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Abstract

Safe mine operations and optimal economical decision making in the context of lignite resources require an adequate level of knowledge about the spatial distribution of critical attributes in terms of geometry and quality in the deposit. Therefore, ore body models are generated using different approaches in geostatistics, depending on the problem to be solved. In this article the analysis of geostatistical methods used for deposits modeling has been presented. Based on exploration data concerning caloric value Q, models of one exemplary lignite deposit has been made. Two models of deposit were prepared using two different methods: ordinary kriging (OK) and sequential Gaussian conditional simulation (SGSIM). Different models of the same deposit were analyzed and compared with source data using criterion of fidelity to statistical attributes like: mean value, variance, statistical distribution. Models, which have been created based on exploration data, were compared with in-situ data gained from survey activities in the exploitation process. As a result of comparison correlation factor and measures of deviations were computed: average relative error, absolute relative error. Models were compared with in situ data, considering statistical features and local variability as well. In conclusion, the study gives valuable information into the benefits of using certain geostatistical approaches for variable tasks and problems in the lignite deposits design process. For the assessment of average values of deposit parameters ordinary kriging provides appropriate effects. Geostatisical simulation (e.g. sequential Gaussian simulation - SGSIM) provides much more relevant information for tasks connected to probability (or risk) of defined threshold exceedences than ordinary kriging. Models made with simulation method are characterized by high fidelity of spatial distribution in comparison to source data.

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Authors and Affiliations

Wojciech Naworyta
Jörg Benndorf
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Abstract

In the paper a transformation between two height datums (Kronstadt’60 and Kronstadt’86, the latter being a part of the present National Spatial Reference System in Poland) with the use of geostatistical method – kriging is presented. As the height differences between the two datums reveal visible trend a natural decision is to use the kind of kriging method that takes into account nonstationarity in the average behavior of the spatial process (height differences between the two datums). Hence, two methods were applied: hybrid technique (a method combining Trend Surface Analysis with ordinary kriging on least squares residuals) and universal kriging. The background of the two methods has been presented. The two methods were compared with respect to the prediction capabilities in a process of crossvalidation and additionally they were compared to the results obtained by applying a polynomial regression transformation model. The results obtained within this study prove that the structure hidden in the residual part of the model and used in kriging methods may improve prediction capabilities of the transformation model.
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Authors and Affiliations

Marcin Ligas
Marek Kulczycki
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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.

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Authors and Affiliations

Jacek Mucha
ORCID: ORCID
Monika Wasilewska-Błaszczyk
ORCID: ORCID
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Abstract

In our article the ordinary kriging interpolation method was used for a spatial presentation of PM2.5 concentrations. The data used in the research was obtained from the unique PM2.5 measuring system, based on low-cost optical sensors for PM2.5 concentration measurements, working on Wroclaw University of Science and Technology campus area. The data from this system was used as an input for the interpolations that were made for three different days characterized by the highest measured values of PM2.5 – 20.01.2019, 17.02.2019 and 30.03.2019. For each of the selected days, variants with the maximum and minimum PM2.5 values recorded on a given measurement day were presented. In the analyses performed, the ordinary kriging technique and cross-validation, was used as the interpolation and the validation method, respectively. Parameters determining the quality of performed interpolation were Mean Error, Mean Standardized Error, Root Mean Square Error, and Average Standard Error. As the main indicator of quality of interpolation RMSE parameter was used. Analysis of that parameter shows that the higher variability of the data used for interpolation affects its quality. The Root Mean Square Error parameter reached 0.64, 0.94 and 1.71 for the lowest concentrations variants characterized by low spatial variability, and 6.53, 7.51, 11.28 for the highest one, which were characterized by high spatial variability. The obtained results of the research with the use of GIS tools shows that the ordinary kriging method allowed for the correct spatial presentation of the PM2.5 concentration variability in areas not covered by the measurement system.
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Authors and Affiliations

Izabela Sówka
1
ORCID: ORCID
Marek Badura
1
Marcin Pawnuk
1
ORCID: ORCID
Piotr Szymański
2
Piotr Batog
3

  1. Wroclaw University of Technology, Faculty of Environmental Engineering
  2. Wrocław University of Science and Technology, Faculty of Computer Science and Management
  3. INSYSPOM, Wrocław
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Abstract

The paper presents the approach for optimization of preventive/technological measures increasing the safety of tailings pond dams. It is based on the combined use of monitoring results as well as advanced 3D finite element (FE) modeling. Under consideration was the eastern dam of Zelazny Most Tailings Storage Facility (TSF). As part of the work, four numerical models of the dam and the subsoil, differing in the spatial arrangement of the soil layers, were created. For this purpose, the kriging technique was used. The numerical models were calibrated against the measurements from the monitoring system. In particular the readings acquired from benchmarks, piezometers and inclinometers were used. The optimization of preventive measures was performed for the model that showed the best general fit to the monitoring data. The spatial distribution and installation time of relief wells were both optimized. It was shown that the optimized system of relief wells provides the required safety margin.
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Authors and Affiliations

Dariusz Łydżba
1
ORCID: ORCID
Adrian Różański
1
ORCID: ORCID
Maciej Sobótka
1
ORCID: ORCID
Paweł Stefanek
2
ORCID: ORCID

  1. Wrocław University of Science and Technology, Faculty of Civil Engineering, ul. Wybrzeze Wyspianskiego 27, 50-370 Wrocław, Poland
  2. KGHM Polska Miedz S.A. Hydrotechnical Unit, ul. Polkowicka 52, 59-305 Rudna, Poland
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Abstract

Determination of High Arctic regions bathymetry is strictly dependent from weather and ice mass quantity. Due to safety, it is often necessary to use a small boat to study fjords area, especially close to glaciers with unknown bathymetry. This precludes the use of modern multi−beam echosounders, and so traditional single−beam echosounders have been used for bathymetry profiling. Adequate interpolation techniques were determined for the most probable morphological formations in−between bathymetric profiles. Choosing the most accurate interpolation method allows for the determination of geographical regionalisation of submarine elevations of the Brepollen area (inner part of Hornsund, Spitsbergen). It has also been found that bathymetric interpolations should be performed on averaged grid values, rather than individual records. The Ordinary Kriging Method was identified as the most adequate for interpolations and was compared with multi beam scanning, which was possible to make due to a previously modelled single beam interpolation map. In total, eight geographical units were separated in Brepollen, based on the bathymetry, slope and aspect maps. Presented results provide a truly new image of the area, which allow for further understanding of past and present processes in the High Arctic.
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Authors and Affiliations

Mateusz Moskalik
Piotr Grabowiecki
Jarosław Tęgowski
Monika Żulichowska
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Abstract

Compacted Graphite Iron (CGI), is a unique casting material characterized by its graphite form and extensive matrix contact surface. This type of cast iron has a tendency towards direct ferritization and possesses a complex set of intriguing properties. The use of data mining methods in modern foundry material development facilitates the achievement of improved product quality parameters. When designing a new product, it is always necessary to have a comprehensive understanding of the influence of alloying elements on the microstructure and consequently on the properties of the analyzed material. Empirical studies allow for a qualitative assessment of the above-mentioned relationships, but it is the use of intelligent computational techniques that allows for the construction of an approximate model of the microstructure and, consequently, precise predictions. The formulated prognostic model supports technological decisions during the casting design phase and is considered as the first step in the selection of the appropriate material type.
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Bibliography

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Authors and Affiliations

Łukasz Sztangret
1
ORCID: ORCID
Izabela Olejarczyk-Wożeńska
1
ORCID: ORCID
Krzysztof Regulski
1
ORCID: ORCID
Grzegorz Gumienny
2
ORCID: ORCID
Barbara Mrzygłód
1
ORCID: ORCID

  1. AGH University of Science and Technology, Poland
  2. Lodz University of Technology, Poland
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Abstract

The purpose of the paper is to analyze the spatial variability of precipitation in Poland in the years 1981–2010. The av-erage annual rainfall was 607 mm. Precipitation in Poland is characterized by high spatial and temporal variability. The lowest annual precipitation was recorded in the central part of the country, where they equaled 500 mm. The highest annual precipitation totals were determined in the south, equaling 970 mm. The average precipitation in the summer half-year is 382 mm (63% of the annual total). On the basis of data from 53 climate stations, maps were made of the spatial distribution of precipitation for the period of the year and winter and summer half-year. The kriging method was used to map rainfall distribution in Poland. In the case study, cross-validation was used to compare the prediction performances of three periods. Kriging, with exponential type of semivariogram, gave the best performance in the statistical sense. Their application is justices especially in areas where landform is very complex. In accordance with the assumptions, the mean prediction error (ME), mean standardized prediction error (MSE), and root mean-square standardized prediction error (RMSSE) values are approximately zero, and root-mean-square prediction error (RMSE) and average standard error (ASE) reach values well below 100.

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Authors and Affiliations

Antoni Grzywna
ORCID: ORCID
Andrzej Bochniak
Agnieszka Ziernicka-Wojtaszek
ORCID: ORCID
Joanna Krużel
Krzysztof Jóźwiakowski
Andrzej Wałęga
Agnieszka Cupak
ORCID: ORCID
Agnieszka Mazur
Radomir Obroślak
Artur Serafin
ORCID: ORCID
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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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Authors and Affiliations

Marcin Ligas
Marek Kulczycki
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Abstract

To guarantee food security and job creation of small scale farmers to commercial farmers, unproductive farms in the South 24 PGS, West Bengal need land reform program to be restructured and evaluated for agricultural productivity. This study established a potential role of remote sensing and GIS for identification and mapping of salinity zone and spatial planning of agricultural land over the Basanti and Gosaba Islands(808.314sq. km) of South 24 PGS. District of West Bengal. The primary data i.e. soil pH, Electrical Conductivity (EC) and Sodium Absorption ratio (SAR) were obtained from soil samples of various GCP (Ground Control Points) locations collected at 50 mts. intervals by handheld GPS from 0–100 cm depths. The secondary information is acquired from the remotely sensed satellite data (LANDSAT ETM+) in different time scale and digital elevation model. The collected field samples were tested in the laboratory and were validated with Remote Sensing based digital indices analysisover the temporal satellite data to assess the potential changes due to over salinization.Soil physical properties such as texture, structure, depth and drainage condition is stored as attributes in a geographical soil database and linked with the soil map units. The thematic maps are integrated with climatic and terrain conditions of the area to produce land capability maps for paddy. Finally, The weighted overlay analysis was performed to assign theweights according to the importance of parameters taken into account for salineareaidentification and mapping to segregate higher, moderate, lower salinity zonesover the study area.
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Authors and Affiliations

Sumanta Das
Malini Roy Choudhury
Subhasish Das
M. Nagarajan
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Abstract

The paper discusses some of the recent advances in kriging based worst-case design optimisation and proposes a new two-stage approach to solve practical problems. The efficiency of the infill points allocation is improved significantly by adding an extra layer of optimisation enhanced by a validation process.

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Authors and Affiliations

Yinjiang Li
Mihai Rotaru
Jan K. Sykulski
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Abstract

Material parameters identification by inverse analysis using finite element computations leads to the resolution of complex and time-consuming optimization problems. One way to deal with these complex problems is to use meta-models to limit the number of objective function computations. In this paper, the Efficient Global Optimization (EGO) algorithm is used. The EGO algorithm is applied to specific objective functions, which are representative of material parameters identification issues. Isotropic and anisotropic correlation functions are tested. For anisotropic correlation functions, it leads to a significant reduction of the computation time. Besides, they appear to be a good way to deal with the weak sensitivity of the parameters. In order to decrease the computation time, a parallel strategy is defined. It relies on a virtual enrichment of the meta-model, in order to compute q new objective functions in a parallel environment. Different methods of choosing the qnew objective functions are presented and compared. Speed-up tests show that Kriging Believer (KB) and minimum Constant Liar (CLmin) enrichments are suitable methods for this parallel EGO (EGO-p) algorithm. However, it must be noted that the most interesting speed-ups are observed for a small number of objective functions computed in parallel. Finally, the algorithm is successfully tested on a real parameters identification problem.

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Authors and Affiliations

Emile Roux
1
Yannick Tillier
2
Salim Kraria
2
Pierre-Olivier Bouchard
2

  1. Université Savoie Mont-Blanc, SYMME, F-74000 Annecy, France.
  2. MINES ParisTech, PSL Research University, CEMEF-Centre de mise en forme des matériaux, CNRS UMR 7635, CS 10207 rue Claude Daunesse, 06904 Sophia Antipolis Cedex, France
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Abstract

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.
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Authors and Affiliations

Adam Piasecki
1
ORCID: ORCID
Wojciech T. Witkowski
2
ORCID: ORCID

  1. Nicolaus Copernicus University, Faculty of Earth Sciences and Spatial Management, ul. Lwowska 1, 87-100, Toruń, Poland
  2. AGH University of Science and Technology, Faculty of Mine Surveying and Environmental Engineering, Krakow, Poland

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