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EN
Grade control is crucial for ensuring that the quality of extracted ore aligns with the geological model and mining plan. This process optimises production, reduces dilution, and maximises profits. It involves geological modelling, sampling, assaying, and data analysis. However, adhering to short-term planning in mining operations can be challenging due to operational bottlenecks that arise during the grade control process and blast design, along with their associated costs. Industry standards for grade control require acquiring extensive information and knowledge to achieve a high level of certainty, which takes time. Despite that, time constraints may necessitate making decisions under risk with incomplete information. In such cases, it is important to consider the opportunities, risks, likelihood, consequences, and potential success associated with each alternative. This study presents the testing results of alternative quantitative analytical methods on samples from the Barruecopardo tungsten deposit in Spain. Spectrometric techniques, including Delayed Gamma Neutron Activation Analysis (DGNAA), Laser-induced Breakdown Spectroscopy (LIBS), and Field Portable X-ray Fluorescence (FPXRF), were employed to determine the tungsten content. Based on the findings of this investigation, a real-time decision-making tool for grade control in open-pit mining has been developed. This tool utilises representative samples directly from the blasting debris, considering the inherent risks and uncertainties associated with the process.
EN
The rock mechanical properties influence the selection of drilling parameters, optimized drilling trajectory, and appropriate hydraulic fracturing intervals. Estimating the 3-D spatial distribution of these geomechanical properties at the reservoir scale is a challenging task, especially in the case of limited data only at the well locations. Advanced geostatistical techniques can be utilized to represent a reservoir’s inherent spatial variation more realistically. In this study, we investigate the spatial variability of rock mechanical properties, including Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio, as major constituents of the reservoir geomechanical model. The data are extracted from a hydrocarbon field located southwest of Iran and consist of forty wells. We first build a 1-D model of rock elastic moduli at each well by integrating petrophysical and core-based laboratory measurements and then develop a corresponding 3-D model using geostatistical simulation techniques. Thereafter, 3-D seismic data are employed to optimize the geomechanical model. Results show that the integration of well logs with seismic data increases the accuracy of field-wise 3-D elastic moduli models. Furthermore, we used various co-simulation techniques to demonstrate the improving effect of complementary data in constructing a more realistic reservoir geomechanical model.
EN
The paper presents selected aspects of calculations and modelling of variograms from measurements of soil surface magnetic susceptibility for rapid screening of surface soil contamination with Technogenic Magnetic Particles (TMP). In particular, the methodology of variogram analysis in the case of multiple magnetometric measurements in one measurement location with the use of the MS2D Bartington sensor was discussed. A new approach to analysing such measurements was proposed that allows determining and using the nugget effect from standard, already existing measurements. This is of key importance for the quality of spatial analyses, and thus the screening results obtained by means of field magnetometry. In the paper, it was shown, step by step, that averaging the measurements performed at one measurement point during the calculation of the empirical variograms does not result in the loss of information on spatial variability in the microscale. As it was calculated non-averaged measurements were characterised by the nugget-to-sill ratio of about 96 % which was much higher than in the case of averaged measurements (close to 0 %). A range of correlation was similar in both cases and was equal to about 300 m - 400 m. The local variogram revealed a range of correlation of about 80 cm. As a result, the screening results are more reliable than is the case with the traditional procedure. An additional advantage of the work was the performance of all calculations in free R software.
EN
The city of Algiers (Algeria) is a highly seismic area, and therefore, soil liquefaction poses a major concern for structures resting on sandy soil. A campaign of 62 static penetration tests or cone penetrometer tests (CPT) was carried out on a site located in the commune of Dar El Beïda in Algiers. The soil Liquefaction Potential Index (LPI) values were assessed, for each borehole, based on the simplified procedure of Seed and Idriss. On the other hand, the geographic information system and geostatistical analysis were used to quantify the risk of soil liquefaction at the studied site. It is worth mentioning that the (LPI) was taken as a regionalized variable. In addition, the experimental variogram was modeled on the basis of a spherical model. Also, the interpolation of the LPI values in the unsampled locations was performed by the Kriging technique using both isotropic and anisotropic models. Kriging standard deviation maps were produced for both cases. The cross-validation showed that the anisotropic model exhibited a better fit for the interpolation of the values of the soil liquefaction potential. The results obtained indicated that a significant part of the soil is liable to liquefy, in particular in the northwestern region of the study area. The findings suggest that there is a proportional relationship between the risk of liquefaction and the increase or decrease in seismic acceleration.
EN
The paper presents the results of research on variability of basic physical and chemical parameters of peats from a small fen in the Struga Wodna valley on the Lubartów Plateau. The variability of organic matter content, moisture content, pH and cation exchange capacity (CEC) was analysed. Apart from descriptive statistics, geostatistical methods were also used, including the analysis of semivariograms. All determined parameters showed high variability, including spatial variability. The analysis of the semivariograms showed that for each of the parameters there is a nugget effect, indicating high local variability. The statistically highest variability, expressed by the coefficient of variation, was shown by peat moisture content, while the moisture content showed the highest spatial autocorrelation. The use of geostatistical methods allowed identifying zones with different properties within the fen, and describing the spatial autocorrelation of individual parameters.
EN
The study presents the possibility of using geostatistical methods for monitoring groundwater quality. Poland is one of the largest copper producers in the world. However, the extraction and production of copper requires constant care for the natural environment. Reservoir Żelazny Most which is situated in South – Western Poland was designed to store flotation tailings out of nearby copper mines. It is one of the biggest industrial dumps in the world. The reservoir stores huge amounts of tailings and industrial water. Water migrating from dump to groundwater could be a potential source of contamination with chlorides, sulphates, heavy metals, and other hazardous substances used in ore separation process in the copper mining industry, like detergent and phenols. Monitoring system around Żelazny Most dump, which was designed to track harmful substances concentrations in groundwater, contains measuring wells and piezometers. They are used to collect groundwater samples for chemical analyses. The idea of the study was to integrate information provided by chemical analyses and geoelectrical measurements by cokriging method, utilizing correlation between electrical resistance of the soil solution and total dissolved solids concentration in groundwater. This enabled to obtain spatial distribution of total dissolved solids concentrations in groundwater at the part of eastern foreground of Żelazny Most dump.
EN
The work focused on forecasting changes in lake water level. The study employed the Triple Diagram Method (TDM) using geostatistical tools. TDM estimates the value by information from an earlier two periods of observation, refers as lags. The best results were obtained for data with an average a 1-week lag. At the significance level of 1σ, a the forecast error of ±2 cm was obtained. Using separate data for warm and cold months did not improve the efficiency of TDM. At the same time, analysis of observations from warm and cold months explained trends visible in the distribution of year-round data. The methodology, built on case study and proposed evaluation criteria, may function as a universal solution. The proposed methodology can be used to effectively manage water-level fluctuations both in postglacial lakes and in any case of water-level fluctuation.
EN
Understanding the spatial variability of soil organic matter (SOM) is critical for studying and assessing soil fertility and quality. This knowledge is important for soil management, which results in high crop yields at a reduced cost of crop production and helps to protect the environment. The benefits of an accurate interpolation of SOM spatial distribution are well known at the agricultural, economic, and ecological levels. It has been conducted this study for comparing and analyze different spatial interpolation methods to evaluate the spatial distribution of SOM in Sidi Bennour District, which is a semi-arid area in the irrigated scheme of the Doukkala Plain, Morocco. For conding this study, it was collected 368 representative soil samples at a depth of 0–30 cm. A portable global positioning system was used to obtain the location coordinates of soil sampling sites. The SOM spatial distribution was performed using four interpolation methods: inverse distance weighted and local polynomial interpolation as deterministic methods, and ordinary kriging and empirical Bayesian kriging as geostatistical methods. High SOM levels were concentrated in vertisols, and low SOM levels were observed in immature soils. The average SOM value was 1.346%, with moderate to high variability (CV = 35.720%). A low SOM concentration indicates a continuous possibility of soil degradation in the future. Ordinary kriging yielded better results than the other interpolation methods (RMSE = 0.395) with a semivariogram fitted by an exponential model, followed by inverse distance weighted (RMSE = 0.397), empirical Bayesian kriging (RMSE = 0.400), and local polynomial interpolation (RMSE = 0.412). Soil genetics and the strong influence of human activity are the major sources of SOM spatial dependence, which is moderate to low. Low SOM content levels (< 1.15%) were present in the southwestern and eastern parts of the digital map. This situation calls for the implementation of specific soil recovery measures.
PL
W artykule w przystępny sposób przedstawiono wybrane zagadnienia związane z metodą krigingu zwyczajnego, szeroko wykorzystywaną do estymacji zasobów górniczych. W szczególności opisano te jej właściwości, które choć zazwyczaj mniej znane to decydują o przydatności tej metody i umożliwiają kontrolę dokładności uzyskanych wyników. Szczególną uwagę poświęcono zastosowaniom roli wariancji krigingu, będącej miarą dokładności wyników otrzymanych za pomocą metody krigingu, oraz możliwości jej zastosowania do planowania sieci pomiarowych.
EN
The article presents, in an approachable way, selected issues related to the method of the ordinary kriging, which is widely used for the estimation of mining resources. In particular, such properties of the ordinary kriging were described, which are usually less known but determine its usefulness and accuracy. Particular attention was paid to the role of kriging variance, which is a measure of the accuracy of results obtained using the ordinary kriging. The possibility of using the kriging variance for planning measurement networks was also discussed.
EN
The population is continuously exposed to a background level of ionizing radiation due to the natural radioactivity and, in particular, with radon (222Rn). Radon gas has been classified as the second leading cause of lung cancer after tobacco smoke [1]. In the confined environment, radon concentration can reach harmful level and vary accordingly to many factors. Since the primary source of radon in dwellings is the subsurface, the risk assessment and reduction cannot disregard the identification of the local geology and the environmental predisposing factors. In this article, we propose a new methodology, based on the computation of the Gini coefficients at different spatial scales, to estimate the spatial correlation and the geographical variability of radon concentrations. This variability can be interpreted as a signature of the different subsurface geological conditions. The Gini coefficient computation is a statistical tool widely used to determine the degree of inhomogeneity of different kinds of distributions. We generated several simulated radon distributions, and the proposed tool has been validated by comparing the variograms based on the semi-variance computation with those ones based on the Gini coefficient. The Gini coefficient variogram is shown to be a good estimator of the inhomogeneity degree of radon concentration. Indeed, it allows to better constrain the critical distance below which the radon geological source can be considered as uniform at least for the investigated length scales of variability; it also better discriminates the fluctuations due to the environmental predisposing factors from those ones due to the random spatially uncorrelated noise.
EN
Post-industrial and post-mining areas have often been under strong anthropogenic pressure for a long time. As a result, such areas, after the ending of industrial activity require taking steps to revitalize them. It may cover many elements of the natural or urban environment, such as water, soil, vegetated areas, urban development etc. To carry out revitalization, it is necessary to determine the initial state of such areas, often using selected chemical, geophysical or ecological. After that it is also important to properly monitor the state of such areas to assess the progress of the revitalization process. For this purpose a variety of change detection technics were developed. Post-industrial areas are very often characterized by a large extent, are difficult to access, have complicated land cover. For this reason, it is particularly important to choose appropriate methods to assess the degree of pollution of such areas. Such methods should be as economical as possible and time-effective. A very desirable feature of such methods is that they should allow a quick assessment of the entire area. Geostatistics supplemented by modern remote sensing can be effective for this purpose. Nowadays, using remote sensing, it is possible to gather information simultaneously from the entire, even vast area, with high spatial, spectral and temporal resolution. Geostatistics in turn provides many tools that are able to enable rapid analysis and inference based on even very complicated often scarce spatial data sets obtained from ground measurement and satellite observations. The goal of the article was to present selected results obtained using geostatistical methods also related to remote sensing, which may be helpful for decision makers in revitalizing post-industrial and post-mining areas. The results described in this paper were based mostly on the previous studies, carried out by authors.
EN
The fractured groundwater aquifers, predominantly found in South Africa, show varying groundwater chemical characteristics in various locations. The hydrochemistry of groundwater is affected by the weathering of rock formations in contact and anthropogenic activities. Determination of groundwater chemistry is important for aquifer protection and overall groundwater management. A hydrochemical analysis is a useful tool for identification of water types, chemical composition, its suitability for specified purposes, and an important requirement for water use licensing applications. The hydrochemical data of groundwater from 79 boreholes near Leliefontein, Kamiesberg local municipality of South Africa, were analysed, using integrated statistical, geostatistics and spatial interpolation methods. The result shows Na+ and Cl− to be the abundant cation and anion. The mean concentration of Na at Leliefontein was 267.39 mg/l, and that of Cl was 574.81 mg/l. The ionic concentrations in groundwater was in sequence of Cl− > Na+ > HCO3− > SO42− > Ca2+ > Mg2+ > NO3− > Si > K+ > F-. The analysis indicated that the cation exchanges in groundwater are influenced by limited silicate weathering, with calcite and dolomite dissolution. Geostatistical and spatial analysis interpolation for the major cation (Na) and major anion (Cl), Sodium Adsorption Ratio (SAR), Electrical Conductivity (EC) and Water Quality Index (WQI) was performed using Inverse Distance Weighing method. The hydrochemical data for the Leliefontein groundwater were analysed to classify water for domestic use (drinking) and agriculture (irrigation) purposes, based on the recommended guidelines of the South African National Standard (SANS). The study area was characterised by high salinity of three water types, viz, Na-Cl seawater type, Ca-Cl reverse ion-exchange water type, and Na-HCO3 base ion-exchange water types. About 70–80% of the boreholes in Leliefontein met the requirement for irrigation application for Sodium Adsorption Ratio (SAR) and salinity hazard analysis, while the groundwater generally required further treatment before domestic use.
EN
Slow, long-term ground deformations in the Dąbrowa Basin (southern Poland) were identified based on ERS-1, ERS-2 and ENVISAT Synthetic Aperture Radar (SAR) images that were processed by means of Permanent Scatterer SAR Interferometry (PSInSAR). The Dąbrowa Basin is a region where two major factors can affect surface stability: intensive coal exploitation and neotectonic processes. In this study, in order to clarify the origin of surface deformations, the authors propose applying a newly developed algorithm of spatio-temporal PSInSAR data analysis. This analysis revealed that subsidence is a characteristic feature of the Dąbrowa Basin. A significant correlation exists between slow, long-term ground deformations and the location of the main tectonic structure of this region. The proposed spatiotemporal analysis of the PSInSAR data additionally showed some degree of correlation between mining activity and the studied deformations. This interconnection is a significant achievement of this study since the deformation values determined by means of PSInSAR were identified in earlier works solely on the basis of Dąbrowa Basin neotectonics.
EN
Discrete groundwater level datasets are interpolated often using kriging group of models to produce a spatially continuous groundwater level map. There is always some level of uncertainty associated with diferent interpolation methods. Therefore, we developed a new trend function with the mean groundwater level as a drift variable in the regression kriging approach to predict the groundwater levels at the unvisited locations. Groundwater level data for 29 observation wells in Adyar River Basin were used to assess the performance of the developed regression kriging models. The cross-validation results shows that the proposed regression kriging method in the spatial domain outperforms other physical and kriging-based methods with R2 values of 0.96 and 0.98 during pre-monsoon and post-monsoon seasons, respectively.
PL
Ważnym elementem zarządzania organizacją jest planowanie jej rozwoju i działań operacyjnych. W procesie podejmowania decyzji związanych z tymi działaniami w przypadku wielu przedsiębiorstw niezbędne jest wykonywanie prognoz obszarowo-czasowych, z krótszym lub dłuższym wyprzedzeniem czasowym. Dotyczy to przede wszystkim tych przedsiębiorstw, których działalność obejmuje duże obszary lub zjawiska stanowiące podstawę do podejmowania racjonalnych decyzji, w odniesieniu do rozwiązywanych zagadnień, rozwijających się w układzie powierzchniowym, powierzchniowo-czasowym, a także przestrzennym. Przykładem mogą tutaj być kopalnie surowców mineralnych, instytucje zajmujące się badaniem i ochroną środowiska naturalnego, przedsiębiorstwa sieciowe, np. telekomunikacyjne czy energetyczne. Przedstawiono metodykę badawczą wykorzystującą metody geostatystyki liniowej i nieliniowej, zastosowanej do modelowania, szacowania i prognozowania (2D, 3D) wartości parametrów opisujących różnorodne zmienne zregionalizowane. Dane wejściowe do analiz przestrzennych stanowiły wartości parametrów geologicznych, pochodzące z opróbowania wyrobisk górniczych w kopalniach rud miedzi, tj. zawartość Cu, miąższość i zasobność złoża (bilansowego), oraz wartości mocy elektrycznej w węzłach sieciowych najwyższych napięć 220 i 400 kV dla obszaru Polski. Zastosowane techniki pozwoliły na szczegółowe odwzorowanie zróżnicowania wartości badanych parametrów, wydzielenie anomalnych stref, określenie przedziałów ufności na odpowiednim poziomie ryzyka, oszacowanie niepewności i analizę zmienności tego ryzyka.
EN
A major element of managing an organization is the planning of its development and operations. As part of the relevant decision making process it is necessary for many enterprises to make areal-temporal forecasts more or less ahead of time. This particularly applies to enterprises whose activity covers large areas or phenomena, which constitute the basis for making rational decisions concerning the problems being solved, developing in the areal system, the areal-temporal system as well as in the spatial system. Industrial mineral mines, institutions studying and protecting the natural environment and network (telecommunications or power) companies are examples here. A research methodology using methods of linear and non-linear geostatistics applied to the (2D, 3D), modelling, estimating and forecasting of the values of parameters describing various regionalized variables is presented. The input data for the spatial analysis were the values of the geological parameters: Cu content, (recoverable) deposit thickness and endowment coming from the sampling of mine workings in copper ore mines and electric power values in the nodes of 220 and 400 kV ultra-high voltage distribution networks for area of Poland. Thanks to the above techniques the variation in the values of the investigated parameters was mapped in detail, anomalous zones were distinguished, confidence levels at an appropriate risk level were determined, uncertainty estimated and the variation of the risk was analysed.
EN
Geostatistics was used in a typical alluvial fan to reveal its applicability to spatial distribution analysis and controlling mechanisms of groundwater chemistry. Normal distribution test and optimal geostatistical interpolation models for various groundwater quality indicators were discussed in this study. The optimal variogram model of each indicator was determined using prediction error analysis. The infuences of human activities and structural factors on the groundwater chemistry were also determined by variability intensity and the sill ratio. The results showed that nitrate content can be served as groundwater quality indicator, which was most sensitive to human activities. The nitrate concentration of both shallow and deep groundwater showed a decreasing trend from the northwest to the southeast. In addition, the spatial distribution of groundwater nitrate was associated with the land-use type and the lithological properties of aquifer. Rapid urbanization in the northwestern part intensifed groundwater extraction and aggravated the pollutant input. The central area showed little increase in nitrate content in the shallow and deep groundwater, and the efect of lateral recharge from the upstream water on the deep groundwater in the central area was greater than that of the vertical recharge from shallow groundwater. The present study suggests that geostatistics is helpful for analyzing the spatial distribution and distinguishing the infuences of anthropogenic and natural factors on groundwater chemistry.
EN
The phenomenon of erosion on mountain and submontane areas influences directly on high variability of soil properties. In the work there were presented results of analysis of spatial variability of bulk density, total porosity, organic matter content and saturated hydraulic conductivity, on eroded slopes of the Kasińczanka stream basin. Geostatistical analysis was carried out using the kriging method, based on irregular network, consisted of 52 points, situated by means of the GPS. Taking into account the calculated variability coefficient it was stated, that on the investigated area, the most flexible spatially was saturated hydraulic conductivity, while the less flexible turned out total porosity. Using the determined models of semivariance, the maps of spatial variability of chosen parameters were drafted. It was stated that high value of variance influenced on higher smoothing of spatial distribution in interpolation. Results of geostatistical analysis will allow to find locations for new measuring points, what has substantial significance in mountain areas, for precision analysis of soil properties. Based on the obtained results, it can be stated that the kriging method may be useful tool for determination spatial variability analysis of soil properties on an areas of mountain basins.
EN
In Indonesia, there are underground mines for mineral metal such copper (Cu) and gold (Au), built by tunneling towards the mineral location. The purpose of this study was to determine the mapping a concentration of diesel particulate matter (DPM) and assess the impact on health by severity measurement of airflow obstruction of the miners experiencing chronic obstructive pulmonary disease (COPD). The data of DPM were measured with NIOSH method no. 5040 and applied a geostatistical method in mapping concentration at the area of underground mining. A spirometric measurement was conducted to diagnose COPD that is done to the 314 miners. The results showed that the concentrations exceeding the permissible exposure limit (PEL) and spirometric measurement were found for 26 miners (8.3%) who experience COPD (post bronchodilator <0.70). The severity measurement of airflow obstruction of the miners experiencing COPD, severity of airflow limitation for moderate (GOLD 2) was obtained for 14 miners (54%); severe (GOLD 3) for 10 miners (38%) and very severe (GOLD 4) for 2 miners (8%). It can be concluded that the amount of DPM exposure against the severity of airflow limitation with COPD by 0.03, in which the other factors also affect the severity.
EN
The aim of this study was to assess the spatial distributions of total trace elements content in the bottom sediments of Dzierżno Duże water reservoir, along with the comparison of the accuracy and characteristics of Kriging and IDW interpolations. On the basis of regular measurement grid consisting of 53 points, bottom sediments samples were collected. Mean values of total trace elements content in bottom sediments of Dzierżno Duże were as follows: Zn – 410 mg/kg, Pb – 57 mg/kg, Cr – 36 mg/kg, Cu – 40 mg/kg, Cd – 5 mg/kg, Ni – 16 mg/kg and Ba – 267 mg/kg. According to the geochemical quality classification, the concentrations of Cd in 32% of samples were assigned to class IV (heavily contaminated), 45% to class III (contaminated), Zn in 42% samples to class III with 1 sample in class IV and 26% to class II (slightly contaminated), Pb in 9% to class III and 58% to class II, Cu in 4% to class III and 68% to class II, Cr in 17% to class II, Ni in 55% to class II, Ba in 8% to class III and 61% in class II. Coefficient of determination was determined between each case of trace elements content. The highest correlation (R2 in range from 0.81 to 0.96) was observed between Zn and Pb, Zn and Cu, Zn and Cr, Zn and Ni, Pb and Cu, Pb and Cr, Cu and Cr, Cr and Ni. Significant correlation (R2 in range from 0.70 to 0.80) occurred between: Zn and Cd, Pb and Ni, Cu and Ni, Cd and Ni. The lowest correlations (R2 in range from 0.25 to 0.70) were observed between concentration of Ba and the rest of trace elements. Two different interpolation methods were chosen for the purpose of generating spatial distributions – Inverse Distance Weighted and Ordinary Kriging. These methods were chosen for purpose of obtaining optimal accuracy result of spatial distributions. The distributions of trace elements content were classified by means of geochemical criteria. In the case of accuracy comparison between IDW and Ordinary Kriging, the former had slightly better results in terms of mean value and root mean square. The generated spatial distributions allowed to determine the most contaminated areas, which were mainly northern-central and southern-central parts of water Dzierżno Duże reservoir.
20
Content available remote Spatio-temporal analysis of annual rainfall in Crete, Greece
EN
Analysis of rainfall data from the island of Crete, Greece was performed to identify key hydrological years and return periods as well as to analyze the inter-annual behavior of the rainfall variability during the period 1981–2014. The rainfall spatial distribution was also examined in detail to identify vulnerable areas of the island. Data analysis using statistical tools and spectral analysis were applied to investigate and interpret the temporal course of the available rainfall data set. In addition, spatial analysis techniques were applied and compared to determine the rainfall spatial distribution on the island of Crete. The analysis presented that in contrast to Regional Climate Model estimations, rainfall rates have not decreased, while return periods vary depending on seasonality and geographic location. A small but statistical significant increasing trend was detected in the inter-annual rainfall variations as well as a significant rainfall cycle almost every 8 years. In addition, statistically significant correlation of the island’s rainfall variability with the North Atlantic Oscillation is identified for the examined period. On the other hand, regression kriging method combining surface elevation as secondary information improved the estimation of the annual rainfall spatial variability on the island of Crete by 70% compared to ordinary kriging. The rainfall spatial and temporal trends on the island of Crete have variable characteristics that depend on the geographical area and on the hydrological period.
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