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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
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.
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.
EN
A 3D model of collected time-domain induced polarization (IP) and electrical resistivity tomography (ERT) data is compiled by geostatistical methods as well as studying spatial correlation among the database. Mesgaran copper deposit, located in Birjand eastern Iran, was chosen to compile and verify the model, leading to five parallel surveyed IP and ERT profiles with dipole–dipole arrays. The collected data were inverted, and then 2D models of IP and ER were prepared; also 3D inversion was done. Afterward, the 3D model has been built by geostatistical methods. Correspondingly, the anomalies threshold was detected by fractal methods and the estimation variance and Kriging efficiency were calculated to validate the modeling. The mineralization zones were determined according to the classified anomalies and those with the lowest error. Results indicated a high correlation between anomalies identified from the model and mineralization. The results made it possible to construct 3D models from surveyed 2D data with acceptable error level.
EN
This paper presents the problem ofparameter selection in geotechnical engineering design. The statistical methods with a literature review to estimate the characteristic parameter value are described. The literature review includes the description of the geotechnical parameters used for statistical analysis. In addition, the field tests (CPT and DMT) are presented together with the interpretation of the obtained results. The empirical relationships serving to calculate the parameter values were analyzed. Then, the Nielisz embankment was characterized, where the objectfor which studies were subjected to the CPT and DMT tests. Finally, the selected parameters using the statistical method ofclassical and bayesian approach were determined.
EN
The paper presents a selection of a semivariogram model in the study of spatial variability of soil moisture in a loess agricultural catchment. Soil moisture tests were carried out in the Moszenki village, 15 km northwest of Lublin. Soil moisture measurements were performed at two dates at 104 points, located on a rectangular surface measuring 700 × 1200 m. These points were laid out in the corners of a grid of squares with sides 100 m. In addition, 6 measurements were made at a distance of less than 100 m from the nearest points. Soil moisture was measured in the soil surface (0–5 cm). ArcGis software with Geostatistical Analyst extension was used for modelling semivariograms. In both terms, five models of semivariograms were used: stable, circular, spherical, exponential and Gaussian. Kriging was used for the estimation of soil moisture values. Among the semivariogram models analyzed in this study, the largest errors in the determined values of soil moisture relative to the empirical data were observed for the exponential model, and the smallest for the Gaussian model. However, it should be emphasized that the values of the analysed errors for the individual semivariogram models were similar. Application of the ordinary kriging method for interpolation of spatial distribution of soil moisture yields good results, but it has to be kept in mind that the final shape of the spatial distribution is influenced by the choice of the semivariance function model.
PL
W pracy zaprezentowano dobór modelu semiwariogramu w badaniach przestrzennej zmienności wilgotności gleby w lessowej zlewni rolniczej. Badania wilgotności gleb przeprowadzono na terenie wsi Moszenki, 15 km na północny zachód od Lublina. Pomiary wilgotności gleby przeprowadzono w dwóch terminach w 104 punktach, rozmieszczonych na powierzchni w kształcie prostokąta o wymiarach 700 × 1200 m. Punkty te wytyczono w narożnikach siatki kwadratów o bokach 100 m. Dodatkowo wykonano 6 pomiarów zlokalizowanych w odległości mniejszej niż 100 m od najbliższych punktów. Wilgotność mierzono w powierzchniowej warstwie gleby (0–5 cm). Do modelowania semiwariogramów wykorzystano program ArcGis z rozszerzeniem Geostatistical Analyst. W obu terminach do analiz wykorzystano pięć modeli semiwariogramów: stały, kołowy, sferyczny, wykładniczy, Gaussa. Do estymowania wartości wilgotności na analizowanym obszarze wykorzystano kryging zwyczajny. Spośród analizowanych modeli semiwariogramów największe błędy wyznaczonych wartości wilgotności gleby w stosunku do danych empirycznych zanotowano dla modelu wykładniczego, natomiast najmniejsze dla modelu Gaussa. Wykorzystanie krygingu zwykłego do interpolacji rozkładu przestrzennego wilgotności gleb daje dobre rezultaty, jednak na efekt końcowy rozkładu przestrzennego wpływ miał dobór modelu funkcji semiwariancji.
PL
Proces przenikania wody opadowej z atmosfery do pedosfery składa się z wielu przejściowych elementów. Jednym z nich jest ekosystem leśny. Zróżnicowanie ilości wody docierającej do dna lasu zależy przede wszystkim od wielkości i budowy koron drzew ale także od odległości od pnia. Zdolność do czasowego zatrzymania wody opadowej to proces intercepcji. W warunkach polowych pomiar intercepcji jest ze względu na trudności metodyczne i techniczno - organizacyjne, zadaniem trudnym do wykonania. Celem prezentowanych badań było skonstruowanie aparatury do pomiaru ilości wody docierającej pod korony drzew, precyzyjna kalibracja i testowanie przyjętej metodyki. Szesnaście urządzeń pomiarowych ustawiono pod koroną każdego analizowanego drzewa, siedemnaste urządzenie zostało zmodyfikowane do badania spływu wody opadowej po pniu a osiemnaste mierzyło opad poza drzewostanem. Przyrosty opadu zapisywano w określonych krokach czasowych co w rezultacie dawało przestrzenno czasowy obraz pojemności wodnej koron drzew. Do realizacji tego etapu wykonano deszczomierze zawierające zbiorniczek przelewowy. Rejestrator zliczał liczbę przechyleń skalibrowanego zbiorniczka i na tej podstawie określono objętości (wysokość) opadu w czasie. Jednorazowo doświadczenie celowo przeprowadzono pod koroną pojedynczego drzewa. Taki zabieg będzie pozwalał w przyszłości na komputerowe modelowanie wyników w zależności od zadanego zwarcia. Efektem wykonanych pomiarów jest graficzna interpolacja danych przestrzennych. Badania zrealizowano na terenie Leśnego Zakładu Doświadczalnego w Krynicy Zdroju (Południowa Polska). Do badań wybrano drzewo z prawidłowo rozwiniętą koroną. W przyszłości planowane jest wykorzystanie wytworzonej aparatury i rozszerzenie badań na powierzchnie zawierające zbiorowiska leśne.
EN
The process of penetration of rainwater from the atmosphere into the pedosphere consists of a multitude of transitional elements. One of them is the forest ecosystem. Variation in the amounts of water reaching the forest floor depends primarily on the size and construction of tree crowns (canopies), but also on the distance from the trunk. The ability to temporarily catch the rainwater is called interception. In the field, measurement of the interception, due to the methodological and technical complication is a difficult task to perform. The aim of the present study was to construct an apparatus for measuring the amount of water reaching under the crowns of trees, precise calibration and testing accuracy of methodology. 16 measuring devices were set under the crown of each of the trees included in the study, the 1th apparatus was modified to test the rainwater runoff on the trunk, while the 18th measured rainfall outside the beech stand. Increases in precipitation were recorded at certain intervals, which in turn provided a spatial-temporal image of the water storage capacity of tree canopies. For the realization of this stage, rain gauges containing overflow cylinders were prepared. The counter counted the number of tilts of the calibrated cylinder, and on this basis the volume (amount) of precipitation during a given time interval was determined. Once, the test was intentionally carried out under the canopy of a single tree. This treatment will allow in the future for computer modeling of the results, depending on the desired leaf canopy size. The result of measurement work carried out is a graphical interpolation of the spatial data. The study was carried out in Experimental Forests of University of Agriculture in Krynica Zdrój (southern Poland). For the study, the tree with well-developed canopy were selected. In the future, it is planned to use the equipment manufactured as part of the present study and extend the study to cover other forest tree species.
PL
W artykule przedstawiono wyniki badań eksperymentalnych podjętych w celu określenia zmienności lokalnej zasobności niklu i wanadu dla serii łupkowej we fragmencie złoża „Rudna” Cu-Ag LGOM. Zmienność lokalną zdefiniowano jako zróżnicowanie parametru złożowego w próbach pobranych w bezpośrednim sąsiedztwie. Wybór pierwiastków towarzyszących złożom miedzi do badań nie był przypadkowy, wybrano pierwiastki strategiczne dla Polski. Badania przeprowadzono metodami statystycznymi i geostatystycznymi. Stwierdzono, że zmienność zasobności jednostkowej niklu i wanadu w serii łupkowej dla całego złoża i w skali lokalnej jest duża (rzędu 70 – 80%). Przeprowadzona ocena statystycznej istotności różnic dla danych (próbek) sparowanych za pomocą testów: t-Studenta, testu rangowanych znaków wykazała, że otrzymane wyniki oznaczeń Ni i V nie są obarczone błędem systematycznym. Badania geostatystyczne wykazały, że na wielkość zmienności lokalnej zasobności obu pierwiastków znacznie większy wpływ (prawie dwukrotnie) ma naturalna zmienność pierwiastków, niż błędy związane z procesem opróbowania.
EN
The paper presents the results of the research on local variability of the accumulation index of nickel and vanadium for the shale ore in a part of the Cu-Ag LGOM “Rudna” deposit . The local variability was defined in this case as the variation of the reservoir parameter in samples taken at the smallest distance from one another. The choice of elements accompanying (Ni, V) copper deposits for the analysis was not coincidental – this elements are strategic importance for Poland. To analyse the results of the experimental sampling, statistical and geostatistical methods were used. It was ascertained that the variability of nickel and vanadium the shale ore for the whole deposit and in the local scale is high (coefficients of variation from 70 to 80%). The performed estimation of statistical significance of differences for the data paired using the t-test and the signed rank test showed that the received results of determining are not encumbered with statistical error. The geostatistical description of the local variability showed a much greater (almost twice higher) effect of natural variation of nickel and vanadium on the magnitude of local variability than errors related to the sampling process.
EN
The paper presents possible implementation of ordinary cokriging and geophysical investigation on humidity data acquired in geotechnical studies. The Author describes concept of geostatistics, terminology of geostatistical modelling, spatial correlation functions, principles of solving cokriging systems, advantages of (co-)kriging in comparison with other interpolation methods, obstacles in this type of attempt. Cross validation and discussion of results was performed with an indication of prospect of applying similar procedures in various researches.
EN
This paper presents selected results of research connected with the development of a (3D) geostatistical hydrogeochemical model of the Kłodzko Drainage Basin, dedicated to the spatial variation in the different quality parameters of underground water in the water intake area (SW part of Poland). The research covers the period 2011–2012. Spatial analyses of the variation in various quality parameters, i.e., contents of: iron, manganese, ammonium ion, nitrate ion, phosphate ion, total organic carbon, pH redox potential and temperature, were carried out on the basis of the chemical determinations of the quality parameters of underground water samples taken from the wells in the water intake area. Spatial variation in the parameters was analyzed on the basis of data obtained (November 2011) from tests of water taken from 14 existing wells with a depth ranging from 9.5 to 38.0 m b.g.l. The latest data (January 2012) were obtained (gained) from 3 new piezometers, made in other locations in the relevant area. A depth of these piezometers amounts to 9–10 m. Data derived from 14 wells (2011) and 14 wells + 3 piezometers (2012) were subjected to spatial analyses using geostatistical methods. The evaluation of basic statistics of the quality parameters, including their histograms of distributions, scatter diagrams and correlation coefficient values r were presented. The directional semivariogram function γ(h) and the ordinary (block) kriging procedure were used to build the 3D geostatistical model. The geostatistical parameters of the theoretical models of directional semivariograms of the water quality parameters under study, calculated along the wells depth (taking into account the terrain elevation), were used in the ordinary (block) kriging estimation. The obtained results of estimation, i.e., block diagrams allowed us to determine the levels of increased values of estimated averages Z* of underground water quality parameters.
19
Content available remote Analysis of Spatial Variability in the Depth of the Water Table in Grassland Areas
EN
The kriging spatial statistical analysis technique was used to analyze spatial variability in the groundwater levels in irrigated grassland catchment in the Piwonia River valley. The geostatistical analysis in this study was performed using ArcGIS software, and the spatial distributions on fluctuations in groundwater levels were also studied. The objective of study was to evaluate the applicability of the kriging method for the analysis of the groundwater level. Field observation data collected in Sosnowica in 2011 were used (Western Polesie). The study area is located in Eastern Poland in the province of Lublin and has an temperate climate with temperature extremes -30°C and 35°C. (average 8°C). The annual rainfall in the area is about 600 mm, 40% of which occurs between June and September, and the evapotranspiration potential is high. The catchment area of the ditches is 0.46 km2 and is 86% of area is used as a one-crop seminatural meadows land. The soil cover is dominated by degraded soil muck-peat (MtII). In the catchment area 75% of the habitat moorshed and moist with a high groundwater level. In spring and summer, flooding of grassland in the eastern part of the study area was observed. It was caused by seepage of water from the pond and the supply of water after ice thawing or after rainfall. The obstruction of drainage including neglected ditches had also impact on flooding. The groundwater level in the western part of the study area decreased excessively in the fall because of drainage influence of the river which depth is 2 m. The dataset consisted of groundwater level measured at 15 points in three test periods (spring, summer and autumn). The measured groundwater levels were used to construct experimental semivariograms to characterize the spatial variability in the levels. A range of theoretical models (spherical, exponential, Gaussian models) were fitted to the experimental semivariograms. The models were validated using cross-validation statistics. Surface generated hydroizohipses maps were produced to illustrate spatial variations in the groundwater level in the study area. The spatial analysis of the groundwater level data from the piezometers led to the following conclusions: groundwater levels in the study area were autocorrelated in the distance between 203.5 and 300 m – depending on series, the groundwater level depth was smallest in the vicinity of the Hetman pond and greatest near the Piwonia river, spatial variability in the groundwater levels was described better by the Gaussian model than by the other models for all test series.
PL
Do analizy zmienności przestrzennej poziomu zalegania wód gruntowych na nawadnianych użytkach zielonych w dolinie zlewni rzeki Piwonia wykorzystano technikę przestrzennej analizy statystycznej w postaci krigingu. W prezentowanych badaniach analizę geostatystyczną obejmującą studium rozkładu przestrzennego wahań głębokości położenia wód gruntowych przeprowadzono przy użyciu oprogramowania ArcGIS. Celem pracy była ocena możliwości stosowania metody krigingu do analizy poziomu wody gruntowej. Wykorzystane zostały dane obserwacyjne zebrane w rejonie Sosnowicy w 2011 roku (Polesie Lubelskie). Badany obszar położony jest we wschodniej Polsce, w województwie lubelskim i charakteryzuje się klimatem umiarkowanym z ekstremalnymi temperaturami od -30°C do 35°C (średnia 8°C). Suma opadów rocznych na obszarze badań wynosi około 600 mm, z czego 40% ma miejsce w okresie od czerwca do września, a potencjalna ewapotranspiracji jest wysoka. Powierzchnia zlewni rowu wynosi 0,46 km2 i jest w 86% użytkowana jako jednokośne półnaturalne łąki. W pokrywie glebowej dominują zdegradowane gleby murszowo-torfowe (MtII). 75% powierzchni stanowią siedliska pobagienne i wilgotne charakteryzujące się wysokim poziomem wody gruntowej w glebie. Podtapianie łąk we wschodniej części obszaru badań na wiosnę i w lecie jest spowodowane filtracją wody ze stawu, doprowadzaniem wody i niedrożnością systemu melioracyjnego w trakcie roztopów lub ulewnych opadów deszczu. Z kolei w zachodniej części badanego obszaru poziom wód gruntowych nadmiernie się obniża z powodu drenującego działania rzeki, której głębokość wynosi 2 m. Zbiór analizowanych danych dotyczył poziomów wód gruntowych mierzonych w 15 punktach w trzech okresach badawczych (wiosna, lato, jesień). Pomierzone poziomy wody gruntowej zostały wykorzystane do skonstruowania semiwariogramów eksperymentalnych charakteryzujących poziomą zmienność przestrzenną. Gama modeli teoretycznych (model sferyczny, wykładniczy i Gaussa) została dopasowana do semiwariogramów eksperymentalnych. Modele zostały sprawdzone za pomocą statystyki krzyżowej. W celu ilustracji zmian przestrzennych głębokości położenia wód gruntowych na obszarze badań utworzone zostały mapy hydroizohips. Analiza przestrzenna danych poziomu wód gruntowych z piezometrów doprowadziła do następujących wniosków: - autokorelacja poziomu wód gruntowych w obszarze badań ma zasięg od 203,5 do 300 m – zależnie od serii, - głębokość położenia zwierciadła wód gruntowych była najmniejsza w pobliżu stawu Hetman, a największa w pobliżu rzeki Piwonia, - przestrzenna zmienność głębokości położenia wody gruntowej dla wszystkich serii badań była lepiej opisana przez model Gaussa niż przez inne modele.
PL
Niniejszy artykuł porusza problem doboru parametrów geotechnicznych w projektowaniu inżynierskim. Przedstawione zostały metody statystyczne mające na celu oszacowanie parametru charakterystycznego. Przegląd stanu wiedzy zawiera opis parametrów geotechnicznych wykorzystanych do analizy statystycznej. Dodatkowo przedstawione zostały badania polowe (CPT i DMT) wykonane na zaporze czołowej w Nieliszu wraz z interpretacją uzyskanych wyników oraz zależnościami empirycznymi służącymi do określenia wartości analizowanych parametrów. W podsumowaniu artykułu zaproponowano także dobór parametrów z wykorzystaniem klasycznej metody statystycznej oraz metody geostatystycznej krigingu zwyczajnego.
EN
This paper presents the problem of parameter selection in geotechnical engineering design. The statistical methods with literature review to estimate the characteristic parameter value was described. The literature review includes the description of the geotechnical parameters using for statistical analysis. In addition, the field tests (CPT and DMT) are presented together with the interpretation of the obtained results. The empirical relationships serving to calculate the parameter values was analyzed. Then Nielisz embankment was characterized, where the object for which studies were performed the CPT and DMT tests. Finally, the selected parameters using the statistical method of classical and geostatistical methods of ordinary kriging was carried out.
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