithological units within the exploited copper and silver deposits (Lubin, Polkowice-Sieroszowice and Rudna). In general, when it comes to Cu-Ag LGCD deposits (or their large parts), the relative diversity of estimates of average bulk densities of ores based on the results of experimental sampling (more than 1,600 samples from different individual lithological units were collected at 500 sampling points in mining excavations) and reference values is low (with a median not exceeding 3%). The results of studies indicate, however, that the application of reference bulk densities at the local observation scale may result in significant underestimation (up to nearly 20%) or overestimation (up to 11%) of real bulk densities of the main lithological units. This may have a noticeable impact on the correct estimation of ore and metal resources in small parts of deposits and, as a consequence, hinder the reconciliation of the planned and actual ore mining production.